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The impact of gateway distribution on the system capacity of CDMA mobile satellite systems Liang, Hongyi 1999

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The Impact of Gateway Distribution on the System Capacity of CDMA Mobile Satellite Systems By  Hongyi Liang B . Eng.(EE), Harbin Institute of Technology, 1992  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E DEGREE OF MASTER OF APPLIED SCIENCE in T H E F A C U L T Y OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH COLUMBIA April 1999 © Hongyi Liang, 1999  In presenting this thesis in partial fulfilment  of the  requirements for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or by  his  or  her  representatives.  It  is  understood  that  copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  A^)r i g ,  <4<?7  Abstract Recent research indicates that satellite diversity is a practical means of mitigating the effects of satellite fading for M o b i l e Satellite Systems ( M S S ) employing C D M A . However, the underlying assumption of such research is that satellite diversity is available all the time, which is not true in reality. We w i l l investigate the impact of improper gateway distribution on the system capacity of M S S . We investigate the principle of distributing the gateways to ensure single and. double satellite service and present some strategies of searching for the optimal gateway distribution for single and double satellite service. To analyze the impact of gateway distributions on the system capacity of M S S , we classify the general mobile terminal environments into five states. B y computing the required power margin of each state to reach the same average Bit-Error Rate ( B E R ) and taking the occurrence probability of each state into account, the capacity of a M o b i l e Satellite System, expressed as the average number of mobile terminals per satellite over the area ranging from South 80° to North 80°, is analytically derived and thoroughly validated by means of computer simulations. After comparing the system capacity of a M S S with improper gateway distributions to that with the optimal gateway distribution, we show that the capacity of a M S S is decreased considerably due to improper gateway distributions. Moreover, the quantitative results indicate that a M S S in a propagation environment of light shadowing suffers more capacity loss due to improper gateway distribution than a M S S in an environment of heavy shadowing.  Contents Abstract  ii  List of Tables  vi  List of Figures  vii  Acknowledgment  x  Chapter 1  Introduction  1  1.1  Motivation and Objectives  1  1.2  Thesis Outline  5  Multiple Satellite Service Availability Analysis  7  2.1  Terminology .".'  7  2.2  Multiple Satellite Coverage Analysis  Chapter 2  .  9  2.2.1  J. G. Walker Constellation and Sub-satellite Equations . . 9  2.2.2  Coverage Analysis  10  2.3  Multiple Satellite Service Availability  14  2.4  Optimal Gateway Distribution  19  2.4.1  Optimal Gateway Distribution for Single Satellite Service . 19  2.4.1.1  Problem Statement  2.4.1.2  : Sufficient Condition of Gateway Distribution Ensuring  19  Single Satellite Service 2.4.1.3  Refined Sufficient Condition Ensuring the Single Satellite Service  2.4.1.4  20  . 21  Gateway Distribution Employing General Solution Algorithm  22 iii  2.4.1.5  Gateway Distribution Employing Local Solution Algorithm . 24  2.4.2  Optimal Gateway Distribution for Double Satellite Service . 25  Chapter 3  Impact of Gateway Distribution to Mobile Satellite System Capacity  3.1  30  Definitions and System Outline  31  3.1.1  System Capacity  31  3.1.2  System Outline  32  3.1.3  Channel Model  35  3.2  Analysis of Average Probability of Error  37  3.3  Power Margins for Each Scenarios  41  3.3.1  SS/C: Single Satellite Service/LOS Path  41  3.3.2  SS/S: Single Satellite Service/Shadowing Path  42  3.3.3  DS/CC: Double Service/Both Paths are LOS  3.3.4  DS/SS: Double Service/Both Paths are Shadowed  3.3.5  DS/CS: Double Service/One Path is LOS, Another Path is  . . . 43 .... 45  Shadowed  47  The Average Interference for Each Scenario  49  3.4.1  Fraction of Double Satellite Service Links  49  3.4.2  Terminology  54  3.4.3  Effect of gateway distribution on PSS distribution  57  3.4.4  Interference Calculations  3.4  iv  . 61  3.5  Capacity Calculation  3.6  Numerical and Simulation Results . .  .63 1  65  3.6.1  Numerical Results  3.6.2  Simulation Results .  .69  3.6.2.1  Simulation Algorithm  .69  3.6.2.2  Simulation Results  .71  Chapter 4  66  Conclusion and Discussion  Bibliography  74 76  Appendix A  List of Abbreviations and A c r o n y m s  80  Appendix B  Supporting Calculations  81  B.1  DS/SS Calculation  .81  B.2  DS/CS Calculation  81  Appendix C  Supporting Figures  83  Appendix D  Simulation Programs in Matlab  84  V  List of Tables Table 1  Recently proposed LEO/MEO satellite systems  Table 2  Power margins for different scenarios  Table 3  The average number of pairs of links providing double satellite service and the average p  ds  2 48  for the Globalstar  System  53  Table 4  The average p  Table 5  Path States  55  Table 6  Summary of States  56  Table 7  Double satellite service transition matrix  60  Table 8  The system capacity comparison for GW distribution 4 and  ds  for different GW distributions  . 54  GW distribution 5 under different channel conditions . . . 69 Table 9  The simulation results for system capacity on channel condition (B=0.3, c=10)  vi  72  List of Figures Figure 1  Satellite diversity  3  Figure 2  Gateway distribution and satellite diversity  4  Figure 3  Satellite diversity  8  Figure 4  Globalstar satellite constellation  10  Figure 5  Half-Central angle  11  Figure 6  Satellite coverage analysis model . . .  12  Figure 7  Satellite coverage analysis for NYC  13  Figure 8  Average fraction of time when multi-satellite coverage is available at different latitudes  14  Figure 9  Overlapping coverage circles centered at MT and GW . . 15  Figure 10  Satellite service analysis model  Figure 11  Satellite Service analysis for New York city  18  Figure 12  Gateway distribution 2  21  Figure 13  Optimal gateway distribution for single satellite service . . 22  Figure 14  Gateway distribution 3: GW distribution without  . 17  considering satellite orbits Figure 15  23  The optimal gateway distribution for single satellite service  ,  24  Figure 16  Gateway distribution 4 employing local solution  Figure 17  Gateway distribution for double satellite service model . .26  Figure 18  The Max—Min satellite distance vii  25  28  Figure 19  Gateway Distribution 5 ensuring double satellite service between North (South) 25° and 45° in the Globalstar system  29  Figure 20  The isoflux antenna of Globalstar  31  Figure 21  System model  33  Figure 22  Two-Arm Rake receiver. . .  34  Figure 23  Channel model  37  Figure 24  Uplink of reverse link scenarios  41  Figure 25  SS/C: Single satellite service/LOS channel  41  Figure 26  SS/S: Single satellite service/Shadowing path  42  Figure 27  DS/CC: Double satellite service/Both paths LOS  44  Figure 28  DS/SS: Double service/Both paths are shadowed  45  Figure 29  DS/CS: Double service/One path is LOS, another path is shadowed  47  Figure 30  The required power margins for different scenarios . . . . 49  Figure 31  Interference calculation  Figure 32  One pair of satellite links capable of providing double  50  satellite service  52  Figure 33  Path and satellite service analysis .  58  Figure 34  The tree diagram of PS—>PSS  59  Figure 35  Distributions of PSS states of Globalstar system  62  Figure 36  Multiple access interference in the Globalstar system . . . 64  Figure 37  BER Vs. p  ds  (Varied system capacity J)  66  Figure 38  BER Vs. p  ds  (varied B)  67  Figure 39  Capacity Vs. p  68  ds  viii  Figure 40  3912 MTs equally distributed on the Earth  .70  Figure 41  The simulation diagram  71  Figure 42  The theoretical and simulation results (B=0.3,c=10) . . . . 72  Figure 43  Flowchart for calculating satellite service  ix  83  Acknowledgment I would like to express my gratitude to my research supervisor, Prof. Victor C . M . Leung, for his direction, guidance and support throughout my studies at University of British Columbia. His helpful comments and critical questions made research interesting for me. This work is funded by the Canadian Institute for Telecommunications Research (CITR) through a Research Assistantship provided by Prof. Leung. A l s o , I would like to thank my friend M r . Wee Liat E r for his kind help to review this thesis. Further, special thanks to my colleagues and staff in the department for their help. Finally, I would like to thank my family for their encouragement and consistent support for me to pursue my personal goal. Without them nothing would have been possible.  Chapter 1 Introduction 1.1 Motivation and Objectives The concept of the Mobile Satellite Systems ( M S S ) [1], providing Personal M o b i l e Satellite Communication System ( P M S C S ) , holds the promise of truly global ubiquitous hand-held low-delay real time communications for mobile telephony and data transmissions, without the need for complex ground-based infrastructures required by existing land-based cellular systems. P M S C S w i l l complement terrestrial cellular systems by offering service in regions where the cellular systems cannot economically be deployed. A number of M S S s based on low or medium earth orbiting ( L E O , M E O ) satellites, as shown i n Table 1 [2][3], have been proposed. Currently, some of these systems are under development and some of them are already in service. These systems employ two distinct architectures for which the Iridium [4] and Globalstar [5] systems are archetypal. In the Iridium system, satellites with onboard-switching and onboard-processing capabilities are networked together through intersatellite links and interconnected to the terrestrial public switched telephone network (PSTN) v i a a small number of gateways (GWs) (11 G W s are planned [2]). In the Globalstar system, communications employ Code Division Multiple Access ( C D M A ) [6] [7] over mobile satellites bent-pipe transponders which work like frequencytranslating repeaters [8], and all. the necessary data switching and processing are completed in the G W s , which interconnect the M S S to the P S T N . The Globalstar system generally requires a larger number of G W s (200 G W s are required [2]), as a mobile terminal ( M T ) and at least one G W must be simultaneously illuminated by the same satellite in order to communicate with each other over this satellite. 1  Chapter 1.  Introduction  Description  ARIES  CALLING  ELLIPSO  GLOBALSTAR  IRIDIUM  Service  Cellular-like  Cellular-like  Cellular-like  Cellular-like  Cellular-like  voice,  voice,  voice,  voice,  voice,  Positioning-  Positioning-  Positioning-  Positioning-  Positioning-  RDSS,  RDSS,  RDSS,  RDSS,  RDSS,  Paging,  Paging,  Paging,  Paging,  Paging,  Messaging  Messaging  Messaging  Messaging  Messaging, Data Transfer  Coverage  CONUS  Global  CONUS  Global  offshore US  offshore US Total Active  CONUS  46  840  17  48  66  7 circlular  21 circular  2 elliptical  6 circular  6 circular  inclined, 1  polar  inclind  inclined (52°)  polar(86.5°)  8  11  Satellites Orbit Planes  circular  (116.6°), 1  equatorial  circular equatorial  Satellite Per  5 in each  40  5 in each  Orbital Plane  inclined orbit,  inclind orbit, 7  11 in equatorial  in equatorial  orbit  orbit  Switching and  ground-based  onboard cellular  ground-based  ground-based  onboard  Processing  switching  switching,  switching  switching  cellular  inter-satellite  switching,  link  inter-satellite link  Multiplexing  CDMA  TDMA/FDMA  FDMA/CDMA  CDMA  FDMA/TDMA  Modulation  PN/QPSK  DQPSK  Capacity  2,400  1,100  Table 1 Recently proposed L E O / M E O satellite systems The main advantages of the Globalstar system over the Iridium system are lower system complexity and cost, tighter integration with terrestrial networks, and most importantly, the capability of employing satellite diversity, a key feature of M S S s employing C D M A . 2  Chapter 1.  Introduction  F i g u r e 1 Satellite diversity In essence, satellite diversity as shown in F i g . 1 allows signals transponded over multiple satellites to be coherently combined at the Rake receivers in the G W s and MTs.  It has been shown [9][10] that satellite diversity is an effective method to combat  blocking and shadowing effects and thus considerably improves the link quality through a noticeable reduction of Signal-to-Noise Ratio ( S N R ) variations. This immediately leads to a reduction of outage probability, i.e., the probability that S N R falls below a specified minimum value dictated by the kind of application. Propagation measurements performed with several aircrafts simulating satellites indicate that the required link margin can be reduced by up to 70% [11] when two or three simultaneous paths are available.  A  modified Rake receiver suitable for the small delay between two satellite paths has also been developed [12]. Note that performance improvements due to satellite diversity depend heavily on the spatial distribution of GWs,  as diversity reception is possible only v i a those satellites  which simultaneously illuminate the M T and the G W connecting it to the P S T N . Consider the two cases shown in Fig. 2 where a M T is illuminated by two satellites. With a proper GW  distribution as in case (a), there exists at least one G W illuminated by the same 3  • .  Chapter I.  Introduction  two satellites. Transmissions from the M T are received by each of the two satellites and re-transmitted to the G W ; diversity reception is performed at the G W and the reception performance at the G W is improved due to satellite diversity. However, i f the G W serving the M T is only illuminated by one of the two satellites, which path to the M T is shadowed as in case (b), not only would diversity reception at the G W be impossible, but the M T would also have to increase its transmit power to maintain the desired performance. A s a result, the M T generates additional interference to the other satellite. Since the number of M T s lacking satellite diversity to a G W at any specific time period may be large, the cumulative impact on system capacity could be significant. SAT1  SAT2  Figure 2 Gateway distribution and satellite diversity  So far, a host of papers evaluating the system capacity and the link performance of L E O M S S systems have been published. Especially, an elaborated analysis for reverse (mobile-to-satellite) link performance of multi-beam multi-satellite C D M A is found in [13] and a detailed performance analysis of the forward  (gateway-satellite-mobile) link  performance is reported in [14]. A l l the papers have assumed that satellite diversity is  4  Chapter 1.  Introduction  always available. This assumption might not be realized for reasons of geographical limitations (e.g. sea, desert), economical, or political considerations. U p to date, analysis of satellite service availability and the effects of G W distribution on M S S capacity, have not yet been found in the literature. A detailed examination of the relationship between satellite system capacity and G W distribution is necessary. In this thesis, we mainly address the following problems: 1.  For a given satellite constellation, analyze the effects of G W distribution on satellite service availability and present some strategies to find the optimal gateway distribution.  2.  For a given G W distribution, analyze its effects on the system capacity, based on the reverse link performance of a M S S .  1.2 Thesis Outline In chapter two, we analyze the percentage of time satellite coverage and satellite service are available to a specific location under a given G . J Walker L E O satellite constellation. To ensure satellite service availability, we present the optimal G W distribution including a general solution and a local solution for single satellite service, and some strategies to find the optimal G W distribution for double satellite service. The results in this chapter w i l l be applied in the capacity evaluations by analytical and simulation methods. In chapter three, we classify the general M T environment into five distinct scenarios. B y computing the required power margins for each scenario to achieve the same probability of Bit-Error Rate ( B E R ) and taking the occurrence probability of each scenario into account, the reverse link capacity is analytically derived and thoroughly validated 5  Chapter 1.  Introduction  by means of computer simulations. The summaries of this thesis are presented in chapter four.  6  Chapter 2 Multiple Satellite Service Availability Analysis 2.1 Terminology The capacity of a C D M A - b a s e d M S S is largely constrained by the required S N R at the M T and G W receiver. The G W distribution has a significant effects on S N R calculations as it determines whether satellite diversity can be exploited. Therefore, a complete and detailed analysis of satellite coverage and service for a given G W distribution is necessary. In this chapter, we w i l l analyze satellite coverage and satellite service for a M T under a given satellite constellation. Furthermore, we w i l l try to search for the optimal G W distribution for single and double satellite service, or, a G W distribution providing single or double satellite service when the optimal distribution is very difficult to pursue. Based on these results, we w i l l be able to investigate the relationship between system capacity and system coverage and services in the next chapter. To facilitate further discussions, a consistent terminology is necessary. We distinguish the concepts of satellite coverage and satellite service as follows, •  Satellite Coverage — A G W or M T is covered by a mobile satellite i f the satellite's elevation angle is higher than a specified minimum value (assumed to be 10° in this thesis).  •  Satellite Service — A M T may receive service from a satellite enabling it to communicate with some G W i f the satellite covers both the M T and G W . We can further extend these definitions as follows:  •  Single Satellite Service — the M T and at least one G W are covered by the same satellite(s); it is the minimal condition for a M T to receive service;  7  Chapter 2. Multiple Satellite Service Availability Analysis  EEBQEEB  LEGEND  c •  GATEWAY MOBILE TERMINAL SATELLITE  Figure 3 Satellite diversity  Double Satellite Service — the MT and at least one GW are under double satellite coverage of the same set of satellites; it is a precondition for satellite diversity to be enabled. In the snap shot shown in Fig. 3, the ellipses represent the 10 degrees elevation  contours of mobile satellites SAT 1 and SAT 2. GW a and MT A receive double satellite coverage from both satellites while GW b and MT B receive single satellite coverage from SAT 2 only. Thus MT A may receive single satellite service from SAT 2 via GW b, or double satellite service from both SAT 1 and SAT 2 via GW a, in which case satellite diversity is enabled. However, MT B may only receive single, satellite service from SAT 2 via GW a or b, without the availability of satellite diversity. Note that the coverage and service each MT receives may change over time due to satellite movements. For any given MSS constellation, we address the following problems in this chapter. 1. Given the GW distribution, to determine the fraction of time a MT at any given location receives single satellite service while it has single coverage, single satellite service while it has double coverage, and double satellite service while it has double coverage. 8  Chapter 2. Multiple Satellite Service Availability Analysis  2.  To find the optimal G W distributions guaranteeing single satellite service for M T locations receiving single satellite coverage. Since all the computation is based on spherical geometry, all distances are angular  measured (in degree) with respect to the Earth's surface in the following discussions.  2 . 2 Multiple Satellite Coverage Analysis 2.2.1 J. G. Walker Constellation and Sub-satellite Equations  A number of constellation schemes have been proposed [15][16][17] for M S S . However, the J . G . Walker Constellation [18] by J . G Walker has been proved the optimal satellite constellation, which requires a minimum number of satellites for global or zone coverage of the earth, for inclined circular orbits. The J . G . Walker constellation is specified by a reference code T/P/F, where there are a total number of T satellites in P orbital planes having the same inclination angle rj, with a F x 360°IT phase increment.  The phase increment is defined as the angle between a satellite and its  ascending node when its easterly neighbor satellite is crossing the equator (ascending node is the intersection of the orbit with the plane of the equator, the satellite crossing this plane from south to north). Globalstar employs the J . G.Walker 48/8/1 constellation. There are a total of 48 satellites in. 8 planes with 45° separation between ascending nodes of adjacent planes, and 7.5° delay between 2 correspondent satellites between two adjacent satellite orbital planes. The satellite constellation of the Globalstar system is illustrated in F i g . 4. For a given constellation, the orbital period To is given by  (2.1)  9  Chapter 2. Multiple Satellite Service Availability Analysis  Figure 4 Globalstar satellite constellation where H is the satellite altitude. In Globalstar, H is 1389 Km and To is 113 minutes. For a given T7F7F J. G. Walker constellation, in the following sections, we assume that the right ascension angle of first orbit plane is —180°. Therefore, the sub-satellite position of the jth satellite of the zth orbital plan at time t is given by .  .  2TXF  .  2TXP  2itt  ° = * ~Y~ +) * ~Y~ ~r~ 1  la = s i n  +  - 1  (sin (5) * sin (r/))  (2.2)  2TT  lo = —7r + i * — + t a n  - 1  (tan (6) * cos (n))  where la and lo are the latitude and longitude of the sub-satellite position (the satellite's projection posistion on the Earth) respectively.  2.2.2 Coverage Analysis For a given minimum elevation angle, the half-central angle r (i.e., the radius of the satellite coverage area, or, footprint) is given by,  r = cos  - l  COS  (j)  COs(l + egyg )  where 4> is minimum elevation angle. 10  (2.3)  Chapter 2. Multiple Satellite Service Availability Analysis  Minimal Elevation Angle Satellite Altitude Half-central Angle center of Earth  Figure 5 Half-Central angle In the Globalstar system, we assume the minimum elevation angle is 10°. Therefore, the radius of satellite coverage is 2 6 ° , which equals to 1842 K m . In contrast to geosynchronous earth orbiting ( G E O ) satellites, L E O satellites are continuously moving relative to the Earth. A s such, satellite coverage for a given M T is a time-dependent variable. To analyze satellite coverage for a given M T , an algorithm is developed. There are three procedures. 1.  Determine which orbital planes are visible to the M T .  2.  Determine the connection time, the period of time the M T is illuminated by some satellites of a visible orbital plane.  3.  Combine all the connection time periods from all visible orbital planes. Step 1 is accomplished by computing the displacements between orbital planes and  the M T . A l l the orbital planes whose displacements from the M T are less than the radius of satellite coverage are visible to the M T . A s illustrated in Fig. 6, the displacement from 11  Chapter 2. Multiple Satellite Service Availability Analysis  a given M T to the ith orbital plane is given by  rf = s i n - ^ s i n ( c ) . s i „ ^ n - ' ( ^ j - , j j  (2.4)  where n is the orbit's inclination angle, la and lo are the M T ' s latitude and longitude, respectively, and c is the great circle distance between the right ascending node of ith orbital plane and the M T , calculated as:  c = cos  -1  (cos (la) * cos (lo — i * — ^ ^  (2.5)  Figure 6 Satellite coverage analysis model  Step 2 is achieved by computing the satellite crossing points ( X I and X 2 in F i g . 6). Since we know the satellite speed with knowledge of the satellite constellation, we w i l l be able to derive satellite connection time based on the distance between 2 crossing points. Referring to F i g . 6, the distance from X I and X 2 to the ascending node is given by: • - l I( — x = sin  — J\ \^sin (c) * cos ((f) + cos (c) J i / cos(c) \ -tan- ! ' \sin{c) * cos(ip) j c o s  2  ( ) r  2  1  2  K  where c is given by Eqn. (2.5). Step 3 find the overlapping period from different orbital planes. 12  Chapter 2. Multiple Satellite Service Availability Analysis  A s an example, the latitude and longitude of New York is North 40.7517° and West 73.9942°, respectively. Assuming the Globalstar constellation and the right ascension of the first orbital plane is West 180°. The satellite coverage for each orbital plane and the overall satellite coverage for N e w York City ( N Y C ) are calculated and illustrated in F i g . 7  Coverage Analysis for NYC by orbit  Overall Coverage Analysis for NYC 5 4.5 <u  1  4  V)  o 3.5 » o>  3  o>  5)  8  2 1.5 1 0.5 0  10 12 Time (Minute)  14  16 .  18  Figure 7 Satellite coverage analysis for N Y C  A C program is written to analyze satellite coverage for a total of 360 * 180 sample points on the Earth in an increment of 30 seconds to show the percentile of one satellite period, averaged over all longitudes, during which a given latitude receives the indicated satellite coverage.  Note that, since the satellite pattern repeats itself when a satellite 13  Chapter 2. Multiple Satellite Service Availability Analysis  moves to the precedent satellite's position, it is only necessary to analyze 113*60/6=1130 seconds for the Globalstar system. The overall satellite coverage for the whole system is illustrated in F i g . 8  100r  I  I  I I  90 -  \  I \  80 O  70 -  Q. 60 15  single coverage  double/  0  ~m  7 I  coverage  50 -  3 or m o r e  o 40 o  satellites  •.  30 -  V  20 -  ^^jxJnore_saatellites  10 0 -90-80  -60  -40  20  0  20  40  60  80 90  Latitude -  LEGEND:  single c o v e r a g e  3 or m o r e satellites  -- double coverage  4 or m o r e satellites  Figure 8 Average fraction of time when multi-satellite coverage is available at different latitudes From F i g . 8, we can see that single satellite coverage is guaranteed in the areas with latitudes between North and South 70° latitude, and double satellite coverage or even higher satellite coverage is guaranteed in the areas with latitudes of South 25° to 45° and North 25° to 4 5 ° .  2.3 Multiple Satellite Service Availability To determine the satellite service available at a M T location, a graphical analysis, as shown in F i g . 9, which consists of two overlapping circles having the same radius as the satellite coverage pattern, is performed. The MT circle is centered at the M T location 14  Chapter 2. Multiple Satellite Service Availability Analysis  for which service is being evaluated, and the GW circle is centered at a GW which may provide service to the MT. The GW circles of more than one GWs may overlap the MT circle, but we only show one GW circle in the figure for clarity. The following scenarios exist for satellite service availability at the MT location: 1. No GW exists which GW circle overlaps the MT circle. It is not possible for any satellite to simultaneously cover the MT and any GW. Therefore, no satellite service is available at the MT location. 2.  No satellite orbital plane goes through the overlapping area between the MT circle and any GW circle (e.g., SAT2 does not go through the overlapping area in Fig. 9). Again, no satellite simultaneously covers the MT and any GW, so that no satellite service is available at the MT location. \ mt end  SAT3 4  l  srv  tstart SAT ,1  SAT2  LEGEND:  r  GATEWAY  SATELLITE  MOBILE TERMINAL  ORBITAL P L A N E  Figure 9 Overlapping coverage circles centered at M T and GW 15  Chapter 2. Multiple Satellite Service Availability Analysis  3.  There exists one satellite orbital plane (e.g., SAT1 in F i g . 9) intersecting the overlapping area between the M T circle and a G W circle. Single satellite service is available from time t%l to t ™ over a satellite in this orbital plane via the respective G W . s  rt  4.  d  If at least two satellite orbital planes intersect the overlapping area between the M T circle and the respective G W circle, double satellite service is available via the G W during the times when the satellites on at least two of these orbital planes are located simultaneously within the overlapping area. A t other times only single satellite service is available. Based on the above considerations, a satellite service algorithm, similar to previous  section but more complicated, is presented to evaluate the satellite service availability at a specific M T location. The algorithm consists three steps as follows: 1.  Determine which G W s ' circles overlap the M T circle;  2.  For each G W , find the orbital planes going through the overlapping area of the M T and G W circle;  3.  Determine the satellite service time. Step 1 is accomplished by computing the distances between the M T and nearby G W s .  A l l the G W s at a distance less than the diameter of the satellite coverage pattern from the M T are selected. Step 2 is accomplished by calculating the displacements from the G W s or the M T to each orbital plane.  With the aid of F i g . 10, the displacement d between an orbit  plane specified by the inclination angle rj and the longitude of the ascending node and a specific M T (or G W ) location is given by, d = sin~ (sin(l) l  * sin(9)) (2.7)  0 = tan~ (tan(la)/sin(lo)) 1  16  — n  Chapter 2. Multiple Satellite Service Availability Analysis  where lo and la are the differences in longitudes and latitudes between center O of the 1  M T / G W circle and the ascending node E of the orbit, and / is the distance between E and O. If the displacements of the M T and G W to an orbit and the distance between the G W and M T are less than the radius of the satellite coverage pattern, the orbit goes through the overlapping area of the M T and G W circles  Satellite Orbit  Ascending Node  Equator  L  F i g u r e 10 S a t e l l i t e s e r v i c e a n a l y s i s m o d e l  Step 3 is accomplished by computing the crossing points X I and X2 of the orbital plane and the M T / G W circle and calculating overlapping satellite service time. The distance x between the ascending node and the crossing point X I or X2 of the orbital plane and the M T / G W circle is determined by  -l /  .  c o s  ( ) r  y/sin (l) * cos (9) + cos (I) J 2  -tan- ( l  2  (2 8)  ^ \sin(l) * cos(0) J C  °  2  S { 1 )  where r is the radius of the satellite coverage pattern. The satellite coverage time t ^ 1  for the M T , which is the time period that the M T is illuminated by the satellite, is 17  Chapter 2. Multiple Satellite Service Availability Analysis  determined by, X2 — I * OJ  ±mt  V  xi  mt  t start 4  tX  i  —  *  OJ  (2.9)  v  j.mt j.mt = t"end „A ~ t start e  c  where X2 and x\ are the distances between X I , X 2 and the ascending node given by Eqn. (2.9), and t™ , art  t™^ , as shown in Fig. 9, are the start and end time of the satellite  trajectory crossing the M T circle, i is the satellite orbit number, OJ is the phase increment of ith orbital plane, and v is the satellite angular velocity. for a G W circle can be derived by similar method.  The satellite crossing time  Thus, the single satellite service  time, which is the intersection of the satellite crossing time intervals of the M T and G W , can be obtained. 3r  2.5-  o  a) co  0.5  10 12 Time (min.)  14  16  18  Figure 11 Satellite Service analysis for New York city The flowchart for calculating satellite service is shown in F i g . 43 in Appendix C . With a G W distribution as described later in F i g . 12 ensuring single satellite service, the overall satellite service for New York City is illustrated in Fig. 11. From the figure above, we conclude that the G W distribution shown in F i g . 12 does not guarantee double satellite service for N Y C , and more G W s are needed.  Chapter 2. Multiple Satellite Service Availability Analysis  2.4 Optimal Gateway Distribution The optimal Gateway distribution is defined as a minimum number of G W s guaranteeing satellite service when the satellite coverage is available. When a single G W is dropped, the same level of satellite service can not be maintained everywhere. Although in reality it is impossible to employ an optimal G W distribution obtained by mathematical calculation, because of geography limitation or economic or even political considerations, . the intention to pursue an optimal G W distribution is to present a best scenario. This information is very useful for M S S system design.  2.4.1 Optimal Gateway Distribution for Single Satellite Service  2.4.1.1 Problem Statement Let  MT be a set of K M T s on the Earth mt\,  satellite points sti(t),st2(t),  mi'i  mt}., ST a set of M sub-  stM(t) of the corresponding satellites 1 to M respectively.  The positions of the members of S T are time-variant and are governed by E q n . (2.2), and GT the set of TV G W s gt\,gt2,  gt^  on the Earth. The computation of the minimum  G W distribution for single satellite service can be restated mathematically as follows: min(N)  (2.10)  under the constraint that, for any given mt^ £ MT,  there exist gt  n  £ GT, stk £  ST  such that the following two conditions are satisfied: \mt k  st (t)\ m  <r  Vt (2.11)  \st (t) - gt \ m  n  <r  where r is the radius of satellite coverage. Before we go into further analysis of optimal G W distribution for single satellite service, we w i l l first derive the sufficient condition of G W distribution ensuring single satellite service. 19  Chapter 2. Multiple Satellite Service Availability Analysis  2.4.1.2 : Sufficient Condition of Gateway Distribution Ensuring Single Satellite Service Proposition: For a given J. G . Walker Constellation, or any other constellations, where single satellite coverage is available, i.e., there exist st^ \mtk — st (t)\ m  <  r  V i at any  mt^  G  ST  such that  M T , the sufficient condition on the G W dis-  tribution providing single satellite service is that Explanation:  £  \st (t) m  — gt \ n  <r  Vt,  A s illustrated in F i g 8, the inherent design of the J. G . Walker  Constellation already ensures that most areas receive single satellite coverage, and the mid-latitudes receive double satellite coverage most of the time. Consider a M T location where  \mtk — st (t)\ m  <  r,  Vt is satisfied. If each satellite in the constellation is able to  communicate with at least one G W at any time, then condition \st — gt \ < r, Vt is m  n  met for the M T . B y the definition, single satellite service is guaranteed. We w i l l now propose two G W distributions in order to a) investigate the basic characteristics of G W distribution patterns satisfying Proposition / to refine the sufficient condition of optimal G W distribution, and b) provide some useful G W distribution configurations in the future capacity analysis and simulations. Gateway Distribution 1: Uniformly distribute the G W s along the satellite orbital planes at an interval equal to the diameter of the satellite coverage pattern. 40 G W s are required to ensure single satellite service. Gateway Distribution 2: Distribute the G W s between adjacent orbital planes at the intersections of coverage patterns of satellites orbiting these planes, which is shown in F i g . 12. 32 G W s are required to ensure single satellite service. A p p l y i n g the similar terminology in the previous section, the circles in G W distribution 2 are called the G W service circles. The center of a G W service circle is located at G W gt , n  and its radius is r. 20  Chapter 2. Multiple Satellite Service Availability Analysis  --150  -100  -50  .0 longitude  50  100  150  Figure 12 Gateway distribution 2 After studying G W distributions 1 and 2, we notice that i f the satellite tracks (satellites' trajectory on the Earth) are completed covered by the service circles of the G W s , Proposition I is satisfied.  Therefore, a refined sufficient condition of G W  distribution ensuring single satellite service is derived.  2.4.1.3 Refined Sufficient Condition Ensuring the Single Satellite Service Proposition II: Let SK be the set of M satellite tracks (satellite's trajectory on the Earth) on the Earth ski,sk-2,.:....skM, If all members of SK  resulting from a given constellation of M Satellites.  are completely covered by G W service circles, single satellite  service is ensured. Explanation: Because ski is the trajectory on the Earth of the ith satellite, therefore, ski = sti(t)  Vt. If SK is completely covered by GT, at any time t, there exists gt _ G T  such that|sii(i) — gtf \ < r  V i . Therefore, Proposition I is satisfied. . 21  Chapter 2. Multiple Satellite Service Availability Analysis  Based on Proposition II, the problem to search for an optimal G W distribution ensuring single satellite service becomes a problem of searching for a G W distribution covering all the satellite tracks with a minimum number of G W s . To cover an object using a number of other kinds of objects is called a Packing and Covering Problem [19] [20]. Covering a square by circles is one of the well-known Packing and Covering Problem [21]. U p to date, there are a few proven optimal solutions to the packing problem and covering. For majority of cases, especially problems involving a large number of circles, searching for an optimal solution is extremely difficult. In the optimal theory, there are two algorithms which can be applied to search for the optimal G W distribution [22], namely, General Solution algorithm and Local Solution algorithmThe General Solution can be applied to a diverse set of problems.  But, it does not  necessarily yield the optimal solution for each specific case. The local solution, although it produces a better solution, is usually only applicable to one specific situation.  2.4.1.4 Gateway Distribution Employing General Solution Algorithm The general solution algorithm is obtained by constructing a G W distribution without considering the satellite orbits. If a G W distribution completely covers the areas under  EQUATOR  GATEWAY Figure 13 Optimal gateway distribution for single satellite service 22  Chapter 2. Multiple Satellite Service Availability Analysis  Figure 14 Gateway distribution 3:  GW  distribution without considering satellite orbits the satellite orbits which lie from South 52° to North 52° in the Globalstar system, all the satellite tracks are covered by G W . service circles. In plane geometry, the hexagon has been proved to be the optimal covering solution in the plane [23]. The equivalent solution in spherical theory is to place circles in such a pattern that the centers of any 3 closest circles form an equilateral triangle and these circles intersect of only one common point. The pattern in F i g . 13 results in the minimum number of G W s to completely cover the satellite tracks. F r o m F i g . 13, the distance between two G W gt  A  dAB = cos  -1  (cos (R) — sin (R) 2  2  and gtg is given by:  * COS(OAOB))  (2.12)  where R is the radius of satellite coverage, and OAOB is 120°. In the Globalstar system, d  AB  is 4 4 ° . 23  Chapter 2. Multiple Satellite Service Availability Analysis  If the areas with latitude from South 52° to North 52° are covered, then the boundary of these area must be covered as well. On the latitude side, ^  = 2.36, therefore, three  layers-are required to cover the boundary. On the longitude side, since maximal distance between 2 points in the same latitude occurs in the equator, ^  = 8.18, 9 G W s per layer  are required. The lower bound of the number of G W is given by N > 27. Fig. 14 illustrates the location of G W s for G W distribution 3 in the Globalstar system employing the general solution. The scheme requires 27 G W s in total to ensure that M T s between South 70° and North 70° receive single satellite service.  2.4.1.5 Gateway Distribution Employing Local Solution Algorithm General Solution Orbit-  Local Solution satellite track S K I Gateway Service Circle  —satellite track S k 5 Figure 15 The optimal gateway distribution for single satellite service  B y investigating in more detail the G W distribution derived from the general solution in F i g . 15, we find that as long as the service circle gw\ covers A, the intersection point between gw  2  ski  and sk^, and B, the intersection point between gwz and ski, satellite tracks  and sk^ are still completely covered by G W s service circles. Thus, the G W service  circle Cl may be centered at a higher latitude and the total number of G W s may be reduced. Based on the local solution algorithm, G W distribution 4, a distribution of 21 GWs  for the Globalstar system is illustrated in F i g . 16. 24  Chapter 2.  Multiple Satellite Service Availability Analysis  Figure 16 Gateway distribution 4 employing local solution In F i g . 16, 7 G W s are placed along the equator in the first layer and 7 G W s are in the layers on North and, South 32.3°. The areas shown between the two horizontal lines on South 52° and North 52° denote the satellite orbital areas. Note that i f the radius of G W service is changed, G W distribution 4 may no longer be valid.  2.4.2 Optimal Gateway Distribution for Double Satellite Service Since the derivation of the optimal G W distribution for double satellite service is far more complicated and difficult than that for single satellite service, and for the reason that our main goal is to present a G W reference system for further capacity analysis, we w i l l attempt to develop an algorithm for constructing a G W distribution to provide double satellite service, rather than pursuing an optimal distribution as we did for single satellite service. 25  Chapter 2. Multiple Satellite Service Availability Analysis  In order to construct a G W distribution GT to provide double satellite service, we equally distribute G W s i n a hexagonal pattern pn the spherical surface, as shown i n the right picture of F i g . 17. If the separation distance d between 2 closest G W s is sufficiently small, GT w i l l ensure that at least one G W is available within any double satellite coverage areas. A s a result, double satellite service is available to the M T s i n those areas. The minimum number min(N)  of G W s is obtained when d is maximum.  LEGEND \~  .  |  GATEWAY MOBILE TERMINAL  ™*W  M  SATELLITE  Figure 17 Gateway distribution for double satellite service model To maximize the value of d, let us consider a case illustrated i n F i g . 17. A t any given time t, a M T mt^ £ MT illuminated by m(t) > 2 satellites i n {sti,st2  st } m  satisfies the following condition: \st (t) - mtk\ < r  (2.13)  m  For clarity, only sti • £ ST and st  2  satellite coverage area of st . m  £ ST are shown in the figure. Let C t  s m  denote  Based on double satellite service analysis i n the previous  section, i n order to ensure that mt^ receives double satellite service from sti and st , 2  there must exist at least one G W gt , in the junction or overlapped area of the satellite n  26  Chapter 2. Multiple Satellite Service Availability Analysis  coverage of st\ and sti, i-e.  f]C t -  To simplify the analysis, we assume that the  s 2  satellite coverage patterns of st\ and stq, are fixed, and Cg^ f] C t s  2  is free to be oriented  in any direction. The distance d of GT guaranteeing that there is always a G W located in C  stl  H Ct s  2  is given by al = c o s ,  where d \- t2 st  s  - 1  (cos l V  * cos ( — j j V / /  + sin l  2  2  (2.14)  3  dst\—st  2  is the width of  P| C i . a  2  dsh-st , 2  which is closely related to the  distance between st\ and st2, is calculated as:  d t\-st2 s  =  2*r -  d  (2.15)  st2  tiStu  where r is the radius of satellite coverage area and d t t2 t s ltS  is the distance between  5^1 and 5^2 at time t. Clearly, the closer the satellite distance is, the larger the G W separation distance is.  ,  Since there are m(t) satellites visible to the typical M T mtk and only one pair of them is needed to provide double satellite service, the G W separation distance can be /m(t)\ maximized by choosing d t t, i.e. the minimum distance of I m  k  J possible distances  between m(t) satellites for mtk at time t. The G W distribution GT derived from the above algorithm w i l l ensure that at least one G W is located within one double satellite coverage area.  Subsequently, for all the M T s or sample points, the G W separation  distance d ensuring all M T s receiving double satellite service is d = m&x(d ) mtk  (2.16)  The M a x - M i n distance d t for the Globalstar system in the areas with latitude from m  North 25° to North 4 5 ° , (i.e. areas which receive 100% double satellite coverage as shown i n F i g . 8), is illustrated i n F i g . 18. The figure shows that the satellite separation  27  Chapter 2. Multiple Satellite Service Availability Analysis  distance d  mt  is larger in the mid latitude than high latitude. This result can be justified  since the orbit separation at lower latitude is larger than higher latitude.  Figure 18 T h e M a x — M i n satellite distance  The M a x - M i n distance of the Globalstar system in the areas with latitude from North 25° to North 45° is 39.4°. Accordingly, the G W separation distance d equals to 10.38°. Providing double satellite service to these areas requires their boundaries being covered. On the latitude side,  ss 2 layers are required to cover the boundary. O n the longitude  side, since the rhumb distance at the latitude of North 25° is 326°,  ~ 32 G W s per  layer are required. Therefore, the lower bound of number of G W s is given by N > 6 4 . Based on the above analysis, G W distribution 5, a distribution of 200 G W s for the Globalstar system is illustrated in F i g . 19.  28  Chapter 2. Multiple Satellite Service Availability Analysis  gateway  80 60  ^ I! • • •! I ^"" | ^ I! • • * I "  " |" ^!' • '5("  40  * *" | * C 5 • • •! * * |" | ) ' I • • •  ^fr*  ¥fc  20  ^« ^  ^  ^  ^  ^  ^f*  m  *^f^ ^i^* ^  ^(^*  4^ ^fr.  ^  ^fr*  ^  ^  ^  ^  ^  • ^*  *^)^ ^  ^  ^  *^.  ^  0)  3  0*-20 -40^  * ^»  . '. ::«••:: i  -60  «^ *  * ^»  »^ *  '. ::••>::)... ;:: i satellite orbit  "  jj^  ^ «^ *^  \ \...',;: i • •::;  ^ * ^«  ;::••«::;...'.:: i  *  •»:: *.  I  I..  -80 -150  -100  -50  0 longitude  50  100  150  Figure 19 Gateway Distribution 5 ensuring double satellite service between North (South) 25° and 45° in the Globalstar system  In F i g . 19, 32 G W s are placed in each of the layers of North and South 2 5 ° , 33.4° and 41.8° and 8 G W s are placed along the Equator. M T s in the areas with latitude between North 25° to 45° and South 25° to 4 5 ° , which are guaranteed to receive double satellite coverage as shown in F i g . 8, are ensured to properly receive double satellite service all the time. M T s in the areas with latitude from South 25° to North 25° are also guaranteed for single satellite service all the time.  29  Chapter 3 Impact of Gateway Distribution to Mobile Satellite System Capacity Diversity techniques in conjunction with D S - C D M A have been very effective for terrestrial cellular systems [24], where line-of-sight ( L O S ) signals are usually absent and Rayleigh fading is experienced. Furthermore, the terrestrial system capacity is generally interference limited. O n the contrary, satellite system are typically power limited and are forced to exploit the L O S signal. The intention of this chapter is to offer some insight on the relationship between.the system capacity and G W distribution. The focus is on the reverse link (mobile-satellitegateway).  Because both mobile terminals and mobile satellites have limited transmit  power due to government communication and health regulations, and battery constraint in mobile terminals, the reverse link results in the system capacity bottleneck.  The  analytical model presented hereafter is of general applicability, whereas numerical results are specific to the Globalstar system. Although coding and interleaving are essential to maximize the system capacity, they have been excluded from the analysis to make our results independent from specific system design parameters such as bit rate and frame length. A s discussed in the previous chapter, satellite service is closely related to G W distribution. The analytical model, drawing on established theory, w i l l be verified with the use of simulation.  30  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  3.1 Definitions and System Outline 3.1.1 System Capacity  To maximize frequency utilization efficiency and increase system capacity, all modern mobile satellites employ multiple spot beam antennas. A s we know, in terrestrial cellular systems, the near-far problem is a big concern for system design. However, in mobile satellite systems, because a M T is almost stationary compared to a high speed mobile satellite, a proper antenna design can alleviate the effects of near-far problem.  3 direction of flight path  Figure 20 The isoflux antenna of Globalstar  The  radiation pattern of an isoflux antenna of the Globalstar system [25] is shown  in F i g . 20. The circle in the figure shows satellite coverage area. The coverage area is divided by 6 elliptical beams with their major axes aligned parallel to the satellite flight path. Due to the path difference between satellites and MTs, the path loss between a M T located at the sub-satellite point and a M T located at the edge of the coverage with 10 degree of minimum elevation angle is as high as 8dB [25]. To ensure that the C D M A system functions properly, the antenna gains on the Earth's surface should be maintained as uniform as possible. This is accomplished by shaping the radiation patterns of each 31  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  coverage beam in a way that antenna directivity increases proportionally to the path loss. In the following sections, we assume that all MTs in the spot beam of the satellite in interest are illuminated equally with one unit of gain. Since all MTs are illuminated by equal gain and reuse of the entire frequency band for each beam is assumed, we may analyze the MSS capacity per satellite rather than per satellite beam. In this case, the satellite coverage and service analysis in the previous chapters for single spot beam satellite system are still valid for multiple spot beam systems. System capacity is defined as the average number of simultaneously active users per satellite with a given average probability of error. Suppose there are totally S  mobile satellites, n t MTs the 5th satellite is able to accommodate at time t, and T Si  samples per satellite over the time, the system capacity is given by: ST  3.1.2 System O u t l i n e  The mobile satellite system to be analyzed is depicted in Fig. 21. It consists of three parts: MTs, mobile satellites (SATs) and GWs. The link from a GW to a MT via a SAT is called the forward link or feeder link; and the link from a M T to a GW via a SAT is called the reverse link or user link. On the forward link, a pilot channel, which is transmitted by each GW to each satellite beam, is used for CDMA synchronization and GW identification. On the reverse link, the signal of a MT is uplinked to a SAT using an omnidirectional antenna, and then transparently resent to a GW by the satellite's pent-pipe transponders. In the GW, the satellite signal is despreaded and decoded accordingly. For analytical convenience and in order to determine the basic performance of a MSS, we assume that the baseband signal of a MT is encoded by BPSK modulation 32  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  User Link  Handset  Gateway  r Information BPSK  Modulator!  A PN Sequence  LEGEND  |nforrrjatiqD BPSK  PN Sequence  Omindirection Antenna  High Gain Tracking Antenna  F i g u r e 21 System model and decoded by coherent detection. While traditional frequency or time division multiple access is widely used in terrestrial mobile communication, C D M A [26] [27] is frequently selected as the access scheme because of its noteworthy low-power flux density emission, time-domain signal discrimination, and interference resilience. Please note that different types of C D M A technologies are adopted for the forward and the reverse link.  Typi-  cally, synchronous C D M A ( S - C D M A ) [28] is adopted for the forward link to avoid the intrabeam self-noise effect since all the signals are transmitted together and they could be coordinated by the satellites. However, because signal synchronization can not be reasonably achieved on the reverse link, asynchronous C D M A ( A - C D M A ) is employed. Each M T is assigned with a different random-like pseudo-random noise (PN) to distinguish signals from different other M T s . Performance of C D M A - b a s e d mobile satellite systems can be improved by employing satellite diversity with the use of Rake receivers [29].  B y using the autocorrelation  characteristics of a C D M A signal, correlators or arms of a Rake receiver synchronize the 33  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  signals of a particular M T ' s P N code and separate the incoming signal into multiple path signals. A n d then each of these signals is fed to a diversity combiner and thus signal level attenuation due to fading is reduced. The best diversity combining techniques is maximal ratio combining [30].  X,  PNi  Rake, Finger 1 Active  Received Signal  Rake, Finger 3 Listening Rake, Finger 2 Active  CD c  £ o O  Estimated • Signal  PN 2  T 2  Two Arm RAKE Receiver Figure 22 Two-Arm Rake receiver The advantages introduced by satellite diversity generally increase as the number of diversity branches increases, but the complexity also increases. A s indicated in [11][14], a two-arm Rake receiver yields sufficient performance to exploit diversity advantages in most situations. Therefore, we assumed that G W s employ a modified version of the twoarm Rake receiver as shown in F i g . 22. Two arms of the Rake receiver despread their received signals by correlating them with locally generated replicas of the assigned P N code. The signals from the two arms are combined to decode the transmitted information while the third arm listens to and searches for pilot signals from other satellites and compares the S N R s to the active arms. When the listening arm finds a signal with a 34  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  better S N R , the Rake receiver will switch one of the active arms and the listening arm according to the preset rules. To achieve the same average probability of error or B E R at the G W for M T s in the different satellite services (i.e. single satellite service or double satellite service) with different channel conditions (i.e. L O S or shadowed channel), we assume that a simplified closed-loop power control is used. When a M T is illuminated by two satellites, the M T detects the pilot channels of both satellites and reports the signal strengths to the G W . Based on satellite and G W identification information and by comparing S N R of the received signal to a threshold, the G W is able to determine the satellite service and channel condition of the M T . Accordingly, the G W then sends out a command to have the M T increase or decrease its transmit power margin to a preset value. The power m a r g i n is defined as the increase in transmit power needed to achieve a specific average B E R , compared to the transmit power of a non-shadowed and non-fading M T . Since the large round trip time delay is in the order of 10 to 20 ms even for a L E O system [13], closed loop power control is not very effective, and rapid fades such as those experienced in the vehicular mobile environment cannot be mitigated.  3.1.3 C h a n n e l M o d e l  The propagation between a satellite and a mobile terminal is classified as either unshadowed or L O S when the mobile receiver has unobstructed L O S path to the satellite, or shadowed when the L O S path is obstructed by either terrain, vegetation, or man-made structures. T h e overall multipath-fading propagation is related to many factors, such as the elevation angle, the particular type of environment, the aerial directional characteristics, 35  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  the relative mobile-satellite speed, etc. A mobile terminal located in open areas (rural or suburban environment) receives a LOS link from satellites most of the time, apart from temporary shadowing. However, a mobile terminal in urban areas lacks LOS link and experiences shadowing. The measurement results in [31] indicate that the fraction of shadowed users is in the range of 0.2-24% on highways, corresponding to satellite elevations from 43° to 13°. In urban areas, the fraction of shadowed users is much higher from 55% to 90% for the same range of elevation angle above. In our simulation, we will verify the effect of GW  distribution on system capacity based on different levels  of shadowing. For ease of analysis, we take the channel model from [32]. It is assumed that a certain fraction, B, of the MTs experience shadowing. For simplicity, we neglect fading for non-shadowed MTs. For shadowed MTs, the probability density function of the received amplitude given by the Rayleigh distribution [13] [32]:  f (R) R  = ^e~^  (3.2)  = -e?  (3.3) .. •  or /() 7 7  7 where 2a  2  is the average received power of a shadowed user experiencing Rayleigh  fading and T is the average signal-to-noise-plus-interference ratio given by: 7_ T  R/(N  + l).  2o /(N  + l)  2  K  '  J  The overall PDF of the received amplitude is given by a combined density function in Eqn. (3.5) and is illustrated in Fig. 23,  36  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  1-B Line-of-Sight  B Rayleigh Fading F i g u r e 23 C h a n n e l model Conforming to the notation introduced in [31], we define the direct-to-multipath signal power ratio c as: 1  (3.6)  2a' Then, f (R) R  = 1-  2.*B*ce'-cR  2  B +  (3.7)  3.2 Analysis of Average Probability of Error  For S N R calculations, it is assumed that only one M S S is available, and there is no other interference from other M S S or terrestrial communications systems. Furthermore, it is assumed that the downlink (SAT to G W ) of the reverse link does not introduce further interference and the noise can be neglected. This is a reasonable consideration because the tracking antenna of the G W must have a high directivity and a high figure of merit  G/T.  Therefore, the signal-to-noise-plus-interference-ratio of reverse link can be calculated as [33]: 'I + N \  fl  + N S  S  MT-SAT  (3.8)  +  SAT-GW  S  s  J + J N  Reverse  V + # )  (3.9) MT-SAT  where / is the multiple access interference ( M A I ) from other active users.  37  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  It is assumed that a mobile satellite can communicate with a total of J users under the satellite coverage of the M T . The transmitted signal of ith M T is given by  (t) =  Si  AtPi'UiWPNiWcosiuct)  (3.10)  In E q n . (3.10), s,-(i) is the overall B P S K signal, di(t) is the ith user's data sequence, which is a sequence of unit amplitude, positive and negative, rectangular pulses of duration T and is assigned a P N waveform PNi(t), which consists of a periodic sequence of unit amplitude, positive and negative, rectangular pulses of duration of T and A is c  t  the equal transmitted power for all M T s . Pi represents the power margin of M T i relative to a non-shadowed and non-fading MT. The transmission from a M T is received by a S A T and re-transmitted to a G W , where demodulation is actually performed. The total received signal at a G W from one mobile satellite is j  r(t) =  ^2A * t  G at 3  * y/pl'* Ri *di(t-  Ti)  *  PNi(t -Ti)*  COs(u t c  + Oi)  (3.11)  i=i  +n (t) w  where R=  the independent flat fading  T=  the independent deplay satellite antenna gain the phase of the carrier additive white Gaussian noise with the two-sided power spectral desity No/2  M o b i l e terminals are assumed to have omnidirectional antennae. A * G t is the t  sa  amplitude of received signal in the non-fading and non-shadowing environment. 38  With  Chapter 3. ' Impact of Gateway Distribution to Mobile Satellite System Capacity  isoflux antenna design, we assume that At * G t is a constant and it equals to A. sa  Therefore, by assuming an ideal correlation receiver, the received signal is calculated as: ./  VFi * Ri * di(t - Ti) * PNi(t - n) * cos{u t + 0 )  r(t) = A  c  t  i=i  (  '  +n (t) w  The test statistics for the user of interest, or the reference user r, is given by, J  D (T) r  = Ajv~ *R *T*d r  r  + Aj2^/P~i* i* h{T) R  r  (3.13)  i=i  +N(T) where  Ii(T) = J di(t - Ti) * PNi(t - Ti) * PN {t - T )cos(e )dt r  r  t  . (3.14)  o The computation of M A I h{T) is the subject o f a host of papers.  The standard  assumption [34] [35] to perform a reasonably accurate yet simple analysis is to model interference coming from other J-1 users as an additional zero-mean Gaussian random variable or Gaussian noise. This assumption turns out to be particularly well founded when the number of interfering users is not small (not less than 5 users) or/and processing gain G is large [27]. p  A n improved and more accurate Gaussian approximation is presented in [36]. H o w ever, for ease of analysis, the standard Gaussian approximation [34][35] is used. The variance of M A I contributed from one M T is given by: VMAI = var{Ii{T)) =  (3.15)  Because Ri and Ii are independent random processes, therefore, the interference from other M T s is A ^ erf = — * 22 Pi * 2  v a r  39  i i) R  (3-16)  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  The average signal-to-noise-plus-interference-ratio for a particular M T and the average total interference including white Gaussian noise and the interference from other M T s are given as follows: SNR  r  N  =  (3.17) 1  J  _  1  r i=l  G  Before further calculation of the variance of noise plus interference a , we notice 2  ot  that there are five distinct scenarios which can arise as depicted in F i g . 24. M T s can be distinguished as follows: •  satellite service: single satellite service (SS) and double satellite service (DS) for a two-arms Rake receiver  •  channel condition: unshadowed or clear of any obstruction (C) in the line-of-sight path or shadowed (S) path In F i g . 24, the two M T s in the left communicate with satellite #1 without satellite  diversity.  M T #1 experiences a L O S channel, and M T #2 experiences a shadowed  channel.  The three M T s in the right communicate with two satellites using satellite  diversity: M T #4 experiences two L O S channels, M T #4 experiences one shadowed channel and one L O S channel, and M T #5 experiences two shadowed channels. Realizing the fact that the power margin for each scenario w i l l be different (a M T , receiving double satellite service is augmented by less power margin than a M T receiving single satellite service, and a M T experiencing a L O S channel requires less power margin than a M T experiencing shadowing), to compute of, and have to a.  quantify the power margin, pi, for each scenario;  b.  calculate the average variance of interference, var(R?), for each scenario.  40.  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  SAT2  SAT1  Single Satellite Service | Double Satellite Service Figure 24 Uplink of reverse link scenarios We w i l l address this topics in the following two sections.  3.3 Power Margins for Each Scenarios 3.3.1 SS/C: Single Satellite Service/LOS Path  In this scenario, the uplink channel is a L O S channel. This scenario occurs when: •  A M T is illuminated by only one satellite and experiences a L O S channel;  •  A M T is illuminated by two or more satellites. However, due to lack of proper G W distribution, the M T is not able to reach the same G W v i a two different satellites and one of the channels is a L O S channel. SAT1  L E G E N D  MOBILE TERMINAL SATELLITE  Figure 25 SS/C: Single satellite service/LOS channel 41  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  Since the M T experiences a non-faded and non-shadowed L O S channel, by definition, the power margin of M T in S S / C is P /c ss  = 1-  Suppose the variance of white Gaussian noise plus interference from other M T s is cr£ , t  the B E R of B P S K [30] is given by  *=Mv*y-  -  <3 i9)  3.3.2 SS/S: Single Satellite Service/Shadowing Path  In this scenario, a M T communicates only one satellite and experiences a shadowed channel. This scenario occurs when: •  A M T is illuminated by only one satellite and experiences a shadowed channel;  •  A M T is illuminated by two or more satellites. However, due to lack of proper G W distribution, satellite diversity is not enabled and the channel experiencing shadowing is the only channel to reach the G W . SAT1 EEQQEffl LEGEND ^ ,  t  Blockage MOBILE TERMINAL  m^m  SATELLITE  Figure 26 SS/S: Single satellite service/Shadowing path Based on Eqn. (3.17), for a given fixed R , r  the B E R for M T in SS/S scenario is  given by 1 / P(e\R ) = -erfcU r  42  Pssls * Rr \ " / ^ [  (3.20)  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  Since R is Rayleigh-distributed, R has a chi-square probability distribution with 2 2  r  degree of freedom. The P D F of R is given by [30]: 2  r  x = Rt  i  2a  -x/2a  2  (3.21)  2  ce~  cx  Therefore, the average B E R is given by, / f 1  Pe  I  /  N  Pss/s *  Ice  x  J-2 {\l-^r  dx  cx  (3.22)  erfc  i  and 7(, = M^-, therefore,  Let 7fc ''"tot  tot  La  OO  f1 1 2k / 77 / (v 7i)= 76 J 2 7i  e=  P  e r  c  /  e 7 6 c ?  (3.23)  After integration,  1 -  lb  (3.24)  Finally, the average B E R is given by -1/21+  (3.25)  p,ss/s  For a given required B E R P , the power margin is given by e  _  API- 4p  76 = - 1  +1 4p2 —4p e  e  ^L(4Pe-4p ss/s  2  Pe  e  +l )  (3.26)  - 2p^  3.3.3 DS/CC: Double Service/Both Paths are LOS  In this scenario, a M T employs satellite diversity. The M T is illuminated by two satellites, and the transmission from the M T is received by two different mobile satellites 43  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  SAT2  SAT1  LEGEND Blockage MOBILE TERMINAL SATELLITE  F i g u r e 27 D S / C C : Double satellite service/Both paths L O S and re-transmitted to the same G W on the ground. Diversity reception is then performed in the G W . The channels between the two satellites and the M T are L O S channels. This scenario happens when a M T is illuminated by 2 or more satellites and at least 2 channels to the satellites are L O S channels. Using the same notation as in Eqn. (3.13), with maximal ratio combining technique [29], the test statistic for Rake receiver is given by:  D {T) r  =A^f - *R *T* r  rl  r  J2V&* i* R  d + AR  2  v  rl  »=i  *i(T)  J + A^p- * R  2  T  +-Rri *  r2  * T* d + AR r  +Rr2  r2  (3.27)  ^r^/pl*Ri* Ii(T)  *N  2  where R \ and R 2 are the effects of fading via SAT1 and S A T 2 respectively. T  T  The desired signal power m and variance cr of interference are given by 2  S = m2 rn =  E(D (T)) r  (3.28) = Ay/pi * R? * T * d + Ay/p'r * R *T 2  rl  A(R  2 rl  +  r  R )Td 2  r2  r  44  r2  *d  r  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  cry —var(D (T)) T  J =A R c2  Pi2 * Ril  2  Tl  MAI  i=l +  J  A R o Y P 2*Rl 2  2  2  r2  MAI  J  (3-29)  i  2=1  + R NT  +  2  rl  0  R NT 2  r2  Q  ••(R i + R ) I Aa \ i=l and R , the BER is given by 2  2  2  2  For fixed R \ r  2  MAI  r2  P(e | R R ) rl  r2  = lerfc I J  |  (3.30) 'tot  Because R i = 1 and R T  r2  = 1, therefore,  j  where a  2 0t  = 3 ^ - ]T Pi^f + JJF' which is same as Eqn. (3.18). i=l P  3.3.4 DS/SS: Double Service/Both Paths are Shadowed  In this scenario, a M T employs satellite diversity. The M T experiences shadowed on both channels to the two satellites. This scenario arises when a M T is illuminated by 2 or more satellites and no channel is a LOS channel. SAT1  SAT2  jr  LEGEND  [ I }•  ^ MOBILE TERMINAL SATELLITE  Figure 28 DS/SS: Double service/Both paths are shadowed 45  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  Similar to D S / C C scenario, for a fixed set of R i and R 2, the B E R is given by:, r  1  2  , /  IP s/ss(R  where o  2  rl  ~2cT 'tot 2  \  J  + R 2)  2  d  V  6 r f C  r  N  = ^ E P 4 + 27? 0  2 ot  1=1  Since i ? n and R\ are Rayleigh distributed, i ? ^ and R 2  with 2 degrees of freedom.  Therefore, R\ + i?f x  are Chi-square distributed  2  2  2  is a chi-squared variable with four  2  degrees of freedom. Accordingly, the P D F of R\ + R  2  x  2  [30] is given by  =4 /(x) =  * 1  x l - e- ' n  2  l  x  (3.33)  2(T2  -xe-^  2  T*2 2' 2  =  ,  /  c xe2  cx  o  (3.34)  oo  = ^  /  e-  i2  (-2e*l«lPto, t -e-^*l «>" 2  - e ~ ^ ^ »  P  aa  + l)  o For the details of derivation of Eqn. (3.34), please refer to Appendix B . Let 76 =  0  , after integration,  i°  P  Pe =  (3.35)  where u, by definition, is given by:  1  + 7i  For a required B E R , the power margin is derived as ^cr u 2  p  2  0i  ^ds/ss  _2  x  u  I((i/3 + r / ) + zV3(V 2 1 3  U  6  =  b=2  Pe  - 1+  2^/pj-pe  4 6  /3  -6- / )) 1  3  (3-37)  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  3.3.5 D S / C S : Double Service/One Path is L O S , Another Path is Shadowed  In this scenario, a M T employs satellite diversity. The M T experiences a shadowed channel and a L O S channel from the satellites. This scenario occurs when a M T and a G W are illuminated by 2 or more satellites, and only one channel is L O S while others are shadowed. SAT2  SAT1  LEGEND Blockage MOBILE TERMINAL •  SATELLITE  Figure 29 DS/CS: Double service/One path is L O S , another path is shadowed Similar to DS/SS scenario, for a fixed set of R \ and R 2, the B E R is given by, r  r  , , x 1 / ds/cs(R n P(e | Rn,Rr2) = g e r / c j \ / \*2 P  2  +Rr ) 2  (3.38) •pi  I  p  \  1  t  I  ds/cs(±  P  +  i f f  2  )  The detailed derivation of Eqn. (3.38) can be found i n Appendix B . Therefore, the P D F of R? is a chi-squared variable with two degrees of freedom. r2  The average B E R is given by  x =  Pds/csO- +  /r (/ r/c  = —er fc 2 1  )  x  2*L  ce  "dx (3.39)  cs  --erfci A c +  J  +1  47  P,dsjcs  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  For a given B E R , there is no closed-form solution for  P^s/cs-  With the same noise-plus-interference from other M T s , to ensure the same B E R P  e  at the G W , the power margins for each scenario are listed in Table 2.  senario  power margin  SS/C  . Pss/c = 1  (3.40)  SS/S c c r  L (4p? - 4p + 1) \ 2p - Ipl e  Pss/s =  i  o  t  e  (3.41)  1  0  2  e  DS/CC  Pos/cc = 1/2  (3.42)  DS/SS PDS/SSu  X  _  Y  2  = -I((ti/3 +  /3(6 / -6- / )) 1  + i >  6 = 2p - l + 2\/p2 _ e  DS/CS  p  3  1  (3.43)  3  e  No closed-form solution. A computer program is written to solve for Pd,/cs  Table 2 Power margins for different scenarios  Suppose that the carrier-to-multipath ratio is c = 10, the required power margins for different scenarios to meet the same required B E R from 1 0  - 3  to 1 0 ~ are shown 2  in F i g . 30. For M T s experiencing shadowed channels, it can be seen from F i g . 30 that satellite diversity dramatically reduces the required power margins to maintain the same B E R at the G W . However, satellite diversity, is less effective when one satellite is seen with a L O S channel. For example, when we choose BER = 1 0  - 3  as our goal, M T s employing  satellite diversity (DS/SS) require 12.87 dB less power margin than M T s without satellite diversity (SS/S) to meet the same B E R . When at least one L O S channel can be exploited, the difference in power margin between S S / C and D S / C C scenario is merely 3.01 d B . 48  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  30  SS/C DS/CS  DS/CC 5  6  Bit Error Rate  9  10 x10"  3  Figure 30 The required power margins for different scenarios  3.4 The Average Interference for Each Scenario  3.4.1 Fraction of Double Satellite Service Links  To reveal the relationship between G W distribution and system capacity of a M S S and provide some meaningful results in this thesis, our first challenge is how to assess a G W distribution. The natural and straightforward assessment method is to use the probability of double satellite service, which is defined as the average fraction of time of M T s receiving double satellite service while they have double satellite coverage. However, the use of the probability of double satellite service to assess the quality of a G W distribution has some shortcomings. Let us quantify the interference results in F i g . 2 in Chapter 1 to show the reasons. 49  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  SAT1  S  A  T  SAT1  2  c) LEGEND  Single  ^~ GATEWAY | MOBILE TERMINAL  SAT2  Satellite S e r v i c e  EBQ-gffl  SATELLITE  ^  Blockage  Figure 31 Interference calculation For ease of comparison, F i g . 2 is re-drawn in F i g . 31 and a M T in SS/S scenario is added in the figure. In Fig. 2 a), MT A is illuminated by two satellites and experiences one shadowed channel and one L O S channel. Ideally, MT A would employ satellite diversity and thus reduce its transmit power. However, due to an improper G W distribution, MT A may not be able to take advantage of satellite diversity and is forced to transmit more power to maintain the same performance. In a pessimistic scenario, MT A communicates 50  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  with SAT 1 via the shadowed channel and generates severe interference to SAT 2 as shown in Fig. 31b). We assume that both MT A and MT B are interfering MTs, the average interference contributed by MT A in a) and b) and the interference contributed by MT B in c) are given by:  (3.44)  c where PDS/CS  a n  d Pss/s denote the power margins for MTs in DS/CS and SS/S  respectively, and c denotes the direct-to-multipath signal power ratio. For c=10 and B=0:3, the average interference for a), b) and c) are P,- = -2.59 dB, P;^ = 24.69 dB )a  and Pi  tC  = 17.29 dB respectively. As indicated in our power margin analysis, usually,  Pss/s ^> PDS/CS-  s  i  n  c  e  c > 1, therefore, P  hb  > Pj  jC  > P;, . a  From the. above analysis, it shows that. 1.  although both MT A in b) and MT B in c) receive single satellite service, the average interference contributed by MT A in case b) is much higher than MT B in case c);  2.  the average interference is determined by not only the satellite service a M T receives, but also its satellite coverage. Apparently, the probability of satellite service is not good enough to compute the  average interference contributed by a M T and it is necessary to find an "indicator" reflecting MT's satellite service and satellite coverage to compute the average interference contributed by a MT. The fraction of double satellite service links is introduced. The computation of the average p  ds  does not include MTs with single satellite coverage. 51  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  Definition: fraction of double satellite service links, pd is calculated by counting s  the average number of satellite-link pairs which provide double satellite service to a M T as a fraction of the possible combinations of satellite-link pairs accessible by the M T . The concept fraction of double satellite service links only applies to M T s receiving double or higher satellite coverage. Example: For a M T in N e w York City as shown in F i g . 32, its connection status generated by a simulation is shown as follows TIME  MT ID  2 2 2  120 120 120  SAT  52 52 0  ID  2 8 2  22 22 13  2  120  43  15  12  GW ID  Elevation  LEGEND [j""  G A T E W A Y  |  M O B I L E  T E R M I N A L  S A T E L L I T E  Figure 32 One pair of satellite links capable of providing double satellite service  Since there are three satellites visible to the M T , the total number of combinations of satellite-link pairs are C ( 3 , 2 ) = 3. Because only one pair of satellite links (MT-Sat # 0 - G W # 2 and M T - S A T # 5 2 - G W #2) is able to provide double satellite service to the 52  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  M T , Pds = I- Therefore, for any pair of satellite links for this particular M T , the chance to. provide double satellite service to the M T is For a M T receiving m-fold satellite coverage, suppose there are  pairs of satellite  links which are able to provide double satellite service to the M T , pd is given by s  Pds =  nds C(m,2)  (3.45)  A pair of satellite links providing double satellite service is considered to be independent from each other because each M T has its own S A T links and G W links. Therefore, p  ds  has a consistent value for M T s in different satellite coverage. Our simulation results  support our observation. For the Globalstar system with the G W distribution shown i n F i g . 16, the average number of pairs of satellite links capable of providing double satellite service and average p  ds  for M T s receiving single, double, triple and four-fold satellite  coverage are shown in Table 3 respectively. The average pd is obtained by computing s  the average value of all the sample M T s ' pds °  v e r  the time.  Single  Double  Triple Satellite  four-fold  Satellite  Satellite  Coverage  satellite  Coverage  Coverage  Percentage of Total Time  12%  40.3%  37.9%  10%  Average # of Satellite-Link Pairs  0  0.524  1.5337  3.1639  0  0.5241  0.5100  coverage  providing double satellite service  Total Possible Combinations of Satellite-link Pairs Average p  ds  0- 00.5267  Table 3 The average number of pairs of links providing double satellite service and the average pd for the Globalstar System s  The average p  ds  for G W distribution 1 on p. 20, G W distribution 2 in F i g . 12, G W  distribution 3 in Fig. 14, G W distribution 4 in F i g . 16 and G W distribution 5 in F i g . 19 are 53  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  shown i n Table 4. Based on the results of confidence interval calculations, we conclude that fraction of double satellite service links is a inherent and consistent indicator for the performance of G W distributions. # of G W s  (p ) (means) ds  99% Confidence  Variation i n terms of  Interval  pencentage of mean  GW 1  40  0.6557  [0.6377,0.6736]  2.73%  GW 2  32  0.6456  [0.6330,0.6581]  1.94%  GW 3  27  0.6196  [0.6299,0.6637]  2.61%  GW 4  21  0.5190  [0.5014,0.5365]  3.37%  GW 5  200  0.8923  [0.8803,0.9034]  1.34%  Table 4 The average p  ds  for different G W distributions  Pds has a close relationship with probability of double satellite service. B y definition, for M T s receiving double satellite coverage, p  ds  equals the fraction of double .satellite  service. For M T s receive m-fold (m>2) satellite coverage, the probability of the M T s receiving single satellite service is the probability that all pairs of satellite links of the M T fail to provide double satellite service to the M T . Therefore, the probability of double satellite service is given by:  Pr(double satellite service) = 1 — (1 — p ) ' ^ C(jn 2  ds  Based on the above analysis, we conclude that p  ds  G W distribution. A higher value of p  ds  (3.46)  is a good indicator to assess a  results in a higher probability of double satellite  service. The contrary is also true that a higher probability of double satellite service yields a higher value of p ds  3.4.2 Terminology  To facilitate further analysis, a consistent terminology is necessary. 54  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  Definition: Path State (PS) is defined as the state of channel condition of a M T . PS is introduced to characterize a particular propagation environment of a M T . A s described before in the channel model, a M T experiences a shadowed channel (S) for B fraction of the time and a clear of path ( Q channel for 1-B fraction of the time. The P S sample space consists of two discrete states PS € {C, S} Let Pr(PS  = (k,m — k)) denote the probability of a M T experiencing k L O S  channels and m-k shadowed channels and let Pr(CG  = m) denote the probability of  a M T receiving m-fold satellite coverage. Suppose that a M T receives m—fold satellite coverage, the conditional probability of a particular PS for the M T is given by: P (PS r  = (k,m-k)\CG  = m) = C(m,k)(l  - B) B k  m  (3.47)  k  Because satellite coverage is an independent event from satellite channel propagation, the probability in a particular PS is given as follows: , p (PS r  = (fc, m - Jfej, CG = m) = C(m, k)(l - B) B - Pr(CG k  m  k  = m)  (3.48)  For the Globalstar system, which has up to four-fold satellite coverage as shown in F i g . 8, all 14 possible propagation or PSs are given in Table 5. Single  Double  Triple  4-fold  Satellite  Satellite  Satellite  Satellite  Coverage  Coverage  Coverage  Coverage  C  CC  ccc  cccc  S'. '  CS  CCS  CCCS  ss  CSS  1  cess csss. ssss  Table 5 P a t h States For example, for a M T receiving triple satellite coverage, the probability of a M T in the C S S P S is given by 3 £ ( 1 - B)Pr(CG 2  55  = 3).  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  DehnitiomSatellite Service State (SSS) is denned as the state of satellite service of a M T . SSS is introduced to characterize a particular satellite service a M T receives. For a G W distribution guaranteeing single satellite service, a M T receives either single satellite service (SS) or double satellite service (DS). The SSS sample space consists of two discrete states SSS e  {SS,DS}.  A s mentioned i n Eqn. (3.46), for a given p , the probability of the a M T receiving ds  single and double satellite service given m-fold satellite coverage are given by: Pr(SSS  = SS\CG = m) = (1  -p f ' {m  2)  ds  (3.49) Pr(SSS  = DS\CG  = m) = 1 - (1 -  Pdsf ' {m  2)  Definition '.Path and Satellite Service State (PSS) is defined as a combination of PS and SSS state of a M T . A s discussed in the previous section, an in-service M T with a twoarmed Rake receiver w i l l be in one of five scenarios, i.e., SS/C, SS/S, D S / C C , D S / C S and D S / S S . Since each scenario is unique, we can classify the general M T environments into five PSS states. The PSS sample space consists of five discrete states PSS € {SS/C, SS/S, D S / C C , D S / C S , D S / S S } , which can be ranked in order of decreasing link performance as D S / C C , D S / C S , S S / C , D S / S S , SS/SS based on the required power margin. Each P S S state has a certain occurrence probability 7, which is a function of the channel propagation and satellite service availability. If a G W distribution ensuring single satellite service is assumed, the sum of all the probabilities is unity. For the Globalstar system, the state diagram describing all 5 PSS states and 14 possible path states is illustrated i n F i g . 33. The summary of the above three states is shown iri Table 6. Name  Symble  Sample Space  Path State  PS  C, S  Satellite Service State  SSS  SS, D S  Path and Satellite Service State  PSS  D S / C C , D S / C S , D S / S S , S S / C , SS/S  Table 6 S u m m a r y o f States 56  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  3.4.3 Effect of gateway distribution on PSS distribution  If a G W distribution guaranteeing double satellite service is assumed, a M T w i l l ideally employ a PSS state with less required power margin (the solid line in F i g . 33 corresponds the preferred PSS). For example, a M T in the (PS=(0,2)) PS w i l l employ PSS state D S / S S . However, under an improper G W distribution, the M T may not be able to employ the preferred PSS state and may be forced to employ a less performing PSS state (the dashed line in Fig. 33). A s a result, the M T needs to transmit at a higher power level and generates more interference to the M T s ' connections. For example, a M T in the (PS=(0,2) PS employs PSS state SS/S. B y definition, the probability of a PSS state is a function of satellite service and channel propagation. Since satellite service, which depends on the satellite constellation and G W distribution, and channel propagation, which depends on the environment of M T s , are independent events, the probabilities of PSSs can be rewritten as:  n Pr(PSS)  =  i  E P ( SS\CG »=i j=o r  *Pr(CG = E  E  n  Pr(PSS\CG  is  the  maximal  = i,PS=(j,i  — j))  = i,PS  = i,PS  satellite  j))  = (j,i-j))  Pr{PSS\CG  *Pr(CG  where  = i, PS = (j, i -  p  =  (  = i, PS = (j, i -  3  5  Q  )  j))  (j,i-j))  coverage  a  MT  can  receive  denotes the transition probability from  and a par-  ticular PS state to a desired PSS state. A convenient way of describing and computing Eqn. (3.50) is by using a tree diagram (CG=3 as a example) as illustrated in F i g . 34. 57  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  Single Satellite Coverage  Double Satellite Coverage  Triple Satelite Coverage  Four-fold Coverage  1  P  LOS  cccs  cess  V^6(1-EJBV transition probability  /  (1-Ft|S)/2. /  [DS/CS, V OD  '- M *  ,  ^  Shadowed  Prefered PSS state Legend:  Less Performing PSS state  Path and Satellite Service State  SSSSf—  Probability of PS SS Figure 33 Path and satellite service analysis  58  P  a  t  n  s  t  a  t  e  probabilty of path state  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  Path and Satellite Service State  Path State  Single Satellite Service  P_| '  Pr(SICG=i,PS=0,i-j))  f  Pr(CG=  1  Pr(PS=(j, i-j))  3  "  Double Satellite Service  Pr(PSICG=i, PS=(j,i-j))  Figure 3 4 T h e tree d i a g r a m of P S — > P S S Therefore, E q n . (3.50) can be further derived as follows:  n Pr(PSS)  i  = ]T Pr(PS\CG i=l j=o • * Pr(SSS\CG = ^Pr(CG  = i,PS = (j, i - j))Pr(CG  = 'i, PS = (j, i - j))Pr(PS  = i)Pr{SSS\CG  = i)  = (j, i -  j))  = i)  (3.51.)  i=l  i * £  Pr(PS\CG  = i, PS = (j, i - j))Pr(PS  = (j, i -  j))  i=o =Pr(PS)  Pr{CG = i)Pr(SSS\CG  = i)  i=l  Based on the above equations, the overall probabilities of single and double satellite service under different satellite coverage situations are given by m  Pr(SSS  = SS) =  (1 - p ) ' Pr{CG C(l 2)  ds  = i)  i=l  (3.52)  m  Pr(SSS  = DS) = J2(±-  {l-Pds) ' )Pr{CG C{l 2)  i=l 59  = i)  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  The probabilities of S S / C and SS/S P S S states are given by: m  l  = {l-B)^{l- .) ^Pr{CG  = i)  c  t l h  Pi  m  i  =  (3-53)  1  = B J2 (1 - p f^ Pr(CG  = i)  2)  l s s / s  ds  and the probabilities of D S / C C , D S / C S and DS/SS PSS states are given, by: m  7<W« = (1 - 5 ) ^ 2  t= l m T d s / c s  ( l - (1 -W 3 )  = (1 - B)B  C ( i  ' ) 2 )  Pr(CG = 0  ( l - (1 - Pdsf ) li,2)  1  Pr(CG = i)  (3.54)  =1  m  Single  Double  Triple Satellite  Four-fold  Satellite  Satellite  Coverage  Satellite  Coverage  Coverage  P3 =  Coverage  Pi =  P2 =  Pr(CG  Pr(CG=l)  Pr{CG = 2)  1  \~Pda  (1 -Pdsf  1  1-Pds  (1 - Pdsf  DS/CC  0  Pds  HI-Pds)  DS/CS  0  Pds  l-(l-Ws)  0  Pds  Hi-Pds)  SS/C  = 3) Pr(CG  = 4)  (1 - P d s )  6  (1 - B) SS/S B l-(l-Pds)  3  3  6  H^-Pdsf  2B(l-B) DS/SS  £  3  2  Hi-Pds)  6  Table 7 Double satellite service transition matrix  The probability for each PSS state is listed in Table 7. The probability of a particular PSS state is the product of the probability of satellite coverage, the probability of single (double) satellite service and the probability of PS. For example, the probability of D S / C S 60  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  is given by: Iss/s = s(pi  + (1 - Pds)P2 + (1 - Pdsf Pi + (1 - Pdsf Pi)  pi = Pr(CG  = 1)  p = Pr(CG  = 2)  p = Pr(CG  = 3)  p = Pr(CG  = 4)  2  3  4  (3.55)  For Globalstar system with the G W distribution in F i g . 16, the distributions of M T s in a particular PSS under the condition where B=0.3 and the heavy shadowed channel condition where B=0.9 are shown in F i g . 35. Note that pd = 100% corresponds to an s  ideal situation where all the satellite pairs capable of providing double satellite service. This may not be realized because an enormous number of G W s are required. Fig. 35 a) and c) show the PSS state probabilities for M T s under normal (B=0.3) and heavy shadowed (B=0.9) channel conditions with an improper G W distribution. F i g . 35 b) and d) show the PSS state for the same channel condition with a proper G W distribution. It can be seen from figure that an improper G W distribution prevents a significant portion (close to 1/3) of M T s receiving double satellite coverage from acquiring double satellite service. The G W distribution has less impact on M T s receiving triple or higher satellite coverage than M T s receiving double satellite service.  3.4.4 Interference Calculations  Suppose that a M T is illuminated by m satellites and experiences k L O S channel and m-k shadowed channel, and the transmit power is P, the average interference generated by the M T is given by  p(k +  E(Pi) = -±  61  -)  m  m  k  —!-  c  (3.56)  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  b) PSS distfibution,B=0.3,pds=  PSS distribution.B=0.3.pds=0.52  4-fold CVG Triple CVG  4-fold CVG Triple CVG Double CVG Single CVG Satellite  Double CVG  Coverage rj\ PSS distribution, B=09 .p , ds=1  PSS distribution,B=0.9.pds=0.S  4-lold CVG Triple CVG Double CVG Satellite Single CVG  DS/CC DS/CS DS/SS  Satellite Coverage  Coverage  4-fold CVG Triple CVG Double CVG Satellite Single CVG  DS/CC DS/SS  Coverage  Figure 35 Distributions of PSS states of Globalstar system where c denotes the direct-to-multipath ratio. Accordingly, based on Eqn. (3.50), the expected interference given by a specific PSS state is as follows:  n  E(Pi\PSS)  i  =J2H  Pr{PS\CG  = i, PS = (j, i - j))Pr(CG  = i)  i=l j=0  * Pr(SSS\CG  = {j, i - j))  (3-57)  *)  .('• +  *  = i, PS = (j, i - j))Pr(PS  : i  Suppose a M T is in PS = (k.m — k), the probability that the first channel selected in PSS state is a L O S channel is ^ . If the first channel is L O S , then the probability that 62  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  the second is a L O S channel is ^ M j - . Thus, the probability that all channel in the PSS state are L O S channels is given by  Pr(PS  = CC\PS  = (k,m-k),CG  = mm).= — * ^ ~ \ m ( m — 1) X  (3.58)  Similarly, the probabilities for other PSS states are given by: Pr(PS = C\PS = (k,m-  k), CG = m) = — m fY)  Pr(PS=S\PS=(k,m-k),CG  h  = m) =  »"(».-*)' Pr(PS = CS\PS = (fc, m - k), CG = m) = — * ± m (m — 1) Pr(PS = SS\PS = (Jb, m - k), CG = m) =  (  m  ~^  * ^"['t^y  < 3 5 9 )  '  3.5 Capacity Calculation Based on the previous results, we w i l l now derive the system capacity of a mobile satellite system. Eqn. (3.18) can be further derived as follows: 2 -^0 1 °tot = ^42 + 3 ^ " l u "  *  Pt  V a r  / r>2\ y i ) R  (3.60)  1 = 1  rh 2A  2  +  3  E p  where E(Pi\PSS)  E(P \PSS)PV(PSS) 1  G  Vpss  is the expected interference for a specific P S S state given in  Eqn. (3.57) Applying the same parameters in the analysis in F i g . 35 and based on the power margin analysis in Section 3.3, the multiple access interference is shown in F i g . 36. It can been seen from F i g . 36 a) and c) that due to improper G W distribution, the M T s receiving double and triple satellite coverage are forced to be in the SS/S P S S state and thus they contribute the most interference to other M T s . When a proper G W distribution 63  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  a)  b)  4-lold C\ Triple CVG Double CVG satellite Single CVG  -Mold CVG Triple CVG Double CVG  coverage  singi.cvG  c)  satellite coverage  d)  4-fold CV Triple CVG Double CVGsatellite Single CVG  4-fold CVG Triple CVG Double CVG Single CVG  coverage  satellite coverage  Figure 36 M u l t i p l e access interference i n the Globalstar system is available, the interference generated by M T s receiving double satellite coverage is fairly low, as shown in F i g . 36 b) and d). When the system capacity J in Eqn. (3.60) is sufficiently large, we assume that the multiple access interference from all M T s other than the M T of interest contribute an equal amount of interference to the M T of interest. Therefore, the noise-plus-interference a  2 ot  of the M T of interest is given by: 1 tot  a  =  erfcinv(p ) e  64  (3.61)  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  where erfcinv(p ) e  is, the inverse complimentary error function for a given  BER.  Therefore, the system capacity is given by: . j =  3  p ( l t - J & ) E{Pi\PSS)Pr(PSS) G  a  ,  l  (  3 K  6  2  ) }  VPSS  There is no closed-form solution to solve the system capacity / . We develope an algorithm to compute the system capacity and a computer program based on this algorithm is written.  3.6 Numerical and  Simulation Results  In this section, we will first present numerical results of the system capacity of a CDMA-based mobile satellite system with different values of pd based on Eqn. s  (3.62).  Then, we will verify the theoretical computations with simulations. We will demonstrate how important it is for a proper G W distribution to be employed. In this sub-section, we will use fraction of double satellite service links p  to assess a  ds  GW  distribution. As we discussed in sub-section 3.4.1, a higher value of p  ds  corresponds  to a higher probability of double satellite service. Hence, a higher value of p  ds  a better G W distribution. Note that achieving p  ds  indicates  = 100% is economically prohibitive  in reality because it requires an enormouse number of GWs.  Also, p  ds  = 0% implies  that double satellite service link pairs are not available. Therefore, the numerical results for  p  ds  = 100% and p  ds  = 0 should be considered as the upper and lower bounds of  the system capacity of a MSS.  65  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  3.6.1 Numerical Results  The numerical results shown in F i g . 37, F i g . 38 and F i g . 39 are based on E q n . (3.62) and computed for code length G  p  = 1024 and  = 30dB. We assume c = lOdB as a  typical value in a L E O channel [31].  B E R Vs. Pds  . _0 1 0  p  1 1  1  1  i  i  1  1  i  i  1  i  1  ri  1  .  10"' J = 1 2 0  B=0.3  J=100  c=10  \ \ \  J=8o\\\ ;  -3  \ :  BER=10  0  "  \-  i  i  i  i  i  i  i  t  i  10  20  30  40  50  60  70  80  90  100  fraction of double satellite service links pds (%)  Figure 37 BER Vs. pd  s  (Varied system capacity J)  In F i g . 37, we show the bit error probability vs.  the fraction of double satellite  service links for a given fixed number of M T s per satellite. We choose B = 0.3, a value as a compromise between a large value, representing an urban area, and a smaller value, representing a suburban or rural environment.  It can be seen from the figure that the  average B E R of M T s are dramatically decreased when the pd  s  66  is increased. A proper  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  GW distribution, ensuring that most MTs receive double satellite service while receiving double satellite coverage, is critical to the performance of a MSS. In Fig. 37, when the p  value for J = 80 and J = 100 are less than 94% and  ds  97% respectively, the average BER of MTs cannot achieve the desired BER level of 10 . -3  As shown in Table. 4, even GW distribution 5 with 200 GWs can only achieve  Pds = 89%. A GW distribution with an enormous number of GWs is required to reach. Pds = 97%. We conclude that the MSS referred in Fig. 37 is under-designed for the assumed fading channel. BER Vs. Pds (varied B) 1  i  1  i  B=0.1^  I  '  1  I  ^^^^  1  1  B=O.5  :  X  V v : >\ • > / i B=U7 \ / \  \.  B=0.9\ 1  •  /  -  G=1024 J=80 c=10  i  0  10  20 .  30  40  i  50  i  i  i  60  70  80  i  90  100  fraction of double satellite service links pds (%)  Figure 38 BER Vs. p  ds  (varied B)  In Fig. 38, we show the average BER of the MTs vs. pd under different channel s  conditions for a fixed number of MTs per satellite (J=80). It is shown that the performance of MTs is more sensitive to an improper GW distribution under a lightly shadowed channel condition than under a heavily shadowed channel condition. The results are justified 67  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  because the interference is usually dominated by M T s receiving double or higher satellite coverage but working in the SS/S PSS state as shown in F i g . 36,. Now, let us examine the relationship between system capacity and G W distribution. We choose B E R of 1 0  - 3  as our goal.  The Capacity Vs. Gateway Distribution 300 -  B=0.1  fraction of double satellite service links pds(%)  Figure 39 Capacity Vs.  p  ds  It can be shown from Fig. 39 that a G W distribution imposes a tremendous effect on the system capacity of a C D M A - b a s e d M S S satellite system. Under a normal channel condition where B=0.3, deploying G W distribution 5 in F i g . 19 improves the system capacity from 13 M T s with G W distribution 4 in F i g . 16 to 60 M T s . The numerical results of the system capacity of a M S S deploying the G W distribution 5 in F i g . 19 and G W distribution 4 in F i g . 16 are listed in Table 8 under different channel conditions.  68  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  channel condition  G W 4,  B=0.1  40  141  B=0.3  13  60  B=0.5  12  41  B=0.7  11  33  B=0.9  10  31  =0.52  Pds  G W 5,  =0.S9  Pds  Table 8 The system capacity comparison for G W distribution 4 and G W distribution 5 under different channel conditions  Table 8 and F i g . 39 also show that a M S S in a lightly shadowed propagation environment suffers more capacity loss due to improper G W distribution.  3.6.2 Simulation Results  In this subsection, the main objectives of simulations are twofold: 1) to provide the statistics of satellite coverage, satellite service and fraction of double satellite service links Pds of the Globalstar system; and 2) to verify the numerical results based on E q n . (3.62) with the simulations. G W distribution 1 on p. 20, G W distribution 2 in F i g . 12, G W distribution 3 in F i g . 14, G W distribution 4 in F i g . 16 and G W distribution 5 i n F i g . 19 are used i n our simulations. Each simulation runs for 113 minutes, which is the orbital period of the Globalstar system. The system capacity of the M S S is obtained by calculating the average value of the capacities of .48 mobile satellites over 113 minutes.  3.6.2.1 Simulation Algorithm A simulator consisting of two sub-simulators: the Orbital information sub-simulator and the Interference information sub-simulator are used throughout all the simulations.  69  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  Satellite orbital information sub-simulator provides the sub-satellite position (the satellite's projection on Earth) of mobile satellites and the distances between the satellites and the MT-of-interest, and it produces the statistics of satellite coverage, satellite service, and pds of a particular M S S .  The specifications of the Globalstar system are employed  by the sub-simulator as typical system parameters. Equally Distributed M T s on the Earth  sen 60 - /  cu  I  40 <: 20 0  ra -20 -40 -60  -80  -150  -100  -50  0  50  100  150  longitude  F i g u r e 40 3912 M T s equally distributed o n the E a r t h  B y using the hexagon M T distribution pattern as shown in F i g . 13, a total of 3912 sample M T s are equally distributed in the areas between latitudes South 80° and North 80° as shown in F i g . 40. The distance between any two neighboring M T s is the same. Note that more M T s are distributed in the lower latitudes than higher latitude because the orbital separation at a lower latitude is higher than that at a higher latitude. The Interference information sub-simulator is employed in the calculation of the total received interference power and the sigal-to-noise-plus-interference-ratio. It is assumed that each M T has a 10-stage P N linear shift register and is assigned a 2  1 0  bits P N  sequence. Fig. 41 illustrates the simulation flow diagram. A M T , which is randomly chosen by the simulator to avoid the correlation between MTs, sends a channel request to a G W via 70  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  MT randomly chosen by simulator Orbital Information Sub-simulator  Time increment  Gatway, Satellite Position  Check the satellite service and channel condition  N  Send Channel request to all visiable satellites Interference Information Sub-simulator  If All satellites are in full capacities  GW compare the total received interference to maxium tolerable interfrence reject  Grant the request  Transmite the power margin based its path and satellite service  RECORD the inference, # of MTs served  Figure 41 The simulation diagram a mobile satellite. If the B E R of the requested satellite is not higher than the required B E R , the G W w i l l grant the request and the M T is able to transmit its signal based on its PSS state. However, i f the B E R of the requested satellite is higher than the required B E R , the satellite has already reached its capacity limit and w i l l reject the channel request of the MT-of-interest accordingly. A computer program based on F i g . 41 are enclosed in Appendix. D .  3.6.2.2 Simulation Results  The simulation results for the system capacity of a M S S under a normal channel condition where B=0.3 and c=10 are listed in Table 9. 71  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity  G W distri-  # of  (Pds)  Theoriticalsystem Simulation  bution  GWs  (means)  capacity (No of  system capacity  MTs)  (No of M T s )  GW 1  40  0.6557  24  35  GW 2  32  0.6456  23  37  GW 3  27  0.6196  22  35  GW 4  21  0.5190  17  25  GW 5  200  0.8923  57  81  Table 9 The simulation results for system capacity on channel condition (B=0.3, c=10) In Table 9, it shows that the simulation results are higher than the theoretical results. It could be attributed to the fact that the theoretical results do not consider any resource managements of a M S S . Using the channel management as described in F i g . 41, M T s with larger power margin would be more likely denied access by the M S S than M T s with smaller power margin. Therefore, a . M S S is able to accommodate more M T s . simulation results  0  10  20  30 40 50 60 70 Fraction of Double Satellite Service Links  80  90  100  Figure 42 The theoretical and simulation results (B=0.3,c=10) 72  Chapter 3. Impact of Gateway Distribution to Mobile Satellite System Capacity J  Nevertheless, our simulation results confirm our previous finding that a G W distribution is very important for the system capacity of a M S S . A s shown in F i g . 42, deploying a G W with a higher value of pd results in a higher system capacity. s  73  Chapter 4 Conclusion and Discussion In this thesis, we have investigated the principle of gateway distribution to ensure single and double satellite service and presented an analysis of the effects of gateway distribution on a C D M A - b a s e d L E O M S S . A well-designed gateway distribution is critical for mobile satellite system design. Accordingly, we have proposed some strategies to derive the optimal or sub-optimal gateway distributions for single satellite and double satellite service. To ensure single satellite service for Globalstar system, 27 gateways are required by the general solution algorithm and 21 gateways are required by the local solution algorithm. To ensure double satellite service, at least 64 G W s are required by employing the M a x - M i n satellite distance algorithm to ensure M T s in the areas with latitude between North 25° and 4 5 ° . A 200 G W s distribution is proposed to ensure double satellite service in the areas with latitude between North and South 25° and 45° and single satellite service from South 80° to North 80°. To analyze the impact of gateway distributions on the system capacity of a C D M A based L E O mobile satellite system, we classified the general mobile terminal environments into five states. B y computing the required power margin of each state in order to reach the same average probability of error and taking the occurrence probability of each state into account, the capacity of the mobile satellite system, expressed as the average number of M T s per satellite, was analytically derived and validated by means of computer simulations. We have shown that an improper gateway distribution have a detrimental effect on the system capacity of the mobile satellite system. For example, under a condition where 30% of the time a M T experiences a shadowed channel, our numerical results indicate 74 .  Chapter 4. Conclusion and Discussion  that a M S S is able to accommodate 60 M T s with G W distribution 5 in F i g . 19, but only 13 M T s with G W distribution 2 in F i g . 12. Our simulation results confirm this  finding.  A l s o , the system capacity of a M S S under a lightly shadowed channel is more sensitive to the gateway distribution mismatch than that under a heavily shadowed channel. A s a final observation, we would like to point out that the C D M A  performance  results presented in this thesis, which we take the channel model from [32], are optimistic because we assumed that non-shadowed M T s experienced no fading at all, although in practice they experience a Rician fading channel. 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Technol, pp. 738-742, A u g . 1994.  79  Appendix A List of Abbreviations and Acronyms  A-CDMA  Asynchronouse C D M A  BER  Bit Error Rate  CDMA  Code Division Multiple Access  CG  Satellite Coverage  CONUS  ContientUS  DS  Double Satellite Service  DS/CC  Double Satellite Serivice/Two L O S Channels  DS/CS  Double Satellite Service/One L O S , One Shadowed Channel  DS/SS  Double Satellite Service/Two Shadowed Channel  GW  Gateway  LEO  L o w Earth Orbiting Satellite System  LOS  Line-of-Sight  MAI  Multiple Access Interference  MEO  M e d i u m Earth Orbiting Satellite System  MSS  Mobile Satellite System  MT  Mobile Terminal  PMSCS  Personal M o b i l e Satellite Communication System  PN  Pseudonoise Code  PS  Path State  PSS  Path and Satellite Service State  PSTN  Public Switched Telephone Network  SAT  M o b i l e Satellite  S-CDMA  Synchronouse  SNR  Signal-to-Noise Ratio  SS  Singal Satellite Service  SS/C  Single Satellite Service/LOS Channel  SS/S  Single Satellite Service/Shadowed Channel  CDMA  80  Appendix B Supporting Calculations  B . l DS/SS Calculation  oo  o  iot  oo  oo  = -)=/  :  J  e- dtc xe-™dx t2  2  (B.l)  =  ^/=J ^  J  0  0  oo  = ~Je- (-cxe-™ t2  c xe- dxdt 2  cx  - e-')\l '" *-'"dt a  t/p  0  oo  B.2 DS/CS Calculation  Let Pio = P r f / s  cs  81  82  Appendix C Supporting Figures Check whether MT and GW have common oevrlapped Area Compare the distance bwteen MT and GW to radius of satellite coverage Distance is less than radius Check which Orbital Plane go through MT and GW circle Compare the distance from MT or GW to Orbital Plane to radius of satellite coverage Distance is less than radius Check whether the Orbital Plane go through overlapped area Caculate the starting and ending time of crossing GW and MT circle  The starting time of crossing GW(MT) is in the period of crossing GT(MT) Check wether the double satellite service is applicable Compare starting and ending time of all crossing orbital planes to find the MT can be illuminated by two satellites  F i g u r e 43 F l o w c h a r t for calculating satellite service  83  Appendix D Simulation Programs in Matlab % % % % % %  The S c e n a r i o S i m u l a t o r Usage: [SATCAP,S,SENREC,SATCVG]=simulation(BER,c,SHADOW,L) S : percentage of S i n g l e S a t e l l i t e S e r v i c e B: Percentage of Shadow C : Multipath Ratio L: l e n g t h of PN Code f u n c t i o n [SATCAP,S,SENREC,CVGREC]=simulation(BER,c,B,L) % f u n c t i o n [SATCAP,CAPFLAG,SO,SI,Sll,S1000,S10] %=simulation(BER,c,B,L) tic constant; QMAX=qmax (1, BER, 1, c).; % A s s i g n PN code f o r each MT l o a d data/pncode; l o a d data/mtdata; [MTN,tmp]=size(MT); [sm,sn]=size(PN); i f sm ~= MTN | .sn ~= L PN=mt_pncode(MTN,L); end NOISE=0; PNref=pngen(L); % The r e f e r e n c e MT l o a d data/mtdata; Sl=[]; • S10=[]; Sll=[]; S1000=[]; , . , S0=[] ; R= [ ] ; SATCAP= [•] ; CAPFLAG=[ ] ; CVGREC=[ ] ; SENREC=[]; f o r time=l:1 %  Initialization  CAPFLAG=zeros (PERIOD, 48) ;• % The s a t e l l i t e c a p a c i t y F l a g Matrix'; 1: r e a c h the c a p a c i t y S1=[S1; zeros(1,48)] ; S0=[S0; zeros(1,48)] ; S11=[S11; z e r o s ( 1 , 4 8 ) ] ; S10=[S10; zeros(1,48)] ; S1000=[S1000; z e r o s ( 1 , 4 8 ) ] ; R=[R; ones(1,48).*NOISE]; % Receive Power White N o i s e SATCAP=[SATCAP; z e r o s ( 1 , 4 8 ) ] ; %' # of u s e r s CVGREC=[CVGREC; ones(1,MTN)*(-1)]; SENREC=[SENREC; ones(1,MTN)*(-!)];  84  M=MTN; TMP=[] ; MTTMP=MT; % Determine the c a p a c i t y f o r each s a t e l l i t e a t g i v e n time f o r counter=l:MTN % Random Access MTS. row=ceil(M*rand); mtn=MTTMP(row,1); [TMP,MTTMP]=movedata(TMP,MTTMP,row); [M,tmp]=size(MTTMP); % Connection A n a l y s i s CONN=connection(MT(mtn,:),time); isempty(CONN)== 1 CVGREC(time,mtn)=0; else % Check the s a t e l l i t e coverage i s a v a i l a b l e or not SAT=unique(CONN(:,3)); % visible satellites [SATN,tmp]=size(SAT); %"# of v i s i a b l e s a t e l l i t e s SEN=senario(CONN); % r e c o r d the s e n a r i o f o r a MT CVGNO=satcvg(CONN); % S a t e l l i t e Coverage SENREC(time,mtn)=SEN; % r e c o r d the s e n a r i o f o r a MT CVGREC(t ime,mtn)=CVGNO; % r e c o r d the s a t e l l i t e coverage f o r a MT % checkcap=capcheck(SAT,CAPFLAG,QMAX); % Check the v i s i b l e s a t e l l i t e checkcap=l; % d i s a b l e capcheck' f u n c t i o n if  if  checkcap== 1 %%% S a t e l l i t e Coverage  & Service Information  %%% I n t e r f e r e n c e C a c u l a t i o n P=pmargin(SEN,BER,QMAX,c); 1= ( p n p n ( P N r e f , P N ( m t n , : ) , d e l a y ( L ) ) ) " 2 ; %%% C o n n e c t i o n Request % c a l c u l a t e the MAI between 2 MTs % MT Request the c o n n e c t i o n t o the v i s i b l e s a t e l l i t e s % I f one s a t e l l i t e has reached the c a p a c i t y , % which means the i n t e r f e r e n c e % i s h i g h e r than the a l l o w e d l e v e l , and thus d e c l i n e s % the c o n n e c t i o n , the % MT w i l l not be a b l e t o connect t o o t h e r % s a t e l l i t e s , even the c o n n e c t i o n % i s avaiable flag=[]; Pnew=[]; % The update R e c e i v e d Power Jnew=[]; % . C a p a c i t y % the c o n n e c t i o n f l a g . f l a g = l , which means % s a t e l l i t e a l l o w e s the new c o n e c t i o n  85  for  satn=l:SATN . SATID=satconv(SAT(satn,1)); % c o n v e r t s a t e l l i t e . Only use f o r v a r i a b l e s  % C a l c u l a t e the i n t e r f e r e n c e LOS=CONN(find(CONN(:,3)==SAT(satn,1)),4); los=LOS(1,1); Prev=I*(channel(los,P,c))"2; % The r e c e i v e d power Pnew(SATID)=R(time,SATID)+Prev; Jnew(SATID)=SATCAP(time,SATID)+1; i f Pnew(SATID) <= QMAX f l a g = [ f l a g ; 1] ; else f l a g = [ f l a g ; 0]; CAPFLAG(time,SATID)=1; % r e a c h the c a p a c i t y end end % MT Request P r o c e s s i n g CHECK=find(flag==0) ; i f isempty(CHECK) ==1 % MT's r e q u e s t i s granted, s i n c e a l l the % s a t e l l i e s have not reached % the t o t a l l a l l o w e d i n t e r f e r e n c e % R=Ptotal, add 1 u s e r s t o s a t e l l i t e r e c o r d f o r satn=l:SATN SATID=satconv(SAT(satn,1)); R(time,SATID)=Pnew(SATID); SATCAP(time,SATID)=Jnew(SATID); % Record S i n g l e S a t e l l i t e S e r v i c e . % & Double S a t e l l i t e S e r v i c e % S1/S2 > S a t e l l i t e and SENREC > MTs i f SEN ==1 SI(time,SATID) = SI(time,SATID)+1; e l s e i f SEN == 0 SO(time,SATID)=S0(time,SATID)+1; e l s e i f SEN == 10 S10(time,. SATID)=S10(time,SATID)+1; e l s e i f SEN == 1000 S1000(time,SATID)=S1000(time,SATID)+1; e l s e i f SEN ==11 S11(time,SATID)=S11(time,SATID)+1; end end end end % checkcap end % CONN? empty end % counter end % time % S=S1./(S1+S2);  >  86  save r e s u l t SATCAP CAPFLAG SENREC CVGREC S i S10 S l l S1000 SO %S SENREC CVGREC toe % Check the v i s i b l e s a t e l l i t e s have y e t reached the c a p a c i t y % 1: c a p a c i t y i s s t i l l a v a i b l e function [TEST]=capcheck(SAT,CAPFLAG,QMAX). Il=[]; I2=[];  [m,n]=size(SAT); f o r counter=l:m 1 1 = [ I I ; satconv(SAT(counter,1) ) ] ; end I2=find(CAPFLAG==l); M=intersect(II,12) ; TEST=isempty(M); % 1: No i n t e r s e c t i o n . % No s a t e l l i t e r e a c h the c a p a c i t y  87  

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