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Characterization of ultrawideband radiowave propagation within the passenger cabin of a Boeing 737-200… Chuang, James Tzu-Ho 2007

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CHARACTERIZATION OF ULTRAWIDEBAND RADIO W A V E PROPAGATION WITHIN T H E PASSENGER CABIN OF A BOEING 737-200 AIRCRAFT by  JAMES TZU-HO C H U A N G B . A . S c , The University o f British Columbia, 2004  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS F O R THE D E G R E E OF M A S T E R OF APPLIED SCIENCE  in  THE F A C U L T Y OF G R A D U A T E STUDIES (Electrical and Computer Engineering)  T H E UNIVERSITY OF BRITISH C O L U M B I A October 2007  © James Tzu-Ho Chuang, 2007  Abstract In 2002, ultrawideband ( U W B ) systems gained prominence in the field o f radar, communications and sensor networks when F C C made their ruling on the unlicensed commercial use o f the 3.1-10.6 G H z spectrum. Channel modeling for U W B thus became extremely important for the evaluation o f newly proposed systems. Currently, based on the envisioned applications, standard channel models based on the Saleh-Valenzuela (SV ) model have been developed by two dedicated I E E E task groups, 802.15.3a and 802.15.4a for four environments:  residential, office, outdoor and industrial. However,  with increasing demand for wireless connectivity, wireless devices are being deployed i n more areas that have not yet been well characterized. One such environment is the public transportation.  In this thesis, we have made three major contributions.  First, the  identification o f clusters is the essential first step needed for the extraction o f S - V model parameters; however,  this process  is still being done  through  subjective  visual  inspections. Here, we remove that subjectivity and make the process more consistent by developing an automated cluster identification algorithm based on performing regression analysis on exponentially decaying clusters expressed i n semi-logarithmic scale. Second, based on extensive measurements, we characterize the large-scale aspects o f U W B propagation in the passenger cabin o f a Boeing 737-200 aircraft; an environment that is fundamentally different from environment previously considered due to its confined volume, cylindrical structure and high passenger density.  Several noteworthy aspects  include: (1) the coverage within the passenger cabin is found to follow a chevron shape contour where it is the greatest along the aisle and the weakest around window seats which suggests that the path gain also depends on the seat location and (2) high passenger density can introduce significant excess path loss.  Third, based on more  extensive measurements, we model the small-scale aspects o f U W B propagation which focused on the shape and duration o f the channel impulse response and the small-scale fading o f multipath components.  In most cases, our results take the form o f the  parameters o f the standard channel models and can be used directly for those planning to simulate, evaluate and deploy U W B systems in the aircraft environment. ii  Table of Contents Abstract  •  ii  Table of Contents  iii  List of Tables  vi  List of Figures  vii  List of Abbreviations  x  Acknowledgments  xi  Co-Authorship Statement Chapter 1  xii  Introduction  •  1  1.1  General Background and Motivation  1  1.2  Thesis outline  4  References  5  Chapter 2  Automated Identification of Clusters in UWB Channel Impulse Responses 6  2.1  Introduction  '.  2.2  Cluster Identification Approach  2.3  Description of the Cluster Identification Algorithm  6 7 11  2.3.1  Local Smoothing in the Time Domain  12  2.3.2  Initial Search for Clusters  12  2.3.3  Iterative Search for Clusters  12  2.3.4  Recursive Partitioning  13  2.3.5  Generalized Cross-Validation Criterion  14  2.3.6  Additional Rules  14  2.4  Validation of the Cluster Identification Algorithm  19  2.4.1  Validation Using Simulated Channel Impulse Responses  19  2.4.2  Validation Using Measured Channel Impulse Responses  20  2.5  Possible Sources of Error  : iii  24  2.5.1  Noise and Small-Scale Fading  2.5.2  Overlap between clusters  2.5.3  Anomalous clusters and additional rules  26  2.5.4  Coupling between input parameters  26  2.6  24 '  25  Conclusions  31  References  32  Chapter 3  UWB Radiowave Propagation within the Passenger Cabin of a Boeing 737-200 Aircraft  .'  34  3.1  Introduction  34  3.2  Measurement Approach  35  3.2.1  UWB Channel Sounder  35  3.2.2  Channel Sounder Calibration  36  3.2.3  Data Collection  37  3.2.4  Measurement Database  3.3  -.  Path Loss in the Aircraft Environment  39 42  3.3.1  Distance Dependence of Path Loss  42'  3.3.2  Three Dimensional Coverage Model  44  3.3.3  Frequency Dependence of Path Loss  51  ' 3.4  Time Dispersion in the Aircraft Environment  54  3.4.1  Delay Spread  55  3.4.2  Number of Dominant Paths  59  3.5  Conclusions  61  References  ••  Chapter 4  62  U W B Channel Impulse Response within the Passenger Cabin of a Boeing 737-200 Aircraft  . 65  4.1  Introduction  65  4.2  Measurement Approach  66  4.2.1  Channel Sounder Configuration and Calibration  66  4.2.2  Data Collection  67 iv  4.2.3 4.3  Measurement Database  68  Models of Multipath Characteristics  72  4.3.1  Initial Processing of the Channel Impulse Response  72  4.3.2  Modeling Strategy...  72  4.3.3  Shape of the Power Delay Profile  74  4.3.4  Interdependence of MPCs  81  4.3.5  Small-Scale Fading  82  4.3.6  Delay Spread within a Local Area  86  4.4  A Simulation Model for U W B CIR in Aircraft Passenger Cabin  86  4.5  Conclusions  90  References Chapter 5  91 Conclusions and Recommendations  94  5.1  Conclusions  :  5.2  Recommendations for Further Work  96  Appendix A  Useful Tables  97  Appendix B  Detailed Setup of E8362B PN A  98  Appendix C  Calibration of Antennas  101  Appendix D  Detailed Measurement Plan  103  Appendix E  Matlab Code of the Automated Cluster Identification Algorithm  105  v  94  List of Tables Table 2.1. User-supplied parameters used in the validation trials  20  Table 2.2. Comparison of actual and estimated parameters for different environments..21 Table 2.3. Consistency check for CM5 - 50 trials  21  Table 2.4. Estimated parameters from measured data in office and underground mine..21 Table 2.5. Algorithm parameters used for office and underground mine environments.21 Table 2.6. Evolution of RMS Error  27  Table 3.1. UWB Channel Sounder Link Budget  36  Table 3.2. Parameters of the distance dependent path gain model  46  Table 3.3. Parameters of shadowing effects  46  Table 3.4. Parameters of the frequency dependent path gain model  53  Table 3.5. RMS delay spread increase rate, a  56  :  Table 3.6. Mean excess delay, RMS delay spread, number of significant paths, and energy captured for different thresholds levels  59  Table 4.1. Power delay profile model parameters  76  Table 4.2. Small-scale fading parameters  83  Table 4.3. Time dispersion parameters within a local area  86  Table A. 1. Dimensions of modern aircraft  97  Table A.2. Large-scale parameters of conventional environments  97  Table A.3. Time dispersion parameters of conventional environments  97  Table B . l . E8362B P N A option 014 port description  98  Table B.2. Setting of E8362B P N A  99  Table B.3. Link budget of the UWB channel sounder  99  vi  List of Figures Figure 2.1. Model of the sparse multi-cluster channel impulse response (S-V Model).. 10 Figure 2.2. Model of the dense single-cluster channel impulse response with uniformly distributed ray arrivals  10  Figure 2.3. Flow chart of the automated cluster identification algorithm  16  Figure 2.4. Locally smoothed power delay profile where the black dots represent the smoothed MPCs  17  Figure-2.5. Evolution of the cluster identification process in a C1R generated from C M 3 . - Office LOS model. Here, (a) two clusters are broken into (b) three clusters, the second of which is broken on (c) the next iteration to yield four clusters..  18  Figure 2.6. (a) Identification of clusters in a CIR measured in an office, (b) Example of an anomalous cluster in a CIR measured in an office  22  Figure 2.7. (a) Identification of clusters in a CIR measured in an underground mine, (b) Example of anomalous clusters in a CIR measured in an underground mine  23  Figure 2.8. A PDP with its features buried by small-scale fading  28  Figure 2.9. Components of the residual error  28  Figure 2.10. Identified clusters for CM5. The total number of clusters is 12 and are marked using crosses while the estimated number of clusters is 10 represented by straight lines  29  Figure 2.11. Typical CIR for CM2  29  Figure 2.12. Change in the reduction of RMS error for different smooth interval, N . ... 30 Figure 2.13 Change in reduction of RMS error for penalty coefficient, a  30  Figure 3.1. Location of the transmitting, "A, and receiving, O, antennas on a Boeing 737200 aircraft for (a) the p-to-mp and (b) p-to-p configurations during the development runs. In the production runs, only one side of the aircraft and only one transmitting antenna location at the font aircraft are considered  40  Figure 3.2. Cross-section of the passenger cabin and the typical antenna mounting positions for the point-to-multipoint and point-to-point configurations Figure 3.3. A photograph of the typical receiving antenna location (armrest) vii  41 41  Figure 3.4. Distance dependent path gain for p-to-mp configuration. Dotted squares represent receiving antenna mounted on the headrest of aisle seats  47  Figure 3.5. Distance dependent path gain for p-to-p configuration  47  Figure 3.6. Log-normal fit to location variability for p-to-mp configuration  48  Figure 3.7. Log-normal fit to location variability for p-to-p configuration  48  Figure 3.8. U W B coverage within the passenger cabin of a Boeing 737-200 aircraft with the receiving antenna mounted at headrest, (a) is the measured coverage and (b) is the regenerated coverage. The unit for the colorbar on the right is dB.  49  Figure 3.9. Shadowing region and the corresponding distances that describe it  50  Figure 3.10. Multiband-UWB spectral map. ' O ' = Usable bands, ' X ' = Unusable bands, and ' A ' = Usable bands only with detect and avoid schemes  53  Figure 3.11. Power delay profile of a typical LOS channel (ceiling to headrest)  57  Figure 3.12. Power delay profile of a typical LOS channel (ceiling to footrest)  57  Figure 3.13. RMS delay spread obtained for p-to-mp configuration  58  Figure 3.14. RMS delay spread obtained for p-to-p configuration  58  Figure 3.15. CDF of the number of significant paths for p-to-mp configuration  60  Figure 3.16. CDF of the number of significant paths for p-to-p configuration  60  Figure 4.1. Layout of a Boeing 737-200 aircraft. Circles represent the location of the receiving antennas and the triangles represent the location of the transmitting antenna, in each transmitting antenna location, spatial sampling is performed according to the measurement grid. The squares represent the measurement taken from our first measurement campaign as described in [12]  ; 70  Figure 4.2. Cross-section of the passenger cabin and the typical antenna mounting positions for the point-to-multipoint and point-to-point configurations  71  Figure 4.3. A photograph of a typical receiving antenna location (armrest)  71  Figure 4.4. APDP measured with receiving antenna mounted at the headrest of row 19. ...77 Figure 4.5. APDP measured with receiving antenna mounted at the armrest of row 19. 77 Figure 4.6. APDP measured with the receiving antenna mounted at the footrest of row 19  78 viii  Figure 4.7. Excess amplitude of the LOS path, Kr, as a function of distance for LOS channels  -.  '.  79  Figure 4.8. Confirming the log-normality of the deviation of excess amplitude of LOS path, sK  79  Figure 4.9. Exponential decay rate, y, as a function of distance for N LOS channels  80  Figure 4.10. Confirming the log-normality of the deviation of exponent decay rate, sy. 80 Figure 4.11. Averaged spatial correlation as a function of antenna separation with the receiving antenna mounted on the footrest of row  84  Figure 4.12. A fit of the path amplitudes against theoretical distributions  84  Figure 4.13. Estimated m-factors as a function of delay for receiving antenna mounted on the headrest of row 19  85  Figure 4.14. The lognormal fit of m-factors for the receiving antenna mounted at the footrest of row 19  85  Figure 4.15. Comparison of the measured and regenerated APDP  88  Figure 4.16. Comparisons of the distribution of the simulated and measured R M S delay spread for LOS and NLOS channels  88  Figure 4.17. Comparisons of the RMS delay spread with respect to distance for NLOS channels  89  Figure B. 1. Connections of the UWB channel sounder  100  Figure C . l . Measurement setup of the antenna transfer functions  102  Figure C.2. Averaged antenna transfer functions  102  :  Figure D . l . Detailed measurement plan of p-to-mp configuration for (a) empty aircraft, (b) half full aircraft and (c) full aircraft. ( A = transmitting antenna, O = receiving antenna, • = passengers)  '.  :  1  Figure D.2. Detailed measurement plan of p-to-p configuration. (A = transmitting antenna, O = receiving antenna)  1  •ix  List of Abbreviations AoA  :  Angle o f arrival  APDP  :  Averaged power delay profile  ATF  :  Antenna transfer function  BER  :  Bit error rate  CDF  :  Cumulative distribution function  CIR  :  Channel impulse response  CM#  :  Channel model #  CTF  :  Channel transfer function  DS-SS  :  Direct-sequence spread spectrum  IFT  :  Inverse Fourier transform  LOS  :  Line-of-sight  MB-OFDM  :  Multiband orthogonal frequency division multiplexing  MLE  :  M a x i m u m likelihood estimation  MPC  :  Multipath component  NLOS  :  Non-line-of-sight  PDP  :  Power delay profile  PNA  :  Performance network analyzer  p-to-mp  :  Point-to-multipoint  p-to-p  :  Peer-to-peer  RMS  :  Root mean square  S-V  :  Saleh-Valenzuela  UWB  :  Ultra-wideband  VNA  :  Vector network analyzer  x  Acknowledgments This work was supported by grants from B e l l Canada (through its B e l l University Laboratories R & D program), N o k i a Canada, and the Natural Sciences and Engineering Research Council o f Canada. We are grateful to the management and staff o f the B C I T Aerospace Technology Campus at Vancouver International Airport for providing our research group with access to their Boeing 737-200 aircraft (a donation from WestJet Airlines) during the course o f this study. I thank my colleagues N i X i n and Shahzad Bashir and undergraduate students Ivan Chan, A l e x Lee, Chris Pang, Cecilia Yeung, and Chad Woodworm for their considerable assistance during the data collection phase o f this study. I also thank Dr. Michelson for the all the useful guidance, suggestions, and patience over the past three years.  xi  Co-Authorship Statement A version o f Chapters 2, 3 and 4 in this thesis w i l l be submitted to I E E E transactions for publication,  [1]  J. Chuang, S. Bashir and D . G . Michelson, "Automated Identification o f Clusters in U W B Channel Impulse Responses," to be submitted to IEEE Transactions on  Wireless Communications. [2]  J. Chuang and D . G . Michelson, " U W B radiowave propagation within the passenger cabin o f a Boeing 737-200 aircraft," to be submitted to IEEE  Transactions on Vehicular Technology. [3]  J. Chuang and D . G . Michelson, " U W B channel impulse response within the passenger cabin o f a Boeing 737-200 aircraft," to be submitted to IEEE  Transactions on Vehicular Technology.  Each project was identified and initiated by Dr. Michelson. In the first paper, Dr. Michelson provided useful suggestion on validating the algorithm using both simulated and measured data.  Both M r . Bashir and Dr. Michelson provided useful discussions  during the development o f the automated cluster identification algorithm and more importantly, the preparation o f the manuscript. In the second and third manuscripts, Dr. Michelson was in charge o f acquiring access to a Boeing 737-200 aircraft from British Columbia Institute o f Technology, recruiting volunteers to collect the measurements. Dr. Michelson also helped with the planning o f all the measurement campaigns that took place in the passenger cabin o f the Boeing 737-200 aircraft, and contributed greatly to the organization and editing o f the two manuscripts.  xii  Chapter 1 Introduction 1.1  General Background and Motivation U W B signals are defined as signals with an absolute bandwidth greater than 500  M H z or with a relative bandwidth greater than 20% o f its center frequency.  The wide  bandwidth have attracted great interest and created many new possibilities i n the field o f radar, communications and sensor network.  Some o f the benefits o f the U W B signals  include: 1.  excellent ranging and positioning capabilities,  2.  no significant multipath fading due to fine time resolution,  3.  multiple access due to wide bandwidth,  4.  possibility o f very high data rate  5.  covert communication due to low transmit power, and  6.  possible easier material penetration due to the wide bandwidth transmitted [1].  In 1990s, U W B system gained prominence when W i n and Scholtz published their groundbreaking work on time-hopping impulse radio systems [4]-[6]. In 2002, the ruling made by the Federal Communications Commission ( F C C ) granted the unlicensed commercial use o f U W B spectrum from 3.1 to 10.6 G H z and fueled the development o f UWB  systems.  Currently, two major industrial alliances, Multiband Orthogonal  Frequency Division Multiplexing ( M B - O F D M ) Alliance or M B O A  and  WiMedia  Alliance, are formed in support o f the two major U W B schemes, M B - O F D M and direct sequence spread spectrum (DS-SS). Other than the industrial support, two dedicated task groups, I E E E 802.15.3a and I E E E 802.15.4a, are also formed to regulate the P H Y layer designs as well as the channel modeling aspects.  In addition, the U W B technology has  been adopted by poplar commercial applications like Wireless U S B and Bluetooth 3.0. The performance limitations o f any communications systems are determined by the channel it operates in. After the F C C made their ruling i n 2002, the channel modeling 1  subcommittee i n the 3 a task group immediately started developing a standard channel model for U W B . Their main goal is to find a suitable model for the U W B channel such that different systems can use it to make fair comparisons against one another [7]. During the course o f their work, they have adopted the well-known Saleh-Valenzuela (SV ) model as the basis for their standard channel models. Their decision to use the S - V model was based on whether or not the model is capable o f reproducing several key channel parameters such as power delay profile (PDP), R M S delay spread, and number o f significant M P C s [7].  In their final report, based on the intended applications for  U W B , i.e., high data rate multimedia access and data transfer, the 3a task group created the first four standardized models for two different environments: residential line-of-sight ( L O S ) , residential non-line-of-sight ( N L O S ) , office L O S , and office N L O S . Later, the increased interest in creating sensor networks using U W B technology has led to the formation o f the 4a task group.  The 4a task group focused on new  environments such as outdoor (suburban microcell) and industrial (dense scatterers) environments where the sensor networks are most likely to be deployed. Several changes and improvements were made to the standard models developed by the 3 a task group which include introducing a new shape for the P D P for dense scattering environments with a "soft" onset, modeling the number o f cluster and M P C s i n the S - V model as a random variable, and incorporating the effect o f frequency dependent path loss [2]. B y the end o f 2004, again through a series o f measurement campaigns, the 4a task group, other than modifying the original four channel models, created four more standardized channel models: outdoor L O S , outdoor N L O S , industrial L O S and industrial N L O S . In addition, they have also created a new model for body area networks which includes correlated shadowing.  Their work on channel modeling eventually replaced the work  done by the 3a task group. Despite the enormous effort put into channel modeling by the task groups, there are still a quite a few unresolved issues regarding the measurement and modeling o f U W B propagation. Specifically, there are four major issues, 1. the identification o f clusters within the C I R , 2. the impact o f antennas on propagation measurements, 3. the effect o f run time compensation, and 2  4. the finite bandwidth effect and the effect o f windowing [1]. (1) The identification o f clusters is the essential first step i n extracting the relevant parameters used in the S - V channel model; however, they are still being done through subjective manual visual inspections which leads to rather arbitrary extracted model parameters [1] [9].  (2) The impact o f antennas on propagation measurements is i n  general very difficult to remove.  Different researchers have reported using different  techniques to remove the effect o f antennas and some o f have reported results including the effects o f antennas [1] [10]. (3) Spatial sampling within a local area is often used to determine small-scale effects; however, due to the fine time resolution, as the receiving antenna is moved from one spatial point to another, the M P C s tend to migrate from one delay bin to another.  This effect on the small-scale fading statistics is still unclear [1].  (4) The effect o f finite bandwidth which leads to the leakage o f power in the time domain is also another major issue.  Although techniques such as C L E A N ,  S A G E , and  windowing can be utilized to reduce the effect o f leakage, each o f them has their own weakness.  For example, C L E A N and S A G E algorithms require the assumption o f a  template waveform [10]. For windowing, although when it is applied the leakage power in the side lobes is greatly reduced, the resolution i n time domain solution is also reduced  [1]. W i t h more and more mobile devices being built and the demand for wireless connectivity increasing, wireless devices are finding themselves deployed in more and more environments. One such environment is the vehicles used in public transportation, e.g., aircrafts, buses, trains and subways. What all these environments have in common is that they are typically in a confined volume, in a long cylindrical structure and the density o f obstacles, such as passengers and luggage, can change quite significantly. These channel conditions thus make public transportation environment unique from the conventional environments previously investigated by the 3a and 4a task groups. Although  i n the  past, numerous  propagation  measurements that  facilitated  the  deployment o f traditional narrowband systems were made within those environments, none o f them characterized the channel for U W B signals. There are three main objectives in this thesis. The first objective is to address the main issues i n the process o f U W B channel modeling process. Due to time constraints, 3  we focused only on the first o f the four main issues, the identification o f clusters in the SV model. Our intension is to develop an automated cluster identification algorithm that w i l l be more consistent and robust than the current manual techniques. objective  Our next  is to characterize the U W B propagation i n vehicles used for public  transportation.  Specifically, we w i l l focus on characterizing the U W B propagation  within the passenger  cabin o f a Boeing 737-200 aircraft a subset o f the public  transportations environment. Through extensive measurements, we w i l l first characterize the large-scale aspects o f U W B propagation.  Our data reduction efforts w i l l then focus  on comparing those propagation characteristics with other conventional environments. Our final objective is to characterize the small-scale aspect o f U W B propagation, again through extensive measurements and create models suitable for the design and evaluation of system performance.  The results derived here w i l l be broadly applicable to a wide  variety o f modern aircraft due to the similarities in their cross-sections (See Table A . l ) .  1.2  Thesis outline This thesis is organized as follows.  cluster identification algorithm.  In Chapter 2, we presented an automated  The algorithm removes subjectivity and unifies the  definition o f clusters in C I R . Chapter 3 presents the measurement data collected within the passenger cabin o f a Boeing 737-200 aircraft, and with the measurement  data,  analysis o f how the structure o f the aircraft affects the coverage and reliability o f U W B communication.  In Chapter 4, a statistical channel model is developed for the U W B  propagation within the passenger cabin o f a Boeing 737-200 aircraft.  The statistical  model can be used for system simulations. Finally, in Chapter 5, we draw conclusions, assess the limitations o f the present work and offer recommendations for future work.  4  References [1]  A . F . Molisch, "Ultrawideband Propagation Channels-Theory, Measurement, and Modeling," IEEE Trans. Veh. Technol, vol. 54, no. 5, pp. 1528-1545, Sep. 2005.  [2]  A . F . Molisch, et al., " A Comprehensive Standardized M o d e l for Ultrawideband Propagation Channels," IEEE Trans. Antennas Propag., vol. 54, no. 11, N o v . 2006, pp. 3151-3166.  [3]  A . A . M . Saleh, and R . A . Valenzuela, " A Statistical M o d e l for Indoor Multipath Propagation," IEEE J. on Sel. Areas in Commun., v o l . 5, no. 2, pp. 128-137, Feb. 1987.  [4]  R . A . Scholtz, "Multiple access with time-hopping impulse modulation," Proc. IEEE MILCOM1993,  [5]  pp. 447-450, 1993.  M . Z . W i n and R . A . Scholtz, "Impulse radio: H o w it works," IEEE Commun. Lett., vol. 2, pp. 36-38, Feb. 1998.  [6]  M . Z . W i n and R. A . Scholtz, "Ultra-wide bandwidth time-hopping spreadspectrum impulse radio for wireless multiple-access communications," IEEE Trans. Commun., vol. 48, pp. 679-691, A p r . 2000.  [7]  J. Foerster et al, "Channel Modeling Subcommittee Final Report," Tech. Rep., I E E E 0249r0P802-15_SG3a, 2003.  [8]  A . F . M o l i s c h et al, " I E E E 802.15.4a Channel Model-Final Report," Tech. Rep., I E E E 802.1504-0062-02-004a, 2005.  [9]  O . H . W o o n and S. Krishnan, "Identification o f clusters  i n U W B channel  modeling," Proc. IEEE VTC 2006 - Spring, M a y 2006. [10]  B . A l l e n et al, Ultra-wideband Antennas and Propagation, Wiley, 2007.  5  Chapter 2 Automated Identification of Clusters in UWB Channel Impulse Responses 2.1  Introduction The tendency for multipath components ( M P C s ) in wideband channel impulse  responses (CIRs) to form exponentially decaying clusters was first reported by Saleh and Valenzuela over twenty years ago [1]. Their model, often referred to simply as the S - V model, was later adopted by both the I E E E 802.15.3a and 802.15.4a W P A N task groups as the basis for standardized models o f the ultrawideband ( U W B ) CIRs that one is likely to encounter in residential, office, outdoor and industrial environments [2]-[5]. Because the M P C s observed i n certain dense scattering environments are often so closely spaced in time that clustering can no longer be observed i n the C I R , I E E E 802.15.4a also specified a dense single-cluster model to be used i n cases such as N L O S channels i n office and industrial environments where the sparse multi-cluster S - V model is not appropriate [6]-[8]. Other models for representing U W B CIRs have been proposed including the twocluster model proposed in [9] and the lognormal-exponential model with a single cluster proposed in [10].  Some have raised concerns that clustering is often not apparent in  CIRs measured i n many conventional environments [11]. However, experience has shown that the two models proposed by I E E E 802.15.4a cover the vast majority o f CIRs observed. Accordingly, we have focused on identifying clusters within a C I R assuming that the underlying model is the multi-cluster S - V model proposed by 802.15.4a.  The  dense single-cluster model can be treated as a special case. Despite the tremendous effort that has been applied to U W B channel measurement and modeling i n recent years (and the importance o f cluster identification to the process),  A version of this chapter has been submitted for publication: J. Chuang, S. Bashir and D . G . Michelson, "Automated Identification of Clusters in U W B Channel Impulse Responses," submitted to IEEE Transactions on Wireless Communication, 12 October 2007.  6  most researchers still identify clusters i n CIRs through time-consuming manual techniques that rely on subjective assessment by the analyst. Although a reliable automated U W B cluster identification algorithm has the potential to make cluster identification less subjective, more consistent and less time-consuming, three factors have limited their adoption: (1) a surprising lack o f agreement concerning the criteria for identifying a cluster, e.g., [4] [5] [12], (2) a lack o f sufficiently robust algorithms, as noted in [8][13], and (3) the effort required to implement or tune existing algorithms, e.g., [12][14]. Our efforts to develop a better cluster identification algorithm differs from past work in three ways: (1) we focus on the manner i n which clusters o f M P C s o f given start time, duration, and exponential decay profile introduce discontinuities i n the shape o f the entire C I R , (2) we have explicitly considered the coupling between the parameters o f the algorithm and (3) we have verified the correct operation o f our algorithm (and the validity o f our approach) by conducting estimation trials using both: (a) simulated U W B S - V CIRs with known channel parameters that correspond to residential, office and outdoor environments and (b) measured CIRs collected i n both office and underground mine L O S environments.  W e also acknowledge the  potential to  use  such an  algorithm as the basis for either an autonomous reduction tool or as an interactive aid to the analyst. The remainder o f this paper is organized as follows: In Section 2.2, we briefly review the U W B standard channel models adopted by the I E E E 802.15.4a task group and summarize our own cluster identification approach. In Section 2.3, we describe the steps that comprise our cluster identification algorithm. In Section 2.4, we present the results o f our efforts to validate the algorithm using both U W B CIRs generated using I E E E 802.15.4a's C I R simulation code and measured CIRs from both office and underground mine environments. In Section 2.5, we consider factors that could affect the performance of the algorithm. In Section 2.6, we summarize our contributions.  2.2 Cluster Identification Approach Our approach to cluster identification is based on identification o f discontinuities in the shape o f the C I R . The I E E E 802.15.4a task group has recommended using either a 7  sparse multi-cluster or a dense single-cluster model, as appropriate, to represent U W B CIRs [3]. The sparse multi-cluster model is based upon the well known S - V model and is given by MO = Z I v a  /=0  e x  P ( M , / )S(t-T,-T ) kJ  (2.1)  k=0  where the M P C s are modeled as Dirac delta functions, d\.), and a^i and fai are the amplitude and phase o f the M i M P C in the /th cluster. L is the total number o f clusters i n the C I R and K is the total number o f M P C s within the /th cluster. T/ and z>_/ represent the t  arrival time o f the /th cluster and the kth M P C i n the /th cluster, respectively. The expected shape o f the P D P , here defined as the square magnitude o f the C I R , is described as the product o f two exponential functions, E  {k' | } 2  0 0e x p  (  - T  ' ) 1  r  e x p  y)  [~ k,i  1  T  (-) 2  2  where T and y are the cluster and intracluster decay constants respectively as depicted i n Figure 2.1. The arrival time o f the clusters and M P C s , T/ and x^i, are found to follow the Poisson distribution with arrival rates, A and X, respectively. For the dense single-cluster model, /'. e., without any discontinuities, the shape of the C I R has the following form  \\ kj \  E  a  2  cc  1-^exp  (2.3)  exp \  yrise J  where x denotes the attenuation o f the first component,  y i r  s e  determines how fast the P D P  rises to its local maximum, y\ represents the decay at later times. The arrival rate o f the M P C s is fixed, At, given by the inverse o f the signal bandwidth as depicted i n Figure 2.2. In both models, the small-scale fading follows the Nakagami distribution. The shape o f a cluster may be greatly distorted by the effects o f noise and smallscale fading. A s a result, our observation o f the power delay profile is,  y{r) = f(T)  +  s  (2.4)  where fix) takes the form o f either (2) or (3) and e is a random variable from a combination o f white noise and small-scale fading. B y expressing the P D P on a semilogarithmic scale, the exponential decays are expressed as straight lines. Then, using linear regression techniques, we find a set o f non-overlapping piecewise regression lines, such that  8  b +br  t <z <t  b +b z  t <r < r  ]0  n  20  lx  x  2  2  3  (2.5)  where Z?,o and bn are the intercepts and slopes o f the best fit lines, respectively, and t are t  the estimated arrival times for each o f the estimated L clusters. Each regression line in g(f) corresponds to a cluster and the estimated arrival times, t  h  correspond to the  discontinuities in the PDP. A s a result, when g(z) is accurately estimated, t w i l l provide t  us with the accurate location o f the clusters. Then, from the estimated arrival time o f each cluster, the channel parameters needed in the S - V model are extracted.  9  03  3  -> 1/A  delay  -> 1A,  Figure 2.1. M o d e l o f the sparse multi-cluster channel impulse response ( S - V Model)  Yrise  / \  AV  PQ D  T3  3 As  I  delay At  Figure 2.2.  M o d e l o f the dense single-cluster channel impulse response with uniformly  distributed ray arrivals.  10  2.3  Description of the Cluster Identification Algorithm The goal o f our cluster identification algorithm is to determine the combination o f  exponentially decaying clusters that best fit the most significant M P C s i n the power delay profile. Whether measured in the time or frequency domain, a measured channel response has a finite bandwidth that is determined by the instrument and/or the measurement process. The result is equivalent to convolving the true C I R with a sine function whose duration is inversely proportional to the bandwidth o f the measurement. Before processing a measured C I R using our cluster identification algorithm, one must first remove the effects o f the finite bandwidth either by windowing or deconvolution. Other pre-processing steps that must be performed include setting thresholds for noise, suppressing small-scale fading, and so forth, as outlined in [15]. Because the first set o f results presented in the next section is based upon simulated PDPs, we were able to omit this pre-processing step. The second set o f results is based upon measured P D P s that we suitably processed before applying our cluster identification algorithm. Computing the spatial average o f several P D P s over a local area is one method for suppressing small-scale fading, and it should be applied whenever possible to obtain a better estimate o f the shape o f the P D P . Because the first set o f results is based upon randomly simulated P D P s , spatial averaging could not be applied. Accordingly, we developed an alternative method for small-scale fading suppression that involves using an average filter i n the time domain to smooth the rapid variations within the C I R caused by small-scale fading. This approach has been used in image processing to reveal edges against background noise [16]. Using such techniques allows one to apply our cluster identification algorithm to either spatially-averaged or instantaneous PDPs. A flow chart o f our cluster identification algorithm is depicted in Figure 2.3. It includes the three main steps that we describe i n more detail below: (1) local smoothing in the time domain, (2) the initial search for clusters by identifying gaps i n the P D P , and (3) the iterative search for clusters based upon trial fitting o f intracluster decay curves to the P D P .  11  2.3.1  Local Smoothing in the Time Domain The first step is to suppress small-scale fading through local smoothing i n the time  domain. The P D P w i l l typically be sampled at an interval, t , that is inversely s  proportional to the bandwidth o f the measured signal. In the U W B case, the bandwidth w i l l typically range from a minimum o f 500 M H z to a maximum o f 7.5 G H z yielding 0.13 n s < / , < 2 n s . We smooth the P D P by applying an averaging filter defined by, N/2  i  PDP [m] = —  PDP[mN + i]  s  M  (2.6)  ,=-jv/2  where N is the user-defined smoothing interval and M w i l l nominally equal TV + 1. Downsampling i n this manner increases the sampling interval to Nt . In certain cases, a s  given tap may not contain any energy after  we apply an amplitude threshold.  Accordingly, we may use a value M < N + 1 i n (2.6) to compensate. A representative P D P that has been generated using the standard channel impulse response generator developed by the I E E E 802.15.4a channel modeling committee is given in Figure 2.4. The dots represent the components o f the P D P that result when the averaging filter given i n (2.6) is applied with N = 9.  2.3.2  Initial Search for Clusters If the interval between successive M P C s exceeds a user-defined threshold, we  consider this to be a gap between distinct clusters. The number o f such gaps plus 1 gives the initial number o f cluster Zj j . Such gaps often arise in simulated P D P s but, in our n  t  experience, rarely arise i n measured ones. The user can usually select an appropriate value for this threshold by inspecting the P D P . Figure 2.5a shows a P D P that has been split into two clusters that are separated by a large gap that appears near T = 200 ns.  2.3.3  Iterative Search for Clusters Our cluster identification algorithm is based upon expression o f the M P C s on a  semi-logarithmic scale so that exponential intracluster decay profiles w i l l be displayed as straight lines with given slopes. W e use linear regression methods to determine the  12  particular combination o f straight lines that best fits contiguous groups o f significant M P C s (given by PDP [m] in (2.6)) i n a least squares sense. s  The search begins with the assumption that the initial number o f clusters is L -  L  mit  as determined by the methods described i n Section 2.3.2. The algorithm then estimates goodness-of-fit by calculating the R M S error, (2.7) where M is the total number o f smoothed M P C s identified and g[m] is g(r) sampled at intervals Nt . If the resulting R M S error o f any cluster exceeds a specified threshold, it is s  assumed that an unidentified cluster is causing a discontinuity i n the P D P . In response, the algorithm increments the number o f clusters by 1, tries all possible combinations o f L straight lines that one might fit to contiguous groups o f M P C s to form L clusters, then selects the combination that yields the best fit, i.e., the lowest R M S error. If the best fit satisfies the error threshold criterion, the process ends, and the number o f clusters in the C I R is reported as L . Otherwise, it is assumed that the number o f clusters must be incremented further and the process is repeated. A typical sequence is depicted in Figure 2.5.  2.3.4 Recursive Partitioning A n exhaustive search o f all possible cluster configurations w i l l ensure that the best possible solution is ultimately found. However, the number o f possible combinations increases  very rapidly as the  number  o f clusters  increases  and  soon  becomes  computationally intractable. During trials conducted upon both simulated and measured CIRs, we have observed that incrementing the number o f clusters used to represent a C I R almost always involve subdividing an existing cluster. In statistics, this approach is referred to as recursive partitioning [18]. Here, the decision to further subdivide an existing cluster is also based upon whether or not the R M S error can be further reduced. M a k i n g this a rule in our search strategy and eliminating all other possibilities reduces the number o f trials that we must conduct from OiM ' ) to just OtM) where M is the total 1 1  number o f smoothed M P C s in the P D P and L is the number o f clusters in the C I R . 13  Implementing  such a partitioning strategy  dramatically reduces  the number o f  combinations that must be examined compared to an exhaustive search. This partitioning strategy plays an important role i n making our algorithm tractable.  2.3.5  Generalized Cross-Validation Criterion A s mentioned before i n Section 2.3.3, a R M S error threshold sets the stopping  condition for the algorithm. However, i n order to ensure that the fast variations o f the i  P D P are not interpreted as clusters, we make the stopping condition more robust by adopting the generalized cross-validation ( G C V ) criterion,  GCV =  RMSE aB M  l  (2.8)  that has been used in Error! Reference source not found, and elsewhere. Here, B is the number o f parameters that we seek to estimate (in our case, the slope and intercept o f each o f the identified clusters), M is the number o f smoothed M P C s and a is the userdefined penalty coefficient. A s the number o f identified clusters increases, the GCV w i l l initially decrease with the R M S error. Past a point defined by the penalty coefficient, the increasing number o f parameters B w i l l cause the GCV to increase. The results presented in Section 2.4 suggest that a penalty coefficient o f 1 to 2 is adequate for U W B cluster identification. Based on the GCV criterion, the algorithm w i l l stop: (1) when the value o f GCV is below the user-defined threshold or (2) when the penalty prevents the value o f GCV from being reduced further.  2.3.6  Additional Rules  In order to ensure the correct operation o f the cluster identification algorithm, we enforce three additional rules: 1. The clusters must exceed a minimum length. 2.  The power level at the start o f a given cluster must be greater than the residual power level extrapolated from the previous cluster.  3.  The slopes o f the regression lines that we fit to the M P C s must be negative because the S - V model assumes that the clusters decay. 14  The three additional rules are jointly enforced during recursive partitioning by applying a multiplicative penalty coefficient, B , where i denotes the additional rule. The t  decision to split an existing cluster is now based on the lack-of-fit ( L O F ) criterion,  LOF = ftfrfrGCV = 0 J3 6 }  2  R M S E 3 r  -, aB n  x  (2.9)  M . where the penalty coefficient, /?,, is set to 1 by default and set to an alternative value when the z'th additional rule is violated. Based on our experience, the optimal choices for these alternative values are: B\ = 10, B = 2 and 2  = 2. The increase in the L O F criterion  that occurs when an additional rule is violated w i l l reduce the likelihood that a cluster w i l l be subdivided. However, it w i l l not completely stop the algorithm from identifying clusters that have violated the rules i f there is sufficient reduction in the R M S error.  15  i  Measured CIR data User Inputs  1 - Smoothing Interval [samples]  Local smoothing in the time domain using an averaging filter  2 - Maximum separation between MPCs [ns]  Initial search for clusters based on gaps in the PDPs  a) Exhaustive Search: Find the best linear fit amongst all possible combinations of L clusters  3 - Apply penalty coefficients, a, /?,.  b) Recursive Partitioning: Find the best linear fit by subdividing a cluster into two clusters at all possible points within that cluster for every clusters in the PDP  4 - Acceptable R M S error threshold e IdBl  Extract model parameters  Figure 2.3. F l o w chart o f the automated cluster identification algorithm  16  Time [ns]  Figure 2.4. Locally smoothed power delay profile where the black dots represent the smoothed M P C s .  0  50  100  150  200  250  300  Time [ns]  (a) Figure 2.5. Evolution o f the cluster identification process i n a C I R generated from C M 3 - Office L O S model. Here, (a) two clusters are broken into (b) three clusters, the second o f which is broken on (c) the next iteration to yield four clusters. 17  Figure 2.5. Evolution o f the cluster identification process in a C I R generated from C M 3 - Office L O S model. Here, (a) two clusters are broken into (b) three clusters, the second o f which is broken on (c) the next iteration to yield four clusters.  18  2.4 Validation of the Cluster Identification Algorithm 2.4.1 Validation Using Simulated Channel Impulse Responses W e validated our algorithm by: (1) generating random CIRs for different scenarios using the standard channel impulse response generator developed by the I E E E 802.15.4a channel modeling committee then (2) estimating the relevant model parameters based upon the clusters identified using our algorithm. The eight standard channel models correspond to line-of-sight ( L O S ) and non-line-of-sight ( N L O S ) instances o f residential ( C M 1 and 2), office ( C M 3 and 4), outdoor ( C M 5 and 6) and industrial environments ( C M 7 and 8), respectively. The parameters that define each o f the channel models are the average number o f clusters, Z  m e a  n ; the cluster decay factor, T; the cluster arrival rate, A ;  the intracluster decay factor, y; the M P C arrival rate, X; and the shadowing term, a. The I E E E 802.15.4a C I R generator presets the interval between samples, t , to 125 psec. s  For each channel model, we generated 50 CIRs and converted them to P D P s in accordance with the procedures outlined i n [3]. W e then estimated the number o f clusters, their peak amplitudes, and arrival time by applying our cluster identification algorithm to each P D P i n turn using the user-defined parameters given in Table 2.1. Next, we normalized the amplitude and arrival time o f the clusters and superimposed them i n order to estimate T and A , then repeated the process for the M P C s in order to estimate y and X. Details o f the parameter extraction are outlined i n [3]. The actual and estimated values o f the S - V model parameters are given in Table 2.2. Since our interest is identification o f clusters, only parameters related to clusters and their exponential decay are shown. Even though all o f the CIRs are affected greatly by both small-scale fading and the randomness o f the Poisson distributed cluster arrival time, the  estimated  parameters are very close to the parameter settings that had been applied to the simulator. A l s o , the algorithm has correctly recommended that a single cluster be used to represent the environments that were simulated using the single-cluster dense scattering model. A s a further check o f the performance o f the cluster identification algorithm, the steps described above were repeated fifty times using CIRs based upon the C M 5 19  (Outdoor - L O S ) model. We chose this model because it tends to exhibit the greatest number o f clusters. W e compare the mean and standard deviation o f the estimates to the actual values o f the parameters in Table 2.3. Once again, our estimates and the actual values generally agree.  2.4.2 Validation Using Measured Channel Impulse Responses To further validate our algorithm, we have also applied it to U W B CIRs that we measured  under  line-of-sight  conditions  i n both  office  and  underground  mine  environments. T w o CIRs that are representative o f those observed i n each case are presented i n Figure 2.6a and Figure 2.7a. The lines represent the identified clusters, and the dots represent the smoothed M P C s . Our estimates o f the model parameters are summarized in Table 2.4. The input parameters used to derive these results are listed in Table 2.5. The office L O S parameters are based upon 49 measured CIRs; the underground mine CIRs are based upon 27 CIRs. In each case, the values are similar to what a human analyst might extract but were obtained with far less time and effort. Moreover, the algorithm functioned correctly and robustly despite the presence o f significant departures from the ideal S - V case.  Table 2.1. User-supplied parameters used i n the validation trials.  Algorithm Parameter Smooth Interval, N [samples] Smooth Interval, N t [ns] Maximum Separation Time [ns] Minimum R M S Error Threshold [dB] Penalty Coefficient for Additional Splits, a Minimum Cluster Length [samples] Penalty Coefficient for Additional Rule 1, /?i Excess Amplitude of New Clusters [dB] Penalty Coefficient for Additional Rule 2, /? Penalty Coefficient for Additional Rule 3, /? s  2  3  Residential CM1 CM2 LOS NLOS 9 9 1.125 1.125 20 20 2 2 1 1 2 2 10 10 2 2 2 2 2 2  CM3 LOS 11 1.375 20 2 1 5 10 3 2 2  20  Office CM4 NLOS 11 1.375 20 2 1 5 10 3 2 2  Outdoor C M5 CM6 LOS NLOS 11 11 1.375 1.375 20 20 2 2 1 1 5 5 10 10 3 3 2 2 2 2  industrial CM8 CM7 NLOS LOS 11 7 0.875 1.375 20 20 2 2 1 1 2 5 10 10 2 3 2 2 2 2  Table 2.2. Comparison of actual and estimated parameters for different environments. Residential CM1 CM2 LOS NLOS 3.0 3.5 2.66 2.58 22.6 26.3 19.2 20.8 0.047 0.12 0.034 0.02 17.5 12.53 9.02 12.6  Actual Estimate Actual Estimate Actual Estimate Actual Estimate  Office CM4 CM3 LOS NLOS 5.4 1 5.5 1 N/A 14.6 N/A 16.3 N/A 0.016 0.022 N/A 11.84 6.4 10.65 9.9  Outdoor CM5 CM6 NLOS LOS 13.6 10.5 12.52 10.1 31.7 105 33.44 95.4 0.024 0.045 0.027 0.036 9.3 3.7 11.62 6.8  Industrial CM7 CM8 NLOS LOS 1 4.75 4.22 1 N/A 13.5 N/A 13.4 N/A 0.071 N/A 0.059 85.36 0.65 14.64 93.29  Table 2.3. Consistency check for CM5 - 50 trials Channel Parameters •^mean  r A y  Actual  Mean of the Estimates  13.6 31.7 0.045 3.7  11.2 34.4 0.041 6.3  Standard Deviation of the Estimates 0.37 0.61 5.2e-4 1.74  Table 2.4. Estimated parameters from measured data in office and underground mine. Channel Parameters  Underground Mine 3.05 20.77 0.0302 14.79  Office LOS 7.0 23.32 0.067 8.79  ^•Tnean  r A 7  Table 2.5. Algorithm parameters used for office and underground mine environments. Algorithm Parameters Smooth Interval, N [samples] Smooth Interval, Nt [ns] Maximum Separation Time [ns] Minimum R M S Error Threshold [dB] Penalty Coefficient for Additional Splits, a Minimum Cluster Length [samples] Penalty Coefficient for Additional Rule \,B Excess Amplitude of New Clusters [dB] Penalty Coefficient for Additional Rule 2, B Penalty Coefficient for Additional Rule 3, B  Office L O S 9 1.125 20 2 1 3 10 2 2 2  s  X  2  3  21  Underground Mine 9 1.125 20 2 1 3 10 2 2 2  22  Or  200  Time [ns]  (a)  23  2.5  Possible Sources of Error Several factors may affect the performance of the algorithm including: (1) noise  and small-scale fading, (2) overlap between clusters, (3) the presence of anomalous clusters and (4) coupling between the input parameters. We discuss each of these in more detail below.  2.5.1  Noise and Small-Scale Fading  The L M S linear regression techniques that we use to fit trial PDPs to groups of MPCs can be sensitive to extreme values or outliers that affect the slope and offset of the resulting regression lines. In U W B propagation measurements, small-scale fading is always present and can significantly mask the shape of the PDP [4]. For example, a PDP whose features are buried by small-scale fading is depicted in Figure 2.8 To illustrate the effect of small-scale fading on cluster detection, assume that there are only L clusters in the PDP and we have fit L regression lines. When L*L , the residual error can be expressed as the sum of two components, error (T) = bias (T) + X . 0  (2.10)  as depicted is Figure 2.9. The random variable, X , is the combination of small-scale a  fading and measurement noise and the bias term is the difference between the envelope of the PDP and the current best regression line, g(r). The bias term in decibel scale can be described as, bias ( r ) = 10 log E {|a(r)f} - y (r) dB  10  (2.11)  where E{\a(f)\ } is the envelope of the PDP as described in (2.2) and (2.3) for the multi2  cluster and single cluster cases, respectively.  Since the random error cannot be  eliminated, the success of the algorithm rests on whether or not we can successfully reduce the R M S error by reducing the bias term with a better estimate, i.e., generate a more accurate g(r). For example, the error in the first regression line in Figure 2.5a can be reduced while the error in the second regression line cannot. As a result, cluster detection will be difficult when small-scale fading is significant.  24  In Table 2.6, how R M S error changes as a function of the number of clusters, L, based on our recursive partitioning is summarized in more detail. Here, we see how the algorithm breaks up clusters in order to identify new clusters. The algorithm stopped at iteration 9 because the R M S error for the entire PDP is no longer reducible.  2.5.2 Overlap between clusters The identification of clusters is also directly related to how the clusters arrive. In the extreme case, when the arrivals of all clusters are too close in time, the clusters become indistinguishable based on the shape, e.g., the dense single-cluster model used in dense scattering environment. Figure 2.10 shows an example of the identified clusters in a channel realization from C M 5 , the outdoor LOS environment. The lines represent the identified clusters and the crosses indicate where the actual clusters start. While most clusters are easily resolved, two clusters around 190 ns and two more around 250 ns cannot because the clusters within the two groups of clusters are not distinct To a lesser extent, the cluster decay rate T and the M P C decay rate y also affects our ability to distinguish the start of a new cluster. Assuming that the first cluster has a continuous decay profile, the arrival of a second cluster A T after the start of the first inserts a discontinuity of height, exp(-Ar/r)  exp(-Ar/x) or, on a decibel scale, as f  \  1^  J  r  (2.13)  where Ti is the arrival time of the new cluster and k is lOlogio(e). This discontinuity is essentially the bias term in (2.11). As the M P C decay rate increases, the clusters can arrive increasingly closer in time and still be successfully identified. From (2.13), we calculated the average magnitude of the discontinuities in the PDP for the standard channel models assuming that, on average, A T is the inverse of the cluster arrival rate, A . A l l channel models give reasonably distinct clusters except for C M 2 where the discontinuities, on average, are only 0.7 dB. The relatively small discontinuities make the algorithm an unsuitable one for identifying the clusters defined 25  by C M 2 . O n the other hand, because all channel models have their clusters identified by the same set o f procedure and rules, relative to other channel models, it would reasonable to conclude that C M 2 is best represented by the single-cluster model. Figure 2.11 shows a typical C I R for C M 2 . Compared to the C I R in Figure 2.5 for C M 3 , the clusters i n C M 2 are difficult to distinguish whether by human analyst or by algorithm.  2.5.3  Anomalous clusters and additional rules In measured C I R data, either because o f small-scale fading or the nature o f the  reflectors i n the environment, the shape o f the P D P does not always follow the S - V model.  A s mentioned before, in these cases, we add a penalty to the R M S error  calculated so that the identified clusters w i l l more likely follow the underlying shape o f the S - V model.  Figure 2.6a and Figure 2.6b depict the identified clusters when  additional rules are enforced and not enforced in the office environment. Figure 2.7a and Figure 2.7b depict the identified clusters when additional rules are enforced and not enforced i n the underground mine environment. H o w well the clusters should follow the S-V model is up for the analyst to decide when he sets the penalty coefficients /?,.  2.5.4 Coupling between input parameters Correct operation o f the cluster identification algorithm requires that the smoothing interval, the penalty coefficients and the R M S error threshold be appropriately set. The smoothing interval averages out the rapid variations i n the P D P . Although the process is aided by increasing the interval, this also increases the risk o f smoothing out the discontinuities that we are trying to identify. The analyst must therefore take care when setting the value used. Results obtained by applying the cluster identification algorithm to the C I R i n Figure 2.10 for different smoothing intervals N are given i n Figure 2.12. The intervals are given in samples where the sampling time is 0.125 ns. Each curve ends when the R M S error has reached its minimum value. In general, when the smoothing interval is very small and the penalty coefficient, a, is not large enough to prevent the creation o f apparent clusters that are merely artifacts o f small-scale fading, the algorithm w i l l tend to overestimate the number o f clusters. A s the smoothing interval increases, the algorithm 26  converges to the correct value and the R M S error drops rapidly. Past a certain point, excessive smoothing blurs the transition between clusters and the number o f clusters is underestimated. Figure 2.13 shows the reduction in R M S error as the penalty coefficient, a, increases. Each curve ends when the R M S error has reached its minimum (except for the case a = 1). Increasing the penalty coefficient, a, inhibits cluster splitting and thereby increases the rate at which the algorithm achieves the minimum R M S error. For all cases, the minimum R M S error threshold, here, 2 d B , has little effect because the R M S error never drops to that value.  Table 2.6. Evolution o f R M S Error  #of Iter.  RMS Error of Clusters [dB]  1.90 1 1.90 1 1.90  9.71  RM S Erro rof entir e PDP  9.13 I  8.49 1 8.07 I  I  7.29  1.90  I  I  6.40  1.90 i 1.90 I 1.90 I 1.90 1 1.90  4  5.82 I  5.49 1  5.13 1 5.05  27  Cluster 1 Cluster 2 O  Sig. MPCs  delay Cluster 1  Cluster 2  Figure 2.8. A P D P with its features buried by small-scale fading.  Best Fit E{\a(r)\ } 2  CQ -a  • i  u  3  delay Cluster 1  Cluster 2  Figure 2.9. Components of the residual error.  28  Or  Time [ns]  Figure 2.10.  Identified clusters for C M 5 . The total number o f clusters is 12 and are  marked using crosses while the estimated number o f clusters is 10 represented by straight lines.  1 Clusters  Time [ns]  Figure 2.11. Typical C I R for C M 2 .  29  13  Number of Identified Clusters  Figure 2.12. Change i n the reduction o f R M S error for different smooth interval, N .  11  7  I  ,  ,  5  10  :  ,  1  15  20  Number of Identified Clusters  Figure 2.13 Change i n reduction o f R M S error for penalty coefficient, a.  30  2.6  Conclusions W e have developed an automated cluster identification algorithm that determines  how a U W B channel impulse response (CIR) can be most effectively represented by either o f the I E E E 802.15.4a standard channel impulse response models: (1) a single exponentially decaying cluster (a straight line when expressed on a semi-log scale) or (2) a sequence o f exponentially decaying clusters described by the Saleh-Valenzuela model, as appropriate. Trials conducted using U W B CIRs generated by a simulation code developed by I E E E 802.15.4a and U W B CIRs measured in office and underground mine environments have confirmed the validity o f our approach. Although the algorithm works best when applied to CIRs that have been expressed as spatially averaged PDPs, our use o f local smoothing allows us to apply it to instantaneous P D P s with considerable success. Compared to previous work, our algorithm has several key features that contribute to its success: (1) W e focus on the manner in which clusters o f M P C s o f given start time, duration, and exponential decay profile introduce discontinuities in the shape o f the entire C I R , (2) W e employ recursive partitioning to dramatically reduce the number o f cluster combinations that must be checked and thereby make the algorithm tractable. (3) The iterative nature o f the algorithm and the manner in which we layer the cluster selection rules makes it possible to use the algorithm as the basis for either (a) an autonomous tool for batch mode processing or (b) an interactive tool for use by analysts. Compared to current manual approaches, the proposed algorithm makes cluster identification more consistent and less time-consuming. Thus, the algorithm should be a useful aid for those engaged in analysis o f U W B channel impulse responses.  31  References [I]  A . A . M . Saleh and R. A . Valenzuela, " A statistical model for indoor multipath propagation," IEEEJ. Sel Areas Commun., vol. 5, no. 2, pp. 128-137, Feb. 1987.  [2]  A . F. M o l i s c h , J. R. Foerster, and M . Pendergrass, "Channel models for ultrawideband personal area networks," IEEE Wireless Commun., vol. 10, no. 6, pp. 14-21, Dec. 2003.  [3]  A . F. M o l i s c h et al., " I E E E 802.15.4a channel model - final report," Tech. Rep., I E E E 802.15-04-0662-00-004a, N o v . 2004.  [4]  A . F. M o l i s c h , "Ultrawideband propagation channels - Theory, measurement, and modeling," IEEE Trans. Veh. Technol, vol. 54, no. 5, pp. 1528-1545, Sep. 2005.  [5]  A . F . M o l i s c h et al, " A comprehensive standardized model for ultrawideband propagation channels," IEEE Trans. Antennas Propagat., vol. 54, no. 11, pp. 31513166, N o v . 2006.  [6]  U . Schuster and H . Bolsckei, "Indoor U W B channel measurements from 2 G H z to 8 G H z , " Tech. Rep., I E E E 802.15-04-0447-00-004a, A u g . 2004.  [7]  J . Karedal, S. Wyne, P. Aimers, F. Tufvesson and A . F . Molisch, " U W B channel measurements i n an industrial environment," Proc. IEEE Globecom 2004, pp. 3511-3516, N o v . 2004.  [8]  J. Karedal, S. Wyne, P. Aimers, F. Tufvesson and A . F . M o l i s c h , "Statistical analysis o f the U W B channel i n an industrial environment," Proc. IEEE VTC 2004 -Fall, pp. 81-85, Sep. 2004.  [9]  S. Venkatesh, J. Ibrahim, and R. M . Buehrer, " A new two-cluster model for indoor U W B channel measurements," 2004 IEEE APS Int. Symp. Dig, vol. 1, pp. 946949, Jun. 2004.  [10]  S. S. Ghassemzadeh, L . J. Greenstein, T. Sveinsson, A . Kavcic, and V . Tarokh, " U W B delay profile models for residential and commercial indoor environments, IEEE Trans. Veh. Technol, vol. 54, no. 4, pp. 1235-1244, Jul. 2005.  [II]  L . J. Greenstein, S. S. Ghassemzadeh, S-C Hong, and V . Tarokh, "Comparison study o f U W B indoor channel models," IEEE Trans. Wireless Commun., v o l . 6, no. l , p p . 128-135, Jan. 2007.  [12]  O . H . W o o n and S. Krishnan, "Identification o f clusters in U W B channel modeling," Proc. IEEE VTC 2006 - Spring, M a y 2006.  [13]  C - C . Chong and S. K . Y o n g , " A generic statistical-based U W B channel model for high-rise apartments," IEEE Trans. Antennas Propag., v o l . 53, no. 8, pp. 23892399, A u g . 2005.  [14]  D . Shutin and G . Kubin, "Cluster analysis o f wireless channel impulse responses with hidden Markov models," Proc. IEEE ICASSP, pp. 949-952, M a y 2004.  [15]  A . F. M o l i s c h , U . G . Schuster, and C - C . Chong, "Measurement procedure and methods on channel parameter extraction," Tech. Rep., I E E E 802.15-04-0283-00004a, M a y 2004.  [16]  I. Gijbels, A . Lambert, and P. Q i u , "Edge-preserving image denoising and estimation o f discontinuous surfaces," IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 7, pp. 1075-1087, Jul. 2006.  [17]  S. C . Chan and Z . Zhang, "Robust local polynomial regression using m-estimator with adaptive bandwidth," Int. Symp .Circuits Syst., M a y 2004, pp. III-333III-336.  [18]  J. H . Friedman, "Multivariate adaptive regression splines," The Annals of Statistics, vol. 19, no. 1, pp. 1-141, Mar. 1991.  33  Chapter 3 UWB Radiowave Propagation within the Passenger Cabin of a Boeing 737-200 Aircraft 3.1  Introduction To date, a variety o f studies have been conducted i n support o f deployment o f  personal wireless technology aboard passenger aircraft, includes studies conducted by researchers at the German Aerospace Centre ( D L R ) (under the aegis o f the European Union's WirelessCabin project), The Vahala lab at O l d Dominion University, Boeing, Intel and elsewhere, e.g., [l]-[9]. In general, these studies have emphasized: (1) systems engineering studies and field trials for conventional wireless technologies such as cellular telephones, wireless L A N , and Bluetooth, (2) simulation o f aircraft interiors using industry standard R F coverage prediction tools, and (3) measurement o f R F coverage using client devices. In one instance, the wideband channel impulse response within the cabin was characterized using a commercial channel sounder [7]. For airlines, U W B wireless technology operating within the frequency band between 3.1 and 10.6 G H z holds great promise for enabling deployment o f high data rate multimedia and network access services within aircraft passenger cabins and for facilitating operations and maintenance through deployment o f sensor networks and precise positioning systems.  However, past efforts to develop  measurement-based  models o f the U W B propagation channel have focused on residential, office, industrial and outdoor environments [ 10] [ 11 ]. W i t h its confined volume, cylindrical structure, and high density o f occupancy, the passenger cabin o f a jet aircraft is fundamentally different from those environments considered previously. The effect o f human presence or body shadowing in confined spaces or over U W B channels has been considered i n [8] [12]. To the best o f our knowledge, however, no previous published study has characterized either the U W B propagation channel within aircraft passenger cabins or explicitly considered the effect o f human presence on U W B propagation within such environments.  34  Here, we seek to characterize large-scale aspects o f U W B propagation within the passenger cabin o f a typical mid-size airliner. Based upon frequency response data collected over the range 3.1 - 10.6 G H z aboard a Boeing 737-200 aircraft with the cabin empty, with a small group o f passengers occupying half o f the seats i n a portion o f the cabin, and with that small group o f passengers occupying virtually all o f the seats i n a smaller portion o f the cabin, we have characterized three large-scale aspects o f U W B channel that affect coverage and reliability, i.e., the distance dependence o f path loss, the frequency  dependence  o f path loss and the location variability.  W e have also  characterized time dispersion parameters such as the R M S delay spread, the number o f significant multipath components ( M P C s ) and the corresponding percentage o f energy captured by those M P C s . In Section 3.2, we describe our V N A - b a s e d U W B channel sounder, our procedure for calibrating the channel sounder, our data collection procedure, and our measurement database. In Section 3.3, we present the results o f our path loss investigation. In Section 3.4, we present the results o f our time dispersion investigation. Finally, we summarize our key findings in Section 3.5  3.2  Measurement Approach  3.2.1 UWB Channel Sounder Our U W B channel sounder consists o f an Agilent E8362B vector network analyzer ( V N A ) , a laptop-based controller equipped with a G P I B interface, a pair o f 15-m L M R 400 UltraFlex coaxial cables, a pair o f Electro-metrics 6865 omni-directional U W B biconical antennas, and suitable tripods and fixtures for mounting the antennas at various locations throughout the aircraft. During data collection, a M A T L A B script running on the laptop controlled the V N A and logged the received data. The system link budget is given in Table 3.1. The transmit power was set to 5 d B m . The loss from each measuring cable is 9.1 d B .  The intermediate  frequency  bandwidth o f the V N A was set to 3 k H z ; this led to a noise floor o f -107.2 d B m and a minimum sweep time o f approximately 2 sec. A s a result, channel sounders o f this type can only be used i n situations where the channel is effectively static. Using the Friis 35  transmission formula with a pathloss exponent 2.2, we determined that our channel sounder can measure responses with an S N R ^ 10 dB at transmitter-receiver separation distances o f up to 15m. During data collection, the V N A was configured to sweep from 3.1 to 10.6 G H z over 6317 frequency  points.  The frequency  sampling interval o f 1.1875 M H z  corresponds to a maximum unambiguous excess delay o f 842 ns or a maximum observable distance o f 253 m. The frequency span o f 7.5 G H z gives us a time resolution of 133 ps or 40 mm.  Table 3.1. U W B Channel Sounder L i n k Budget Values 5 dBm -9.1 dB* OdBi -82.1 dB** OdBi -9.1 dB* -95.3 dBm -107.2 dBm 11.9 dB  Links Transmitted Power Cable Loss Transmit Antenna gain Path Loss Receiver Antenna gain Cable Loss Received Power Receiver Sensitivity System Margin  * Calculated from datasheet at the highest frequency 10.6 G H z ** Calculated using Friis transmission formula with a path loss exponent of 2.25 at a distance of 15m  3.2.2 Channel Sounder Calibration Before use, the channel sounder must be calibrated so that systematic variations in the amplitude and phase o f the measured frequency response due to factors other than the propagation channel can be removed. The process involves two steps. The first step is to use the V N A ' s built-in calibration routines which are based upon a 12-term error model to compensate for all distortion between the points where the transmitting and receiving cables attach to the transmitting and receiving antennas, respectively. The second step, which is much more difficult, is to compensate for the distortion introduced by the antennas themselves. In [13], M o l i s c h considered how antennas can distort channel measurements and reviewed the various techniques that researchers have used i n the past to compensate for 36  such effects. Although it is a relatively simple matter to compensate for the return loss o f the antenna over the range o f frequencies o f interest, one must also account for the manner i n which the antenna radiation pattern varies over the range o f directions that rays may depart the transmitter and impinge on the receiver. It is generally very difficult to completely remove the effect o f antennas from measurements. Not only does the nonuniform frequency response o f U W B antennas significantly distort the arriving M P C , but the distortion is different for rays arriving from different directions.  A s a result,  complete removal o f antenna-related distortion requires knowledge o f the angle o f arrival ( A o A ) o f each M P C . Acquiring this information requires a space-time channel sounder with a real or virtual antenna array at the receiving end.  However, the limited space  available within the passenger cabin makes it difficult to deploy such an antenna array. Here, we use the approximate approach described in [14] to calibrate our antennas. It is based upon the assumption that all o f the M P C s are uniformly incident from all directions. To obtain the correction data, we measured the frequency response between the ports o f the transmitting and receiving antennas: (1) with both antennas in open space, (2) with the receiving antenna located in the principal plane o f the transmitting antenna and (2) with the receiving antenna successively mounted i n all possible orientations with respect to the transmitting antenna. We then average the set o f frequency responses in order to determine the mean effective gain at each frequency. W e refer to the result as the antenna frequency response ( A F R ) . We use the result to remove a good portion o f the effect o f the antenna by taking the ratio o f the measured channel frequency response ( C F R ) and the average antenna frequency response. We measured the antenna frequency response o f our antennas on the rooftop o f the Electrical and Computer Engineering building at U B C . We avoided reflections from the surrounding environment by carefully placing the antennas away from local scatterers and mounting them on 3.4-metre high tripods.  W e minimized ground reflection by  placing the antennas such that the transmission path spanned the gap between the two perpendicular wings o f the building. A s expected, we found that the magnitude o f the averaged A F R decreases with increasing frequency with a frequency dependent pathloss coefficient K o f approximately 0.8.  3.2.3  Data Collection 37  W e collected our channel frequency response measurements within the passenger cabin o f a Boeing 737-200 aircraft.  The aircraft is 21 m in length overall, 3.54 m i n  width and 2.2 m in height. It can carry over 100 passengers. Plan and cross-sectional views o f the passenger cabin are shown i n Figure 3.1 and Figure 3.2, respectively. A photograph o f the receiving antenna mounted at the armrest is shown i n Figure 3.3. Because modern mid-sized airliners have similar cross-sections, our results should be generally applicable to a wide range o f modern aircraft such as the A 3 2 0 family from A i r B u s , the A R J 2 1 family from A C A C and the C R J series from Bombardier, as depicted in Table A . 1. In our measurement campaign, we considered two wireless system configurations: point-to-multipoint (p-to-mp) and peer-to-peer (p-to-p). In the p-to-mp configuration, the transmitting antenna, in the manner o f an access point, was mounted on the ceiling, as suggested in Figure 3.2, and the user terminals, in the manner o f mobile devices, were placed at the headrest, armrest and footrest level o f the passenger seats throughout the aircraft as shown i n Figure 3.3. In the p-to-p configuration, the transmitting antenna was mounted on the headrest, armrest and footrest level o f a passenger seat. After accounting for reciprocity, this configuration yielded six unique antenna combinations. During our development runs for the point-to-multipoint configuration, we verified the static nature o f the channel and the consistency o f our measurements by comparing ten consecutive channel frequency response measurements over selected paths within the cabin. This verified that we could take just one sweep per location during production runs and thereby dramatically reduce the number o f measurements needed to characterize the aircraft. W e introduced further redundancies into our measurement database by: (1) putting the transmitting antenna at different locations and (2) measuring on both sides o f the bilaterally symmetric passenger cabin, as shown i n Figure 3.1.  In particular, we  collected channel response data at every other seat on both sides o f the aircraft from row 4 to row 19, i.e., at 53 different seats, for each o f three transmitting antenna locations. Once we had verified that the expected symmetries and similarities appeared in the results, we were able to take advantage o f them to further reduce the number o f measurements required to characterize the aircraft, e.g., by focusing only on the port side o f the aircraft and using only one transmitting antenna location.  38  3.2.4 Measurement Database In our development runs, for an empty aircraft using the p-to-mp configuration, we collected data at 24 seats, i.e., at every other seat on one side o f the aircraft from row 4 to row 19.  When measurement data were collected with people aboard the aircraft, 19  volunteers occupied seats on the port side.  In the first instance, they occupied every  other seat, i.e., seats next to where the receiving antennas are placed, from row 4 to 16. A total number o f 19 seats were sampled for this instance. In the second instance, the volunteers occupied every seat from row 4 to 10 and we sampled at every seat which gave a total number o f 21 seats sampled.  For p-to-p configuration, two transmitting  antenna locations at the window and aisle seat o f row 4 were examined.  Again, the  receiving antenna is mounted at every other seat on the port side but only from row 4 to 18 to sample the aircraft.  The sampling strategy gave us a total number o f 22 seats  sampled for each o f combination o f transmitting and receiving antenna mounting positions.  In total, the passenger cabin is sampled in great detail at 564 different  locations.  39  CD  (a)  (b)  Figure 3.1. Location o f the transmitting, A , and receiving, O, antennas on a Boeing 737200 aircraft for (a) the p-to-mp and (b) p-to-p configurations during the development runs.  In the production runs, only one side o f the aircraft and only one transmitting  antenna location at the font aircraft are considered.  40  INTERIOR TRIM-TO-TRIM 139.2 IN (3.54 M)  66 IN (1.68 M)  xAntem  1  f  1  \  I  I  1  1  86.6 N (2.20 M) 62.2 IN (1.58 M)  /  148 IN (3.76 M)  Figure 3.2. Cross-section o f the passenger cabin and the typical antenna mounting positions for the point-to-multipoint and point-to-point configurations.  Figure 3.3. A photograph o f the typical receiving antenna location (armrest).  41  3.3  Path Loss in the Aircraft Environment The U W B path gain model adopted by the I E E E 802.15.4a channel modeling  committee is given by, f j\-"f  j-\-  lK  G {d,f) = k  (3.1)  p  where d and / are distance and frequency, respectively, do and f  c  are the reference  distance and frequency, n and K are the distance and frequency exponents, and A: is a constant that represents the path gain at the reference distance and frequency. The two independent variables, d and / , are assumed to be independent from one another and as a result, they are modeled separately. In this study, we refer to the path gain as the mean received power multiplied by the gains o f the transmitting and receiving antennas divided by the transmitting power as measured by the V N A . That is,  G J£&p p  v  (3.2) y  3.3.1 Distance Dependence of Path Loss Distance dependent path loss is the most fundamental and most important parameter to characterize for wireless devices and is especially important for U W B devices due to their regulated l o w transmit power. The path gain model parameters derived here are very important for system designers to determine the coverage and reliability o f wireless systems within the passenger cabin o f an aircraft. A l s o , the peerto-peer model is useful for understanding the effect o f interference from other wireless devices aboard the aircraft. Following  the  recommendation by the  IEEE  802.15.4a channel modelling  committee, we took the average o f the measured complex channel frequency responses across the entire span from 3.1 to 10.6 G H z in order to obtain the mean distance dependent path gain,  1  •>  M  42  where M is the number o f frequency steps.  Path gain decreases with increasing  transmitter-receiver separation due to the combined effects o f spatial spreading and obstruction by cabin fixtures, seats and human presence. In decibels, the path gain with respect to distance is,  GP(d) = GP -lOn\og 0  + X ,d>d  ]  a  (3.4)  0  \ oj d  where GPo, the intercept point, is the path gain at the reference distance, do, and I0nlog\o(d/do) is the excess path gain referenced to 1 m , n is the path gain exponent and X is a zero-mean Gaussian random variable with a standard deviation o f a. B y fitting a a  linear regression line to the path loss data with respect to distance, we are able to determine the path loss exponent n and the intercept point GPo- The standard deviation of X  a  is found by subtracting the mean values from the path loss data and fitting the  differences to a Gaussian distribution. Figure 3.4 shows how path gain varies with respect to distance for the different receiving antenna mounting positions in the p-to-mp configuration. From Figure 3.4, we can see, as expected, that the path gain data points for the headrest channels are always greater than the armrest and footrest channels.  Note that some data points from the  armrest and footrest channels are receiving higher power because they are placed too close to the aisle as shown i n Figure 3.3. A l s o , some o f the headrest positions are not exactly line-of-sight ( L O S ) because some o f the positions are shadowed by overhead compartments. If we only consider the case where the receiving antenna is placed on the headrest o f an aisle seat, then the path loss exponent drops to 1.83 with an intercept o f 39.5 d B m and location variability o f 0.42 d B .  Depending on the mounting position o f  the receiving antenna, path loss is expected to increase between 5 and 10 dB at greater distances. The difference shown here is expected to increase as more obstacles such as passengers and luggage are brought aboard the aircraft.  The fit o f X to a Gaussian a  distribution is shown in Figure 3.6. The slightly deviation o f the data from a Gaussian distribution is because o f the difference in mounting positions creating two significantly different channel conditions. For peer-to-peer  configuration, because both the transmitting and receiving  antennas are below the height o f the seats for all the antenna mounting combinations considered, the path gain parameters derived are all very similar. The only exception is 43  when both the transmitting and receiving antennas are mounted at the headrest level. Figure 3.5 shows how path gain varies with distance for the p-to-p configuration. W e have also, in Figure 3.5, marked the headrest to headrest data separately to show the difference. Unlike the point to multipoint case, the location o f the receiver, whether it is on an aisle or window seat does not matter. In terms o f shadowing, X , as shown in a  Figure 3.7, fits the Gaussian distribution very well. Table 3.2 gives a complete summary o f how path gain varies for all the cases considered. In free space environments, the path loss exponent is equal to 2 as a consequence o f spatial spreading.  In conventional environments with L O S condition, the path loss  exponent for U W B signals is often less than 2 because other than the L O S component, additional energy is being collected from the reflections from scatterers [15].  For  example, i n the industrial L O S channels with a lot o f metallic scatterers, the path loss exponent is only 1.2 (See in the Appendix). In the aircraft passenger cabin environment, the channel is enclosed within a metallic cavity so we might expect that the path loss exponent to be around the same as industrial L O S channels. measured path loss exponent is not as low as expected.  In practice, however, the  We believe this is due to the  large amount o f R F absorbers within the cabin, e.g., seats, overhead compartments, etc. O n the other hand, because there are no metallic objects that can completely block signals and energy often finds its way to the receiver due to the dense set o f scatterers i n the environment, the path loss exponent for non-line-of-sight ( N L O S ) channels is never too high (See Table A . 2 in the Appendix for comparisons).  3.3.2 Three Dimensional Coverage Model Because o f the large yet predictable variance i n path loss observed with respect to the different scenarios considered, a simple distance dependent path loss is no longer adequate.  For instance, Figure 3.8a shows the two-dimensional coverage within the  passenger cabin based on measurements.  The degree to which the coverage is affected  by the overhead compartments and the seats is apparent. To more accurately account for the path gain measured within the passenger cabin, path gain is decomposed into three components: (1) L O S path gain assuming there are no  44  obstacles within the aircraft, (2) deterministic shadowing due to the furnishings within the aircraft, and (3) random shadowing. The complete path loss equation is, GP(^) = GP -10n 0  L O S  log  -GP,+X , a  1 0  d>d  0  (3.5)  \d ; 0  where we simply added a GP term to (3.4) to account for the deterministic shadowing S  and modified the path loss exponent, «LOS, such that it is derived from a reference case with no obstacles in between, i.e., with the receiving antenna mounted on the headrest o f the aisle seats.  To model the deterministic shadowing, three shadowing conditions,  shadowing by overhead compartment only, by seats only, and by both, are identified. Each o f these shadowing conditions corresponds to one or more antenna mounting configuration, e.g., i n p-to-mp configuration, the receiving antenna is shadowed by both the overhead compartments and the seats when mounted at the armrest and is shadowed only by the overhead compartments when mounted at the headrest.  The effect o f  shadowing is then quantified as,  GP (d ,d ) s  x  y  = ad + 3d x  (3.6)  2  where the two new distances, d and d , account for how far the receiving antenna is in x  y  the shadowing region as shown in Figure 3.9. The corresponding coefficients, a and B, are then derived by applying linear regression techniques with respect to the reference case for each row and then averaged over all rows. Finally, the random shadowing is modeled using a zero mean Gaussian random variable. summary o f the coverage models in the aircraft.  Table 3.3 gives a complete  The use o f this model simplifies the  different scenarios into a compact form and at the same time, it models more accurately the shadowing effects caused by the overhead compartments and seats.  Figure 3.8b  shows the reconstructed coverage within the passenger cabin without the random component.  45  Table 3.2. Parameters o f the distance dependent path gain model. System Configuration Point to Multipoint  Peer to Peer  Mounting Point  Path loss exponent, N 2.2 2.1 2.2 2.3 2.2 2.0 1.7 1.7 1.8 2.3 2.3 2.6 2.6 2.5  All C-to-H C-to-A C-to-F All H-to-H H-to-A H-to-F A-to-H A-to-A A-to-F F-to-H F-to-A F-to-F  1-m intercept, P L [dBm] -40.5 -39.3 -40.7 -42.6 -41.7 -40.7 -44.5 -45.7 -43.5 -41.3 -41.4 -38.5 -38.9 -39.9 0  Location variability, a [dB] 2.7 1.6 2.3 1.3 1.8 1.3 1.8 0.7 1.0 1.5 1.6 0.8 1.2 1.3  (C = Ceiling, H = Headrest, A = Armrest, F = Footrest)  Table 3.3. Parameters o f shadowing effects. Shadowing Condition Overhead Compartments Seats Both  a [dB/m] 3.5 1.1 1.5  P [dB/m]  -  3.30 5.07  Example p-to-mp, C-to-H p-to-p, H-to-A p-to-mp, C-to-A  (C = Ceiling, H = Headrest, A = Armrest, F = Footrest)  46  -45  -50  ~  -55  I" CD  ^ a  D D  60  03 Q.  -65  -70  -75  -  Best Fit  •  Headrest  o  Armrest  V  Footrest 3  4  7  5  6  7  8  vO  9 10  Distance [m]  Figure 3.4.  Distance dependent path gain for p-to-mp configuration.  represent receiving antenna mounted on the headrest o f aisle seats.  -45  Distance [m]  Figure 3.5. Distance dependent path gain for p-to-p configuration.  47  Dotted squares  0.999 F  0.001  -I  I  -5  -4  -3  -2  -1  0  1  2  3  4  Location Variability, Xo- [dB] F i g u r e 3.7.  L o g - n o r m a l fit to l o c a t i o n v a r i a b i l i t y for p-to-p c o n f i g u r a t i o n .  48  5  Headrest Measured  4  -70  -65  6 8 Distance [m]  -60  -55  10  -50  12  -45  (a)  £  1  4  -70  -65  6 8 Distance [m]  -60  -55  10  12  -50  -45  14  (b) Figure 3.8. U W B coverage within the passenger cabin o f a Boeing 737-200 aircraft with the receiving antenna mounted at headrest, (a) is the measured coverage and (b) is the regenerated coverage. The unit for the colorbar on the right is dB.  49  Figure 3.9. Shadowing region and the corresponding distances that describe it.  50  3.3.3 Frequency Dependence of Path Loss The I E E E 802.15.4a channel modeling committee has adopted the following relationship for modeling the frequency dependence o f path gain where, (3.7) In a free space environment, the frequency dependence o f path loss comes from the antennas only.  F o r a typical omnidirectional antenna with constant gain, path loss  increases with frequency with K = 2 [16]. This is a consequence o f the effective aperture o f the antenna scaling with frequency. In a real channel, frequency dependence can also be introduced by one or more o f the following physical aspects o f the channel: (1)  diffraction across blocking objects,  (2)  scattering from rough surfaces,  (3)  wall  penetration,  with material reflection coefficients being  frequency-  dependent, (4)  frequency-selective reflection from metallic objects o f specific geometric shapes such as railings and gratings; and  (5)  vector superposition o f overlapping signal waveforms i n a dense multipath channel, altering the frequency content o f individual M P C [16].  Frequency dependent path loss is a serious problem, because it greatly affects the coverage at different frequencies.  It is especially important i n systems that use  Multiband Orthogonal Frequency Division Multiplexing ( M B - O F D M ) . Figure 3.10 shows a typical frequency dependent  For instance,  U W B C T F and the different  government regulations on the unlicensed use o f U W B systems for the United States, Europe, Japan, and Korea. Here, we see that i n order to implement a worldwide design, the system designer needs to know how path gain changes with frequency to adapt to the different regulations set by the different regions o f the world. A l s o , it has been reported in Error! Reference source not found, that depending on the value o f K, the channel w i l l either act as an integrator or a differentiator that severely distorts the transmitted waveform and degrades the performance o f coherent receivers.  51  Based on (3.7), K is estimated by converting the frequency axis o f the C T F into logarithmic scale and fitting a regression line across the C T F . The slope divided by 2 o f regression line is then the desired K. Table 3.4 gives a complete summary o f K observed at the different mounting combinations where ju is the mean o f K observed and o K  deviation.  K  antenna  is the standard  The results are given in terms o f both the radio and the propagation channels  where K for the radio channel is defined as the channel including the effects o f the antennas, i.e., from anything in between the transmitting and receiving antenna connectors, and K for the propagation channel is defined as the channel after we have applied the antenna calibration procedure described i n Section 3.2 and removed the effects o f the antennas. The most significant result here is the huge difference in the K observed for the radio and propagation channel. The K observed for the propagation channel is expected because in environments with similar geometry such as tunnels, path loss has been shown to decrease with increasing frequency due to the waveguide effect [17].  This unique  effect also has not been reported previously in the U W B channel modeling. Comparing the K observed at the different receiving antenna mounting positions, we see that K varies slightly with respect to the different mounting configurations.  This slight variation is  mainly cause by the different antenna mounting positions having slightly different A o A distributions. W e can also see that the variation in K is greater for the p-to-mp configuration, and this is because the difference in height between the transmitting and receiving antennas is greater for the p-to-mp configuration and this greater difference in height caused greater change in the A o A distribution. The propagation channel has less to do with this variation because the materials with the aircraft are consistent everywhere. For p-to-p configuration, the K obtained indicates that path loss is decreasing with the square o f frequency. Comparing the K measured with the K used i n the I E E E 802.15.4a channel models, we can see that the aircraft environment is closest to rich scattering environment like the industrial environment.  Although i n [18], we have observed a  slight dependency between K and the separation distance possibly due to a cumulative effect o f the materials within the aircraft, because the dependency is small, we w i l l assume, for simplicity, that this distance dependency is negligible and is just a part o f a . K  Our analysis here is applicable due to the large amount o f scenarios considered 52  Table 3.4. Parameters o f the frequency dependent path gain model.  Point to Multipoint  Peer to Peer  Propagation Channel o -1.52 0.40 0.33 -1.86 0.38 -1.46 0.22 -1.24 0.17 -1.11 0.17 -1.36 0.24 -1.11 0.08 -0.94 0.09 -1.09 0.17 -1.08 0.15 -1.16 -1.14 0.13 0.11 -1.09 0.11 -1.13  Radio Channel o 0.40 0.43 0.33 0.09 0.37 0.49 0.22 0.71 0.17 0.77 0.17 0.51 0.24 0.81 0.08 0.93 0.09 0.78 0.17 0.79 0.71 0.15 0.13 0.73 0.11 0.78 0.11 0.75  Mounting Point All C-to-H C-to-A C-to-F All H-to-H H-to-A H-to-F A-to-H A-to-A A-to-F F-to-H F-to-A F-to-F  System Configuration  K  K  (C = Ceiling, H = Headrest, A = Armrest, F = Footrest)  o CO  O O O o o o  o o o  o  us  X  X  EU  o o o  A A O  X  X  X  A O  X  X  X  X  X  o o o o o  X  Japan  A A O  X  X  X  X  X  o 0 o o o  X  Korea  X  3.168  o o o o  X  X  6.864  10.56  Frequency [GHz]  Figure 3.10. M u l t i b a n d - U W B spectral map. ' O ' = Usable bands, ' X ' = Unusable bands, and ' A ' = Usable bands only with detect and avoid schemes.  53  3.4  Time Dispersion in the Aircraft Environment The channel impulse response (CIR) can be described in term o f a power delay  profile (PDP) as such,  ^*H%)| =XM(*-**)| 2  (-)  2  3 8  k  where ak is the amplitude coefficient and S(r — T0 is the impulse function at different delays. Figure 3.11 and Figure 3.12 depict the shape o f typical P D P s measured for L O S and N L O S channels, respectively. A general sense o f the shape, duration and structure of the C I R can be obtained by estimating the R M S delay spread, r , and the number o f rms  dominant paths. Such information is very helpful when evaluating the performance o f U W B wireless communications systems. For instance, the ratio o f R M S delay spread o f a channel to the symbol period is often strongly correlated with the bit-error-rate ( B E R ) experienced by a wideband system. The number o f dominant paths is also very useful information for the design o f rake receivers in U W B systems because it determines how many rake fingers are required. Whether measured in the time or frequency domain, a measured channel response has a finite bandwidth that is determined by the instrument and/or the  measurement  process. The result is equivalent to convolving the true C I R with a sine function whose duration is inversely proportional to the bandwidth o f the measurement.  Before  processing a measured C I R , one must first remove the effects o f the finite bandwidth either by windowing or deconvolution. Here, we apply a Kaiser window with /? = 7 to the channel frequency response (CFR)  in order to suppress dispersion o f energy between delay bins. Then, we convert  the C F R s into channel impulse responses (CIRs) using an inverse Fourier transform (IFT). Specifically, the transformation was done directly in the complex baseband and without any zero padding i n the frequency domain. The CIRs are then normalized to unit energy. Next, i n order to remove the initial propagation delay, we define the start o f the CIRs. For L O S channels, we define the start o f the C I R as the first M P C that arrives within 10 d B and 10 ns o f the peak M P C . For N L O S channels, we define the start o f the C I R as the first M P C that arrives within 10 d B and 50 ns o f the peak M P C . W e remove 54  the propagation delay by setting the start time o f the first arriving M P C to zero. These procedures are based upon the recommendations contained i n Appendix I V o f the final report o f the I E E E 802.15.4a channel modeling committee [19].  3.4.1  Delay Spread The mean excess delay,  r  ,  o f a P D P is defined as the normalized first-order  mean  moment,  r  "  =^=  (3.9)  mea  k  The R M S delay spread,-  r , rms  is defined as the square root o f the second central  moment o f a P D P , =JT \  2  T  rms  mean  f  -(T \  (3.10)  mean }  '  v  where  1mean  \p I \ L, »\ k)  (3-11)  n  P  T  k  Before any o f the S - V model parameters are extracted, all M P C s with amplitudes that are more than 25 dB below the peak M P C are removed. This ensures that only significant M P C s are considered. The results obtained from the aircraft measurements are shown in Figure 3.13 and Figure 3.14. For both p-to-mp and p-to-p configurations, R M S delay spread increases with distance which agrees with the measurements o f the aircraft environment that were presented in [7] and results for other environments that were presented i n [20]. increase i n x  rms  This  as a function o f distance is related to the decrease i n power at greater  distances and is very well known.  A summary o f how x  rms  changes with respect to  distance, d, is presented in Table 3.5 where y is the distance dependent exponent as dJ. The large spread in  r  rms  shown in Figure 3.13 and Figure 3.14 can be easily  explained with the different channel conditions associated with the different antenna mounting points. For p-to-mp configuration, whenever the receiving antenna is placed at the headrest, the channel can roughly be classified as a L O S channel. A s a result, the 55  P D P w i l l always have a strong spike as shown in Figure 3.11, and the presence o f the strong spike w i l l result i n a much smaller in  x  rms  T  RMS  as shown in Figure 3.13. The large spread  in the headrest case itself is a result o f shadowing caused by the overhead  compartments.  Whenever the receiving antenna is placed at the armrest or footrest, the  channel is almost always N L O S except for a few rare cases along the aisle. A s a result, irms  is always larger.  variation i n  T  RMS  However, since N L O S channels do not have a strong path, the  is much smaller. For peer-to-peer configuration, since L O S condition  only exists for headrest to headrest configuration, only the data points corresponding to that particular case showed much lower  T RMS  Although the increase o f R M S delay spread with respect to distance is observed, the measured R M S delay spread is not as large as the results obtained in [7]. This is expected because as pointed out in [21], the range o f R M S delay spread depends heavily on the measured bandwidth. Although the aircraft environment is enclosed i n a relatively small metallic cavity, the R M S delay spread is still comparable to values obtained for residential and office environments.  O n the other hand, i f we compare the R M S delay  spread observed to larger environments, such as outdoor or industrial settings, we can see that the R M S delay spread for the aircraft environment is much smaller.  Table 3.5. R M S delay spread increase rate, a. System Configuration Point to Multipoint  Peer to Peer  Mounting Point All C-to-H C-to-A C-to-F All H-to-H H-to-A H-to-F A-to-H A-to-A A-to-F F-to-H F-to-A F-to-F  a 1.08 0.63 1.35 1.00 1.85 0.98 1.29 1.60 1.61 1.88 1.84 1.95 2.07 2.04  (C = Ceiling, H = Headrest, A = Armrest, F = Footrest)  56  0  50  100  150  200  250  Delay [ns] Figure 3.12. Power delay profile o f a typical L O S channel (ceiling to footrest).  57  35 30  I 25 •o CO CD  I.  - Best Fit  •  Headrest  o  Armrest  V  Footrest  „„  20  4  5  6  7  8  9 10  Distance [m]  Figure 3.13. R M S delay spread obtained for p-to-mp configuration.  35 30 CO  c  25  ~o CO 0  20  k_ Q .  00 >^ 15 J2 0  Q  CO  10 Best Fit 5 0  •  Headrest to Headrest  o  All Others  4  5  6  7  8  9 10  Distance [m]  Figure 3.14. R M S delay spread obtained for p-to-p configuration.  58  3.4.2 Number of Dominant Paths To find the dominant paths, we first set 5 different threshold levels: 5 d B , 10 d B , 15 d B , 20 d B , and 25 d B from the maximum peak in a given P D P . Then, any M P C s i n the P D P s are considered to be a dominant path i f the energy o f the M P C is greater than the threshold. Figure 3.15 and Figure 3.16 are the C D F s o f the number o f significant paths seen in the P D P for the p-to-mp and p-to-p configurations respectively. Table 3.6 summarizes the number o f dominant paths observed for each o f the receiver cases and the percentage o f energy captured with those identified paths. If we compare the number o f dominant paths i n the aircraft environment with  other  conventional environment under the same threshold level, we can see that the number o f paths is significantly less when compared with environments like the residential or office environment. The number o f path is about the same however, when we compare with industrial environment that has a rich amount o f scatterers.  This result is a natural  consequence o f propagation inside a large conducting cavity within which the signal can reverberate [8].  Table 3.6.  M e a n excess delay, R M S delay spread, number o f significant paths, and  energy captured for different thresholds levels. System Configuration Point to Multipoint  Peer to Peer  Threshold [dB] 5 10 15 20 25 5 10 15 20 25  tmean [US]  ^rms  6.4 9.6 13.1 16.2 18.5 12.4 17.3 21.6 24.5 26.2  [ns] 4.0 7.3 11.0 14.7 17.9 7.7 12.1 16.2 19.5 21.8  59  Num. of Paths 15 75 180 324 501 33 159 354 572 801  % Power 30 55 74 87 95 27 63 84 94 98  Figure 3.15. C D F o f the number o f significant paths for p-to-mp configuration.  Number of Paths (NP)  Figure 3.16. C D F o f the number o f significant paths for p-to-p configuration.  60  3.5  Conclusions W i t h its confined volume and cylindrical structure, and the dense and regular  layout o f its seating, the passenger cabin o f a mid-sized airliner is physically quite different from the residential, office, industrial and outdoor environments considered by the I E E E 802.15.4a propagation committee.  Based upon an extensive  measurement  database that includes both point-to-point and point-to-multipoint configurations, we have determined the range o f distance and frequency dependent path gain exponents (1.7 to 2.6 and -1.09 to -1.86) and the R M S delay spread (4 to 22 nsec) that characterize this environment.  Based upon these results, we conclude that the passenger cabin most  closely resembles the previously characterized industrial environment. However, our measurements also reveal that the dense and regular layout o f the passenger seats cause the two-dimensional coverage pattern to take the form o f distinctive chevron-shaped contours with path loss increasing most rapidly along the window seats and least rapidly along the aisle seats. This suggests that a comprehensive path loss model for such environment could include antenna separation and distance offset from the cabin aisle, as input parameters. A three-dimensional model could be generating by including distance below the headrest as another input parameter. In most cases, our results take the form o f the parameters o f the corresponding models recommended by the I E E E 802.15.4a channel modelling committee and can be used directly i n simulations o f U W B propagation i n an aircraft interior. Accordingly, our results w i l l assist: (1) those planning U W B deployments and field trials in aircraft, (2) those wishing to verify the results o f electromagnetic simulations o f aircraft interiors, (3) those wishing to simulate U W B aircraft systems with realistic channels, and (4) those wishing to predict the level o f interference that one might experience from wireless devices i n other locations within the passenger cabin.  61  References N . R. D i a z and M . Holzbock, "Aircraft cabin propagation for multimedia communications," Proc. EMPS 2002, 25-26 Sep. 2002. M . Youssef and L . Vahala, "Effects o f passengers and internal components on electromagnetic propagation prediction inside Boeing aircrafts," 2006 IEEE  APS  Int. Symp. Dig., pp. 2161-2164, 9-14 Jul. 2006. M . Jafri, J. E l y and L . Vahala, "Comparative analysis o f interference path loss coupling patterns on B-737 vs B-757 airplanes," Digital Avionics Systems Conference, v o l . 1, pp. 6.B.5 - 61 - 10, 30 Oct. - 3 N o v . 2005, G . Hankins, L . Vahala and J. H . Beggs, "Propagation prediction inside a B767 i n the 2.4 G H z and 5 G H z radio bands," 2005 IEEE APS Int. Symp. Dig, vol. 1A, pp. 791-794, 3-8 Jul. 2005. C. P. Niebla, "Coverage and capacity planning for aircraft in-cabin wireless heterogeneous network," Proc. IEEE VTC 2003 - Fall, pp. 1658-1662, 6-9 Oct 2003. G . A . Breit, H . Hachem, J. Forrester, P. Guckian, K . P. Kirchoff, B . J. Donham, " R F propagation characteristics o f in-cabin C D M A mobile phone networks,"  Digital Avionics Systems Conference, pp. 9.C.5-1—9.C.5-12, 30 Oct. - 3 Nov. 2005. N . R . Diaz and J.E.J. Esquitino, "Wideband channel characterization for wireless communications inside a short haul aircraft," Proc. IEEE VTC 2004 - Spring, pp. 223-228, 17-19 M a y 2004. M . P. Robinson, J. Clegg, and A . C . Marvin, "Radio frequency electromagnetic fields i n large conducting enclosures: effects o f apertures and human bodies on propagation and field-statistics," IEEE Trans. Electromagn. Compat, v o l . 48, no. 2, pp. 304-310, M a y 2006. R. Bhagavatula, R. W . Heath and S. Vishwanath, "Optimizing M I M O antenna placement and array configuration for multimedia delivery i n aircraft," Proc. IEEE VTC 2007 - Spring, pp. 425-429, A p r . 2007.  62  [10]  A . F . Molisch, J. R . Foerster and M . Pendergrass, "Channel models for ultrawideband personal area networks," IEEE Wireless Commun., vol. 10, pp. 1421, Dec. 2003.  [11]  A . F . M o l i s c h et ah, " A comprehensive standardized model for ultrawideband propagation channels," IEEE Trans. Antennas Propagat., vol. 54, no. 11, pp. 31513165, N o v . 2006.  [12]  T . B . Welch et al, "The effects o f the human body on U W B signal propagation i n an indoor environment," IEEEJ. Sel. Areas Commun., vol. 20, no. 9, pp. 17781782, Dec. 2002.  [13]  A . F . M o l i s c h , "Ultrawideband propagation channels: Theory, measurement, and modeling", IEEE Trans. Veh. Technol, vol. 54, no.9, pp. 1528-1545, Sep. 2005.  [14]  C . C . Chong, Y . K i m and S. S. Lee, "Statistical characterization o f the U W B propagation channel i n various types o f high-rise apartments," IEEE Wireless Commun. Networking Conf., vol. 2, pp. 944-949, Mar. 2005.  [15]  J. A . Dabin, A . M . Haimovich, and H . Grebel, " A statistical ultra-wideband indoor channel model and the effects o f antenna directivity on path loss and multipath propagation," IEEEJ. Sel. Areas Commun., vol. 24, no. 4, pp. 752-758, A p r . 2006.  [16]  W . Q . M a l i k , D . J . Edwards and C . J . Stevens, "Frequency-dependent pathloss i n the ultrawideband indoor channel," Proc. IEEE Int. Conf. Commun. 2007, vol. 6, pp. 800-804, Mar. 2007.  [17]  S. R . Saunders and A . Aragon-Zavala, Antennas and Propagation for Wireless Communications Systems, Wiley, 2007.  [18]  J. Chuang, N . X i n , H . Huang, S. Chiu, and D . G . Michelson, " U W B radiowave propagation within the passenger cabin o f a Boeing 737-200 Aircraft," Proc. IEEE VTC 2007 - Spring, pp. 496-500, Apr. 2007.  [19]  A . F. M o l i s c h et al., " I E E E 802.15.4a channel model - final report," Tech. Rep., I E E E 802.15-04-0662-00-004a, N o v . 2004.  [20]  S. S. Ghassemzadeh, R. Jana, C . W . Rice, W . Turin and V . Tarokh, "Measurement and modeling o f an ultra-wide bandwidth indoor channel," IEEE Trans. Commun., vol. 52, no. 10, pp. 1786-1796, Oct. 2004.  63  J. Karedal, S. Wyne, P. Aimers, F. Tufvesson, and A . F. M o l i s c h , " U W B channel measurements in an industrial environment," pp. 3511-3516, 29 N o v . - 3. Dec. 2004.  64  Proc. IEEE Globecom 2004, v o l . 6,  Chapter 4 UWB Channel Impulse Response within the Passenger Cabin of a Boeing 737-200 Aircraft 4.1 ^  Introduction In order to effectively predict and compare the performance o f ultrawideband  ( U W B ) wireless communication systems, the shape and duration o f the channel impulse response (CIR), and the small-scale fading statistics experienced by individual multipath components ( M P C s ) , need to be accurately modeled. The placement o f the fingers in rake receivers, the guard-time required i n O F D M systems, and the design o f mitigation techniques such as insertion o f cyclic prefixes are all affected by time-varying time dispersion due to the propagation channel. The shape o f the C I R also affects  the  performance o f U W B ranging and positioning algorithms because it determines how well the algorithm w i l l be able to detect the first arriving M P C . In recent years, the channel modeling subcommittees o f the I E E E 802.15.3a and 802.15.4a task groups devoted considerable effort to the modeling o f U W B channel impulse responses under both lineof-sight ( L O S ) and non-line-of-sight ( N L O S ) conditions i n residential, office, outdoor and industrial environments at ranges up to 15 m. The standard channel models that they developed allow fair comparison between alternative U W B systems under a range o f channel conditions and deployment scenarios [1][2]. UWB  systems operating between 3.1 and 10.6 G H z hold great promise for  enabling high data rate multimedia and network access within the passenger cabin o f an aircraft or facilitating operations and maintenance through deployment o f low power U W B - b a s e d sensor networks. However, with its confined volume and cylindrical structure, the passenger cabin o f an aircraft is fundamentally different from previously  A version of this chapter has been submitted for publication: J. Chuang and D . G . Michelson, " U W B Channel Impulse Responses within the Passenger Cabin of a Boeing 737-200 Aircraft," submitted to IEEE Transactions on Vehicular Technology, 12 October 2007.  65  modeled environments. Although several research groups have made  considerable  progress i n characterizing aircraft passenger cabins in support o f deployment o f more conventional wireless technologies such as Bluetooth and I E E E 802.11 wireless L A N [3]-[10], no other groups have yet reported results regarding U W B propagation i n the aircraft passenger cabin environment. Previously, we have reported upon the large-scale aspects o f U W B  propagation  within the passenger cabin o f a typical mid-sized airliner [11][12]. Here, we focus on the small-scale aspects o f U W B propagation. Based upon frequency, response data collected over the range 3.1-10.6 G H z between numerous locations aboard a Boeing 737-200 aircraft, we have characterized two principal aspects o f small-scale propagation o f the U W B channel: (1) the shape and duration o f the channel impulse response (CIR) and (2) the  small-scale fading statistics experienced by individual multipath  components  ( M P C s ) . Due to the similarities in the cross-section o f other mid-sized airliners, our results w i l l also be generally applicable to the A 3 2 0 family from A i r B u s , the A R J 2 1 family from A C A C , and the C R J series from Bombardier. The remainder o f this chapter is organized as follows. In Section 4.2, we describe the configuration and calibration o f our V N A - b a s e d channel sounder, our procedure for collecting data i n the aircraft, and our measurement approach. In Section 4.3, we present our proposed model for the shape and duration o f the P D P seen i n the aircraft passenger cabin environment and the small-scale fading statistics measured. In Section 4.4, we describe how we modified the standard channel model simulation code developed by I E E E 802.15.4a to apply to the aircraft passenger cabin environment. W e validate our model by regenerating CIRs and comparing the essential channel parameters with those derived from the measured CIRs. Finally, we summarize our key findings i n Section 4.5.  4.2  Measurement Approach  4.2.1  Channel Sounder Configuration and Calibration The channel sounder configuration and calibration procedure used i n this study are  the same as those used in our recent study o f the large-scale aspects o f U W B  66  propagation. Because a more complete description o f the setup and calibration can be found i n [12], we w i l l only summarize the essentials i n this section. Our channel sounder is based upon an Agilent E8362B vector network analyzer. Two Electrometrics 6865 U W B omni-directional biconical antennas are attached to the VNA  through  two  15-m long L M R - 4 0 0  UltraFlex  coaxial  cables.  During  the  measurements, the start and stop frequencies are set to 3.1 and 10.6 G H z , respectively, the number o f frequency points is 6317, the intermediate bandwidth is set to 3 k H z and the transmit power is set to 5 d B m . W e verified that the channel is static by taking 10 consecutive sweeps in several locations throughout the aircraft. A s expected, we found no significant differences between the sweeps. The V N A and the coaxial cable up to the antenna connectors are calibrated using the 12-term error model that is implemented by the V N A ' s calibration facility. The antennas are calibrated separately using an approximate approach described in [13]. This approach is based upon the assumption that the M P C s are arriving from all directions. A n averaged antenna transfer function ( A T F ) - essentially a measure o f the  average  distortion (averaged over all angle o f arrivals o f the M P C s ) caused by the antennas - is obtained from a set o f A T F measurements collected under free space conditions. Details of how we obtained our antenna correction data are summarized in [12].  4.2.2  Data Collection W e collected our measurement data within the passenger cabin o f a Boeing 737-  200 aircraft. The aircraft, which is 21 m i n length, 3.54 m i n width and 2.2 m in height, can carry over 100 passengers. Plans and cross-section o f view o f the passenger cabin are shown i n Figure 4.1 and Figure 4.2, respectively. Here, we have considered both pointto-multipoint (p-to-mp) and peer-to-peer (p-to-p) wireless system configurations. In the point-to-multipoint configuration, the transmitting antenna is mounted on the ceiling in the manner o f an access point, as suggested by Figure 4.2, and the receiving antenna is placed at the headrest, armrest and footrest level o f the passenger seats throughout the aircraft. The different receiving antenna mounting positions not only represent the typical use cases such as using a cell phone (headrest), a laptop (armrest), or devices that might be contained in passengers' carry-on baggage (footrest) but also represent both line-of67  sight (headrest) and non-line-of-sight (armrest and footrest) channel conditions. In the peer-to-peer configuration, the transmitting antenna is mounted on the armrest level. In this case, all the receiving antenna positions are considered as N L O S . In order to check the consistency o f our results, we have introduced redundancies to the measurements that we collected during our development runs. For example, we compared the results obtained with the transmitting antenna successively placed i n three different locations or with the receiving antenna successively mounted on opposite sides of the bilaterally symmetric aircraft. Exploiting symmetry effects have also allowed us to dramatically reduce the number o f measurements needed to characterize propagation within the aircraft.  4.2.3 Measurement Database In the point-to-multipoint configuration, we collected data in the middle seats on the port side o f the aircraft at row 4, 11 and 19. In each case, the transmitting antenna was mounted on the ceiling o f the passenger cabin i n the aisle beside row 2. A t each row, we collected 49 spatial samples by moving the transmitting antenna across a 7-by-7 grid with a spacing o f 5 cm. B y collecting 49 spatial samples in this manner, we obtained enough data to obtain a good estimate o f the amplitude statistics within a local area [14] [15]. The 5-cm spacing was chosen because it corresponds to half the wavelength o f the lowest frequency. This ensures that the samples are sufficiently independent [14] [15]. W e chose to move the transmitting antenna instead o f the receiving antenna  (as  suggested i n [15]) because: (1) it is too difficult to move the receiving antenna when it is mounted close to the seats and (2) this alternative approach was shown in [13] to successfully characterize the channel. The slant distances from the transmitting antenna to each o f the rows considered are approximately 2, 7 and 13 m, respectively. We have also taken 9 measurements with a 3-by-3 5 cm spacing grid at rows 7 and 15. The measurements taken at these two rows are used only to characterize the shape o f the P D P rather than estimate the small-scale fading statistics. According to [16], 9 measurements are sufficient to average out the small-scale fading and permit the true shape o f the P D P to be recovered. In the peer-to-peer configuration, we collected measurements at row 11  68  with a 7-by-7 grid with 5 cm spacing. Additional data from measurements collected [12] are also used to derive the results in this chapter.  69  5cn  _L T  A A A A A A A  A A A A A A A  A A A A A A A  A A A A AA AA AA A A A A  A A A A A A A  A A A A A A A  •  )  •  )  •  )  •  )  •  )  •  • •  5cm  (•  •  •  [n  •  •  • •  •  (•  •  •  (•  •  •  •  (•  •) •  (•  •  )  •  )  •  (• •  (•  Figure 4.1. Layout o f a Boeing 737-200 aircraft. Circles represent the location o f the receiving antennas and the triangles represent the location o f the transmitting antenna. In each transmitting antenna location, spatial sampling is performed according to the measurement  grid. The squares represent the measurement  measurement campaign as described in [12]. 70  taken from our first  INTERIOR TRIM-TO-TRIM 139.2 IN (3.54 M)  ,20 M)  L Figure 4.2.  148 IN (3.76 M)  -1  Cross-section o f the passenger cabin and the typical antenna mounting  positions for the point-to-multipoint and point-to-point configurations.  Figure 4.3. A photograph o f a typical receiving antenna location (armrest).  71  4.3  Models of Multipath Characteristics  4.3.1 Initial Processing of the Channel Impulse Response Whether measured in the time or frequency domain, a measured channel response has a finite bandwidth that is determined by the instrument and/or the  measurement  process. The result is equivalent to convolving the true C I R with a sine function whose duration is inversely proportional to the bandwidth o f the measurement.  Before  processing a measured C I R using our cluster identification algorithm, one must first remove the effects o f the finite bandwidth either by windowing or deconvolution. Here, we apply a Kaiser window with a beta value o f 7 in order to suppress dispersion o f energy between delay bins. Then, we convert the channel frequency responses (CFRs) into channel impulse responses (CIRs) using an inverse Fourier transform (IFT). Specifically, the transformation was done directly in the complex baseband and without any zero padding i n the frequency domain. The CIRs are then normalized to unit energy. Next, in order to remove the initial propagation delay, we define the start o f the CIRs. For L O S channels, we define the start o f the C I R as the first M P C that arrives within 10 d B and 10 ns o f the peak M P C . For N L O S channels, we define the start o f the C I R as the first M P C that arrives within 10 d B and 50 ns o f the peak M P C . W e remove the propagation delay by setting the start time o f the first arriving M P C to zero. After the initial delays have been removed, we align the spatial samples with respect to a given location and average them directly i n the time domain to give the small-scale averaged power delay profile ( A P D P ) . Finally, before any o f the S - V model parameters are extracted, all M P C s with amplitudes that are more than 25 dB below the peak M P C are removed. This ensures that only significant M P C s are considered i n the channel model. These procedures are based upon the recommendations contained i n Appendix I V o f the final report o f the I E E E 802.15.4a channel modeling committee [15].  4.3.2 Modeling Strategy Our first step is to decide which channel impulse model is the most suitable for the aircraft passenger cabin environment. Two standard U W B models were adopted by the 72  I E E E 802.15.3a and 4a task groups [1][2]. The sparse multi-cluster model is based upon the well known S - V model and is given by h  LK  (0=Z Z kj  e x  a  ;=o *=o  p  (4.1)  (M,/ ) ^ (' - / - ^ ) T  Here, the M P C s are modeled as Dirac delta functions, 8(.), and a ,i and 0*,/ are the k  amplitude and phase o f the /th M P C in the M i cluster. L is the total number o f clusters in the C I R and A' is the total number o f rays within the /th cluster. T/ and x ,i represent the k  arrival time o f the /th cluster and the /th M P C in the M i cluster, respectively. This model is used for residential and outdoor environments. The shape o f the P D P is described as the product o f two exponential functions, £ { | « | } <* e x p ( - T , / r ) e x p ( - T 2  t > /  4>;  Iy)  (4.2)  where Y and y are the cluster and ray decay constants respectively. In the S - V model, the arrival times o f the clusters are modeled by a Poisson distribution such that p(r |7;_ ) = A e x p [ - A ( r - 7 ; . ) ] /  1  /  (4.3)  1  while the arrival times o f the M P C s are modeled using a mixed Poisson distribution such that =  /'(^IV0,') ^  e x p  B( '.'" H.') r  r  + (l-/?)/l exp 2  -^(T.J-T^J)  (4.4)  where the A , Ai and fa are the mean arrival rate o f the clusters and M P C s within the P D P and P is the mixture probability. The dense single-cluster model depicted is used to describe dense scattering environment with a "soft" onset, e.g., the office and industrial environments under N L O S conditions. In these environments, one can no longer discern clustering within the C I R and the envelope o f the P D P can be described as,  \\ kj  E  a  CC  1-^exp  exp rise  J  -r k,l  rx  (4.5) J  where x denotes the attenuation o f the first component, y i determines how fast the P D P r  se  rises to its local maximum, yi represents the decay at later times. If the scattering environment is sufficiently dense, e.g., an industrial N L O S environment, then every time resolution bin contains an M P C . Accordingly, the P D P can be modeled as a tapped delay 73  line with fixed arrival time, At, given by the inverse o f the signal bandwidth.  Where  scatterers are less dense but the single cluster response still applies, e.g., an office N L O S environment, then the arrival rate o f the M P C s is best modeled as a Poisson distribution. Although two models are currently being used by I E E E 802.15.4a task group, we have to stress that the models are only somewhat representative o f the environment because they are only meant for making fair comparisons between the different system schemes and are not used for predicting performance. For example, a simplification made in the standard models is that all model parameters are derived from an average across the entire range o f separation distances. Furthermore, the simplification has led to the use of a constant exponential decay rate to model the industrial N L O S environment from 2 to 8 m. The constant decay, which keeps the shape o f P D P fixed, severely limits the range of R M S delay spread simulated by the channel model while many researchers have reported that the R M S delay spread, a measure o f the time dispersion i n the P D P , increases with distance [9][17][18]. In [17] and [19], the authors have further established the fact that the extended range o f R M S delay spread is mainly caused by a change i n the cluster decay rate, T, in the S V model or the exponential decay rate. Here, we seek to model the multipath characteristics more accurately by introducing the relationship between distance and the shape o f the P D P . This strategy has also been used in [17]. Even though we feel that the industrial N L O S channel model is somewhat inadequate, it is still a good starting point because we have adopted its tapped delay line model for the ray arrival rates and its small-scale fading distribution.  4.3.3  Shape of the Power Delay Profile Figure 4.4 shows the A P D P o f a L O S channel where the transmitting antenna is  mounted on the ceiling and the receiving antenna is mounted on the headrest o f a seat. A s in the case o f industrial N L O S channels, there are no distinct clusters within the aircraft A P D P and the M P C s form a continuous exponential decay. The only exception is a few strong spikes or impulses early in the A P D P that likely correspond to specular reflection of some sort. A P D P s measured at other receiving antenna mounting positions that exhibit similar characteristics are shown in Figure 4.5 and Figure 4.6. The only difference between the different antenna mounting positions is the existence o f a large spike ( L O S 74  component) at the beginning o f the P D P . A l s o , the A P D P s do not display the gentle rise to the maximum peak as described by the standard model in (4.5). Our proposed model o f the P D P in aircraft passenger cabins is as follows. First, because there is no gentle rise to a maximum, we model the shape o f the A P D P with just an exponential decay, (4.6) v  r  where y is the exponential decay rate. For L O S channels, we need to model the excess amplitude o f the L O S path from the exponential decay. Excess amplitude is defined as  5^  K =r  14  1  (4.7) t|LOS  V k  where PjqLos is the power o f the L O S component and the denominator is the expected power at the beginning o f the exponential decay described using (4.6). Using (4.6) and (4.7), we modeled the A P D P s for all three receiver scenarios and for all locations. Next, based on [17] and [19], we model how the shape o f the P D P changes with distance where,  y = Y +P \ogd + e 0  r  (4.8)  r  and K =K -\0B \og d r  0  K  +e  w  (4.9)  K  In (4.8) and (4.9), yo and KQ are intercepts and fi and B are the slopes. e and EK are zeroy  K  y  mean Gaussian random variable with standard deviations, a and OK, respectively, and d y  is the separation distance between the transmitting and receiving antennas. Using linear regression techniques  after  converting d into logarithmic scale, we estimate  the  parameters i n (4.8) and (4.9). The results are shown i n Figure 4.7 and Figure 4.9. Both shape parameters shown are changing with respect to distance in logarithmic scale. A l s o , from Figure 4.8 and Figure 4.10, we can see that both e and EK fit well against a zeroy  mean normal distribution i n logarithmic scale. A summary o f all the model parameters is given i n Table 4.1.  75  Table 4.1. Power delay profile model parameters Model Parameters K PK 0  yo Pi a d y  LOS (headrest) 24.18 -0.35 1.32 15.08 5.00 0.99 2 to 13 m  76  NLOS (armrest, footrest) N/A N/A N/A 12.79 7.94 1.74 2 to 13 m  Or -10 • _  -20  Delay [ns] Figure 4.4. A P D P measured with receiving antenna mounted at the headrest o f row 19.  77  Or -10 „  -20  _!  I  I  !  I  0  50  100  150  200  I  250  I  300  I  350  Delay [ns]  Figure 4.6. A P D P measured with the receiving antenna mounted at the footrest o f 19.  78  Distance [m]  Figure 4.7.  Excess amplitude of the L O S path, K , as a function of distance for L O S r  channels.  -6  -4  -2  0  2  4  6  Deviation of Excess Amplitude of LOS Path, ^ [dB]  Figure 4.8.  Confirming the log-normality o f the deviation of excess amplitude o f L O S  path, E . K  79  80  4.3.4 Interdependence of MPCs When designing systems that utilize spatial diversity, we need to model the dependence o f correlation between antenna elements i n the environment o f interest so that we can realize the desired diversity gain with the minimum antenna spacing. A t the same time, we need to model temporal correlation so that we know how to model the M P C s that have arrived very close i n time in the C I R . The correlation between signals measured at two spatial sampling points is defined as,  /=r,  where r(t, x ) and r(t, xj) are the received signals at grid points x, and x , and d is the t  y  absolute distance between the 2 o f 49 grid points [21]. Figure 4.11 shows the averaged correlation coefficient as a function o f distance for different parts o f the received signal. The  averaging comes from calculating the correlation coefficient o f all possible  combinations o f x and Xj and taking the mean o f the correlations when the separation t  distances are the same. From Figure 4.11, we can see that i f we only look at the first 13.3 ns, the correlation is much stronger and this is because o f the few strong M P C s coming from a narrow angular spread. This result has an important implication for multi-antenna application and that is i f the receiver captures only the few dominant components, then a much larger antenna separation is needed to obtain l o w correlation. The temporal correlation is given by  E{{a -d ){a -d )} k  k  k+x  k+x  where E{.} denotes expectation, a and a +\ are the amplitude o f the M i and (k + l)th k  k  M P C respectively, and a and a \ are their mean values [13]. For all receiving antenna k  k+  positions considered, the temporal correlation for the different delay taps are all below 0.4 with a mean correlation o f only 0.13. Because the delay bins have l o w correlation, we assume them to be uncorrelated with each other and we can now simplify the channel model by assuming that the path amplitudes at each delay bin are independent random variables. 81  4.3.5 Small-Scale Fading To determine the distribution for small-scale fading, 49 amplitude data, \cik,i\, at a certain delay, TO, measured using spatial sampling are fit using the maximum likelihood estimation  ( M L E ) against  several  probability  distributions  commonly  used  in  propagation modeling, including lognormal, Nakagami, Rayleigh, Ricean, and Weibull. Figure 4.12 shows the empirical cumulative distribution function ( C D F ) and the fit against theoretical C D F s . In Figure 4.12, other than the lognormal distribution, all other distributions fit the empirical C D F equally well. From this result, we can conclude that Rayleigh distribution is the best distribution, and the reason all other distributions except for the lognormal distribution fit equally well is because their shape factors, e.g., the mfactor i n Nakagami distribution, have transformed them into near replicas o f the Rayleigh distribution. This result is different from [19] where a lognormal distribution is used to model the fading statistics. The Rayleigh distribution is not an unexpected outcome because i n the aircraft passenger cabin environment, the Rayleigh distribution has been reported to be the small-scale fading statistics in environments with dense scatterers like the industrial environments [22]. Next, we use the Nakagami distribution to characterize the small-scale distribution at different delays because this distribution has the ability to model Rayleigh distribution as well as other types o f propagation scenarios. Moreover, because the 4a task group has adopted Nakagami distribution for small-scale fading, expressing our results in terms o f Nakagami distribution also allows fair comparisons with the other environments. The Nakagami distribution is given by the following equation,  T(m)  m n  x - exp 2m ]  m -x n  (4.12)  where m ^ Vi is the Nakagami m-factor, T(m) is the Gamma function, and Q is the meansquared value o f the amplitude. We estimate the m-factor o f the Nakagami distribution using the inverse normalized variance estimator with respect to the 49 spatial samples collected for all delays [22]. The estimated m-factor is, m=  ^  and 82  ,  (4.13)  where N is the number of spatial sampling points and h is the path amplitude. The scatter t  plot of estimated m-factors at different delays for the receiving antenna mounted on the headrest is shown in Figure 4.13. Although there are a few MPCs at the beginning of the PDP (typically when delay is less than 30 ns) that exhibit the Nakagami distribution, the Rayleigh distribution is still applicable for the majority of the PDP and for all antenna mounting positions in the passenger cabin. The estimated m-factors are found to follow a lognormal distribution by many researchers and the IEEE 802.15.4a task group [16][22]. The lognormal distribution is give by  ft.  (\nm-n ) ^ 2 ^ 2  m  fu( )  =  m  where p  m  and a  m  ^7z= P  (4.15)  ex  lot  are the mean and variance of the m-factors on a natural logarithmic  scale. Here, we also find that the w-factors follow a lognormal distribution. However, like the correlation coefficients, the fit to a lognormal distribution is not as accurate in the beginning of the PDP due to the few strong impulses near the leading edge of the response. The fit of w-factors to the lognormal distribution is shown in Figure 4.14. Although in [15], both ju and a are modeled as a function of delay, we did not find any m  m  evidence of a relationship. The initial spike in the PDP for the LOS channel is modeled using a fixed m-factor, mo, also given in natural logarithmic scale, and is typically much larger. A summary of the small-scale characteristics is presented in Table 4.2.  Table 4.2. Small-scale fading parameters Receiving Antenna Mounting Position Headrest at row 4 Armrest at row 4 Footrest at row 4 Headrest at row 11 Armrest at row 11 Footrest at row 11 Headrest at row 19 Armrest at row 19 Footrest at row 19  Mm  0~  [dB] 0.055 0.012 0.083 0.066 0.092 0.092 0.101 0.145 0.187  [dBl 0.286 0.293 0.267 0.287 0.284 0.269 0.301 0.290 0.318  m  83  m [dB] 4.03 0.92 2.13 2.91 2.87 2.14 2.23 1.91 1.98 0  c 92 'o IE  - 0 —  Entire PDP  -A—  Before 13.3 ns  -H—  After 13.3 ns  CD O  o  c o  JS 0 1  l_  o O  tn  CO ot_ O  10  20  30  40  Distance between spatial sampling points [cm]  Figure 4.11.  Averaged spatial correlation as a function o f antenna separation with the  receiving antenna mounted on the footrest of row  Z_i  0.01  i  i  i  i  i  0.02  0.03  0.04  0.05  0.06  ' I  0.07  Path Amplitude, |a |  Figure 4.12. A fit of the path amplitudes against theoretical distributions.  84  10  Delay [ns]  Figure 4.13. Estimated m-factors as a function of delay for receiving antenna mounted on the headrest o f row 19.  m-factors  Figure 4.14.  The lognormal fit of m-factors for the receiving antenna mounted at the  footrest o f row 19.  85  4.3.6 Delay Spread within a Local Area M e a n excess delay, r  ,  mean  and R M S delay spread, Th™, are two  important  parameters that help to characterize the shape and duration o f the P D P . In the case o f simple digital modulation schemes, the ratio o f T  rms  to symbol period is also known to be  strongly correlated with the bit error rate ( B E R ) . In Table 4.3, we compare the mean excess delay and R M S delay spread within a local area. The relatively small standard deviations o f the mean excess delay and R M S delay spread suggest that the channel is consistent within a local area.  Table 4.3. Time dispersion parameters within a local area. Receiving Antenna Mounting Position Headrest at row 4 Armrest at row 4 Footrest at row 4 Headrest at row 11 Armrest at row 11 Footrest at row 11 Headrest at row 19 Armrest at row 19 Footrest at row 19  4.4  Mean of x [ns] 0.81 5.0 17.2 0.83 24.2 31.0 4.78 29.04 32.83  m e a n  Std of x 0.42 2.51 1.65 0.62 1.62 1.71 1.15 2.12 1.3  m e a n  [ns]  Mean of [ns] 2.0 5.1 12.8 1.94 19.6 22.19 7.81 21.75 23.38  Std of  [ns]  1.0 1.57 1.32 1.22 1.17 1.24 0.82 1.16 0.93  A Simulation Model for UWB CIR in Aircraft Passenger Cabin After modeling the U W B propagation for environments like residential, office,  outdoor and industrial, 4a channel modeling subcommittee developed a simulation code that can generate CIRs typical in those environments. The M A T L A B - b a s e d code has four parts: ( 1 ) assignment o f the channel model parameters, (2) generation o f CIRs using random processes that simulates the arrivals o f the clusters and rays and the path amplitudes based the shape o f the P D P and small-scale fading distribution, (3) prediction of the frequency dependent path loss, and (4) conversion from continuous time to discrete time models. W e have modified the channel simulation code developed by 4a so that it can generate channel impulse response typical o f the aircraft passenger cabin 86  environment. First, we added two more sets o f channel model parameters corresponding the L O S and N L O S channel conditions in the aircraft passenger cabin environment. In particular, we have added the parameters o f small-scale fading. Then, in the part where CIRs are being simulated, instead o f using the shape o f the P D P as described in (6), we used a single exponential decay as described i n (5) in the simulator and inserted codes that randomly generate the exponential decay rate and excess amplitude o f the L O S path in (6) and (7) as a function o f distance using (8) and (9). The modified version o f the channel simulator can be downloaded from [23]. To validate the code, CIRs are generated using the modified channel simulator. Because our model depends on distance, distances from the aircraft measurements are used when we are regenerating the CIRs. A comparison o f measured and simulated A P D P is shown i n Figure 4.15. From the simulated CIRs, we also need to examine how closely the model can reproduce the C D F o f the R M S delay spread. The comparisons between simulated and measured R M S delay spread are shown i n Figure 4.16 and Figure 4.17. From Figure 4.16, we can see that the model has successfully reproduced the C D F o f R M S delay spread. If we look at the scatter plot i n Figure 4.17, we can see that the R M S delay spread is increasing as a function o f separation distance between the transmitting and receiving antennas. Because the clusters o f R M S delay spread represent the small-scale measurements we did for rows 4, 11 and 19, we can see that the range o f R M S delay spread in the aircraft passenger cabin environment is much greater than what one might expect from within a local area.  87  CO  2,  D_ Q CL <  •o 0  L_  3  in co 01  200 CD 73. Q. Q CL < T3 0 -4—'  J9 E  100  CO  200  Delay [ns]  Figure 4.15. Comparison o f the measured and regenerated A P D P .  XI CO  o 0  .a E  o  20  30  40  RMS Delay Spread [ns]  Figure 4.16. Comparisons o f the distribution o f the simulated and measured R M S delay spread for L O S and N L O S channels.  88  CO  c  30 • 25  NLOS simulation NLOS Fit  co (D CL  co >. JS a> Q CO  or  20 15 10  3  4  5  6  7 8 910  6  7 8 910  Distance [m] 30 CO  .g. T3  CO d)  • 25  NLOS Measred NLOS Fit  i_ Q. CO >.  20  is 0) Q  15  CO 10  1  2  3  4  5  Distance [m]  Figure 4.17. Comparisons o f the R M S delay spread with respect to distance for N L O S channels.  89  4.5  Conclusions W e have measured a multiplicity o f U W B channel impulse responses within the  passenger cabin o f a typical mid-size airliner for both point-to-multipoint and peer-topeer configurations. Based upon analysis o f the results, we have proposed a statistical model that describes the multipath characteristics o f the channel including the shape o f the power delay profile and both the spatial and temporal distribution o f the small-scale fading. W e have observed several noteworthy aspects o f U W B channel impulse responses within the passenger cabin o f a mid-size airliner: (1) the shape o f the P D P generally follows I E E E 802.15.4a's dense single-cluster model, but with negligible rise time and, on many occasions, one or more impulses or spikes near the leading edge o f the response, (2) delay spread tends to increase with path length and as the receiving antenna drops from the headrest to the footrest, (3) small-scale fading o f multipath components ( M P C s ) tends to follow a Nakagami distribution with a lognormally-distributed m parameter, as has been found i n other environments, and (4) the mean excess delay and rms delay spread within a local area (several wavelengths) are consistent. In most cases, our results take the form o f the parameters o f the corresponding models recommended by the I E E E 802.15.4a channel modelling committee and can be used directly in simulations o f U W B propagation in an aircraft interior. Accordingly, our results w i l l assist: (1) those planning U W B deployments and field trials in aircraft, (2) those wishing to verify the results o f electromagnetic simulations o f aircraft interiors, (3) those wishing to simulate U W B aircraft systems with realistic channels.  90  References [1]  A . F. M o l i s c h , J. R. Foerster and M . Pendergrass, "Channel models for ultrawideband personal area networks," IEEE Wireless Commun., vol. 10, pp. 1421, Dec. 2003.  [2]  A . F. M o l i s c h et al., " A comprehensive standardized model for ultrawideband propagation channels," IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3151 3165, N o v . 2006.  [3]  N . R . Diaz and M . Holzbock, "Aircraft cabin propagation for multimedia communications," Proc. EMPS 2002, 25-26 Sep. 2002.  [4]  M . Youssef and L . Vahala, "Effects o f passengers and internal components on electromagnetic propagation prediction inside Boeing aircrafts," 2006 IEEE AP-S Int. Symp. Dig, pp. 2161-2164, 9-14 Jul. 2006.  [5]  M . Jafri, J. E l y and L . Vahala, "Comparative analysis o f interference path loss coupling patterns on B-737 vs B-757 airplanes," Digital Avionics Systems Conference, v o l . 1, pp. 6.B.5 - 61 - 10, 30 Oct. - 3 N o v . 2005.  [6]  G . Hankins, L . Vahala and J. H . Beggs, "Propagation prediction inside a B767 i n the 2.4 G H z and 5 G H z radio bands," 2005 IEEE AP-S Int. Symp. Dig, v o l . 1A, pp. 791-794, 3-8 Jul. 2005.  [7]  C P . Niebla, "Coverage and capacity planning for aircraft in-cabin wireless heterogeneous network," Proc. IEEE VTC 2003-Fall, pp. 1658-1662, 6-9 Oct 2003.  [8]  G . A . Breit, H . Hachem, J. Forrester, P. Guckian, K . P . Kirchoff, B . J . Donham, " R F propagation characteristics o f in-cabin C D M A mobile phone networks," Digital Avionics Systems Conference, pp. 9.C.5-1—9.C.5-12, 30 Oct. - 3 N o v . 2005.  [9]  N . R . Diaz and J.E.J. Esquitino, "Wideband channel characterization for wireless communications inside a short haul aircraft," Proc. IEEE VTC 2004 - Spring, pp. 223-228, 17-19 M a y 2004.  [10]  R. Bhagavatula, R. W . Heath and S. Vishwanath, "Optimizing M I M O antenna placement and array configuration for multimedia delivery i n aircraft," Proc. IEEE VTC 2007 - Spring, pp. 425-429, A p r . 2007.  91  [11]  J. Chuang, N . X i n , H . Huang, S. Chiu and D . G . Michelson, " U W B radiowave propagation within the passenger cabin o f a Boeing 737-200 aircraft," Proc. IEEE VTC 2007 - Spring, pp. 496-500, Apr. 2007.  [12]  J . Chuang and D . G . Michelson, "Large-scale aspects o f U W B propagation within the passenger cabin o f a Boeing 737-200 aircraft," Submitted to IEEE Wireless Commun., 15 A u g . 2007.  [13]  C . C . Chong, S. K . Yong, " A generic statistical-based uwb channel model for highrise apartments," IEEE Trans. Antennas Propagat., vol. 53, no. 8, pp. 2389-2399, A u g . 2005.  [14]  A . F . M o l i s c h , "Ultrawideband propagation channels: Theory, measurement, and modeling", IEEE Trans. Veh. Technol., vol. 54, no.5, pp. 1528-1545, Sep. 2005.  [15]  A . F . M o l i s c h et al., " I E E E 802.15.4a channel M o d e l - Final report," Tech. Rep. Doc. I E E E 802.15-04-0662-02-004a, 2005.  [16]  C . W . K i m , X . Sun, L . C . Chiam, B . Kannan, F . P . S. Chin, and H . K . Garg, "Characterization o f ultra-wideband channels for outdoor office environment," IEEE Wireless Commun. Networking Conf, vol. 2, pp. 950-955, 13-17 M a r . 2005.  [17]  J. A . Dabin, A . M . M a i m o v i c h and H . Grebel, " A statistical ultra-wideband indoor channel model and the effects o f antenna directivity on path loss and multipath propagation," IEEEJ. Sel. Areas Commun., vol. 24, no. 4, pp. 752-758, A p r . 2006.  [18]  S. S. Ghassemzadeh, R . Jana, C . W . Rice, W . Turin, and V . Tarokh, "Measurement and modeling o f an ultra-wide bandwidth indoor channel," IEEE Trans. Commun., vol. 52, no. 10, pp. 1786-1796, Oct. 2004.  [19]  S. S. Ghassemzadeh, L . J. Greenstein, T. Sveinsson, A . K a v c i c and V . Tarokh, " U W B delay profile models for residential and commercial indoor environments," IEEE Trans. Veh. Technol, vol. 54, no. 4, pp. 1235-1244, Jul. 2005,  [20]  L . J. Greenstein, S. S. Ghassemzadeh, S-. C . Hong and V . Tarokh, "Comparison study o f U W B indoor channel models," IEEE Trans. Wireless Commun., vol. 6, no. l , p p . 128-135, Jan. 2007.  [21]  B . A l l e n et al, Ultra-wideband Antennas and Propagation, Wiley, 2007.  [22]  J. Karedal, S. Wyne, P. Aimers, F. Tufvesson, and A . F . M o l i s c h , "Statistical analysis o f the U W B channel i n an industrial environment," Proc. IEEE VTC 2004 - Fall, vol. 1, pp. 81-85, 26-29 Sept. 2004.  [23]  J. Chuang and D . G . Michelson, "Simulation Code for U W B CIRs in Passenger Aircraft," U B C Radio Science Lab, A u g . 2007, http://rsi. ece. ubc. ca/codes/'aircraft, html  93  Chapter 5 Conclusions and Recommendations 5.1  Conclusions This thesis  has  been  concerned  with the  identification o f clusters  within  ultrawideband ( U W B ) channel impulse responses (CIR) and the U W B propagation characteristics within the passenger cabin o f a Boeing 737-200 aircraft. In this thesis, we have made three major contributions to the modeling o f U W B propagation. First, we developed an automated cluster identification algorithm which makes the identification o f clusters more consistent and less subjective.  The algorithm also  determines how a U W B C I R can be most effectively represented by either the single exponentially decaying cluster model or the standard Saleh-Valenzuela (S-V) model. Compared to past work, ours is innovative i n four ways: (1) we implemented a novel significant M P C search algorithm that reduces small-scale fading that is inherent in channel measurements,  (2) our bounded search drastically reduced the number o f  searches required and made the algorithm more tractable, (3) only five input parameters are needed which is far less complicated than schemes proposed previously and (4) the iterative nature o f the algorithm and the manner in which the cluster selection rules are layered makes it possible to be used either as an autonomous tools or an interactive aid for the analysts. Furthermore, The validity o f our approach was verified using both the simulated U W B CIRs generated from the simulation code developed I E E E 802.15.4a task group and the measured CIRs from office and underground mine environments. Second, we characterized large-scale aspect o f U W B propagation within the passenger cabin o f a Boeing 737-200 aircraft which includes distance and frequency dependent path loss and time dispersion parameters such as R M S delay spread and number o f significant M P C s . From the measurements, we determined that the passenger o f a Boeing 737-200 aircraft is unique from the other conventional environments i n three ways. (1) The coverage within the passenger cabin is found to follow a chevron shape contour where the coverage is the greatest along the aisle and the weakest around 94  window seats. This result suggests that the path gain within the passenger cabin depends not only on the separation distance but also on the seat location and the mounting point. (2) When antenna effects are not as strong, e.g., i n p-to-p configurations, frequency dependence o f path loss is found to decrease with the square o f frequency, (3) x  r m s  is  found to vary greatly from 3 to 29 ns, with respect to the L O S and N L O S channel conditions associated with the different antenna mounting points and (4) the presence o f human increased the path loss and decreased delay spread. Third, based on extensive measurements, we developed statistical models that describe the small-scale aspects o f U W B propagation within the passenger cabin o f a Boeing 737-200 aircraft. Specifically, we looked at two major aspects: the shape o f the power delay profile (PDP), and the distribution o f small-scale fading. Four noteworthy aspects were discovered: (1) the shape o f the P D P generally follows the dense singlecluster model used to describe the channels like the industrial non-line-of-sight ( N L O S ) environment^ (2) delay spread tends to increase with path length and as the receiving antenna lowers, (3) small-scale fading can be modeled using Nakagami distribution with a lognormally-distributed m-factor, as found in other environments and (4) the mean excess delay and rms delay spread within a local area (several wavelengths) are fairly consistent.  In most cases, our model follows the form o f the parameters o f the  corresponding channel models recommended by I E E E 802.15.4a and can be used directly i n simulations. B y developing the automated cluster identification algorithm i n Chapter 2, we have resolved a major issue regarding the U W B channel modeling process. In Chapter 3 and 4, the measurements and modeling o f U W B propagation in the passenger cabin o f an aircraft is an essential first step i n the modeling o f propagation i n the public transportation environment.  The results are going to help (1) those planning U W B  deployments and field trials in aircraft, (2) those wishing to verify the results o f electromagnetic simulations o f aircraft interiors, (3) those wishing to simulate U W B aircraft systems with realistic channels, and (4) those wanting to understand the effect o f interference from other wireless devices aboard the aircraft.  95  5.2  Recommendations for Further Work While this study has demonstrated the practical issues in identification o f clusters  in U W B channel modeling and the modeling o f the U W B propagation in the aircraft environment, there are still many limitations to our work and we recommend that several topics o f considerable practical interest be pursued i n the very near future. In the automated cluster identification algorithm, we recommend adding smoothing techniques, such as applying a running average, used i n image processing. In channel measurements, we feel that more measurements are needed still to fully characterize the aircraft environment.  Due to time constraints and other administration issues, only  limited data were collected to characterize the effect o f human presence. Nevertheless, we have demonstrated that the effect o f human presence is important and should be examined with great scrutiny. More importantly, it should be extended to the small-scale aspects o f U W B propagation. Finally, in order to investigate the commonality between other types o f vehicles used in public transportation, measurement campaigns should be carried out for other types o f aircrafts as well as other types o f vehicles.  96  Appendix A Useful Tables Table A . 1 . Dimensions o f modern aircraft. Manufacturer Boeing Boeing ACAC AirBus Bombardier Embraer  Aircraft Family 737 757 ARJ21 A320 CRJ E-Jet  Cabin Width 3.54 m 3.54 m 3.14m 3.7 m 2.53 m 2.74 m  Recent model 737-900 757-300 ARJ21-700 A321 CRJ 1000 E-175  Cabin Height 2.20 m 2.20 m 2.03 m 2.22 m 1.85 m 2m  Table A . 2 . Large-scale parameters o f conventional environments. Environment CM1 CM2 CM3 CM4 CM5 CM6 CM7 CM8  Residential-LOS Residential-NLOS Office-LOS Office-NLOS Outdoor-LOS Outdoor-NLOS Industrial-LOS Industrial-NLOS  PG [dBm] -43.9 -48.7 -35.4 -57.9 -45.6 -73.0 -56.7 -56.7 0  X [dB] 2.22 3.51 1.9 3.9 0.83 2 6 6  n  a  1.79 4.58 1.63 3.07 1.76 2.5 1.2 2.15  K  1.12±0.12 1.53±0.32 0.03 0.71 0.12 0.13 -1.103 -1.427  Table A . 3 . Time dispersion parameters o f conventional environments. Environment  tfnean  trms  NP 10dB  CM1 CM2 CM3 CM4 CM5 CM6 CM7 CM8  [ns] 16.36 19.68 8.816 17.49 26.31 70.94 5.55 114.3  [ns] 17.75 19.09 10 13.25 30.24 75.4 8.65 90  15.28 35.04 20.14 54.84 23.16 30.44 15.94 355.4  Residential-LOS Residential-NLOS Office-LOS Office-NLOS Outdoor-LOS Outdoor-NLOS Industrial-LOS Industrial-NLOS  97  Appendix B Detailed Setup of E8362B PNA Figure B . l shows the connections o f the U W B channel sounder used to measure the U W B channel i n the passenger cabin o f a Boeing 737-200 aircraft.  The P N A is set to  work in the forward operation, i.e, to measure the S-parameter, S21, by taking the ratio o f receiver B ' s measurement over receiver R l ' s measurement. B y utilizing option 014 on the P N A , we avoided entering the directional coupler across the ports i and j , and went directly into receiver B . The bypass gave us an extra 12 dB gain. A detailed description of each port on the P N A is given i n Table B . l . The settings o f the P N A are summarized in Table B . 2 . The extra gain allowed us to increase the coverage up to 15 metres with at least 10 dB o f signal-to-noise ratio. The link budget o f the channel sounder is shown in Table B . 3 .  Table B . l . E8362B P N A option 014 port description. Description Source output Receiver R l input Source output Directional coupler Port 1 Directional coupler Receiver A input Receiver B input Directional coupler Port 2 Directional coupler Source output Receiver R2 input Source output  Ports a b c d e f g h i j k 1 m n  98  through arm  arm through  Table B . 2 . Setting of E8362B P N A . P N A Settings Start Frequency Stop Frequency IF Bandwidth Number of Sampling Points Input Power  Values 3.0 G H z 10.6 G H z 3 kHz 6401 5 dBm  Table B . 3 . L i n k budget of the U W B channel sounder Links Transmitted Power Cable Loss Transmit Antenna gain Path Loss Receiver Antenna gain Cable Loss Received Power Receiver Sensitivity System Margin  Values 5 dBm -9.1 dB* OdBi -82.1 dB** OdBi -9.1 dB* -95.3 dBm -107.2 dBm 11.9 dB •Calculated from data sheet at the highest frequency 10.6 G H z **Path loss is calculated using Friis formula with an exponent of 2.25 at a range of 15m.  99  E8362B Performance Network Analyzer  15mLMR-400 Coaxial Cable  15 m LMR-400 Coaxial Cable  ^  Channel  EM6865 UWB Omni direction Bicone Antenna  EM6865 UWB Omni direction Bicone Antenna  Figure B . l . Connections o f the U W B channel sounder.  100  Appendix C Calibration of Antennas In order to calibrate for the effect o f antennas, the angle o f arrival ( A o A ) o f multipath components ( M P C ) is needed. To determine the A o A , virtual or real antenna array are often used. However, due to the limited space available in the passenger cabin, it is too difficult to deploy such an array.  We have, instead, decided to use an  approximate approach to calibrate the effect o f the antenna.  First, we have to assume  that the M P C s are arriving uniformly from all directions. Next, we measure the antenna transfer function ( A T F ) with respect to all orientations o f the receiving antenna i n open space. The measured A T F s are then averaged to form the averaged A T F . This averaged A T F is then deconvolved from the measured channel transfer function (CTF) directly in the frequency domain. Figure C . l shows a picture o f the measurement setup used to measure the A T F s .  The measurements were done on the roof top o f an L-shaped  building with the antennas mounted on a 3.4 metres high tripod to minimize reflections from the environments. The ground reflection is also minimized by placing the antennas along the two wings o f the building, and as a result, the antennas are 14.4 metres apart. The measured averaged A T F is shown in Figure C.2. In total 24 A T F s were taken with respect to the different elevation angles over the range from 0 to 345 degrees with 15 degree increments.  A l s o , 12 A T F s were taken with respect to the different azimuth  angles over the range from 0 to 330 degrees with 30 degree increments. Since there are very little cancellations in the A T F s , we can conclude that the antennas are placed in a nearly free space environment and thus, only contain the effect o f the antennas.  Note  that, the averaged A T F is showing the typical response o f an receiving antenna with constant gain where the effective aperture o f the antenna is decreasing with increasing frequency. The decrease i n effective aperture leads to the decrease i n the received power with increasing frequency.  101  Figure C . l . Measurement setup o f the antenna transfer functions.  Frequency [GHz] Figure C.2. Averaged antenna transfer functions.  102  Appendix D Detailed Measurement Plan  •• •  ro  (a)  (b)  (c)  Figure D . l . Detailed measurement plan o f p-to-mp configuration for (a) empty aircraft, (b) half full aircraft and (c) full aircraft.  (A = transmitting antenna, O = receiving  antenna, • = passengers)  103  P'  CD  Figure D.2.  CEO  Detailed measurement plan of p-to-p configuration.  antenna, O = receiving antenna)  104  (A = transmitting  Appendix E Matlab Code of the Automated Cluster Identification Algorithm %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% /o /o% 0  0  main.m - begin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% env = 'demo'; load('demo'); h = h_demo; % parameters of the algorithm Nloc = length(h(l,:)); % number of CIR from 'h' zone = 7; % local maxima search zone [samples] sep = 8; % maximum separation time before two local maxima are considered as two clusters [ns] power_diff = 2; % power difference of old and new clusters [dB] minclusterlength = 3; % this is the length with respect to how many local maxima min_error_threshold = 1; %2.7 % minimum error threshold [dB] sig_peak = 0.1;% when finding local maxima, the local maxima have to be greater than the rest by [dB] % othe parameters of the algorithm maxnumclusters = 100; % a fail-safe stopping condition for the while loop minerrorreduction = 0.01; % stopping condition when increasing the number of clusters does not significantly decrease the residual error [dB] (normally not used) max_delay = 2500; % maximum delay, rays beyond this delay are not considered [ns] add_ruleCheck = 0; % set to zero if you need to enforce the additional rules. add_boundaryCheck = 0; % set to zero if you need to check the boundaries of the clusters, saveresults = 0; % set to zero i f you do not want to save the results in a workspace. step_by_step = 0; % set to 1 if you want to see the evolution of cluster ID process, showresult = 1; % for output graph control enable_axis_control = 1; xmin = 0; xmax = 350; ymin = -80; ymax = 0; for(i= l:Nloc) threshold = max(20*logl0(abs(h(:,i)))) - 100; noise_floor(i) = threshold; % noise floor, rays below this value are not considered end; % loop through all the CIRs for(i= l:Nloc) No_of_CIR = i % put the CIR into the algorithm [bp Nbp p d p l p t_lp Carr Camp Cnum Rarr Ramp Rnum Rbp Rarrindex... error_vector] = clusterAlgorithmTest(h(:,i), t, zone, sep, power_diff,...  105  max_num_clusters, .min_error_threshold, min_cluster_length, min_error_reduction, sig_peak,. noise_floor(i), max_delay, add_ruleCheck, add_boundaryCheck, step_by_step); % for plotting purposes only pdp = 20*logl0(abs(h(:,i))); if(show_result == 1) % show identification result figure(4); elf; hold on; plot(t, pdp); plot(Carr_sim_plot, Camp_sim_plot, 'r. , 'MarkerSize', 16); plot(t_lp(bp), pdp_lp(bp), 'ms', 'MarkerSize , 8); for(k= l:Nbp) start = bp(k); if(k == Nbp) stop = length(pdplp); else stop = bp(k+l)-l; end; coef = polyfit(t_lp(start:stop), pdp_lp(start:stop), 1); line = coef(l)*t_lp(start:stop) + coef(2); plot(t_lp(start:stop), line, 'k', 'linewidth', 1.5); end; hold off; xlabel(Time [ns]'); ylabel('PDP [dB]'); % title([env,' -', int2str(i)]); if(enable_axis_control == 1) axis([xmin xmax ymin ymax]); end; 1  1  % show RMS error figure(5); for(nz= l:length(error_vector)) if(error_vector(nz) ~= 0) break; end; end; nz hold on; plot(nz:length(error_vector), error_vector(nz:length(error_vector)), '-v'); xlabel('Number of Identified Clusters'); ylabel('RMS Error for entire PDP [dB]'); axis([0 14 0 20]); end; % save them all into a big workspace if(save_results == 1) Cnum_all(i) = Cnum; if(i==l) Carr_all(:,l) = Carr'; Camp_all(:,l) = Camp'; else if(length(Carr_all(:,l)) > Cnum) Carr_all(l:Cnum,i) = Carr; 106  else Carr_all = [Carr_all; zeros(Cnum-length(Carr_all(:,l)),i-l);]; Carr_all(:,i) = Carr'; end; if(length(Camp_all(:, 1)) > Cnum) Camp_all(l :Cnum,i) = Camp; else C a m p a l l = [Camp_all; zeros(Cnum-length(Camp_all(:,l)),i-l);]; Camp_all(:,i) = Camp'; end; end; save([env, 'dervied'], 'Cnum_all', 'Carr_all', 'Cnumall'); end; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% main.m - end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %  0  / o % % % % %  cluster iteration.m - begin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [bp Nbp pdp_lp t i p Carr Camp Cnum Rarr Ramp Rnum Rbp Rarrindex error_vector]... = clusterAlgorithmTest(h, t, zone, sep, power_diff, max_num_clusters,... min_error_threshold, minclusterlength, min_error_reduction, sig_peak, noisefloor,... maxdelay, .addruleCheck, add_boundaryCheck, stepbystep); % % % %  this function is used the incrementing the number of clusters in the automated cluster identification algorithm. At the end of this script, the identified clusters and major rays along with their arrival time and amplitude will be saved in a workspace.  % % % % % % % % % % %  INPUTS h —> CIR in linear voltage units t --> time axis in [ns] zone —> local maxima search zone in [samples] sep —> maximum separation time power_diff --> power difference of new and old clusters dip --> not used maximum_num_clusters --> safety parameter so the loop won't run forever min_error_threshold —> when the algorithm stops incrementing the number of clusters [dB] noise_floor —> rays that drops below this threshold will not be used [dB] max_delay —> rays that are beyond this delay value will not be used [ns]  % error_weight --> weight used to change the relative importance of postive residue and negative residue % OUTPUTS % % % % % % % % % %  bp --> the breakpoints in the power delay profile or the start/end of clusters (used for generating plots) Nbp —> the number of breakpoints (used for generating plots) pdp_lp —> power delay profile of identified local maxima (used for generating plots) t_lp —> time of the identified local maxima (used for generating plots) Carr —> cluster arrival time [ns] Cnum --> number of clusters (Nbp + 1) Camp --> cluster amplitude, strongest ray within a cluster [dB] Rarr --> ray arrival time [ns] Ramp --> ray amplitude [dB] Rnum --> number of rays within a cluster  107  % % % %  Rbp --> index of the breakpoints [samples] Rarrjndex —> number of rays in each cluster errorvector —> how error decreases as number of clusters increase illegalcluster —> status flag showing clusters that have not passed the additional rules  Ndata = length(h); % convert to pdp pdp = abs(h). 2; pdp = 10*logl0(pdp); A  % find local maxima index = 1; for(i = 1 :Ndata - zone - 1); if(i <= zone) start = 1; else start = i-zone; end; % conditions to find local maximum include: % 1. It needs to be the maximum within the search zone. % 2. It needs to be greater than the noise floor. % 3. It needs to arrive before the delay cutoff. % 4. the maximum needs to be greater than the second greatest point by 0.5 dB. zone_max = max(pdp(start:i+zone)); if(pdp(i) = zonemax & pdp(i) > noise_floor & t(i) < maxdelay & ... length(find(pdp(start: i+zone)>zone_max-sig_peak))== 1); pdp_lp(index) = pdp(i); tlp(index) = t(i); index_lp(index) = i ; index = index + 1; end; end; Nip = length(pdp_lp); % remove any isolated points (first and last) if(t_lp(Nlp)-t_lp(Nlp-l) > sep) p d p l p = pdp_lp(l :Nlp-l);  t_lp = t_lp(l:Nlp-l);  indexlp = index_lp(l:Nlp-l); Nip = length(pdplp); end; if(t_lp(2)-t_lp(l)>sep) pdp_lp = pdp_lp(2:Nlp); t_lp = t_lp(2:Nlp); index_lp = index_lp(l:Nlp-l); Nip = length(pdp_lp); end; % remove any isolated points (in the middle) index = 1; remove = 0; for(i = 2:Nlp-l) if((t_lp(i)-t_lpO-1 )>sep)&(t_lp(i+1 )-t_lp(i))>sep) remove(index) = i ; index = index + 1; 108  end; end; iffremove ~= 0) for(i = l:length(remove)) pdp_lp = [pdp_lp(l:remove(i)-l) pdp_lp(remove(i)+l:length(pdp_lp))]; U P [t_lp(l:remove(i)-l) t_lp(remove(i)+l:length(t_lp))]; if(i ~= length(remove)) % reset the index remove(i+l:length(remove)) = remove((i+l):length(remove)) - 1; end; end; Nip = length(pdplp); end; =  % find the smallest R M S error (the iteration starts here) % initialization N c = 1; old_bp = 1; % for all number of clusters, 1 is always present and it is the start of the first cluster all_cluster_error_below_threshold = 0; % check to see if there are large gaps. If there are automatically % increase the number of clusters according to the number of gaps + 1. for(i = 3:Nlp-l) if(t_lp(i+l)-t_lp(i) > sep) % if there is large gap old_bp = [old_bp i+1]; % then record the breakpoint Nc = Nc + 1; % incrememt the number of clusters number_of_clusters = Nc % msg in console end; end; % run the R M S error test for the first time to determine if we actually % want to go into the while loop next iffNc == 1) % calculate the R M S error for the case of one cluster just in case one cluster is the best fit coef = polyfit(t_lp, p d p l p , 1); % considering everything as one cluster and fit a line through it line = polyval(coef, t i p ) ; min_error = sqrt(mean((pdp_lp - line). 2)); % find the variance if(min_error < min_error_threshold) all_cluster_error_below_threshold = 1; bp = old_bp; end; error_vector = min_error; else m i n e r r o r c luster = zeros(l, Nc); N l p c luster = zeros(l, Nc); min_error = 0; for(k= l:Nc) start = old_bp(k); if(k = Nc) stop = Nip; else stop = old_bp(k+l)-l; end; coef = polyfit(t_lp(start:stop), pdplp(startistop), 1); % least square fit min_error_gamma_cluster(k) = -10*logl0(exp(l))/coef(l); line = polyval(coef, t_lp(start:stop)); min_error = min_error + sum((pdp_lp(start:stop)-line). 2); min_error_cluster(k) = minerrorcluster(k) + sqrt(mean((pdp_lp(start:stop)-line). 2)); A  A  A  109  Nlp_cluster(k) = stop-start+1; end; % min_error_gamma_cluster mean_min_error_gamma_cluster = mean(min_error_gamma_cluster) minerror = sqrt(min_error/Nlp); if(isempty(find(min_error_cluster > minerrorthreshold))) all_cluster_error_below_threshold = 1; else all_cluster_error_below_threshold = 0; end; error_vector = zeros(l, Nc); error_vector(Nc) = minerror; if(all_cluster_error_below_threshold == 1) bp = old_bp; end; end; Nip = Nip % minerrorcluster % while(min_error > min_error_threshold | all_cluster_error_below_threshold == 1) while(all_cluster_error_below_threshold == 0) % find the smallest R M S error given the number of clusters, Nc [bp min_error min_error_cluster] = clusterRMSerrorTest(pdp_lp, t i p , Nc, o l d b p , . . . min_error_threshold, min_cluster_length); % check to see if the algorithm failed or not if(bp==0) stop ins^ ~~ ''^^^^'^'^'i''^'^'^'^'^'^ new t)re<iks C3.ii be found ^^^^^^^^^^^^ *^'^'^^ ^ '^^ ^ '^^'^ ^'^^ ^' bp = o l d b p ; break; end; t  %  E  e  e  £  t5  !  min_error_cluster % update the search - increment the number of clusters to reflect the current number of clusters % pass on breakpoint info to the next iteration. Nc = N c + 1; old_bp = bp; % message in the console numberofclusters = Nc % save the changes in the min_error as the number of assumed clusters % increase error_vector(Nc) = min_error; % check to see if the R M S error of each cluster is below the threshold if(isempty(find(min_error_cluster > min_error_threshold))) all_cluster_error_below_threshold = 1; else all_cluster_error_below_threshold = 0; end; % stopping condition in case the algorithm tries to break into too many 110  % clusers when there are not that many local maxima iffNc > length(pdp_lp)/3) stop_msg = '***• Number of clusters greater than significant paths can provide ***** break; end; % stopping condition in case something goes wrong if(Nc > max_num_clusters) stopmsg =***** Number of clusters greater than the user defined maximum number break; end; % used to show the step by step breakdown of the cluster identification % process if(step_by_step == 1) figure(15); elf; hold on; plot(t, pdp); plot(t_lp, pdpjp, W , 'MarkerSize', 4); plot(t_lp(bp), pdp_lp(bp), 'ms', 'MarkerSize', 8); for(k= l:Nc) start = bp(k); if(k == Nc) stop = length(pdp_lp); else stop = bp(k+l)-l; end; coef = polyfit(t_lp(start:stop), pdp_lp(start:stop), 1); line = coef(l)*t_lp(start:stop) + coef(2); plot(t_lp(start:stop), line, 'k', 'linewidth', 1.5); end; hold off; xlabel(Time [ns]'); ylabel('PDP [dB]'); title([int2str(Nc),' Clusters']); axis([0 max(t_lp)+10 min(pdp) max(pdp)+5]); pause; end; end; % message in the console % number_of_clusters = Nc systemmsg = '*********** Cluster identification process completed ***************** % save the number of breakpoints into a variable Nbp = length(bp); % apply additional rules if(add_ruleCheck== 1) [bp] = ruleCheck(pdp_lp, t_lp, bp, power_diff, sep, 1,1); systemmsg = '********** Additional rules successfully applied ****************** end; if(add_boundaryCheck == 1)  111  [bp] = clusterBoundaryCheck(pdp_lp, t_lp, bp); end; Nbp = length(bp); % update the number of breakpoints just in case % returning 4a parameters % stats for the clusters Carr = t_lp(bp); % absolute cluster arrival time = where the breakpoints are for(i= l:Nbp); start = bp(i); if(i == Nbp) stop = Nip; else stop = bp(i+l)-l; end; Camp(i) = max(pdp_lp(start:stop)); % cluster amplitude = strongest path within a cluster end; Cnum = Nbp; % number of clusters % stats for the rays Rbp = indexlp(bp); % reset the start of the clusters as the all rays not just the local maxima Rarrjndex = ones(l, Cnum); Rarr = zeros(length(t), Cnum); Ramp = zeros(length(t), Cnum); for(k = 1 :Cnum) start = Rbp(k); if(k == Cnum) stop = length(pdp)-l; else stop = Rbp(k+l)-l; end; for(m = start: stop) if(m == 1) % check right only for the first point if(pdp(m) > pdp(m + 1)) Rarr(Rarr_index(k), k) = t(m); Ramp(Rarr_index(k), k) = pdp(m); Rarrindex(k) = Rarr_index(k) + 1; end; else % check left and right for all points if((pdp(m)-pdp(m + 1))>0.5 & (pdp(m)-pdp(m - l))>sig_peak & pdp(m) > noise_floor & t(m) <... max_delay) Rarr(Rarr_index(k), k) = t(m); Ramp(Rarr_index(k), k) = pdp(m); Rarrindex(k) = Rarrjndex(k) + 1; end; end; end; Rarrindex(k) = Rarr_index(k) - 1; % you've added one more than needed end; Rnum = sum(Rarr_index); % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %  0  / o % %  cluster iteration.m - end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0^0/OZO/0/0/0/0/0/0/0^0/0^0/0/0/ /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o /o  112  cluster R M S error.m - begin %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [bp minerror minerrorcluster] = clusterRMSerrorTest(pdp_lp, t i p , Nc, o l d b p , . . . min_error_threshold, min_cluster_length); % % % %  this function is used for iterating through all combinations of straight lines given the number of clusters. It will find what the min error is and pass it back to clusterAlgorithmTest to see i f incrementing the number of clusters is still necessary.  % % % % % % %  INPUT p d p l p —> local maxima identified in the PDP t_lp —> time of the local maxima identified in the PDP Nc —> number of clusters for this iteration old_bp - > breakpoint identified w/ one less cluster min_error_threshold --> minimum error threshold [dB] min_cluster_length --> minimum length of a cluster w.r.t. the local maxima  % % % %  OUTPUT bp —> breakpoints or the start of a cluster min_error —> min R M S error found [dB] min_error_cluster --> min R M S error for each cluster found [dB]  Nip = length(pdp_lp); min_error = inf; min_error_cluster = zeros(l, Nc+1); algorithm_fail = 0; % status flag % pre-calculate the residuals of errors to save computations error_cluster_old = zeros(l, Nc); for(k= l:Nc) start = oldbp(k); if(k == Nc) stop = Nip; else stop = old_bp(k+l)-l; end; coef = polyfit(t_lp(start:stop), pdp_lp(start:stop), 1); % least square fit gammaclusterold(k) = -10*logl0(exp(l))/coef(l); line = polyval(coef, t_lp(start:stop)); error_cluster_old(k) = sum((pdplp(start:stop)-Iine). 2); Nlp_cluster_old(k) = stop-start+1; rms_error_cluster_old(k) = sqrt(error_cluster_old(k)/Nlp_cluster_old(k)); % calculate the R M S error end; A  for(i = 3:Nlp-l) n e w b p = zeros(l, Nc+1); % initialize a fresh set of breakpoints error = 0; % error tracker - this is updated per combintation of fit and saved as min_error errorcluster = zeros(l, Nc+1); % error tracker for individual clusters Nlp_cluster = zeros(l, Nc+1); % cluster length tracker % checking to see i f any of the old breakpoints are where % this new iterating breakpoint is conflict = 0; for(k= l:length(old_bp)) 113  if(abs(old_bp(k)-i) <= min_cluster_length) % if it is within close to the +/- 1 of the old breakpoint conflict = 1; break; end; end; % proceed w/ the R M S error calculation if(conflict == 0) n e w b p = [oldbp i]; % add the new breakpoint at the end n e w b p = sort(new_bp); % sort it in ascending order new_bp_i = find(new_bp == i); % find where the new index is errorstatus = 0; % check to see if this cluster is already below the error threshold if(rms_error_cluster_old(new_bp_i-l) < minerrorthreshold) error_status = 1; end; if(error_status = 0) % proceed only if the breakpoint is at a cluster with error greater than threshold % add up the errors before the broken line since only the % error associated with the cluster containing the new % breakpoint has changed for(k = 1 :new_bp_i-2) error = error + errorclusterold(k); error_cluster(k) = error_cluster_old(k); Nlpcluster(k) = Nlp_cluster_old(k); gamma_cluster(k) = gamma_cluster_old(k); end; % calculate error for the broken cluster into two clusters for(k = new_bp_i-l :new_bp_i) start = newbp(k); if(k== Nc+1) stop = Nip; else stop = new_bp(k+1)-1; end; coef = polyfit(t_lp(start:stop), pdp_lp(start:stop), 1); % least square fit gammacluster(k) = -10*logl0(exp(l))/coef(l); line = poIyval(coef, t_lp(start:stop)); error = error + sum((pdp_lp(start:stop) - line). 2); error_cluster(k) = error_cluster(k) + sum((pdp_lp(start:stop) - line). 2); Nlp_cluster(k) = stop-start+1; end; A  A  % add up the errors after the broken line for(k = new_bp_i+l:Nc+l) error = error + error_cluster_old(k-l); error_cluster(k) = error_cluster_old(k-l); Nlp_cluster(k) = N l p c l u s t e r o l d ( k - l ) ; gammacluster(k) = gamma_cluster_old(k-l); end; % complete the 'RM'S error calculation, i.e., take the mean and % then square root everything, error = sqrt(error/Nlp); for(k= l:Nc+l) error_cluster(k) = sqrt(error_cluster(k)/Nlpcluster(k));  114  end; % update the minimum error and breakpoint if necessary if(min_error > error) minerror = error; bp = new_bp; min_error_cluster = errorcluster; minerrorgammacluster = gammacluster; end; end; end; end; if(min_error ~= inf) % min_error_gamma_cluster meanminerrorgammacluster = mean(minerrorgammacluster) end; % i f least squares fit fails, assign something to all outputs if(min_error == inf) bp = 0; algorithm_fail = 1; end;  cluster R M S error.m - end  115  

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