Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Reverse link capacity of cellular CDMA systems employing group successive interference cancellation Silvester, Anna-Marie 2004

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2004-0627.pdf [ 4.37MB ]
Metadata
JSON: 831-1.0065404.json
JSON-LD: 831-1.0065404-ld.json
RDF/XML (Pretty): 831-1.0065404-rdf.xml
RDF/JSON: 831-1.0065404-rdf.json
Turtle: 831-1.0065404-turtle.txt
N-Triples: 831-1.0065404-rdf-ntriples.txt
Original Record: 831-1.0065404-source.json
Full Text
831-1.0065404-fulltext.txt
Citation
831-1.0065404.ris

Full Text

R e v e r s e L i n k C a p a c i t y o f C e l l u l a r C D M A S y s t e m s E m p l o y i n g G r o u p S u c c e s s i v e I n t e r f e r e n c e C a n c e l l a t i o n by Silvester, Anna-Marie B.Eng. , The University of Victoria, 2000 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Department of Electrical and Computer Engineering) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A September 2004 © Silvester, Anna-Marie, 2004 THE UNIVERSITY OF BRITISH Chi I I M R I A FACULTY OF GRADUATE STUDIES L i b r a r y A u t h o r i z a t i o n In p r e s e t t i n g this Ihesis in partial tulfillmenl of the r e o u i r a m e n K fn, . „ s c t o , a r , y w o s e s m a y b e g r a n t e d b y l h e h e a d ; ; ~ ; « « — for ^ , c o p y i n g „ l h l s l n e s i s p U » c a , i „ „ w „ s , „ e s i s f o r ( i n a n c i a l g a i n s h a l l n o , b e a i ™ : ; ™ — * e s - " i s u n d e f S ' ° M - « Name of A T i u T c T f p / e a s e T ^ " " ~ " — - J j l X i L 5 _ _ _ _ _ _ _ _ _ _ Date (dd/mm/yyyy) Title of Thesis: £> — Q i l P U E O ^ D ^ ^ p Year. oiCXy\ Department of ET o The University of i n i s l ^ c S a ^ ^ ^ - — ^ ^ ^ ^ i e * ^ ^ Vancouver, BC Canada A b s t r a c t Successive Interference Cancellation (SIC) is a much studied multi-user de-tection technique capable of increasing reverse link capacity significantly [1, 2, 3, 4]. Current issues blocking industry from adopting multi-user detection include complexity, cost, and detection delay [5, 6, 7, 8, 9, 10, 11]. In this thesis, we evaluate the benefits of a simplified SIC scheme, called group succes-sive interference cancellation (GSIC), in which users are cancelled in groups rather than individually. Canceling users by group has a number of benefits, including reduced detection delay time, and decreased hardware complexity as compared with practical implementations of SIC [7]. We begin by extending a model of inter-cell interference first developed for SIC and presented in [12, 13, 14, 15]. Using the inter-cell interference factor developed in [12, 13, 14, 15] we derive expressions for the outage probability of GSIC. In order to improve system performance we consider four different diversity cases. These diversity cases include selection macro-diversity (SM), when a user is detected based on 1 copy of its signal received at its assigned base station, and combining macro-diversity (CM), when a user is detected based on 3 copies of its signal received at surrounding base stations. We also consider the case of multi-cell cancellation (MGSIC), when a user's detected signal is regenerated and cancelled not only from its assigned base station, but also from 2 other base stations in its vicinity. The group sizes for which we evaluate outage probability are 1, 10, and 20. Our numerical evaluation of the theoretical expressions indicates that higher values of capacity can be obtained from the SIC-SM, SIC-CM, MSIC-SM, and ii MSIC-CM techniques than was previously indicated by [12, 13, 14, 15]. Our research has shown that the work in [12, 13, 14, 15] applies a bound on the inter-cell interference factor. Numerical results show significant increases in capacity for C M as compared to SM, and for MGSIC as compared to GSIC. However, simulation results generated in an environment with good but im-perfect power control, and with looser restrictions on the power distribution of users indicate that gains for MGSIC are not as significant as indicated by theory. Both simulation and numerical evaluation demonstrate that C M pro-vides a significant capacity increase over SM. Increasing group size reduces the number of users a base station can support on the reverse link; however, these losses may be tolerable considering the reduction in detection delay and hardware complexity that accompany increasing group size. On average, group size can be increased to 10 with a 3.5% loss in capacity, while detection de-lay and hardware complexity are decreased by a factor of approximately 1/10. Similarly, group size can be increased to 20 with a 7% loss in capacity, for which detection delay and hardware complexity are decreased by a factor of approximately 1/20. iii C o n t e n t s Abstract ii Contents iv List of Figures vii List of Abbreviations and Symbols ix Acknowledgments xi 1 Introduction 1 1.1 Background - CDMA Detection Schemes 2 1.2 Related Work 3 1.3 Research Contributions 5 1.4 Thesis Outline 5 2 Overview of System Model 7 2.1 Cellular System and Path Loss Models 7 2.2 SNIRofSUD 10 2.3 SNIR of SIC 12 2.4 Combining Macro-diversity 15 2.4.1 SNIR for SUD-CM 16 2.4.2 SNIR for SIC-CM 18 2.5 Multi-cell Cancellation 19 2.5.1 SNIR for MSIC-SM 19 iv 2.5.2 SNIR for MSIC-CM 20 3 Modeling GSIC 22 3.1 Group Cancellation 22 3.2 GSIC-SM 23 3.3 GSIC-CM 24 3.4 MGSIC-SM 25 3.5 MGSIC-CM 26 4 Capacity Analysis and Evaluation 28 4.1 GSIC-SM 28 4.2 MGSIC-SM 32 4.3 GSIC-CM . 33 4.4 MGSIC-CM 35 4.5 Outage Probability for SIC 37 4.6 Outage Probability for SUD 38 4.7 Numerical Evaluation 39 4.7.1 Numerical Results for SM 40 4.7.2 Numerical Results for CM 42 4.7.3 Comparison with Previous Results 43 5 Simulation Results 46 5.1 Computer Simulation Methodology 46 5.1.1 Step I 47 5.1.2 Step II 47 5.1.3 Step III 48 5.1.4 Step IV 48 5.1.5 Step V 49 5.1.6 Step VI 50 5.1.7 Step VII 50 5.1.8 Calculation of Outage Probability . 50 v 5.1.9 Simulation Variables 51 5.2 Simulation Results 51 5.2.1 SUD 53 5.2.2 GSIC-SM 56 5.2.3 MGSIC-SM 59 5.2.4 GSIC-CM 62 5.2.5 MGSIC-CM 63 6 Detection Delay and Hardware Complexity 67 6.1 Detection Delay 67 6.2 Hardware Complexity 70 7 Conclusions 73 A Inter-cell Interference Factor 75 A . l Cumulative Probability Function of Path Loss 75 A.2 Inter-cell Interference Originating from So 77 A.3 Inter-cell Interference Originating from S0 79 A.4 Individual Inter-cell Interference Factors 80 B Power Reduction Factors 81 vi L i s t o f F i g u r e s 2.1 Serving areas of the 0th base station for different values of Nc- • 9 2.2 Block diagram of SIC detection , 1 2 4.1 Numerical results for GSIC-SM and MGSIC-SM 40 4.2 Numerical results for GSIC-CM and MGSIC-CM 42 4.3 Comparison of numerical results with those from [13] 45 5.1 Computer simulation model for evaluation of outage probability. 47 5.2 Reverse link capacity of SUD-SM and SUD-CM (simulation and numerical Results) 52 5.3 Influence of power control on received power ranking for SUD and SIC 53 5.4 Influence of power control on received power ranking for GSIC. . 54 5.5 Reverse link capacity of SUD-SM (simulation and numerical results), numerical results with SNIR of 5.2 dB 55 5.6 Reverse link capacity of GSIC-SM group sizes 1,10 and 20 (sim-ulation and numerical results) 56 5.7 Reverse link capacity of GSIC-SM group size 1 (simulation and numerical results), numerical results with SNIR of 5.2 dB. . . . 57 5.8 Reverse link capacity of MGSIC-SM group sizes 1, 10 and 20 (simulation and numerical results) 58 5.9 Reverse link capacity of MGSIC-SM group sizes 1, 10 and 20 (simulation and numerical results), with a = 5.2 dB for group size 1, x — 1/3-0 dB for all group sizes 60 vii 5.10 Reverse link capacity of GSIC-CM group sizes 1, 10 and 20 (simulation and numerical results) 62 5.11 Reverse link capacity of MGSIC-CM group sizes 1, 10 and 20 (simulation and numerical results) 63 5.12 Reverse link capacity of MGSIC-CM group sizes 1, 10 and 20 (simulation and numerical results), with a — 5.1 dB for group size 1, x — 1/3.0 dB for all group sizes 65 6.1 Normalized delay reduction and capacity for GSIC group sizes 1, 10 and 20 68 6.2 Normalized delay reduction and capacity for MGSIC group sizes 1, 10 and 20 69 6.3 Block diagram of pipelined SIC detection. The variables and r^Q are the in-phase and quadrature components of the received signal after i users have been cancelled 70 6.4 Block diagram of Pipelined GSIC detection, group size 2 (G = 2). The variable a* represents the spreading sequence of the ith user, and the variable Zi represents the decision variable of the ith user, and finally 0j represents the phase of the ith user. . . . 72 B . l Overlapping serving areas, when NQ = 4 82 viii 2G 3G 4G BER cdf CDMA cdma2000 CM EGPP2 EV-DO GSIC IMT-2000 MGSIC MRC MSIC MUD pdf PIC SUD A b b r e v i a t i o n s a n d Second generation Third generation Fourth generation Bit error rate Cumulative distribution function Code division multiple access Code division multiple access 2000 Combining macrodiversity Third generation partnership project 2 Evolution data only Group successive interference cancellation International telecommunications union 2000 Multi-cell group successive interference cancellation Maximum ratio combining Multi-cell successive interference cancellation Multi-user detection Probability density function Parallel interference cancellation Single user eetection S y m b o l s A c r o n y m s IX SIC Successive interference cancellation SM Selection macrodiversity SNIR Signal to noise and interference ratio UMTS Universal mobile telecommuniations system O p e r a t o r s a n d N o t a t i o n H Ceiling £ {•} Expectation [•]T Matrix or vector transposition x A c k n o w l e d g e m e n t s I would like to thank Dr. Schober for his guidance, which was very helpful throughout this process. I would also like to thank Dr. Mathiopoulos for all his input, and for the suggestion of the topic. Finally, I would like to thank Dr. Hong Nie for providing the software that formed the basis of the numerical evaluation and simulation. xi C h a p t e r 1 I n t r o d u c t i o n Achievable data rates for third generation (3G) networks based on the code di-vision multiple access (CDMA) standard are currently fairly limited, "although peak data rates on the order of 1-10 Mbps are advertised for 3G techniques such as EV-DO (for 3GPP2, i.e. cdma2000) ... the actual data rate experi-enced by a typical subscriber is generally less than 100 kbps, and the latency can also be very poor" [5]. Here, cdma2000 is a 3G standard for C D M A as defined by the third generation project partnership 2 (3GPP2), and EV-DO stands for evolution data only, a data only specification of the cdma2000 stan-dard. C D M A is a spread spectrum technique that makes use of voice activity and universal frequency reuse; however, it is an interference limited technique [5, 16]. Therefore, in order to increase network capacity (the number of users the network can support at a given data rate and bit error rate (BER)), and improve the data transmission rate and latency, it is important to address interference. If C D M A is to be a competitive technology considered for adoption as a 4G standard, as has been proposed in [17, 18], interference mitigation will become an even more important issue. The 3G standard improved upon the 2G stan-dard by providing mobile users with features such as image transfer, internet access, database access, large file transfer and video telephony [12]. Similarly, a 4th generation standard will be expected to support a larger range of fea-1 tures, such as global mobility, the ability to tag and track anything mobile, and improved multimedia access [17, 19]. In addition to these features, the number of mobile users and mobile devices is also growing. By 2010 the authors of [17] are predicting there will be more than 500 million mobile terminals in Japan alone. 1.1 B a c k g r o u n d - C D M A D e t e c t i o n S c h e m e s A large part of interference in a C D M A network comes from surrounding users. In a C D M A network, all users are transmitting on the same frequency at the same time. Additionally, on the reverse link it is not possible to synchronize user transmission to guarantee dimensional separation. Therefore, because users on the reverse link can experience large amounts of interference, the reverse link can become a system bottleneck. We will distinguish between interference originating from other mobile devices within a user's cell by calling this interference intra-cell interference, and interference from users outside the user's cell by calling this inter-cell interference, as established in [12, 13, 14]. Since C D M A is limited by interference and a reduction of interference "converts directly and linearly into an increase in capacity" [16], it is important to tackle the problem of both intra-cell and inter-cell interference. Conventional detection schemes predominately use a single-user matched filter [1, 12] although this method is suboptimal [20]. These conventional detection schemes have a very simple implementation but do not combat either intra-cell or inter-cell interference well [12, 21]. As each and every user is detected at the base station it is affected by the interference caused by all the other transmitting users in the network. In addition, these schemes suffer from what is called the near-far effect [2, 22]. Because single user detection (SUD) schemes reach optimal performance when all signals are received at the base station with equal power (resulting in equal B E R for the received signals) [6], users at different locations transmit with varying power. Users located near 2 the base station will tend to overpower users near the cell boundaries. This is a significant problem for C D M A networks using conventional detection. In fact, the power profile for SUD results in increased interference, which reduces capacity, and requires that C D M A networks operate with strict power control [16, 22]. Techniques for increasing the capacity of a C D M A network by mitigating the effect of intra-cell and inter-cell interference include power control, channel error control coding, sectorized antennas or antenna arrays, macro-diversity, micro-diversity, and multi-user detection [12, 16, 21]. In this work, we consider varying combinations of the last three techniques. By making use of information about multiple users, multi-user detection (MUD) can reduce the effect of intra-cell interference. The optimal multi-user detec-tor is the maximum likelihood detector proposed in [20]. However, this detec-tor is too complex for practical use and many suboptimal options have been investigated. Suboptimal techniques include linear multi-user detectors and subtractive interference cancellation detectors [21]. Two types of subtractive interference cancellers are parallel interference cancellers (PIC) and successive interference cancellers (SIC). PIC schemes are generally complex, requiring a large additional amount of hardware [7, 21, 23]. In addition, in the case of unequal user power SIC has significantly better performance [5], therefore we will consider SIC in this work. Although SIC is suboptimum, it can provide a significant performance improvement in comparison with conventional detec-tion. In addition to interference reduction, because users transmit with power disparity, the use of SIC reduces the impact of the near-effect [1, 2, 3, 4]. 1.2 R e l a t e d W o r k A model of intra-cell and inter-cell interference for SIC was proposed in [24]. The model uses a hexagonal cellular structure, and takes into account distance attenuation and log-normal shadow fading. This model produces an average 3 value of inter-cell interference evaluated as path loss is varied from zero to infinity. Based on this value [24] is able to make capacity predictions. In [12, 14] the inter-cell/intra-cell model is extended to be a function of path loss, which allows the interference model to be incorporated into an outage probability calculation. Outage probability can then be used as a more di-rect and useful indicator of capacity. Several other models of inter-cell and intra-cell interference have been developed in order to provide a measure of capacity [16, 3, 25, 26, 27]. In [3], cells are simplified to circles. In [16, 25], user power is based solely on the distance between the mobile user and its assigned base station. This assumption is made to simplify calculations and does not take into account losses other than distance attenuation, such as log-normal shadow fading. In [26], only inter-cell, and not intra-cell, interference is considered. Finally [27], considers interference when users are allowed to be mobile in a limited six cell network. This model does not take into considera-tion log-normal shadow fading. We will be using [12] as a basis for our outage probability calculations. Problems associated with the successive approach to interference cancellation include error propagation and detection delay. Reduction of detection delay has been attempted using a number of different methods. Several schemes have been designed that hybridize SIC with PIC, for example [8, 9, 28, 29]. Simpler schemes that group users together and process the groups successively are [7, 10, 30, 31]. By processing users in groups these schemes reduce detection delay at the cost of interference cancellation. The schemes proposed in [7, 10, 30, 31] evaluate performance by simulation only. Another technique previously mentioned for reducing interference is the use of diversity. To incorporate diversity into a reverse link SIC scheme we con-sider combining or canceling portions of a user's signal received at more than one base station. In a CDMA network this can be considered the equivalent of soft-handoff. Macro-diversity and intra-cell/inter-cell interference have been considered in [12, 22, 32, 33]. Using the schemes proposed by [32, 33], users are 4 decoded based on a combined signal representing information from all base sta-tions in the network. These schemes may incur a delay which currently makes them impractical. In [22], only the inter-cell interference factor is considered as a measure of capacity. 1.3 R e s e a r c h C o n t r i b u t i o n s In this work, we will derive expressions for the outage probability of detection schemes employing group successive interference cancellation (GSIC) in a va-riety of diversity cases. As a basis for our work, we will use the interference model proposed in [12, 14]. Using these derivations we will • investigate the outage probability and detection delay of GSIC for several different cases of diversity, and different group sizes. • simplify our GSIC results to the SIC case to show that significantly higher capacities can be obtained than indicated in [12, 13]. • verify our theoretical analysis using simulation data generated using sys-tem parameters for cdma2000 given in [34, 35]. • consider outage probability and detection delay and show that the group approach to SIC can be used without significant loss in performance for the network. 1 . 4 T h e s i s O u t l i n e The remainder of this thesis is organized as follows. In Chapter 2, we discuss the cellular system models and parameters used in this work. We will also derive expressions for intra-cell and inter-cell interference, and signal-to-noise and interference ratios (SNIR) for single user detection and SIC in different diversity conditions. Chapter 3 will extend the derivations presented in Chap-ter 2 to the GSIC case. In Chapter 4, we will use the SNIR expressions from 5 previous chapters to derive expressions for outage probability for different di-versity cases, and present our numerically evaluated results. In Chapter 5, we will discuss the simulation methodology that we used and compare simulation results to the numerical results of the previous chapter. Chapter 6 will look at the detection delay reduction and hardware complexity of GSIC with respect to conventional SIC. Finally, in Chapter 7 we will draw some conclusions about the practical use of GSIC, and useful group sizes. In Appendix A, derivations of the inter-cell interference factors are taken from [12] and presented as back-ground for the derivation of the inter-cell interference expressions. In Appendix B, a derivation of the power reduction factor is presented based on [12]. The power reduction factor is used in expressions for combining macro-diversity. 6 C h a p t e r 2 O v e r v i e w o f S y s t e m M o d e l In this chapter, we will discuss and derive expressions for the signal-to-noise and interference ratio (SNIR) for several detection techniques as a stepping stone to capacity analysis. We will begin by outlining the cellular system model, and path loss model that we used for this work. Then we look at two detection methods: single user detection (SUD) and successive interference cancellation (SIC). We will briefly discuss the benefits of SIC, and then derive expressions for the SNIR of both SUD and SIC. Next, we will look at these two techniques when combining macro-diversity is applied, and we will again derive expressions for the SNIR. Finally, we will analyze SIC with multi-cell cancellation. 2.1 C e l l u l a r S y s t e m a n d P a t h L o s s M o d e l s In this work, we will use the cellular system model as described in [12, 13, 16, 24], which uses the IMT-2000 standard [34]. This model consists of M identical hexagonal cells, each of which has a base station located at its centre. The base stations are equipped with omni-directional antennas to receive the signals of a set of mobile users that are assumed to be uniformly distributed. The IMT-2000 standard defines several types of mobile user environment and several types of data transmission. According to the standard, possible mo-7 bile user environments include indoor office, outdoor to indoor, vehicular, and pedestrian. Possible types of data transmission include long data delay, low data delay, and speech. We will assume that only one type of user populates the system, and that this user is transmitting speech in a pedestrian environ-ment. It is also assumed that there are an equal number of users assigned to each base station, and this number is denoted as N. The density of mobile users, p, can be written as p — N/Ac, where Ac represents the area of one hexagonal cell. The propagation model we will use is the International Mobile Telecommuni-cation 2000 (IMT-2000) model [13, 34]. In this model, path loss consists of two components, distance attenuation and lognormal shadowing fading. According to [34] distance attenuation, in dB, between a mobile user and the mth base station is expressed as where rm is the distance from the mobile user to the mth base station, fi is the distance attenuation exponent, and D is a constant fixed attenuation common to ah base stations. Lognormal shadowing fading, also in dB, between a mobile user and the mth base station is given by where h and hm are independent zero-mean Gaussian distributed random vari-ables with standard deviation equal to a, and where a and b are constants such that a2 + b2 = 1 [12, 24]. The values ah and bhm correspond to losses caused by obstacles in the field of transmission; ah represents losses in the near field of the user and is therefore common to all base stations, and bhm represents losses due to obstacles in the area of the base station and is therefore particular to a certain base station [24]. In total, the path loss from a mobile user to the mth base station can be expressed as DAm = 10^1og10rm + D (2.1) LSFm = ah + bh, (2.2) PLm = DAm + LSFm = 10/i log 1 0 rm + ah + bhm + D. (2.3) 8 Optimally, a user would be assigned to the base station that receives its signal with the lowest value of path loss. As it is not practical for a user to check all base stations in the network before making a connection, we will use the strategy of serving areas as proposed in [24, 12, 13]. Using the technique of serving areas a user minimizes its path loss among the Nc closest base stations. The term "serving area" refers to the area surrounding a base station in which it is possible for a user to establish a connection. Serving areas of different size are illustrated in Figure 2.1. The area covered by a serving area will be denoted So.as in [12], and can be expressed as So — NQAC-Following the work in [12], since each mobile user is minimizing its path loss among the Nc closest base stations, a mobile user's path loss to its assigned 9 base station must be re-written as (2.4) where {rrij,j 6 [1, Afc]} are the Nc base stations nearest the mobile user. C D M A systems employing SUD detect each and every user independently. Therefore, for users in SUD schemes, the signals of all other transmitting users act as interference. A general form for the reverse link SNIR of the ith mobile user that is assigned to the nth base station is given in [13, 16]. The reverse link SNIR for this mobile user, which we will denote as the (i, n)th user as given in [13, 16], is where Elbn is the power of the ith user's signal at the nth base station as it is used for detection, and 7tOT is the total interference that the ith user experiences at the nth base station during detection. Additionally, P ; n n is the average receiving power of the (i, n)th user as received at the nth base station, R is the information bit rate of the mobile users, BW is the spreading bandwidth of the mobile users, NQ is the single-sided power spectral density of thermal noise, and FN is the noise figure of the base station receivers. Also in Eq. (2.5), I™N and pnn a r e j - n e m t r a-cel l (interference originating from other mobile users assigned to the same base station) and inter-cell (interference originating from mobile users assigned to other base stations) interferences respectively, as experienced by the (i, n)th mobile user when it is received at the nth base station. Following [12, 13], when no cancellation is employed and users are detected individually (SUD), the intra-cell.interference is expressed as 2.2 S N I R of S U D El Tir (7*nn + ILENN)/BW + N0FN' inn (2.5) N rinn \ A O jnn j (2-6) 10 where Pjnn represents the average power of the (j, n)th user as received at the nth base station. Similarly, for SUD, the inter-cell interference can be expressed as f N M - l | jinn = £}j2 £ e ^ P L ^ - p L ^ ] P i m m \ , (2.7) [ j= l ra=0,m^n ) where £ {•} denotes expectation,./? = log 10/10 and PLjmm and PLjmn are the path loss of the (j, m)th user to the mth and nth base stations respectively. If the expression given in Eq. 2.4 is evaluated for user j and the minimum value of path loss is found to be between user j and base station m, Eq. 2.4 becomes the equivalent of PLjmm. A power control scheme is optimal if each user is detected with an equal BER, or equivalently if each user is received with an equal SNIR. Therefore, assuming optimum power control, Pinn for SUD can be simplified as follows Pinn = P, Vi e [1,N] and V n € [0, M-l ] ] . (2.8) Models for inter-cell interference in the case of equal received power, with no cancellation have been investigated in [24, 36]. For these models inter-cell interference becomes f N M - l £ { E E exp \p (PLjmm - PLjmn)} pnn __ U = 1 m=0,m^n y_ jy p e N = ReNP, (2.9) where Re is the inter-cell interference factor, and is for this case independent of N and P. The value of Re in the case of equal received power has been analyzed in [24, 36]. Finally, using the expressions for intra-cell and inter-cell interference developed in Eqs. (2.6) and (2.9) the expression for the SNIR of SUD can be written as (2.10) Elbn P/R It {{N -1)P + ReNP) /Bw + N0FN' Optimal performance for successive interference cancellation does not occur when users are received with equal power. In this case, analysis of I™*1 becomes more complicated. This problem was tackled by [12, 13]. In the next section, we will look at /*"" for SIC, following the analysis done in [12, 13]. 11 2 . 3 S N I R o f S I C SIC takes a serial approach to interference cancellation. At each stage in the detection, the SIC detector decisions, and the signal is regenerated and cancelled from the received signal [12, 21]. The first stage of SIC is illustrated in Figure 2.2. In the first stage a conventional detector is used to detect the strongest signal si from the received signal, r(t), which is composed of all of the transmitting user's signals. After a hard decision is made on s\ the resulting signal d\ is the estimated version of the transmitted signal of user 1. In addition to d\, estimates of timing and amplitude and knowledge of the P N sequence are used to regenerate the received signal of user 1. The term Ai (t — Tb) is an estimate of the amplitude of the signal of user 1 as it was received, delayed by the detection time T&. The term g\ (t — T i — TJ,) is the signature code waveform of user 1 delayed by the detection time, and T\ is an estimate of the timing of the received signal. The estimate of the received signal belonging to user 1, given by s\ (£), can then be subtracted from the delayed version of the received signal (composed of all users). The resulting signal r(i) (t) is a modified received signal with reduced interference from user 1. The SIC detector in its simplest form requires only minimally more hardware than the conventional detector [12, 21]. However, practical implementation is more complex. Matched filter "^ {^ Decision User 1 r(t) Amplitude estimation 91 Figure 2.2: Block diagram of SIC detection. 12 Optimally SIC will detect users starting with those with the lowest path loss, and highest received power (i.e. those with the highest chance of successful detection) and ending with those with the highest path loss, and lowest re-ceived power (i.e. those with the lowest chance of successful detection). Users detected towards the end of the SIC process may have a lower received signal strength (and higher path loss), because they experience less interference due the effects of cancellation. The power disparity that SIC introduces is beneficial in several ways. Users at the border between cells suffer from larger distance attenuation than mobile users closer to the base station. The power disparity introduced by using SIC allows the distant user to transmit with lower power than would be possible in a SUD network (as it can be detected after most other users in the cell when a large portion of interference has already been cancelled). Because the distant user is not required to transmit with high power there is a reduction in inter-cell interference [25], intra-cell interference [1], and the near-far effect [2]. In addition to these interference reduction ben-efits, the power disparity means that on average users are transmitting with lower power, which translates into lower battery power consumption [1]. Users can be ranked by path loss, PLinn, the path loss experienced by the ith user, assigned to the nth base station, as received at the nth base station, as follows PLlnn < PL2nn <...< PLinn <...< PLNnn> Vn G [0, M - 1]. In addition, the power disparity allows us to rank users by received power [3, 12, 13, 25, 27]. We can express this ranking as Pinn > P2nn> •••> Pinn> •••> PNnn, Vn G [0, M - l]. In the analysis of [12, 13, 37], the above ranking is simplified by assuming that mobile users of the same rank in different cells have the same level of received power. This assumption is made on the basis that received power for a mobile user is strongly correlated to its power ranking, and that there are an identical 13 number of users (JV) in each cell. The new expression for power becomes Pinn = Pi, V i G [ 1 , N] and V n G [ 0 , M — 1 ] . Using this expression for power, the intra-cell interference factor for SIC given in [ 1 2 , 1 3 ] can be written as t - l JV I a 2~^i Pjnn + Pjnn 3 = 1 j=i+l = 1>IlPj+ E Pi, ( 2 - 1 1 ) j=l j=i+l where imperfect cancellation is assumed, and tp represents the portion of the signal remaining after cancellation. Using Eq. ( 2 . 7 ) and the new power rela-tion, the inter-cell interference for SIC can be written as JV f M - l jinn _ ^ £ I ^ ^(PLjmn-PLjmn) I p 3 = 1 ^m=0,m^n J JV ( M - l 1 = { E et3(pLjrnm~PLjrnn) > Pj = ( 2 - 1 2 ) where {R?eN = £ j ^PLimm~PL^ I , j 6 [ 1 , JV]} are denoted in [ 1 2 ] as individual inter-cell interference factors. These individual interference factors are independent of Pj. This model will simplify to the SUD model if all users are set to have equal receiving power (Pj = P). Using the expressions given in Eqs. ( 2 . 1 1 ) and ( 2 . 1 2 ) , we can write an expres-sion for the SNIR of SIC as Etn Pi/R ( * - l N N \ U l 2 P j + E PJ+T. Ri Pj IBW + N0FN \ 3=1 j= i+ l J'=l / ( 2 . 1 3 ) A detailed analysis of the individual interference factors, R{N, as a function of path loss is given in [ 1 2 ] . In [ 1 2 ] , a closed form solution for these interfer-ence factors, R{N (Ks) is found, where R{N (Ks) are the individual inter-cell 1 4 interference factors for users whose path loss to their assigned base station is equal to Ks dB. The derivation of the closed-form solution can be found in Appendix A. Because it is relevant to the future analysis of outage probability, we will mention that the analysis of the interference factors is split into two components, using the serving area. The system is assumed to be symmetric, and therefore without loss of generality the authors of [12, 13] consider the inter-cell interference experienced at the 0th base station. Inter-cell interfer-ence generated by users within the serving area of the 0th base station, denoted in [12, 13] as serving area So, but not assigned to the 0th base station is referred to as Rjjtf (Ks). Inter-cell interference generated by users outside of the serv-ing area of the 0th base station, denoted by [12, 13] as area So, is referred to as (K). Together these two components make up the individual inter-cell interference factors, which are expressed as RlN(Ks) = R!°N(Ks) + Rf0N{Ks). (2.14) Both of the techniques we have discussed, SUD and SIC, benefit from the use of diversity. In the next sections, we will discuss diversity and derive the SNIR for SUD and SIC when these techniques employ diversity. 2 . 4 C o m b i n i n g M a c r o - d i v e r s i t y Until now, we have considered only the portion of a mobile user's signal that is received by the base station to which the mobile user is assigned. A digital base station network is able to make use of components of a mobile user's signal that are received by surrounding base stations. The use of these other components can significantly improve performance for the mobile user [15, 33, 38, 39]. In fact, if the base station is able to access all the signal components of a mobile user as they are received at base stations network-wide, inter-cell interference is eliminated. This case has been analyzed by [32, 33]. Although ideal, accessing signal components from base stations network-wide is impractical as it will 15 incur a large delay [15, 39]. Combining signals from a small area helps to improve performance, while incurring a much smaller delay [15, 39]. We will consider the case occurring when signal components from the Nc base stations surrounding a mobile user are used in detection, and we will call this case combining macro-diversity (CM), following the convention set in [12, 39]. The case we previously considered, when only the signal component received at the base station to which the user is assigned is used for detection, we will call selection diversity (SM), again following the convention set in [12, 39]. 2.4.1 S N I R for S U D - C M In the case of SUD-CM users are detected individually, with no cancellation, and the signal received at more than one base station is used to detect a users signal. As we are combining signals received at several base stations we must observe the user's SNIR at each of the base stations separately. First, we write an expression for the SNIR of the user's signal as it is received at its assigned base station Jinn ~ ( 7 i „ „ + j i n n ) jB^ + NQJ?N ' ^ ' > Next we write the SNIR of the user's signal as it is received at the other base stations in its serving area Tpinmj p i r> (2.16) Ilnmj (Cmj + li?mj) /Bw + N0FN' where {n, mi, m 2 , • • •, mjv c_i} are the indices of the Nc base stations nearest to user (i,n). In Eq. (2.16), IT™* and IT™0 are the intra-cell and inter-cell interferences that user (i, n) experiences at the mf1 base station respectively. If we can prove that the denominators in Eqs. (2.15) and (2.16) are identical, and under the assumption of perfect channel estimation we can write the SNIR of combined signal (using maximum ratio combining (MRC)) as Tin Jinn Z—i f h H j=i li t (2.17) 16 The process of proving that the denominators of Eqs. (2.15) and (2.16) are identical is performed in [12, 15], and we will follow the steps detailed there. Using the results for SUD-SM given in Eqs. (2.6) and (2.9), we can write the total interference experienced by the (i, n)th user at the nth base station as JV JV jinn + jinn = £ finn + __ i 2 f (tf S) Pj„„. (2.18) l=l,l^i 1=1 Making a comparison between I™™* and la"13™3, the following expression is obtained JV Tinmj _ Timjmj , p _ ST* p , p. (n 10) Furthermore, making a similar comparison between / * n m j and il™3™3, the fol-lowing expression is obtained JV jinm, = j i r n j m j _ p .^ = £ RIN ^ p ^ _ p . ^ 1=1 Combining Eqs. (2.19) and (2.20) gives the following expression for the total interference experience by the (i,n)th user at the mfh base station JV JV jinm, + jinm, = £ P i m . m . + ^_ (Ks) Plmjmj + Pimjmj ~ Pinmj- (2.21) l=l,ljti 1=1 Assuming that N S> 1, the summation terms Ei=i,<:^i Pim,™, and E i l i R l e N (KS) Pimjmj are much greater than the remaining term, P i m j m j - P i n m j , and using the previous assumption that PiU = Pi, Eq. (2.21) can be re-written as JV JV j l n m j + j i n m j ^ £ P l n n + R1" (KS) P l n n . (2.22) l=l,ljii 1=1 With these assumptions, and using Eqs. (2.22) and (2.18) the expression for the SNIR of SUD-CM can be re-written as Eln Pjn/ R Ji" I N N ' E Plnn+ZRleN(Ks)Plnn) /BW + NQFN \l=l,ljki 1=1 (2.23) where JVc-l Pin = Pinn ^ ] Pinmj- (2.24) 17 By combining signals received at the Nc base stations surrounding a mobile user, the mobile user benefits because it is able to transmit its signal using less power. The average power reduction of the (i,n) user can be expressed as P i ^c - 1 f P 1 *in I _ —^\ „ I 1 mm,- I { 1 ^ } = i + f e{ ^ • ' i n n ' 5=1 ( = 1+ £ 5 ^(P^-PLinmj) [ = i + T i N (Ks), (2.25) where {T;JV (Ks) ,i G [1, AT]} are denoted as power reduction factors in [12, 15]. Also in [12, 15] it is demonstrated that the power reduction factors are equal to the inter-cell interference factors (derivation given in Appendix B), when the inter-cell interference is limited to that originating from within serving area SQ, as given by riN (Ks) = R?N (Ks). (2.26) Using Eqs. (2.26) and (2.25), Pinn can be re-expressed as p. n n n ~ l + TiN(KS) Pin = I + R£(KS)' ( 2 ' 2 7 ) where RfN is derived in Appendix A, and is given in Eq. (A. 15). Finally, using (2.27) and (2.23) the SNIR of SUD-CM can be expressed as Eh™ Pin j R fir 1t I £ — ^ y — - + E fiiN {Ks) T T ^ T ^ T (2.28) /Bw + N0FN 2.4.2 S N I R for S I C - C M Using Eq. (2.27), the expression for intra-cell interference can be written as i - l N i-1 p N p pnn = ^ p . n n + Pjnn = ^ Yl 1^7 + E 1^7 7-j=l j=i+l j=l 1 + RjN (.Ks) j=i+i 1 + RjN (Ks) (2.29) Similarly, the expression for inter-cell interference can be written as jinn = £ pJN { K s ) = J2 Ri» (KS) (2.30) j = l j=l 1 + RjN \Ks) 18 Using Eqs. (2.29) and (2.30), the SNIR of SIC-CM can be expressed as Tin 1t Pin/R i-1 E N + E N + E RJN(Ks)Pin i i 1+R*(KS) l+R%(Ks) jti l+R*°N(Ks) /Bw + N0FN (2.31) 2 . 5 M u l t i - c e l l C a n c e l l a t i o n For SIC to be successful inter-cell interference must be low, because this in-terference is not part of the cancellation process [2]. Higher network capacity can result if interference is cancelled not only at its assigned base station but at surrounding base stations. However, canceling a mobile user's signal from distant base stations may result in delay. In [12, 15], multi-cell SIC (MSIC) is analyzed when interference is cancelled from base stations in the user's serv-ing area. Using the serving area concept, performance is improved without significantly increasing the detection delay [12, 15]. The following expressions leading to SNIR are based on the analysis given in [12, 15]. 2.5.1 S N I R for M S I C - S M When analyzing MSIC, intra-cell interference is unchanged from the SIC case because the MSIC technique only adds inter-cell interference cancellation. Therefore, we can use Eq. (2.11) for intra-cell interference. However, the inter-cell interference cancellation expression must be modified from Eq. (2.12) to include to the inter-cell interference cancellation that is carried out within the serving area. The inter-cell interference that the (i,n)th user experiences at the nth base station must divided into two summation terms, given by I™ = E R% (KS) Pjnn + E RiN (KS) Pjnn- (2.32) j=l j=i In Eq. (2.32), the first summation term is used to calculate the inter-cell interference due to users of rank lower than the current user that have been detected and cancelled from the received signal. The second summation term 19 is used to calculate inter-cell interference due to the users of the same rank as the current user, and other undetected users. When MSIC is applied the user's signal is cancelled from surrounding base stations, which reduces inter-cell interference. Thus the inter-cell interference factor must be modified, and the modified term R{+, is referred to in [12, 15] as the revised individual inter-cell interference factor of the (i,n)th user. The revised individual inter-cell interference factor is split into two components as shown in the following expression Rf+{KS) = V^fiv (KS) + R?N (Ks). (2.33) The first component in Eq. (2.33) represents the reduced inter-cell interference originating from within the user's serving area, due to the multi-cell cancel-lation. The term tp represents the portion of the inter-cell interference that remains after the cancellation. The second component of inter-cell interference originating from outside of the user's serving area is unaffected by multi-cell cancellation. The term R.fN is derived in Appendix A, and is given in Eq. A.16. Finally, combining Eqs. (2.11) and (2.32) into the general equation for SNIR, (Eq. 2.5), we arrive at the following expression for the SNIR of MSIC-SM _ Pinn/R ^ £ [V + RU (Ks)} Pjnn + ReN (KS) Pinn + (2.34) JV E j=i+l E fl + PdN (Ks)} Pjnn}/Bw + N0FN 2.5.2 S N I R for M S I C - C M Once again, the SIC-CM expression for the intra-cell interference that the (i,n)th user experiences at the nth base station given in Eq. (2.29) is valid for the MSIC-CM case. However, the expression for the inter-cell interference experience must be modified and is given by jinn = Y^(Ks)Pjnn + jrRiN (KS)PJnn j=l j=i 20 = ^ i f f (KS) Pjn f RjN (Ks) Pjn ^Xl + R%(KS) U l + R%(KS) (2.35) Combining Eqs. (2.29) and (2.35) into (2.5), the expression for SNIR of user (i, ri) is given by Pin/R ^1 \*+R?£jKs)\Pjn Ri"(Ks)Pin • f \l+RiN(Ks)]P3 f-1, I J . P S O iwl\ ' i l p i ' o / F C ' „ N ' , 2^ IXR^PT/VCT /Bw + N0FN (2.36) 21 C h a p t e r 3 M o d e l i n g G S I C Although there has been much research on the subject of multi-user detection, the technique has not been generally adopted by industry for use in C D M A systems [5]. Many techniques have been proposed to improve different charac-teristics of the SIC technique, including hybridization [8, 9, 28, 29] and group cancellation [7, 10, 30, 31]. In this work, we have chosen to investigate group cancellation because of the simplicity of the technique and its significant bene-fits. We will begin this chapter with a brief overview of the group cancellation technique, and then derive SNIR expressions for group successive interference cancellation (GSIC) employing SM and C M . We will end the chapter with an analysis of GSIC employing multi-cell cancellation (MGSIC), in the two diversity cases, SM and C M . 3 . 1 G r o u p C a n c e l l a t i o n Current issues blocking industry from adopting multi-user detection include complexity, cost, and detection delay [5, 6, 7, 8, 9, 10, 11]. GSIC is one technique proposed in order to address the concerns of hardware complexity and detection delay. When GSIC is implemented, users are ranked in the same way as for SIC; however, the users are processed in groups of size G. Each group is detected using conventional detection and after detection is complete 22 the entire group is cancelled at once from the received signal. Because detection of users within a group is independent, G users can be detected simultaneously. Simultaneous detection of users within a group means that detection delay can be reduced by a factor approximately equal to 1/G as compared with standard SIC. Hardware complexity can also be reduced, as compared with pipelined SIC (discussed in Chapter 6), by a factor approximately equal to 1/G [7]. We will show that detection delay and hardware complexity can be significantly reduced by the use of group cancellation without significant performance loss. Beginning in the next section, we will derive expressions for the SNIR of GSIC, so that we can investigate the relation between performance, intra/inter-cell interference, and group size. 3.2 G S I C - S M In order to form expressions for inter-cell and intra-cell interference we will assume the same received power and path loss ranking applies as in the SIC case. Additionally, we will continue to use the assumption of perfect power control. However, in this case, we will assume that users in the same group have the same received power. The received power ranking for GSIC is an extension of that given for SIC and can be expressed as Pin = Pin = • • • = P G « > P{G+l)n = ••• = P(2G)n > ' ' ' > ^ H - i ) G + i = • • • = PNn, (3.1) where [•] denotes the ceiling function. Alternatively, the received power rank-ing of GSIC can be expressed as P(Group\)n ^ P(Group2)n ^ " " ' ^ P(Groupi)n ^ ' ' ' ^ P f \ > (3-2) [Group^N^Jn where P(GrouPi)n represents the power of all G users belonging to the ith group, (users with a ranking in the range {(i — 1) G + l,iG]). If we apply this assumption to GSIC we may use the derivation of the individual inter-cell interference factors used for the SIC case. First we will consider 23 the case of group cancellation employing SM (when only the signal at the user's assigned base station is used for detection). As no inter-cell interference cancellation takes place in this case, the inter-cell interference expression is unchanged from the SIC-SM case and can be expressed as i r = j^R{NPjnn. (3.3) j=i However, the expression for intra-cell interference must be changed to reflect the cancellation in a group format. The new expression for intra-cell interfer-ence for GSIC-SM is rann = ipjbpjnn+ E P j n n + E Pjnn, (3.4) J'=I i=Ci+i j'=*+i where the assumptions of Section 2.3 are used (ip represents the portion of the signal remaining after cancellation) and where Q represents the number of detected and cancelled users, or alternatively the highest ranked user of the last group completely detected, and is given by 0, 1 < i < G G, G+l<i<2G Ci=< " ~ (3-5) . ( r « i - i ) G , ( r s i - i ) G + i < t < ; v Using Eqs. (3.3) and (3.4), and the general expression for SNIR given in Eq. (2.5), the SNIR of GSIC-SM can be written as El" Pinn/R TF ~~ 7 <i i-1 M N ^ \ ' * U E Pinn + E Pjnn + E Pjnn + E & Pjnn /Bw + N0FN (3.6) 3.3 G S I C - C M The next case we will consider is group cancellation in the case of combining macro-diversity (when portions of a user's signal received at Nc of the base 24 stations in the mobile user's serving area are used in its detection). Once again inter-cell interference is unaffected as compared with SIC-CM and the inter-cell interference expression unchanged' from the SIC-CM case is given by IT = E RiN (Ks) Pjnn = E R{N (KS) 1 - L | 5 " v (3-7) i = l j = l 1 + RjN (Ks) The expression for intra-cell interference, however, must reflect the cancellation in a group format. The new expression for intra-cell interference for GSIC-CM is given by Pr = 1> E PJnn + E Pjnn + E (3-8) Using Eq. (2.27), the expression for intra-cell interference given above can be re-written as C; t - l N E IpPjn E Pjn E Pjn jinn _ J = 1 i j=Ci + l I j=»+l g\ l + R*N(Ks) l + R%(Ks) l + R%(Ks)' The general form for the SNIR of a mobile user that is making use of C M was derived in Section 2.4.1, and is repeated here for convenience E%bn _ Pin/R Tjn (Nc Nc • \ 1 E Hnn + E Unn /Bw + N0FN \J=1 J'=l / (3.10) Using Eqs. (3.7) and (3.9), and the expression for the SNIR of a mobile user employing C M in Eq. (3.10), the SNIR of GSIC-CM can be written as Elbn _ Pin/R Iln ~ ( <i ^p. i -1 p. N p . . (3.11) h ^ ^ ) ' B w + N Q F l 3.4 M G S I C - S M Next we will consider employing multi-cell interference cancellation (when the regenerated version of the mobile user's detected signal is cancelled from Nc of the base stations in the user's serving area) in the SM case. In this case, 25 intra-cell interference is unaffected as compared to GSIC-SM. We can write the expression for intra-cell interference as Ci i - l N Ia = V 'Pjnn + __ Pjnn + _^ Pjnn- (3-12) J=l j'=Ci+l J'=»+I The new component of interference cancellation affects inter-cell interference. The expression given for inter-cell interference in the GSIC-SM case, Eq. (3.3), must be re-written to include the affects of the multi-cell cancellation. The new expression can be written as r r = Y.RiN+{Ks)Pjnn+ __ R{N (Ks)Pjnn, (3.13) J=I i=Ci+i where RlJ^ is given in Eq. (2.33) and once again Q represents the number of completely detected and cancelled mobile users, given in Eq. (3.5). Using Eqs. (3.12) and (3.13), and the general expression for SNIR given in Eq. (2.5), the SNIR of GSIC-SM can be written as E™ Pinn j R ^ ( z k + Rl+.(Ks)}PJnn+ £ \l + RiN(KS)]Pjnn + L J j=Ci+i L J ~t :N~~1 V • ( 3 > 1 4 ) Rf (KS) Pinn + £ 1 + RlN (Ks)\ Pjnn / Bw + N0FN j=i+l1 J / 3.5 M G S I C - C M Finally, we consider the multiple cell cancellation case employing combining macro-diversity. Because the additional interference cancellation of MGSIC-C M , when compared with GSIC-CM, only affects inter-cell interference we may use the GSIC-CM expression for intra-cell interference for MGSIC-CM. Therefore, the intra-cell interference for MGSIC-CM can be expressed as Ci i - l N £ IpPjn £ Pjn £ Pjn jinn _ J= l i J=Ci+l , j=i+l ^gs a ~l + RfN(Ks) 1 + R%(KS) l + R%(Ks)' The expression for the inter-cell interference must be modified from Eq. (3.13), using the power relation developed in Section 2.4.1. The new expression is 26 given by i r = Y.RiN+(Ks)pjnn+ E RiN{Ks)pjnn jzX 1 + R% (Ks) 1 (3.16) + i?^(ir5 ' ^ l i + ^ W Using Eqs. (3.15) and (3.7), and the expression for the SNIR of a mobile user employing combining macro-diversity given in Eq. (3.10), the SNIR of MGSIC-CM can be written as Pin/R ^ \l,+B>»(Ks)\Pjn lfi \l+R{"(Ks)\Pjn Ri»(Ks)Pin 3hi l+R$(Ks) J=cr+1 l+R-°N(Ks) 1+R%(KS) j=i+l i+RjN(Ks) I (3.17) 27 C h a p t e r 4 C a p a c i t y A n a l y s i s a n d E v a l u a t i o n In this chapter, we will follow the steps taken in [12] to calculate outage prob-ability. Using the equations for the SNIR of GSIC, developed in Chapter 3, we will write a set of linear equations to describe Pinn (or P m for CM). The set of equations will be solved using linear algebra techniques to find the minimum value of received power with which a user may still successfully connect to the cellular network. Using this minimum value of received power, a maximum tolerable path loss will be calculated. Finally, employing the maximum tol-erable path loss and the cdf of the path loss of a mobile user, calculated in Appendix A we will be able to calculate outage probability. Once we have the expressions for outage probability we will compare our results with those given in [12]. 4.1 G S I C - S M In order to maintain a required BER for all users connected to the network ginjpn musi D e greater than or equal to a required value, a. Under the assumption of perfect power control the SNIR can be written as {ET/lin = a,Vie[l,N)}. (4.1) 28 Using the expression for the SNIR of GSIC-SM given in Eq. (3.6), and also using Eq. (4.1) we can write an expression for the SNIR for each value of i £ [1,N]. If we re-write each equation to isolate P{nn we can form a set of equations for power as a function of mobile user index, ( P m n , i G [1, A7]}. This set of equations can be written as GSIC-SM where A Pnn — P\nn P2nn P — B • T ) B = [aN0FNBw aN0FNBw and AOSIC~SM = A as given below P(N-l)nn -P/Vnn aNQFNBw aN0FNBu A = ai b2 • • bG bG+i bG+2 • • b2G b2G+i • • bN bi a2 . • bG bc+i bG+2 • • b2G b2G+i • • bN h b2 • • aG bG+i bG+2 • • b2G b2G+i • • bN C l C2 • • cG a-G+i bG+2 • • b2G b2G+i • • bN C l C2 • • cG bG+i a-G+2 • • b2G b2G+i • • bN C l c2 • • cG bG+i bG+2 • • a2G &2G+1 • • bN C l c 2 • • cG CG+l CG+2 • • c2G O 2 G + I • • bN C l c 2 • • cG CG+I CG+2 • • c2G ^2G+l • • bN C l C2 • . cG CG+I CG+2 • • c2G C2G+1 • • bN C l C2 • • cG CG+I CG+2 • • c2G C 2 G+1 • • aN (4.2) (4.3) (4.4) .(4.5) where [-]T denotes transpose. Additionally, the terms are representative of the mobile user that is currently being detected, bi are representative of users whose signals have been detected but not yet been cancelled from the received signal, or users who are undetected, and Cj is representative of users 29 whose signals have been detected and cancelled from the received signal. For GSIC-SM, the values for a,i,bi, and Cj are given by ai = Gs-aRf{Ks) k = -a [l + Rf (Ks)] Ci = -a[^ + RiN(Ks)] Gs — Bw j R. Using linear algebra techniques the set of equations given by (4.2) can be solved for the received power of a group, Pdn, where Pcin is the received power of users belonging to the ith group, assigned to the nth base station. Among users whose ranking places them in the same group the expression for received power is identical. To satisfy the SNIR requirement received power for mobile users in a GSIC-SM system is given by aN0FNBw ( 7 - (G - 1) f3)Lai Gin ( LGN-1 E j=0 . l?+l)G (7-f3(G-l)Y E (l + RkeN(Ks)) k=jG+l + _ pGSIC-SM GiN ( 7 - (5 (G - 1))Lgn (Ks), E (1 + RkeN (KS)) k=LGNG+l - 1 (4.6) where 0, 1, m 1 < i < G G <i<2G (\§]-l)G<i<N Ga+ij)a Gs+a _ a(l-ip) ~ Gs+a • 7 = P For the ranking of users by received power given in Eq. (3.2) to hold the term ( 7 — (G — l)/3), in Eq. (4.6), must be less than one. Substituting for the values 7 and f3 using the expressions given in the above produces the following Gs + V« - (G - 1) a (1 - V) 7 - ( G - l ) / 3 = Gs + a Gs + a - G (1 - tp) a Gs + a (4.7) 30 Because the portion of the interference left after cancellation, ip, is always less than one, the expression given in Eq. (4.7) is less than one and the power ranking •GSIC-SM > P: GSIC-SM G2N > ^ pGSIC-SM - rGNN that was an important part of our initial assumption holds. Similar calculations can be performed for all the other cases that we will discuss. In order for the (i,n)th user assigned to the nth base station to satisfy the SNIR requirement that { £ j n / J t i n > a, V i G [1, N]}, its path loss must satisfy the following expression ?max < 101og10 pt» oGSlC-SM V i G [ l , iV] , (4.8) GtN (Ks). where P t m a x is the maximum power a user is capable of transmitting. The largest value of path loss occurs for user N, as shown by the received power ranking proven above. Therefore, the highest path loss that a user may experience while remaining connected to the network, j(GSic-SM^ - g g i v e n D V ^GSIC-SM = 101og10 [P^/PS^N'™ (KS)]}, or more completely as K GSIC-SM = lOlog 10 3max t ( LCN-1 'G.-a E 3=0 ( 7 - / 3 ( G - l ) y E ( l + RkeN (Ks)) k=jG+l v ' aN0FNBw(7-(G-l)P) V -a N (7-/3(G-1))Lgn E (l + RheN(Ks)) - 1 aN0FNBw(1-(G-l)P) Once the expression given in Eq. (4.9) is evaluated the outage probability can be calculated using the cumulative distribution function, F(K), derived in Appendix A. Outage probability for GSIC-SM as a function of N, denoted TJGSIC-SM ^jy^ ^ g i v e n D y th e following U GSIC-SM (N) = l-F(KfIC-SM). (4.10) (4.9) 31 4.2 M G S I C - S M In the same manner as the derivation in the previous section, we begin the derivation of outage probability for MGSIC-SM with the expression for the SNIR of MGSIC-SM given in Eq. (3.14). Under the assumption of perfect power control, {Elbn /1™ = a, V i G [1, N]}, the set of equations for power as a function of mobile user index, {Pinn, i G [l,iV]}, can be written as AMGSIC-SM p _ D (4.11) where P n n and B are given in Eqs. (4.3) and (4.4) respectively, and A M S I C S M = A (A given in Eq. (4.5)), however, now the values of matrix A are given by cn = G s - a R f i K s ) h = -a[\ + R f ( K s ) \ d = - a ^ + RfiKs)] G s = Bw/R. Using linear algebra techniques the system of equations given by (4.11) can be solved and written as a N 0 F N B w U UkG - GE PkG-i „ fc=i \ i=i G i n — G s E i=o j { G-l \ U+l)G U h k G - E P k G - i ) E [1 + R ? N ( K S ) } k=l V '=1 / m=jG+l + LGN I G-l \ 'N R n (IkG — E PkG-l) E [1 + R ? N ( K S ) } k=l \ 1=1 I m=LGNG+l oMGSIC-SM GtN - 1 (4.12) where L>Gi = li Pi 0, 1, rf i - 1 , Gs+^a-a(l-^)R?°(Ks) Gs+a a(l-^)(l+Rf°(Ks)) ~ G3+a 1 < i < G G <i < 2 G ( rg i - i )G<i<jv 32 In order for a user to satisfy the SNIR requirement that {E%bn/I™ > a, V i € [1, iV]}, the path loss in the MGSIC-SM case must satisfy the following expres-sion pmax PLinn < 101og10 TJMGSIC-SM ( is \ ' V i e [1,N] (4.13) The largest value of path loss occurs for user N; therefore, the highest path loss that a user may experience while remaining connected to the network, KGSIC-SM/1S g i y e n b y K: GSIC-SM = 101og10 pmax pMGSIC-SM I TS \ V i e [i,N] (4.14) Once the expression given in Eq. (4.14) is evaluated the outage probability can be calculated using the cumulative probability function, F (K), derived in Appendix A. Outage probability for GSIC-SM expressed as a function of N, denoted U M G S I C ~ S M (N), is given by the following U MGSIC-SM (N) = l - F ( K f G S I C ~ S M ) . (4.15) 4 . 3 G S I C - C M Once again, to calculate the outage probability for GSIC-CM we begin with the expression for the SNIR of GSIC-CM, given by Eq. (3.11). Under the assumption of perfect power control, {Elhn/Iln = a , V i 6 [l,iV]}, the set of equations for power as a function of mobile user index, {Pin, i € [l,iV]}, can be written as A G S I C - C M P n = B, (4.16) where Pnn is given by Pn = \P\n Pin ••• P(N-l)n -PiVn] , (4-17) and where B is given in Eq. (4.4), and A G S I C - C M = A, (A given in Eq. (4.5)), where the values of matrix A are now given by 33 _ r _ cKN(Ks) _ -a\l+R^(Ks)] 0 i - l+Rf(Ks) -a\l>+RiS'(Ks)\ C i ~ \+R?u(Ks) Gs = BwjR. Using linear algebra techniques the system of equations given by (4.16) can be solved and written as aN0FNBw • kU [KG - E ^ l ^ f ' ^ ( LGN—1 E fW k G ^ 1 a\ U P G a+RrN(Ks)).. fc=i J=(fc-1)G+1 m=jG+l + LGN I kG-1 \ N n [ i k G - E A E fc=l \ i = ( f c - l ) G + l / m=LGNG+l _ T3MGSIC-SM = Pi GtN (Ks) (1+R?»(KS)) ( l + * f ° ( f f s ) ) (4.18) where 7i = A = 0, 1, . r s i -Ga(l+R(°)+a GJl+Rf0(Ks))+a Gs(l+R?0(Ks))+a4> Gs(l+R?°(Ks))+a »(1-V0 1 < i < G G < i < 2G ( r g l - 1) G? < t < iV Gs(l+R?°(KS))+* In order for a user to satisfy the SNIR requirement that {Elbn/Iin > a, V i € [1, A7]}, the path loss for the GSIC-CM case must satisfy the following expres-sion PLin < 101og10 pmax TJGSIC-CM (KS) V i e [1,N\. (4.19) Again, the largest value of path loss occurs for user N. Therefore, the highest combined path loss that any user may experience while remaining connected to the network, PLoin, is given by 34 PLGin < 101og10 pmax pUstc-cM^y^P^-^iKs). (4.20) ^GNN \ K S ) . ^GSIC-CM GNN The power reduction factor for a mobile user with a path loss of K dB, em-ploying C M is derived in [12] and is given by 4 s (K)/N q(K) = 10log10 1 + (4.21) SKS (K) where q^s (K) is the total power reduction ratio produced by all mobile users assigned to the 0th base station whose path loss are equal to K dB, in a system where path loss must be less than Ks dB in order for users to be served by the system. This term is derived in Appendix B, and is given in Eq. (B.6). The term fxs (K) is the Ks limited pdf of the path loss for a mobile user, which is given in Appendix A in Eq. (A.7). Using the expression for power reduction and maximum allowable combined path loss, Eqs. (4.20) and (2.25), we can write an expression for the limiting path loss, K%SIC~CM, as follows KGSIC-CM = PLGSICSM fKGSIC-CM^ + q ^GSIC-CM^ ^ Once the expression given in Eq. (4.22) is evaluated the outage probability can be calculated using the cumulative probability function, F (K), derived in Appendix A. Outage probability for GSIC-SM expressed as a function of N, denoted UGSIC~CM (AT), is given by the following rjGSic-CM (j\T) = I — F (KGSIC-CM) . (4.23) 4 . 4 M G S I C - C M Finally, to calculate the outage probability for MGSIC-CM, we begin with the expression for the SNIR of MGSIC-CM, given by Eq. (3.17). Under the assumption of perfect power control, {E%bn/Iln — a , V i . G [1, AT]}, the set of equations for power as a function of mobile user index, i G [1, A7]}, can 35 be written as AMGSIC-CMpn = jg ) ( 4 2 4 ) where Pn and B are given in Eqs. (4.17) and (4.4) respectively, and AMGSIC-°M A, (A given in Eq. (4.5)) where the values of matrix A are now given by U I ~ ^ S 1+R?°(KS) _ -a\l+R^(Ks)} °i ~ i+R?u(Ks) C i - l+R™(Ks) Gs = Bw/R. Using linear algebra techniques the system of equations given by (4.24) can be solved and written as Pi Gin (l+R^(Ks)) LOi f ( G - l ) ( l + i l f g ) ( l - ^ ) a aNQFNBw • ^  { l + R ? 0 ) fcn [ike - G ; ( 1 ; ^ ) + a -( LGN—1 E fc=i f l 7fcG fcG-1 E Pi ; = ( f c - l ) G + l / m = j G + l + LGN "If1 A ^ i = ( f c - l ) G + l / m = L G i v G + l ; = P, MGSIC-SM (Ks) (l+Rf°) (4.25) where LGI = Hi. = li = Pi = 0, 1, 1 < i < G G <i <2G G3(l+Rf0(Ks))+a Gjl+R?°(Ks))+a Gs(l+R?°(Ks))-a(l-il>)R?0{Ks)+TPa Ga(l+Rf°(Ks))+a a(l-^)(l+R?°(Ks)) Gs(l+R?°(Ks))+a • (\§]-l)G<i<N In order for a user to satisfy the SNIR requirement that {Elbn/Iin > a, V i € [l,iV]}, the path loss for the MGSIC-CM case must satisfy the following ex-pression PUnn < 101og10 pmax r>MGSIC-CM i TS \ V i e [1,N] (4.26) 36 The largest value of path loss occurs for user N; therefore, the highest combined path loss that a user may experience while remaining connected to the network, PLGin, is given by PLGin < 101og10 pmax •>MGSIC-CM (J(s) = PL^SNIC~CM (Ks). (4.27) GNN Again, using the expression for power reduction derived in Appendix B, and the maximum allowable combined path loss, Eqs. (4.27) and (2.25), we can write an expression for the limiting path loss as jsMGSIC-CM = pLMGSICsM ^MGSIC-CM^ + g fjsMGSIC-CM^j ^ 2 g ) Once the expression given in Eq. (4.28) is evaluated the outage probability can be calculated using the cumulative probability function, F (K), derived in Appendix A. Outage probability for MGSIC-CM expressed as a function of N, denoted u G S I C ' C M (N), is given by the following rjMGSIC-CM (AT) = 1_ F(KMGSIC-CMy ( 4 2 9 ) 4.5 Outage Probability for SIC If we set the group size equal to one (G = 1) the expressions derived for GSIC-SM, MGSIC-SM, GSIC-CM and MGSIC-CM simplify from GSIC to SIC. The simplified equations, [Eqs. (4.6), (4.12), (4.18), (4.25) with G-l] are given by aN0FNBw • 7*-1 pSIC-SM ( TS \ _ Pinn (KS) ~ N I where 7 G s - a ^ E [1 + ^ (Ks)] 7 * - 1 - ! Gs + ipa Gs + a aN0FNBw • LI 7fc iMSIC-SM (js\ _ fc=l r>MSlu-i>M I TS \ _ Unn \AS) -Gs-a(f: \i + MN(ks)]n7J-i V = i L J fc=i , Gs + -ipa-a(l-^)Rf°(Ks) where 7^  = 37 oSIC-CM (Ks) = aN0FNBw • / ini+ijfojigj j r f Ik Ga a f JV E 1+R?U(KS) j - l n 7/= * ; = i where 7, and / i i = _ Gs [l + i?f° (AT5)] + V><* G s [ l + i?f0(Ars)] + a Ga [l + Rf° (Ks)]+a Gs [1 + Rf° (Ks)} + a aN0FNBw • M n i + g j g n 7fc » - i iMSIC-CM (Ks) = Gx a JV E MJ n 7fc -1 fc=l l + f l f u ( ^ s ) _ G a [ l + i 2 f ° ( ^ s ) l + V a + a ( l - V ) i 2 f 0 ( ^ ) W h e r 6 7 l = G.[l + *r(Ka)] + a _ Ga [l + Rf° (Ks)} + a a n d * ~ Gs [1 + i?f° + a • The above equations that were obtained by simplifying the set of equations we had derived for GSIC (by setting G = 1), are identical to the equations for SIC given in [13, 15, 37]. This result is a confirmation of our derivations. 4 . 6 O u t a g e P r o b a b i l i t y f o r S U D Once again following the technique in [13], using the equations for the SNIR of SUD-SM (Eq. (2.5)), under the assumption of perfect power control we can write a set of equations for power as a function of mobile user index in the case of SUD-SM. Solving the resulting set of equations leads to a closed-form expression for { P m n , i G [1, A7]} given by aN0FNBw P > 1 mn — Gs a E RiN (Ks) + N-1 j = i _ r>SUD-SM (4.30) In order for a user to satisfy the system requirements, its path loss must satisfy the following / pmax PLinn < 101oglo I ^SUD-SM V JV = K •SUD-SM (4.31) 38 The outage probability of the system can now be written as rjSUD-SM { N ) = 1 _ F (K§UD-SMj ( 4 3 2 ) Similarly for SUD-CM, we use the expression for SNIR given in Eq. (2.17) and obtain a relation for power as a function of mobile user index given by a N 0 F N B w 1+R?°(KS) {Gs l+Rf°(Ks) } l+Rf°(Ks) {Gs l+Rf°(Ks) } r _ ccR\"(Ks) h+RJN(Ks)]{Gs[l+flfo(KS)] + a > U s [l+Rf°(Ks)\ h + f i f ° ( K s ) \ { G s {l+Rf(Ks)\+a} EE P S N U D - C M . (4.33) Again, in order for a user to satisfy the system requirements, its path loss must satisfy the following ( pmax \ PSUD-CM) = P L f N D - C M ( K S ) . (4.34) Because we are employing combining macro-diversity we must include the power reduction factor in the expression for the maximum path loss. The expression for the maximum allowable path loss becomes KSUD-CM = p L N N rKSUD-CMj + g ^SUD-CM^ ( 4 35) The outage probability of system can now be written as rjSUD-SM { N ) = 1 _ F 'KIUD-CMJ ( 4 3 6 ) 4.7 Numerical Evaluation In order to assess the benefits and costs of the GSIC scheme we need to evaluate the expressions that we have derived for GSIC. Evaluating these expressions will give a measure of capacity. Once we have performed the evaluation we can make some comparisons between GSIC and SIC. We will take an itera-tive approach to evaluating the outage probability. For each value of N , we calculate the outage probability using the bisection approach, as given in [40]. We begin with an upper and lower limit on the path loss, the upper value 39 Outage Probability for GSIC-SM Outage Probability tor MGSIC-SM Outage Probability Outage Probability Figure 4.1: Numerical results for GSIC-SM and MGSIC-SM. as Ks —• oo and the lower value as Ks —> 0. Using these values of Ks we calculate RleN (Ks), and evaluate the expression for the maximum allowable path loss, Ks = PLGiN (Ks) for SM, and Ks = PLGiN (Ks) + q (Ks) for CM. At each step in the numerical evaluation the window size is reduced by a factor of two, based upon the limit (upper or lower) that brings the expression Ks = PLGiN (Ks) (SM) or Ks = PLGiN (Ks) + q (Ks) (CM) closest to zero. When we arrive at a value of Ks that satisfies the maximum allowable path loss equations, we use this value of Ks in the outage probability calculation. We will use the system parameters for a pedestrian mobile user, using the cdma2000 network as given in the IMT-2000 standard [34]. These parameters are a = b = ^ , a = 10 dB, Nc = 3, [i = 4, R = 9.6 kbps, Gs = 384, a = 5 dB. Additionally, following the analysis in [13], we set the portion of a signal which remains after cancellation, tp, equal to K 4.7.1 Numer ica l Results for S M First we will consider group cancellation in the SM case. From the plots in Figure 4.1 it is obvious that the highest capacity is achieved when the group size equals 1, (equivalent to SIC) and that capacity decreases as group size is increased. This is as we would expect, as group cancellation means 40 reduced interference cancellation. Figure 4.1 also clearly demonstrates that the use of multiple cell cancellation with GSIC increases capacity. For an outage probability of 5 %, as recommended by the cdma2000 standard [34], comparing techniques with groups of size 1 we find that GSIC-SM supports 85 mobile users, while MGSIC-SM supports an additional 9 users for a total 95 mobile users. Also visible on these plots is the appearance of changes in the slope of the outage probability. These changes in slope appear to correspond to group size. Presumably, these slope changes are in response to changes in the amount of inter-cell interference that a mobile user experiences. Just before a cancellation occurs there is a large amount of un-cancelled interference, this un-cancelled interference increases the probability of an outage event occurring (when one or more mobile users cannot transmit with enough power to be successfully detected at the base station). As a result, the un-cancelled interference has a negative affect on outage probability, and increases the slope of the outage probability curve. Immediately after a cancellation, interference is reduced with respect to before the cancellation. Probability of an outage event occur-ring is also reduced, as compared with the probability prior to the cancellation. Therefore, the interference cancellation has a positive affect on outage proba-bility, reducing the slope of the outage probability curve. Accounting for the variations in slope, GSIC-SM with a group size of 10 has a maximum of 5 fewer supported users as compared to the SIC-SM scheme. At the 5 % target outage probability the difference in the number of users supported is only 3. For GSIC-SM with a group size 20 the maximum number of users unsupported as compared with SIC-SM is 10, while at the target outage probability this number drops to 6. For MSIC-SM with a group size of 10 there is a maximum variation of 7 users, as compared to MSIC-SM. However, at the target outage probability the difference drops to 4 users. Finally, for MGSIC-SM with a group size of 20, the maximum variation in the number of users supported is 15, and this number drops to 8 at the target outage probability. 41 Outage Probability (or QSIC-CM Outage Probability for MOSIC-CU Outage Probability Outage Probability Figure 4.2: Numerical results for GSIC-CM and MGSIC-CM. 4.7.2 Numerical Results for C M Now we will consider group cancellation in the C M case. Once again in Figure 4.2, we can see that the slope changes with group size, and the same explana-tion applies as in the SM case. If we compare the plots for C M in Figure 4.2, with the plots for SM in Figure 4.1, we can see an improvement in capacity as expected. In the case of SIC-CM (group size 1), 120 users can be supported at the outage probability of 5 %, as compared with 85 for GSIC-SM, a sig-nificant improvement. MSIC-CM (group size 1), can support 132 users at the 5 % outage probability, which is an improvement of 38 users as compared to MSIC-SM (group size of 1). Looking at the number of users supported with respect to increasing group size we see that GSIC-CM with a group size of 10 has a maximum variation from the group size 1 technique of 5 users. At the target outage rate, however, this number drops to only 3 users. The GSIC-CM technique with a group size of 20 has a maximum difference of 12 users as compared to the group size 1 method, but this number drops to 6 at a 5 % outage probability. Looking at MGSIC-CM we see a maximum variation of 10 users between the group size 1 and 10 technique, which is reduced to 5 mobile users at the target outage rate. Finally, comparing MGSIC-CM using groups of size 1 and 20 we see a 42 maximum difference of 18 users, which improves to only 8 users at the 5 % outage probability mark. 4 .7 .3 Comparison with Previous Results If use the equations for SIC and SUD given in Sections 4.5 and 4.6 we can make some comparisons between the numerical results we have generated, and those produced in [12, 13, 14, 15]. The comparisons between the numerical results that we have generated and those presented in [12, 13, 14, 15] are shown in Figure 4.3. The numerical results generated in [12, 13, 14, 15] tend to have thresholds after which the number of users supported does not increase, whereas the plots we have gener-ated have no strict thresholds. Our investigations suggest that the numerical N results generated in [12, 13, 14, 15] use the bound, { £ ^ ( + 0 0 ) = 0.75iV}, on inter-cell interference for a cellular system with a = 10, Nc = 3, first de-rived in [24]. The bound is calculated by averaging over all values of path loss, from very small values of path loss to the worst case for the cellular system, infinite path loss (Ks —• 00), and is a constant for a given number of users. The use of a bound on the inter-cell interference factor implies that there will be a hard limit on the number of users a base station may admit to the network. However, by iteratively calculating the inter-cell interference factor based on a maximum path loss observed in a simulated network (not equal to infinity), we observe a percentage of instances when users are positioned favorably, and very low values of path loss occur. In these instances more users can be assigned to a base station than are predicted using the technique which applies the bound (averaging over path loss values from zero to infinity). Comparing the two techniques we see that when the number of users is small the maximum path loss permissible for a network connection to be created or maintained can be very high. Therefore, when the number of users connected to the network is small and allowable path loss is high, we calculate the inter-cell interference factor in an interval approaching [0,+OG). If we use this interval our results 43 will agree very well with those presented in [12, 13]. As the number of users increases the maximum permissible path loss decreases, because more users are present in the network causing more interference. If we continue to apply the bound which calculates inter-cell interference over the range [0, +co) the number of users able to access the network will be strictly limited. However, if we consider the possibility that users with a path loss less than a certain limit Ks are still able to access the network and we calculate the inter-cell interference factor in the interval [0, Ks] we will produce a smaller inter-cell interference factor, which indicates that more users are able to access the network. Thus, when the number of users supported by the network is large our results diverge from those presented in [12, 13, 14, 15]. Simulation data produced in [12, 13, 14, 15] confirms the numerical results of [12, 13, 14, 15], shown in Figure 4.3. However, the simulation model employed in [12, 13, 14, 15] also uses an inter-cell interference factor generated using path losses in the interval [0,+oo). Simulated mobile users are generated for only N one cell, and the bound on the inter-cell interference factor, £ R>e N (+oo), is used to determine the total inter-cell interference a user experiences. We would expect simulated data using inter-cell interference generated using path loss in the interval [0, +oo) to match numerical results using the inter-cell interference factor calculated in the interval [0, +oo). We suggest a more realistic simulation model in which inter-cell interference is generated for each simulation instance based on users position and transmit power in a 37 cell, 3 tier model. The simulation model we employ is discussed in more detail in the next chapter. 44 Outage Probability lor SUD-SM Outage Probability (or SUD-CM 1 401--8. 1 60 j-I Numerical Results V-Numerical Results (rom Previous Work |; Outage Probability Outage Probability for SIC-SM - Numerical Results - Numerical Results (rom Previous Work OutageProbability Outage Probability (or SIC-CM a. I 60 140 g 120 8. IOO i D l 60 40 Outage Probability Outage Probability (or MSIC-SM — Numerical Results - - Numerical ResJts (rom Previous Work Outage Probability Outage Probability (or MSIC-CM : : — : — : : : : : i : : — : — T T T T T T : ! : : : : : ; - : i / ' Ui.. I \-\ i 1- i - i -HtH \hi -H-Hi-j Numerical Results J 1 Numerical Results from Previous Work | Outage Probability Outage Probability Figure 4.3: Comparison of numerical results with those from [13]. 45 Chapter 5 Simulation Results In this chapter, we will outline the methodology behind our simulation tech-nique. Then, we will discuss the simulation results generated for SUD-SM, SUD-CM, GSIC-SM, GSIC-CM, MGSIC-SM, and MGSIC-CM. We will make a comparison between the numerical results generated in the previous chapter and our simulation results. Finally, we will discuss numerical and simulation results with respect to group size and performance. 5.1 Computer Simulation Methodology For simulation purposes, following the cellular C D M A model outlined in Sec-tion 2.1, we implement a 3 tier, 37 cell network in software. Outage probability is calculated from outage statistics of the central cell in the network. Sur-rounding cells are populated with users solely to provide data for calculation of inter-cell interference. Users in surrounding cells are, however, expected to conform to the same requirements for connection to the network as required of mobile users in the central cell. User information is generated by employing Monte Carlo simulation techniques. In the following, we will describe the steps used in our computer simulation. 46 Step I N = 0 Step II Add a user to central cell and Tier 1 cells N = N + 1 Step VII Record value No of JV Step III Make a copy of new user in central cell, and copy this to Tier 2 & 3 cells Step IV Step VI Calculate intercell interference at central cell & Tier 1 cells experienced Yes ,Step V No / / O o m p u t e El"/I't" f o r \ ie[l,JV],ne[0,6] X . Does Pln require adjustment \ so that a < E'b"/I'tn < a + e for a least one user? Figure 5.1: Computer simulation model for evaluation of outage probability. 5.1.1 Step I Initially, the 3 tier cellular network is unpopulated, that is N = 0, as shown in Figure 5.1. 5.1.2 Step II In the next step, one user is created for the central cell and each of the cells in the surrounding tier. The new mobile users' positions follow the uniform distribution. A user is generated for each cell independently and if the new mobile user's position is not within the current cell it is discarded and another user is generated. In addition to the user's position, path losses between the base station of the current cell and the base stations of all surrounding cells are randomly generated according to the path loss model. If the lowest value of path loss is not between the mobile user and the base station of the current cell, the mobile user is once again discarded and another is generated. The Nc lowest values of path loss for the user are recorded, as are the corresponding base stations. These base stations now form the serving area for our newly generated user. As new users are generated they are ranked within the cell, according to the 47 value of path loss to their assigned base station. 5.1.3 Step III We require that all cells in the network obey the same rules regarding admit-tance of users to the network. This means that for all independently generated users we must check received SNIR and optimize the users' transmit power. Every change we make to a user will affect all other users in the network through inter-cell interference. Therefore, in order to minimize computation time we use the newly created user in the central cell and make a copy of its position in relation to its assigned base station, and of the values of path loss between the user and its assigned base station, and base stations in its serving area. Next, instead of generating a new user for all cells in the 2 n d and 3 r d tier we place a copy of the position and path loss of the user (taken from the central cell) in the 2 n d and 3 r d tier cells. For users in the 2 n d and 3 r d tier, we make the assumption that if the users in the central cell meet the conditions for connection to the network, the users in the 2 n d and 3 r d tier meet the conditions for connection to the network. 5.1.4 Step IV Next, values of inter-cell interference are generated for the central cell and Tier 1 cells. For example, considering the central cell, the signals of all transmitting users in Tiers 1, 2, and 3 cause interference. Because the majority of inter-cell interference is generated by users in the 2 tiers surrounding a user [12, 13], we calculate inter-cell interference for the central cell by processing each user in each of the surrounding 2 tiers, or eighteen cells. Users in the Tier 1 cells are checked to see if the central base station is in their serving area. If the central base station is within the user's serving area the previously recorded path loss is used along with the users transmit power to calculate this portion of the inter-cell interference. If the user does not have a serving area association, a 48 new path loss is generated randomly according to the path loss model. For Tier 2 users a serving area association is not possible and inter-cell interference is calculated using randomly generated (according to the model) path loss values. Inter-cell interference is calculated similarly for the Tier 1 cells. In this case, the surrounding 2 tiers include the central cell, cells with other independently generated users, and cells containing copies of users in the central cell. For cells neighboring the Tier 1 cells we check serving area associations (for copied users serving area associations are copied geometrically along with the location information). For users that do not have serving area associations, including the copied users, path losses are generated randomly according to the model. 5.1.5 Step V In this step, we calculate the SNIR for all users in the central cell and the Tier 1 cells. Next, using the SNIR calculations the transmit powers of the N mobile users in each of the seven innermost cells {P/n, 6 [1, N], n € [1,6]} are adjusted until we have satisfied the following condition (the transmit power of users in the outer cells is dependent upon the transmit power of users in the central cell) a<-t<a + e, (5.1) 1t where e is a small positive constant, small enough to ensure accuracy but large enough to ensure convergence. We chose e = 0.01 dB, following the work in [12, 13]. The process begins with the first user in the central cell, moves through to the Nth user in the sixth cell of Tier 1. When the transmit power of any single user is adjusted we must return to Step IV and recalculate interference and the SNIR values, and begin again with the first user in the central cell. 49 5.1.6 Step VI When all mobile users in the central cell and Tier 1 have met the condition specified in Eq. (5.1), the values of power must be tested to ensure that none of the users have exceeded the maximum power limitation. If all users require a transmit power less than P t m a x ) then we are free to add another user to each cell in the network and the simulation returns to Step II. If, however, at least one user requires more power than the maximum allowable transmit power we have an outage event. The outage event occurs because the user that requires more power than P t m a x is unable to access the network. When an outage event occurs we move to Step VII. 5.1.7 Step VII In this step we must first check to which base station the mobile user was assigned. We only collect outage statistics for the central cell, and thus if the mobile user that generated the outage event is assigned to a cell in Tier 1 we will discard the outage event and return to Step I immediately. However, if the mobile user which caused the outage event is assigned to the base station in the central cell we record the number of users, N, currently assigned to the central base station and then we return the simulation to Step I. 5.1.8 Calculation of Outage Probability Once the simulation has recorded a sufficient number of outage events we can obtain the pdf of outage events, denoted as ^  (N). The pdf of outage events gives us the relationship between the number of mobile users, N, assigned to a base station and the probability that at least one mobile user assigned to the base station cannot transmit with enough power to meet the SNIR requirement. Because mobile users in the cellular network are independent of one another we can generate the outage probability of the system using the 50 following formulae 1 - X X 0 - .(5.2) rj(iV) = l - f 5.1.9 Simulation Variables As in' the numerical evaluation we will use the cellular system parameters specified in the IMT-2000 cdma2000 cellular standard [34]. The parameters that we apply are a = b — a = 10 dB, Nc = 3, // = 4, R = 9.6 kbps, Gs = 384, a = 5 dB and once again ijj = ^. Additionally, for the simulation we set the value of e in Eq. (5.1) to 0.01 dB. This value for e represents almost perfect power control. 5.2 Simulation Results To allow for comparison, numerical and simulation results are plotted together in Figures 5.2, 5.6, 5.8, 5.10, 5.11. First, we will look at the differences be-tween numerically generated data and simulation data when a small number of users are present in the cellular network. If we look at any of the figures presenting simulation data (Figures 5.2, 5.6, 5.8, 5.10, 5.11), we observe large differences between simulation data and numerical data when a small number of users is present in the network. As the number of users in the network in-creases this difference is gradually reduced. To explain these differences we will discuss the inter-cell interference factor. As presented in the previous chap-ter, if we place no limit on the path loss of mobile users within the cellular system we may use the theoretical bound on the inter-cell interference factor, ' N ' {£ R3e (+°°) — 0.75iV}, derived in [24]. When few users are present in the j=i network this bound is applicable because very high values of path loss are per-missible, as the small number of users generate a small amount of interference. If we simulate the environment recording the inter-cell interference factor for randomly generated users using a uniform distribution and the path loss model described in Chapter 2, and we average over a sufficiently large number of sam-51 Oulaga Probability lorSUD-SM Outaga ProbabiUly lor SUD-CM - Numerical Ratults - Numerical RaiulU using Bound - Simulation Rasulti ' Numaricnl RasulU - Numerical RaauHa using Bound - Simula lion Raiulti Outaga Probability Figure 5.2: Reverse link capacity of SUD-SM and SUD-CM (simulation and numerical Results). N pies, we will arrive at the bound of { RJe (+00) = 0.75iV}. However, the J'=I values of path loss that we encounter are not uniformly distributed, with path loss being biased toward small values and only occasional large values occur-ring. When the large values are averaged with the small values we meet the 0.75iV bound. But, if we randomly generate users with a uniform distribution, apply the path loss model of Chapter 2 and put these users directly into the outage probability simulation, we see a large improvement as compared with the numerical evaluation because of the bias toward small values of path loss. Finally, regarding the differences for a small number of users, we will add that the IMT-2000 standard [34] recommends an operating outage probability of 5 %. It is, therefore, in the range of the 5 % outage mark that we are especially interested in agreement between the numerical and simulation results. At an outage probability of 5 % a large number of users are populating the system for all detection schemes discussed in this work and as a result in this area we generally have much better agreement between the simulation and numerical results. In regard to the work presented in [12, 13], simulation results for SUD, GSIC and MGSIC (Figures 5.2, 5.6, 5.8, 5.10, 5.11) do not show threshold limitations on capacity. Plots for SUD, GSIC, and MSIC indicate a higher capacity than 52 Distribution of Received Power lor SUD Employing Perfect Power Control Distribution ol Received Power for SUD Employing Imperfect Power Control 0.8 -"8 0.8 - • i • 4 . . . 0.2 •• 0 l 1 2 3 4 5 6 7 8 9 10 1 2 3 4 6 6 7 8 9 10 User Rank UMr Rank Distribution of Reoerved Power lor GSIC (Group Size One) Employing Perfect Power Control Distribution ol Received Power lor GSIC (Group Size One) Employing Imperfect Power Control 0.8 I s. I 06 ' 0 4 -•• 0.2 • • ol 1 2 3 4 5 6 7 8 9 10 1 Z 3 4 5 6 7 6 9 10 Uaer Rank User Rank Figure 5.3: Influence of power control on received power ranking for SUD and SIC. is obtained by using the bound on inter-cell interference, R{N (+00), used in [13, 12]. 5.2.1 SUD Simulation and numerical results for SUD employing SM and C M are shown in Figure 5.2. This figure shows that the simulation results match very well in the C M case, and that we have a constant margin between simulation and numerical results in the SM case. This margin may be explained if we look at the profile of transmit and receive power for SUD users. Underlying all of the theoretical analysis was the assumption that users of the same receive power/path loss rank have the same received power at their assigned base I 0.6 -•-0.4k-1 0.6 -0 .4 . 53 Distribution of Received Power for GSIC {Group Size Four) Employing Perfect Power Control Distribution of Received Power for GSIC (Group Size Four) Employing Imperfect Power Control "8 0.6 •s 8 1 2 3 5 6 7 s. Tg 0.6 .a « cr 0.4 1 2 3 5 6 7 8 9 10 Figure 5.4: Influence of power control on received power ranking for GSIC. station. In the theoretical analysis we also assumed that power control was perfect. However, in simulations we have allowed the received SNIR to vary by 0.01 dB around a set point of 5 dB (giving a range of SNIR from 3.155 to 3.170). In practice, this would mean that our power control algorithm is good, but not perfect. Also in the simulation, users of the same ranking in the central cell and the cells in Tier 1 were not required to have the same received power in order to provide a more realistic simulation environment. Limiting all users of the same rank to the same received power was also shown in simulations to have a large negative impact on capacity, because users in some cells experience higher values of path loss. In the case of SUD, in order for the equal BER rate condition to be met all users must be received with the same power [6]. However, because our power control condition is not perfect there will be slight variations between users. Figure 5.3, contains a plot of SUD employing perfect power control and SUD employing imperfect power control. The variations between users for the scheme employing imperfect power control can have a significant impact on system performance. We may treat these fluctuations in received power as additional noise. Also, in our simulation environment, all users of the same rank in the central cell, and Tier 1 cells may not have the same level of received power. These variations can also be treated as noise. The additional noise in the simulation environment results 5.4 io"4 10" 3 10~* 10"' 10° Outage Probability Figure 5.5: Reverse link capacity of SUD-SM (simulation and numerical re-sults), numerical results with SNIR of 5.2 dB. in reduced performance as compared with the theoretical analysis. To verify our explanation, we can increase the value of a in our numerical evaluation (while maintaining the values of all other parameters) to compensate for the additional noise in the simulation environment. When a is increased to 5.2 dB (as compared to the original value of 5.0 dB), as shown in Figure 5.5, we see that the theoretical results match very well with our simulated results. As we have said before, the SUD-CM simulation results, shown in Figure 5.2, match very well with the theoretical results. When CM is employed, as outlined in this work, detection is based on 3 copies of the mobile user's signal. We can equate the combining of the 3 different copies of the user's signal with averaging. Thus, using the CM technique we may observe that the distribution of power used in detection is more even. When the distribution of power used in detection is even, the noise as described in the SM case is dissipated. Therefore, we expect the SUD-CM simulations results to have a better agreement with theoretical results than in the SUD-SM case. 55 Outage Probability lor GSIC-SM Group Size 1 (G=1) Outage Probability for GSIC-SM Group Size 10 (G=10) Outage Probability for GSIC-SM Group Size 20 (G=20) Outage Probability Figure 5.6: Reverse link capacity of GSIC-SM group sizes 1, 10 and 20 (simu-lation and numerical results). 5.2.2 G S I C - S M Next, we will consider the simulation and theoretical results of GSIC-SM, shown in Figure 5.6. Here, we can see that the simulation results for the groups of size 10 and 20 match very well with the theoretical results. Our simulation results do not, however, display the same changes in slope visible in the theoretical curves. Variations in the pdf of outage events, up(N), are suppressed when up (N) is summed over N to obtain the cdf used in the calculation of outage probability, as given in Eq. (5.2). As a result, the simulation curve shown in all plots is equivalent to an outage probability averaged with respect to the number of supported users, N. 56 100 90 80 70 3 60 e 8 50 =3 •5 | 40 Z 30 20 10 0 10"' 10"3 10'* 10"' 10° Outage Probability Figure 5.7: Reverse link capacity of GSIC-SM group size 1 (simulation and numerical results), numerical results with SNIR of 5.2 dB. The plot of GSIC-SM with a group size of 1 shows a more substantial difference between numerical and simulation results than observable in the group size 10 and 20 plots. Presumably, the explanation for this behavior is to be found again in the power distribution of the users. As we have discussed before, the simulation environment we have created does not have perfect power control, and allows users in different cells with the same power ranking to have dif-ferent received powers. As in the case of SUD-SM, these factors may be held responsible for additional noise in the simulation cellular system. Assuming perfect power control, all users in a GSIC cellular system should have different levels of received power, and these levels should be decreasing with increasing rank, as shown in Figure 5.3. If we allow variations in the received power, our ranking will not be as precise as in the case of perfect power control, as shown in Figure 5.3. In this case, cancellation of a user may not result in as significant a reduction in interference as theoretically predicted. Therefore, the variations in received power add noise to the scheme and negatively affect performance. To verify these assumptions, we will once again increase the required received SNIR in our numerical evaluation to account for additional noise in the simulation environment. In Figure 5.7, the theoretical curve uses 57 Outage Probability lor MGSIC-SM Group Size 1 (G»1) Outage Probability tor MGSIC-SM Group Size 10 (G=10) - Numerical Results - Numerical Results using Bound - Simulation Results - Numerical Results - Simulation Results Outage Probability Outage Probability Outage Probability for MGSIC-SM Group Size 20 (G=20) ' Numerical Results - Simulation Results Outage Probability Figure 5.8: Reverse link capacity of MGSIC-SM group sizes 1, 10 and 20 (simulation and numerical results). a value of a equal to 5.2 dB. When this correction is employed, the numerical and simulation results match very well. In comparison, when group sizes are large the differences between received power levels are more significant, as shown in Figure 5.4. Thus, when group sizes are large variations in power due to imperfect power control are less significant, shown in Figure 5.4. As a result, simulation performance is closer to theoretical performance when groups are large in size. 58 5.2.3 MGSIC-SM There is a significant difference between the results of simulation and the nu-merical results for MGSIC-SM for all 3 group sizes, as shown in Figure 5.8. Also, comparing Figure 5.6 and Figure 5.8 we can observe that the simulation results indicate that MGSIC-SM does not offer as large an improvement over GSIC-SM as predicted by the theory. As in the case of GSIC-SM some of the difference between numerical and simu-lation results for a group size of 1 is due to variations in the power distribution of users. As the number of users increases, variations in the power distribution of users are likely to be smaller because there are more levels to the power distribution, and power is restricted within a certain range. However, for MGSIC-SM additional noise may be introduced by the multi-cell cancellation process because of the non-identical power ranking between cells. When group size is small, each user within a cell has a different level of power. Therefore, differences between users of the same rank in different cells can be significant. In the theoretical analysis, this difference is ignored and the amount of inter-ference cancellation is based solely upon the inter-cell interference factor and the power of the current user (or group of users) in the current cell. In this substantial noise component may be introduced in the simulations of MGSIC. When group size is large however, differences between group power levels within the cell are larger. Therefore the difference between group power levels in adjacent cells is less likely to be significant. As a result, when group sizes are large variations between the power distributions of neighboring cells are less likely to introduce a substantial noise component. Because we also observe significant differences for the larger group sizes we must consider other factors. The MGSIC-SM technique involves cancellation of a user's signal from the Nc surrounding base stations. In the theoretical work, this cancellation is performed by a reducing the inter-cell interference factor for interference generated within the user's serving area expressed by the following 59 Outage Probability for MGSIC-SM Group Size 1 (G=t) Outage Probability for MGSIC-SM Group Size 10 (G=10) ' Numerical Results - Simulation Results — Numerical Results! — — Simulation Results Outage Probability Outage Probability Outage Probability for MGSIC-SM Group Size 20 (G=20) ' Numerical Results] - Simulation Result: Outage Probability Figure 5.9: Reverse link capacity of MGSIC-SM group sizes 1, 10 and 20 (simulation and numerical results), with a = 5.2 dB for group size 1, x — 1/3.0 dB for all group sizes. linn^Y^[i;R%(Ks) + R%(Ks)}pjnn+ £ RiN(Ks)Pjnn, (5.3) where Q is given in Eq. (3.5). As previously discussed, the simulation model we use allows users of the same rank in different cells to have different path losses, and different transmit pow-ers. In the previous simulations, the inter-cell interference factor was averaged over all cells in the network so that our simulated value might come close the averaged theoretical value. In the multiple cell cancellation case, we can only average the cancelled signal over the cells in the serving area (SQ), and the 60 serving area consists of only 3 cells. Therefore, the amount of interference • cancelled using MGSIC-SM may be very different from the value predicted by theory, (1 - ip)RfN (Ks). To verify this theory, we will re-evaluate our numer-ical results using a larger value of tp, the portion of the signal remaining after cancellation for the multi-cell portion of cancellation. In order to affect this increase, we must separate the cancellation variables for SIC component and the multi-cell component. We will call the new cancellation variable x- Intra-cell interference is unaffected by the separation and we may use Eq. (3.12), but we must re-write the inter-cell interference given in Eq. (5.3) as ITn = ,t[xRfSr(Ks) + RfN(Ks)\PJnn+ fl RiN(Ks)Pjnn. (5.4) Using the above expression for inter-cell interference, we derive a new expres-sion for Pcin- We may use the expression given in Eq. (4.12), however, the values of ji and $ are changed and given by _ Gs+4>a-<x(l-x)R?°(Ks) '» ~~ Gs+a R _ a ( l - ^ ) + a ( l - x ) ( l + f l f ° ( ^ ) ) The plots shown in Figure 5.9 use a value of x equal to 1/3 dB (0.50118). The larger value for x reflects the inaccuracy of the theoretical value of R.fN (Ks), as compared to the smaller value of 1/a dB (0.31623 when a = 5.0 dB) previously used. To counter the added interference due to noise in the power distribution for MGSIC-SM group size 1, we set a equal to 5.2 dB for this case only. The numerical and simulation results shown in Figure 5.9 show a much better agreement agree than those shown in Figure 5.8. The maximum difference between numerical and simulation results is 5 for a group size of 1, and 6 for groups of size 10 and 20. At the target outage probability (5 %) these differences become 4 for groups of size 1 and 20, and 3 for group size 10. To put these differences in perspective, the total number of users in the system is approximately 90 at the 5 % outage probability (this corresponds to a maximum percentage difference of 4.21 %). 61 Outage Probability (or GSIC-CM Group Size 1 (G=1) Outage Probability (or GSIC-CM Group Size 10 (G=10) Outage Probability Outage Probability Outage Probability lor GSIC-CM Group Size 20 (G=20) 160 I • r -r^-r^ . ...,-H , '/'^'l '~ 140h to" 4 10"3 10*2 10"' 10° Outage Probability Figure 5.10: Reverse link capacity of GSIC-CM group sizes 1, 10 and 20 (sim-ulation and numerical results). The corrections discussed above give a much lower capacity for MGSIC-SM. In fact, using the simulation results, at an outage probability of 5 % MGSIC-SM only improves upon GSIC-SM by a maximum of four users over all group sizes. Considering the added complexity of the multi-cell cancellation technique this is not a significant increase. 5.2.4 GSIC-CM The numerical and simulation results for GSIC-CM, shown in Figure 5.10, match very well. When CM is employed, detection is based on 3 copies of the mobile user's signal. As we previously explained in the discussion of SUD-CM 62 Outage Probability for MGSIC-CM Group Size 1 (G=1) Outage Probability for MGSIC-CM Group Size 10 (G=t0) Outage Probability Outage Probability Outage Probability for MGSIC-CM Group Size 20 (G=20) - Numerical Results - Simulation Results Outage Probability Figure 5.11: Reverse link capacity of MGSIC-CM group sizes 1, 10 and 20 (simulation and numerical results). results, we can equate the combining of 3 different copies of the user's signal with averaging. Therefore, using C M we expect that the distribution of power used in detection is more even than in SM case. When the distribution of power used in detection is even, the noise as described in the SM case is not as significant. Therefore, we expect the GSIC-CM simulations results to agree well with the numerical results. 5.2.5 M G S I C - C M As shown in Figure 5.11, for MGSIC-CM there is a significant difference be-tween numerical and simulation results for all group sizes. As explained in 63 the previous section the use of C M produces a more even power distribution for signal detection, which reduces noise in the detection process. However, as discussed in Section 5.2.3 the non-identical power ranking between cells can introduce noise into the multi-cell cancellation process for small group sizes. Additionally, as discussed in Section 5.2.3, another factor affecting simulation and numerical results, is the theoretical approach to multi-cell cancellation. In the theoretical work for MGSIC-CM, the multi-cell cancellation is performed by reducing the portion of the inter-cell interference factor that corresponds to inter-cell interference generated by users in the current serving area. Inter-cell interference for MGSIC-CM is expressed as J i n n = f (Rs) + R% (KS)) Pjn » Rf(Ks)Pjn e . rftl 1 + R%(KS) ^ l + R^iKsY Our simulation allows users of the same rank in different cells to have different levels of received power at their assigned base station. As defined in this work (Nc = 3), MGSIC cancels interference from only 3 cells. If interference cancellation is averaging over only 3 cells the amount of interference cancelled in simulation may differ significantly from the amount predicted by theory. To verify this analysis, we will re-evaluate the numerical results by replacing ip in Eq. (5.5) with x- Because tp and x represent the portion of the signal remaining after cancellation, we will increase the value of x with respect to ip. Inter-cell interference for MGSIC-CM becomes = ^(xR%(KS) + R%(Ks))pjn N Rf{Ks)Pjn h 1 + RJ°N(KS) J=f+1l + R°°N(KsY We can now derive a new expression for received power PGin- The new expres-sion is identical to Eq. (4.25), however the variables 7* and /3j have changed and are now given by _ Ga(l+Rf0(Ks))-«(l-x)Rf0(Ks)+i><* 7 i ~ Gs(l+Rf°(Ks))+a _ a [ W + ( l - x ) f l f ° ( K s ) ] P i Gs(l+Rf°(Ks))+a • The plots shown in Figure 5.12 use a value of x equal to 1/3 dB (0.50118). Once again, the larger value for x ( a s compared with the smaller value of ip = l a 64 Outage Probability tor MGSIC-CM Group Size 1 (G=1) Outage Probability lor MGSIC-CM Group Size 10 (G=>10) 10"* 10"3 10~* 10"' 10° Outage Probability Figure 5.12: Reverse link capacity of MGSIC-CM group sizes 1, 10 and 20 (simulation and numerical results), with a = 5.1 dB for group size 1, x = 1/3.0 dB for all group sizes. dB (0.31623 when a = 5.0 dB) previously used), reflects the inaccuracy of the theoretical value of RfN(Ks). To account for added noise in the multi-cell cancellation process we set a equal to 5.1 dB for group size 1 only. The value of a equal to 5.1 dB is chosen to reflect noise in the multi-cell cancellation process only (i.e. less added noise than for MGSIC-SM). The numerical and simulation results given in Figure 5.12 show a much better agreement than those results shown in Figure 5.11. The corrections discussed above give a lower capacity for MGSIC-CM. Using simulation results, at an outage probability of 5 % MGSIC-CM only improves upon GSIC-CM by a maximum of 6 users over all group sizes. Once again, 65 considering the added complexity of the multi-cell cancellation technique this may not be a significant enough increase. 66 Chapter 6 Detection Delay and Hardware Complexity One of our primary motivations in undertaking the study of GSIC was to reduce detection delay. Another important issue blocking SIC schemes from adoption by service providers is hardware complexity. In this chapter, we will compare GSIC with the more standard SIC, and discuss the impact of increasing group size on detection delay time, hardware complexity and outage probability for each of our group cancellation schemes. In each case, we will discuss the viability of group cancellation, and possible group sizes for practical implementation. 6.1 Detection Delay Because GSIC allows a group of users of size G to be detected simultaneously, it is obvious that use of this technique will reduce detection delay by a factor approximately equal to 1/G. In order to truly evaluate the scheme we must, however, analyze the performance loss caused by increasing the number of users processed simultaneously. We will use the numerical results generated in Chapter 4 to compare the performance and detection delay for the four different GSIC techniques dis-67 GSIC-SM Capacity vs Normalized Detay Reductkjn lor Groups ol Size 1, 10, 20 -0- • Outage Probability 2% Outage Probability 3"X - 9 - Outage Probability 5"X — a — Outage Probability 7 * 0.3 0.4 0.5 0.6 0.7 0.8 Normalized Factor of Delay Reduction 0.9 GSIC-CM Capacity vs Normalized Delay Reduction lor Groups of Size 1, 10,20 - 0 - • Outage Probability 2 * Outage Probability 3 * - V - Outage Probability 5 * — g — Outage Probability 7% 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Normalized Factor ol Delay Reductttn 1 Figure 6.1: Normalized delay reduction and capacity for GSIC group sizes 1, 10 and 20. cussed in this work. It should be noted that simulation results indicated that small groups have reduced performance as compared to the numerical results, because the more realistic environment with imperfect power control affects smaller group sizes more than larger group sizes. Therefore, the comparisons that we are about to make for all techniques and all group sizes will actually reflect the greatest losses possible in capacity when group size is increased, or alternatively can be considered a worst case scenario for large group sizes. Figure 6.1 shows the normalized delay reduction factor and the number of users that GSIC-SM and GSIC-CM networks support for groups of size 1, 10 and 20. For each outage probability, the number of users supported for a group size of 20 is shown as the far-left point, for group size 10 the centre point, and for group size 1 the far-right point. The curves presented in Figure 6.1 are extrapolated from these points. The normalized delay reduction factor for a given outage probability is calculated using the following expression i-max number of users supported for G = I - I D(G = i) = ± i , ^ f n ' t6-1) max number of users supported tor G = 1 The plots in Figure 6.1 show that GSIC may be used without a large reduction in the number of supported users. Both GSIC-SM and GSIC-CM incur a maximum reduction of 3 mobile users when the group size is increased from 68 MGSIC-SM Capacity vs Normalized Delay Reduction (or Groups of Size 1,10,20 MGSIC-CM Capacity vs Normalized Delay Reduction for Groups of Size 1,10, 20 Normalized Factor of Delay Reduction Normalized Factor of Delay Reduction Figure 6.2: Normalized delay reduction and capacity for MGSIC group sizes 1, 10 and 20. 1 to 10. When the group size is increased from 1 to 20, a maximum of 6 mobile users are left unsupported. At the target outage probability of 5 %, the number of users that become unsupported is similar. Considering GSIC-SM at the target outage, when group size is increased from 1 to 10, and then to 20 the number of users that become unsupported are 2 and 6, respectively. Employing a group of size 1 a total of 85 users can be supported, therefore the reductions in supported users are 3.53 % and 7.06 % for groups of 10 and 20 respectively. Considering GSIC-CM, increasing group size from 1 to 10, 3 users become unsupported, and from 1 to 20, 6 users become unsupported. A total of 121 users can be supported by GSIC-CM with a group size of 1; therefore the.reductions in supported users are 2.48 % and 4.96 % for groups of size 10 and 20 respectively. Now considering MGSIC, in Chapter 5 we mentioned that simulation results showed that the gains in moving from GSIC to MGSIC were not as significant as predicted by the theory. However, we will use the numerical results to look at performance loss for MGSIC as group size is increased. The plots in Figure 6.2 show that the number of users that become unsupported as group size is increased is not large. Both MGSIC-SM and MGSIC-CM incur maximum of 5 additional unsupported mobile users when group size is increased from 69 1 to 10, and 8 users when group size is increased from 1 to 20. At the 5 % outage probability, MGSIC-SM experiences a reduction of 5 supported mobile users for an increase to group size 10, and 8 users for an increase to group size 20. Because MGSIC-SM with a group size of 1 can support 95 users the reductions in supported users are 5.26 % and 8.42 % for groups of size 10 and 20, respectively. At the target outage probability, MGSIC-CM has a reduction of 4 supported users for an increase to group size 10, and 3 users for an increase to group size 20. Considering that MGSIC with a group size of 1 can support 132 users, these values amount to a 3.03 % reduction in supported users for group size 10, and a 5.30 % reduction for group size 20. In all cases but MGSIC-SM, we can increase group size by 10, which means detection delay is reduced by a factor of approximately 0.1, and only forfeit up to 3.5 % (MGSIC-SM, 5.26 % ) of the supported users. The reduction of the number of supported users is slightly more significant for a group size 20, when detection delay is reduced by a factor of approximately 0.05, but the reduction in supported users is between 4.96 and 8.42 % of supported users. 6.2 Hardware Complexity J O ) rI IC filter J i ) 1 » IC filter ^ J ° ) rQ User 1 J D User 2 ^ 1 Symbol estimate Symbol estimate IC filter User N Symbol estimate Figure 6.3: Block diagram of pipelined SIC detection. The variables rf^ and rq are the in-phase and quadrature components of the received signal after i users have been cancelled. It is important for any implementation of an interference cancellation scheme to meet the existing requirements of the communication network in which it is 70 being placed. One important requirement is that the data rate is maintained. In order to meet this constraint for SIC, one possibility is to pipeline interfer-ence cancellation units, as shown in Figure 6.3 taken from [11]. Pipelining the interference cancellation units means that the number of interference cancella-tion units required in hardware is dependent on the number of users, a number that could get quite large. One possibility to limit the number of hardware components and detection delay time is to place a limit on the number of can-cellations performed, after which conventional detection is used [11,6]. Placing a limit on the number of cancellations reduces detection delay and minimizes the required hardware, but negatively affects performance. Assuming that de-tection decisions are based on the output of conventional correlators, we can calculate the hardware complexity of pipelined SIC (without a limit on can-cellation). Each interference cancellation unit shown in Figure 6.3 contains TV (the number of users) complex correlators. Thus, a total of TV2 correlators in total are required for this technique. Interference units for GSIC must also meet data rate requirements, and we also apply the pipelined arrangement. However, for GSIC we may make a detection decision about more than one user at a time. The receiver structure for pipeline GSIC is shown in Figure 6.4 taken from [7]. One set of complex correlators can make a detection decision about an entire group of G signals. The group of G mobile users is processed simultaneously, first by choosing the G strongest outputs of the correlator, then by re-spreading the signals and combining them, and finally by canceling the single resulting signal from the latest version of the received signal. By employing GSIC we can reduce the number of correlators to \^]N, or by a factor of approximately 1/G. We can conclude that by implementing GSIC we can actually reduce hardware complexity in comparison with a practical implementation of the standard SIC scheme. This conclusion was also reached in [7, 10]. 71 Bank of complex correlators LPF Signal at Baseband a\e-s W " 1 Select Max Z i ® am*9* Bank of complex correlators Signal at Baseband S Select Max Figure 6.4: Block diagram of Pipelined GSIC detection, group size 2 (G — 2). The variable a* represents the spreading sequence of the ith user, and the variable Zi represents the decision variable of the ith user, and finally fa represents the phase of the ith user. 72 Chapter 7 Conclusions In this work we have developed expressions for the outage probability of the group successive interference cancellation (GSIC) multi-user detection tech-nique. These expressions have been developed based on work presented in [12, 13, 14, 15]. We have derived expressions for the outage probability of GSIC using two types of diversity: selection macro-diversity (SM) and com-bining macro-diversity (CM). As defined in this work, using the concept of serving areas, C M is similar to soft-handoff. We have also derived expressions in both diversity cases for the outage probability of GSIC when it employs multi-cell cancellation (MGSIC). In total, we consider four cases of multi-user detection: GSIC-SM, GSIC-CM, MGSIC-SM, and MGSIC-CM. Because the expressions for outage probability are too complex to evaluate in closed form, we used numerical evaluation to obtain theoretical values of outage probability for the four cases that we considered. Our numerical results, with group size set equal to 1, showed that higher capacity was possible for these techniques than was previously indicated in [12, 13, 14, 15]. The lower values for capacity presented in [12, 13, 14, 15] are due to the use of a bound on the inter-cell interference factor. Simulation results confirmed our numerical results, once again showing that higher capacities than shown in [12, 13, 14, 15] were possible. However, simu-lation results also showed some discrepancies when compared with theoretical 73 data. These discrepancies have been attributed to the simulation environment, which did not use perfect power control and did not require identical power distribution in each cell. These factors had a larger impact on MGSIC de-tection techniques. In fact, the gains due to MGSIC as compared with GSIC were not significant in simulation. Thus, MGSIC is not as useful a technique as promised for increasing capacity. C M , however, showed a large improvement over SM in both the theoretical and simulation data. The four techniques were evaluated for 3 different group sizes; groups were of size 1, 10 and 20. Numerical and simulation results showed that capacity was not dramatically affected as group size was increased. On average the group size could be increased to 10 with a 3.5 % loss in capacity, and to group size 20 with a 7 % loss in capacity. Additionally, we discussed the reduction in detection delay, and hardware com-plexity resulting from the implementation of GSIC (as compared with SIC). Both hardware complexity (with respect to pipelined SIC), and detection de-lay can be reduced by a factor of approximately l/G with the use of GSIC. Considering all of the information presented in this work, we suggest that GSIC-SM or GSIC-CM.with groups of up to 10 are both promising multi-user detection techniques and that they deserve further study. 74 Appendix A Inter-cell Interference Factor The derivation of inter-cell interference factors given here was first presented in [14, 13, 12], they are reproduced here in concise form for the reader's con-venience. A . l Cumulative Probability Function of Path Loss The mobile users in the system are assumed to be uniformly distributed. It is also assumed that there is an equal number of users assigned to each base station, and this number is denoted as N. The resulting expression for the density of mobile users, p, can be written as p = N/Ac, where Ac represents the area of one hexagonal cell. In accordance with the system parameters presented in this work, and in [14, 13, 12] the path loss from a mobile user to the mth base station is expressed as PLm = DAm + LSFm = 10>log10 rm + ah + bhm + D. ( A . l ) Since each mobile user is minimizing its path loss among the Nc closest base stations, its path loss can be written as PL = min {PLm.}. (A.2) 1>J>NC 75 Combining Eqs. (A.l) and (A.2), and considering a mobile user assigned to the 0th base station at position (x,y), the expression for the probability that path loss is less than K dB becomes Pr{PL<K\(x,y)} = Pr {PL0 < K; PL0 < PLU% G [1, 2 , N c - 1] | (x, • K-Mp-ah bh0 + Mp - Mj , , = Pr{h0< ;hi> ,z G 1, 2 , . . . , Nc - 1 „ K — Mn—ah +oo > C t -oo -oo 1 v +oo e x p U2/2\ where Mt = lG>log 1 0 ri (x,y) + D and Q (z) = / W ; dg. Using Eq. (A.3) and the density of mobile users, the cumulative probability function of the path loss of a mobile user, F(K), can be calculated, and is given by F(K) = ^JjPr{PL<K\(x,y)}pdxdy So K-Mp-ah 2 +oo 6 — ~ Ac JJ J \[2~KG J \/27rcr S0 -oo NUQ(bh0 + ^~Ml) dhpdhdxdy. (AA) When the system is restricted such that a mobile user must have a path loss less that Ks dB in order to be served by the system, the density of mobile users becomes N '*«= A^FVCTY (A'5) Using the new expression for the density of mobile users given by (A.5), the path loss limited cumulative distribution function becomes _ K-M0-ah 2 +oo _jt4 — r — _ i f l _ . 1 rr r e 2^ r e * * 1 F k s { K ) = ACF (Ks) JJ J 72^  J T^c So —oo -oo " f f g ^ O + M Q - M ^ D H O D M X D Y ( A 6 ) 76 Finally, we can write an expression for the probability density function of Ks limited path loss by taking the derivative of Eq. (A.6), given by dFKs (K) dK K-Mn-ah • — - ,?~. 1 r r r e 2 ^ e ACF (Ks) JJ J V2^a y/2^ba So —oo ^ ^ / K - ah- MA „ , , II Q y ^ J dhdxdy. (A.7) i = l As all cells in the network are assumed to be identical, analysis is performed for the 0th base station. The work is divided into two sections, interference caused by users in serving area S 0 (the serving area of the 0th base station) and interference caused by users outside of the serving area So, this area is denoted as So. It is important to note that users in So may be assigned to the 0 t h base station, in which case the interference they generate is not inter-cell, but intra-cell interference. The analysis begins with the inter-cell interference originating from So, which is followed by the inter-cell interference originating from SQ. Combining these two terms produces the final value of the inter-cell interference factor, {R{N ,j G A.2 Inter-cell Interference Originating from So Using Eqs. (A.l) and (A.2), the inter-cell interference at the 0th base station, denoted as (x,y), caused by a mobile user located at (x,y) € So, but not assigned to the 0th base station, whose path loss is less than K dB can be expressed as N c - l I?°(x,y) = £ S{e^PL--pu);PLm<PLhj e[0,Nc-l], m=l j^m-PLm<K\(x,y)} N ^ ™ <• i .Mh—hny i. ^K-Mm-ah_L ^bhm + Mm-Mj Nc~l ( K — M — nh m=l I 77 j e[0,Nc-l],j^m} • 2 K-Mm-ah (hm-bga2)2 b 2 0 2 a 2 TeJ^L f e 2°'2 * fbhm-Mm-M0 + b2Pa2\ t i m J J sfao ba ' T " ~ 1 —oo —oo » \ / II <?( 7 J-]dhmdh, (A.8) where i?™ = r m (x,y) /r 0 (x, y). Using (A.8), the inter-cell interference at the 0th base station produced by all mobile users within serving area So, who are not assigned to the 0th base station and whose path loss is less than K dB can be written as IsN°-Ks(K) = JJl*>(x,y)pKsdxdy So h2 K-Mm-ah (hm-bHv2)1 e JJ h i m J ^ a J V^a W I So — ~ ° ° ~ 6CT j=l,j^m \ / Taking the derivative of (A.9) with respect to K, produces the total inter-cell interference at the 0th base station produced by all mobile users who are within serving area So, but who are not assigned to the 0th base station. Additionally this inter-cell interference is due to users whose path loss is equal to K dB. This inter-cell interference is given by the following * > - K s t t « _ **frKa (*) dK 2 (K-Mm-ah-b2/3a2) fe1 Te~^e ^ n(K-ah-Ma + b2l)a'1 = e^'Jj £ JC / ^ Q c_ m=l _„ ^/2~KO- y/2nba \ ba So -oo  v Nf{ Q (K ^ M A d M x d y , ( A . 1 0 ) 78 A.3 Inter-cell Interference Originating from S{ o Similarly, for mobile users who are located outside of the 0th base station serving area, at (x,y) € So and whose path loss is less than K dB, the inter-cell interference, denoted as i /° (x,y), at the 0th base station is given by Nc lf°(x,y) = J2£{e^PL--pLo);PLm<PLj,je[0,Nc]J^m-PLm<K\(x,y)} m—1 £ R"m£ h m < K-M -ah. < bhm + M m - M j m = l I O f ) je[0,Nc],j^m} Nc-l +°° ~ 4 K-M?-ah _ £ m -m = i J„ vZira J Iff o(6"" + t m " M j " ) ^ (A.ii) = 1.7^771 \ / /27TO" ^g1 rfbhm + Mm-Mi j=i,j¥=m Using (A. 11), the inter-cell interference at the 0th base station produced by all mobile users in the area So, whose path loss is less than K dB can be written as ISN°-Ks (K) = jj if0 (x, y) pKs dxdy So 2 K-Mm-ah (hm-b0<x2)2 Nc + 0 0 _±_ b _\ 1_ /T TTI—1 rv-! T —fY-i e /27R7 So n Q ( b h - + " ; - M i ) d h m d h . (A.i2) Finally, by taking the derivative of (A. 12) with respect to K, we arrive at the total inter-cell interference at the 0th base station produced by all mobile users who are within area So. Additionally, this inter-cell interference is due to user whose path loss is equal to K dB and is given by & - « s m - d I » ' K S W dK 2 (K-Mm-ah-b2Po2Y 2 rr _ . . r e e ^ /V" V /?" f e e JJ ^ m J sfao- V^ba e So T n = L -°° 79 II Q(K f Mj)PKsdhdxdy. (A.13) A . 4 Individual Inter-cell Interference Factors Using (A.6), the probability that a mobile user with a path loss equal to K dB has the ith minimum path loss among the N mobile users assigned to the same base station can be written as Pr.w (K) = CN-\FKS (K) I1 ~  FKs (K)]N-\ (A.14) Now, using (A. 10) and (A.14), the individual inter-cell interference factor due to all mobile users who are within So, but not assigned to the 0th base station, and whose path loss has the ith smallest value among the N users assigned to their base station can be written as Ks R?N (Ks) = J iSN°-Ks (K) Pr*f (K) dK. (A.15) —o  Similarly, the individual inter-cell interference factor due to all mobile users who are within the area So, whose path loss has the ith smallest value among the N users assigned to their base station can be written as Ks (Ks) = J if?'*3 (K) P i f t (K) dK. (A. 16) —oo To complete the derivation, the total interference factor due to all mobile users that have the ith smallest path loss among the N mobile users assigned to their base station- can be expressed as RieN(Ks) = R^(Ks) + R^(Ks). (A.17) 80 Appendix B Power Reduction Factors The derivation of the power reduction factor given here was first presented in [14, 13, 12], it is reproduced here in concise form for the reader's convenience. Combining signals received at the Nc base stations surrounding a mobile user allows the mobile user to transmit its signal using less power. The average power reduction of the (i, n) user can be expressed as where {TW {Ks) ,i £ [l.A7]} are referred to as power reduction factors. The system is assumed to be symmetric, and therefore without loss of generality the authors of [12, 13] consider the power reduction factors of the mobile users assigned to the 0th base station. For a mobile user with a path loss less than K dB, who is assigned to the 0th base station, and whose location is given by (x,y), its power reduction ratio, Qr (x,y), can be expressed as Qr(x,y)= £ £{e^PLo-pL-)-PL0<PLi,j£[l,Nc-\hPU<K\(x,y)}. Because the cellular system is assumed to consist of identical hexagonal cells, if two base stations have overlapping serving areas, as shown in Figure B . l , they are assumed to be symmetrical within the overlapping serving area. Nc-l ' ( , i + £ £ L ' 3 ( P L i - - p L = 1 + TIN(KS), (B.l) Nc-l (B.2) 81 - / y \ / \ / S -„ / \ \ / T >--^ • Figure B . l : Overlapping serving areas, when Nc = 4 Using this assumption, if a mobile user exists at position (x, y) and is assigned to the 0th base station, then there exists another mobile user symmetrically located at position (xm, ym) assigned to the mth base station. These two users satisfy the following relation £{e(3(PLB-PLm). P L q < p L j j e [ h N c - 1 ] ; P L q < K \ (x,y)} = £{SPL"-pLo); PLm < PLj:j G [0, Nc - l j , j ^ m; F L m < # | ( x m , y m ) } . (B.3) Using Eq. (B.3), the expression for the power reduction ratio given in Eq. (B.2), can be re-written as J V b - l Qr(x,y) = J2 S{SPL™-Pu>h PLm < PLhj € [0,NC - 1 ] , m=l j f m; PLm < K | (xm, ym)}. (B.4) Using Eq. (B.4), the total power reduction ratio for all mobile users who are assigned to the 0th base station and whose path loss is less than K dB is given by Q%S(K) = IJQr(x,y)pKsdxdy So Nc-1 r f = E JJ n^^-^^PLm^PL^je^Nc-l], m = 1 So 82 j ^ m; PLm < K \ (xm, ym)}pKs dxdy. (B.5) If Eq. (B.5) is compared with the equation for I^°~Ks (K) given in Appendix A (Eq. (A.9)), it is obvious that Q^s (K) = IsN°~Ks (K). Using this equality, the total power reduction ratio produced by mobile users assigned to the 0th base station, and whose path losses are equal to K dB is given by 4 s (K) = ^gH> = ^ i K ) = $-Ks (*) • (B.6) Using Eq. (B.6) and the probability of a user with a path loss of K dB, having the ith smallest path loss among A?' users assigned to the same base station, P^f (K) given in Appendix A (Eq. (A.14)), the power reduction factor for the (i,0)th user, is given by KS TiN (Ks) = J qNs (K) P r * s (K) dK —oo Ks = j isN°'Ks (K) Pr*f (K) dK = (Ks). (B.7) —OO 83 Bibliography [1] J.G. Andrews and T.H.Y. Meng. Transmit power and other-cell inter-ference reduction via successive interference cancellation with imperfect channel estimation. In IEEE International Conference on Communica-tions, pages 1211-1215, Helsinki, Finland, June 2001. [2] J.G. Andrews and T.H.Y. Meng. Optimum power control for successive interference cancellation with imperfect channel estimation. IEEE Trans-actions on Wireless Communications, 2:375-383, March 2003. [3] D. Warrier and U. Madhow. On the capacity of cellular C D M A with suc-cessive decoding and controlled power disparities. In 48th IEEE Vehicular Technology Conference, volume 3, pages 1873-1877, May 1998. [4] P. Patel and J. Holtzman. Analysis of a simple successive interference cancellation scheme in a D S / C D M A system. IEEE Journal on Selected Areas in Communications, 12:796-807, June 1994. [5] J.G. Andrews. Interference cancellation for cellular systems: A contempo-rary overview. Submitted to IEEE Wireless Communications Magazine, May 2004. [6] K.I. Pedersen, T.E. Kolding, I. Seskar, and J .M. Holtzman. Practical implementation of successive interference cancellation in D S / C D M A sys-tems. In Proceedings of the 1996 Universal Personal Communications Conference, pages 321-325, September 1996. 84 [7] F. van der Wijk, G.M.J . Janssen, and R. Prasad. Groupwise successive interference cancellation in a D S / C D M A system. In Proceedings of the IEEE International Symposium on Indoor and Mobile Radio Communi-cations, pages 742-746, Toronto, Canada, July 1995. [8] B.C.K. Poon, C Y . Tsui, and R.S. Cheng. Composite interference can-cellation scheme for C D M A systems. In Proceedings of the IEEE Global Telecommunications Conference, volume 1, pages 1-5, November 2000. [9] S. Sun, L .K. Rasmussen, H. Sugimoto, and T.J. Lim. A hybrid interference canceller in CDMA. In Proceedings of the IEEE International Symposium on Spread Spectrum Technologies and Applications, pages 150-154, Sun City, South Africa, September 1998. [10] C S . Wijting, T. Ojanpera, M.J . Juntti, K . Kansanen, and R. Prasad. Groupwise serial multiuser detectors for multirate DS-CDMA. In 49th IEEE Vehicle Technology Conference, pages 2510-2514, Houston, USA, May 1999. [11] I. Seskar, K.I. Pedersen, T.E. Kolding, and J .M. Holtzman. Implementa-tion aspects for successive interference cancellation in D S / C D M A systems. Baltzer/ACM Wireless Networks, 4:447-452, 1998. [12] H. Nie. Interference Cancellation and Macro-diversity for Wideband CDMA Systems Employing Software Radio Base Stations. PhD thesis, Department of Electrical and Computer Engineering, University of British Columbia, 2003. [13] H. Nie and P.T. Mathiopoulos. Theoretical analysis of reverse link capac-ity for cellular C D M A systems employing successive interference cancel-lation. Presented in part at IEEE International Conference on Telecom-munications, Beijing, China, April 2003. 85 [14] H. Nie and P.T. Mathiopoulos. Reverse link capacity analysis for cellu-lar C D M A systems employing combining macrodiversity. In Proceedings of International Conference on Communication Technologies 2003, vol-ume 2, pages 774-777, April 2003. [15] H. Nie and P.T. Mathiopoulos. Reverse link inter-cell interference analysis for cellular C D M A systems with controlled power disparities. In Proceed-ings of International Conference on Communication Technologies 2003, pages 788-792, April 2003. [16] K.S. Gilhousen, I.M. Jacobs, R. Padovani, A . J . Viterbi, L .A. Weaver Jr., and C E . Wheatley III. On the capacity of a cellular C D M A system. IEEE Transactions on Vehicular Technology, 40:303-312, May 1991. [17] K. Tachikawa. A perspective on the evolution of mobile communications. IEEE Communications Magazine, pages 66-73, October 2003. [18] D. L i . The perspectives of a large area synchronous C D M A technology for the fourth-generation mobile radio. IEEE Communications Magazine, pages 114-118, March 2003. [19] S.Y. Hui and K . H . Yeung. Challenges in the migration to 4G mobile systems. IEEE Communications Magazine, pages 54-59, December 2003. [20] S. Verdu. Minimum probability of error for asynchronous Gaussian multiple-access channels. IEEE Transactions on Information Theory, IT-32:85-96, Jan 1986. [21] S. Moshavi. Multi-user detection for DS-CDMA communications. IEEE Communications Magazine, pages 124-136, October 1996. [22] A . J . Viterbi, A . M . Viterbi, K.S. Gilhousen, and E. Zehavi. Soft handoff extends C D M A coverage and increases reverse link capacity. IEEE Jour-nal on Selected Areas in Communications, 12:1281-1288, October 1994. 86 [23] J.G. Andrews and T.H. Meng. Multiple access interference cancellation in fading multipath channels: Progress and limitations. In IEEE Vehicular Technology Conference, pages 1804-1808, Rhodes, Greece, May 2001. [24] A . J . Viterbi, A . M . Viterbi, and E. Zehavi. Other-cell interference in cel-lular power-controlled C D M A . IEEE Transactions on Communications, 42:1501-1504, February/March/April 1994. [25] P. Hatrack and J .M. Holtzman. Reduction of other-cell interference with integrated interference cancellation/power control. In 7^<t/j IEEE Vehicle Technology Conference, volume 3, pages 1842-1846, May 1997. [26] R. Akl and A. Parvez. Impact of interference model on capacity in C D M A cellular networks. Accepted for presentation at the 8th World Multi-Conference on Systematics Cybernetics and Informatics, July 2004. [27] D.W. Matolak and A. Thakur. Outside cell dynamics in cellular CDMA. In Proceedings of the 35th Southeastern Symposium, pages 148-152, March 2003. [28] S. Jung and H.M. Kim. An improved hybrid multiuser interference can-cellation scheme based on the clustering algorithm. In Proceedings of the IEEE Vehicular Technology Conference, volume 2, pages 683-687, Octo-ber 2001. [29] R. Malik, V . K . Dubey, and B. McGuffin. A hybrid interference canceller for C D M A systems in Rayleigh fading channels. In Proceedings of the IEEE Vehicular Technology Conference, volume 2, pages 1523-1527, May 2001. [30] A . L . Johansson and L .K. Rasmussen. Linear group-wise successive inter-ference cancellation in CDMA. In Proceedings of the IEEE International Symposium on Spread Spectrum Techniques and Applications, pages 121-126, Sun City, South Africa, Sept 1998. 87 [31] M. Wang, J. Lu, and Z. Zhou. A novel interference cancellation receiver in VSL-CDMA systems. In Proceedings of the 17th International Conference on Advanced Information Networking and Applications, pages 164-167, March 2003. [32] J.L Gorricho, A. Rojas, and J. Paradells. Power control at the combiner output to maximise the uplink capacity on a cellular spread spectrum system. IEEE Communications Letters, 2:273-275, October 1998. [33] S.V. Hanly. Capacity and power control in spread spectrum macrodiver-sity radio networks. IEEE Transactions on Communications, 44:247-256, February 1996. [34] The cdma2000 ITU-R RTT candidate submission (0.18), 2000. [35] P. Chaudhury. The 3GPP proposal for IMT-2000. IEEE Communications Magazine, pages 72-81, December 1999. [36] G.E. Corazza, G.D. Maio, and F. Vatalaro. CDMA cellular systems per-formance with fading, shadowing, and imperfect power control. IEEE Transactions on Vehicular Technology, 47:450-459, May 1998. [37] H. Nie and P.T. Mathiopoulos. Reverse link capacity analysis for cel-lular CDMA systems employing successive interference cancellation. In Proceedings of International Conference on Communication Technologies 2003, pages 770-773, April 2003. [38] A.J. Viterbi. CDMA: Principle of Spread Spectrum Communication. Ad-dison Wesley, Reading, MA, 1995. [39] H. Nie and P.T. Mathiopoulos. A new software radio base distributed base station architecture and its application to 3G UMTS employing sig-nal combining techniques. In Proceedings of IEEE Vehicular Technology Conference 2002, pages 240-244, May 2002. 88 [40] W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery. Numer-ical Recipes in C: The Art of Scientific Computing. Cambridge University Press, New York, 1992. 89 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0065404/manifest

Comment

Related Items