Multiuser Detection for Out-of-Cell Cochannel Interference Mitigation in the IS 95 Downlink

Transcription

1 1 Mutiuser Detection for Out-of-Ce Cochanne Interference Mitigation in the IS 95 Downink D. Richard Brown III, H. Vincent Poor, Sergio Verdú, and C. Richard Johnson, Jr. This research was supported in part by NSF grants ECS , ECS , EEC , and Appied Signa Technoogy. D.R. Brown III is with the Department of Eectrica and Computer Engineering, Worcester Poytechnic Institute, Worcester, MA 01609, USA. H.V. Poor and S. Verdú are with the Department of Eectrica Engineering, Princeton University, Princeton, NJ USA. C.R. Johnson, Jr. is with the Schoo of Eectrica Engineering, Corne University, Ithaca, NY USA. September 19, 2001 DRAFT

2 Abstract This paper considers the appication of mutiuser detection techniques to improve the quaity of downink reception in a muti-ce IS 95 digita ceuar communication system. In order to understand the reative performance of suboptimum mutiuser detectors incuding the matched fiter detector, optimum mutiuser detection in the context of the IS 95 downink is first considered. A reduced compexity optimum detector that takes advantage of the structura properties of the IS 95 downink and exhibits exponentiay ower compexity than the brute-force optimum detector is deveoped. The Group Parae Interference Canceation (GPIC) detector, a suboptimum, ow-compexity mutiuser detector that aso expoits the structure of the IS 95 downink is then deveoped. Simuation evidence is presented that suggests that the performance of the GPIC detector may be near-optimum in severa cases. The GPIC detector is aso tested on a snapshot of on-air data measured with an omnidirectiona antenna in an active IS 95 system and is shown to be effective for extracting weak downink transmissions from strong out-of-ce cochanne interference. The resuts of this paper suggest that the GPIC detector offers the most performance gain in scenarios where weak downink signas are corrupted by strong out-of-ce cochanne interference. I. Introduction An important miestone in the deveopment of persona wireess communication systems occurred in the eary 1990 s when Quacomm introduced a new digita ceuar communication system based on Code Division Mutipe Access (CDMA) technoogy. The proposed ceuar system offered severa advantages over first generation anaog ceuar systems incuding increased capacity and reiabiity as we as improved sound quaity and battery ife. Eary trias of this new ceuar system proved to be quite successfu and, in 1993, the detais of the system were pubished by the Teecommunications Industry Association as the IS 95A standard [1]. Despite the we documented performance benefits of mutiuser detection in the iterature prior to 1993, the IS 95 ceuar standard was designed such that adequate performance coud be achieved by a downink receiver (typicay a mobie handset) using conventiona singe-user matched fiter detection with coherent mutipath combining. The choice of matched fiter detection for the IS 95 downink resuted in the need for strict, cosed-oop power contro on both the upink and downink in order to avoid near-far probems (cf. [2]). One reason for this approach is that, unike power contro, the majority of the mutiuser detectors proposed in the iterature have been regarded as too compex for cost-effective impementation in IS 95 downink receivers. Despite the exponentia perfor-

3 mance improvements in microprocessors and DSPs over the ast decade, these constraints have continued to outweigh the potentia performance benefits of mutiuser detection for the IS 95 downink. In this paper we attempt to bridge some of the gap between IS 95 and mutiuser detection. Toward that goa, severa authors have studied the probem of improving the performance of IS-95 and third generation Wideband-CDMA downink reception in a singe-ce environment. In [3] [12] the authors observe that the orthogonaity of the user transmissions within a particuar ce is destroyed by mutipe paths in the propagation channe between the base station and the IS 95 downink receiver. The authors propose receivers that a share the common feature of a inear equaizer front-end that cances the effects of the mutipath propagation channe and restores the orthogonaity of the users. This approach effectivey eiminates the in-ce mutiuser interference and aows the conventiona matched fiter detector to be used. In [13], the authors propose and compare severa agorithms appicabe to the IS 95 downink for mutipath channe estimation. In [14], [15], the authors deveoped a noninear mutipath canceer to cance the in-ce mutiuser interference caused by mutipath repicas of the base station s piot signa. Our approach here differs from the prior approaches in that we investigate mutiuser detection for the IS 95 downink in a muti-ce environment. Mutiuser detection in a muti-ce environment was considered recenty for the IS 95 upink in [16], [17]. In this paper we consider receivers that mitigate the effects of the out-of-ce cochanne interference from neighboring base stations in the IS 95 downink. To estabish a performance benchmark, we first examine optimum detection for the IS 95 downink and deveop a reduced compexity optimum detector that expoits the structure of the IS 95 downink. We then propose the Group Parae Interference Canceation (GPIC) detector, a suboptimum, ow-compexity mutiuser detector that aso expoits the structure of the IS 95 downink. The resuts of this paper suggest that mutiuser detection may provide modest performance improvements over the conventiona matched fiter detector in scenarios where a strong desired signa is corrupted by weak out-of-ce cochanne interference. On the other hand, our resuts suggest that mutiuser detection may offer significant performance

4 improvements in conditions where an IS 95 downink receiver is detecting a weak desired signa in the presence of strong out-of-ce cochanne interference. Athough this scenario woud be unusua for a subscribing user in an IS 95 ceuar system, the practica impications of our resuts incude: Nonsubscribing users (e.g. eavesdroppers or test/diagnostic receivers) which do not have the benefit of power contro may wish to extract a weak desired signa from strong out-of-ce cochanne interference. Mutiuser detection receivers tend to offer superior performance in these cases. Subscribing users with mutiuser detectors require ess transmit power from their base station to maintain an equa quaity of service. This good neighbor effect eads to a reduced eve of cochanne interference induced on other out-of-ce users in the system. This baance of this paper is organized as foows. In Section II we deveop a concise mode with mid simpifying assumptions for the IS 95 downink that incudes the effects of the time and phase asynchronous, nonorthogona, and non-cycostationary transmissions of a M base station communication system. In Section III we use this mode to understand optimum mutiuser detection in the context of the IS 95 downink. Athough the optimum detector is often too compex for impementation in reaistic systems, its roe is sti important in order to determine the reative performance of suboptimum mutiuser detectors. In Section IV we show that the structure of the IS 95 downink aows the optimum detector to be posed in a computationay efficient form with compexity exponentiay ess than a brute-force impementation. In Section V we deveop a computationay efficient noninear mutiuser detector for the IS 95 downink caed the Group Parae Interference Canceation (GPIC) detector. The GPIC detector is derived from examination of properties of the reduced compexity optimum detector and aso expoits the structure in the IS 95 downink. In Section VI we examine the performance of the GPIC detector reative to the conventiona matched fiter and optimum detectors via simuation and show that the GPIC detector exhibits near-optimum performance in the cases examined and provides the argest benefit when the desired signa is received in the presence of strong out-of-ce cochanne interference. Finay, in Section VII we appy the GPIC detector to a snapshot

5 of on-air data from an active IS 95 system and present resuts that suggest that GPIC detection offers significant performance improvements when extracting weak signas in the presence of severe out-of-ce cochanne interference. II. IS 95 Downink System Mode Figure 1 shows a mode of a singe IS 95 base station downink transmitter. This mode is simpified in the sense that the scrambing and channe encoding operations specified by the IS 95 standard prior to the channeization bock in Figure 1 are not shown. An IS 95 downink receiver typicay consists of four fundamenta stages: mutipath timing and phase estimation (via the downink piot), coded symbo detection (matched fiter with mutipath combining), decoding (convoutiona and repetition), and descrambing. Since this paper focuses on the probem of improving the performance of the detection stage, we consider the portion of the IS 95 downink transmitter inside the coders as shown in Figure 1. piot:m a (m,0) Wash Code {b (m,1) } a (m,1) Wash Code.. PN-Code Puse Shaping z m (t) {b (m,km) } a (m,k 1 ) Wash Code Channeizer Power Contro Fig. 1. Singe base station IS 95 downink baseband transmitter mode. We denote m as the base station index and K m as the number of data streams simutaneousy transmitted by the m th base station, not incuding the piot transmission. Note

6 that K m is typicay greater than the actua number of physica users in the ce since the IS 95 standard specifies that each base station must transmit additiona data streams for ca setup, paging, and overhead information. For the purposes of this paper, we wi henceforth refer to each of these data streams as a user even if the data stream is an overhead channe and not actuay aocated to a particuar user in the ce. The detais of Figure 1 as specified by the IS 95 standard may be summarized as foows: Channeizer: Orthogonaizes the user transmissions by assigning a unique ength-64 Wash code to each user and spreads the input symbos with this code. Each user s Wash code remains fixed for the duration of their connection. The Wash-0 code is aways assigned to the base station s piot signa which transmits a constant stream of binary symbos equa to +1. The remaining 63 Wash codes are assigned as needed to the users in the ce as we as to overhead and paging channes. Power Contro: Sets the gain on each user s transmission to provide a minimum acceptabe transmission quaity in order to avoid generating excessive cochanne interference in neighboring ces. PN-Code: Mutipies the chip-rate aggregate base station data stream by a compex pseudonoise (PN) code in order to cause the cochanne interference observed by the users in neighboring ces to appear noiseike and random [18, pp. 11]. Each base station uses the same PN-code but is distinguished by a unique, fixed PN-phase. The PN-code has eements from the set {1+j, 1 j, 1+j, 1 j} and has a period of 2 15 chips. Puse Shaping: Specified in the IS 95 standard. Note that the tota spreading gain on the coded symbos in the IS 95 downink is 64 and that a spreading occurs in the channeizer bock. The PN-code does not provide any additiona spreading. Since the IS 95 standard specifies universa frequency reuse for a base stations in a ceuar system, it is reasonabe to mode the downink receiver s observation as the sum of transmissions from M base stations and additive channe noise as shown in Figure 2. Each base station s aggregate transmission passes through an individua propagation channe

7 that accounts for the effects of mutipath, deay, and attenuation. The channe noise is modeed as an additive, white, compex Gaussian random process denoted by σw(t) where E(w(t)) = 0 and E(Re(w(t)) 2 )=E(Im(w(t)) 2 )=1/2. The rea and imaginary parts are uncorreated and aso assumed to be independent of the base station transmissions. z 1 (t) Channe 1 z 2 (t) Channe 2 σw (t). r(t) z M (t) Channe M Fig. 2. Baseband IS 95 downink received signa mode. We define the tota number of users in the system as K = M m=1 K m. To faciitate the anaytica deveopment in the foowing sections, we aso make the foowing simpifying assumptions which may be reaxed or eiminated at the expense of greater notationa compexity: We ignore the soft-handoff feature of IS 95 where two base stations may be transmitting identica bit streams to a singe user. We assume the user popuation remains fixed over the receiver s observation interva. This impies that users do not enter or eave the system, users are not handed off between ces, and that voice activity switching does not occur during the observation interva. We ignore base station antenna sectorization. Indexing the users by a two dimensiona index (base station, user number), we denote the (m, k) th user s positive rea ampitude and coded binary symbo at symbo index as a (m,k) and b (m,k) respectivey. We denote the unit-energy normaized combined impuse response of the (m, k) th user s channeization code, PN-code, baseband puse shaping, and propagation channe at symbo index as s (m,k) (t). Note that s (m,k) (t) incudes any inherent

8 propagation deay and asynchronicity between base stations and is assumed to be FIR. We aso denote φ m as the received phase of the transmission from the m th base station. The baseband signa observed at the downink receiver may then be written as M L [ ] K m r(t) = e jφm a (m,0) s (m,0) (t T )+ b (m,k) a (m,k) s (m,k) (t T ) + σw(t). m=1 = L where we have separated the terms corresponding to the non-data-bearing piots with the superscript notation (m, 0). k=1 In order to represent the observation r(t) compacty, we estabish the foowing vector notation. If x (m,k) represents a (possiby compex) scaar quantity corresponding to the (m, k) th user at symbo index, we can construct the vectors x [m] = [ ] x (m,1),...,x (m,km), [ ] x [m] = x [m] L,...,x[m] L, and x = [ x [1],...,x [M] ]. The superscripts x, x and x H denote transpose, compex conjugate, and compex conjugate transpose, respectivey. Define a and b according to this notation and define the vector of signature waveforms as s [m] (t T ) = [ s (m,1) (t T ),...,s (m,km) (t T ) ], [ s [m] (t) = s [m] L (t + LT ),...,s[m] L (t LT )], and s(t) = [ s [1] (t),...,s [M] (t) ]. Finay, define ( [e jφ A = diag 1 a [1],...,e jφ M a [M] ] ) as the K(2L +1) K(2L + 1) dimensiona diagona matrix of user ampitudes mutipied by the appropriate base station transmission phases. We can then write the continuous time observation as r(t) = M L e jφm a (m,0) s (m,0) (t T ) m=1 } = L {{ } piots = p(t)+s (t)ab + σw(t) + s (t)ab }{{} users + σw(t) }{{} AW GN (1)

9 where the piots are denoted as p(t) for notationa convenience. III. Optimum Detection In this section we examine optimum (joint maximum ikeihood) detection in the context of the previousy deveoped IS 95 downink system mode. In a singe-ce scenario with singe-path channes, an IS 95 downink receiver observes the sum of K orthogonay moduated signas in the presence of independent AWGN. It is easy to show that the optimum detector is equivaent to the conventiona singe-user matched fiter detector in this case. In this paper, however, we consider the muti-ce scenario where an IS 95 downink receiver observes nonorthogona out-of-ce cochanne interference and the optimum detector is not the matched fiter detector. We assume that the receiver is abe to acquire the piot (and hence the PN-phase) of each base station m {1,...,M} via correation with the known periodic PN-code of ength This then aows the receiver to estimate the impuse response of the propagation channe and transmission phases of each base station. For each base station, the receiver can then construct a bank of 63 matched fiters, one matched fiter for each of the non-piot Wash codes, in order to determine which users are active in each ce. Since the receiver now knows the Wash codes of the active users, the phase of the PN-code, the propagation channes, and the baseband puse-shaping, we can construct the set of s (m,k) (t) for a users in the muti-ce system. Finay, ampitude estimates are generated for each user and the piots (cf. [19]). For the purposes of the remaining anaytica deveopment, we assume that a of these estimates are perfect and that the ony unknowns in (1) are b and σw(t). Let I represent a compact interva in time containing the support of r(t) and et U represent the set of cardinaity 2 K(2L+1) containing a admissibe binary symbo vectors of ength K(2L + 1). Then the jointy optimum symbo estimates [20] are given by ˆb OPT = arg max ( exp 1σ ) r(t) p(t) s (t)au 2 dt. u U 2 I Manipuation of the term inside the exponent yieds the expression for jointy optimum IS 95 downink symbo estimates as ˆb OPT = arg max u U 2Re[u A H (y p)] u A H RAu }{{} Ω(u)

10 where y = I s (t)r(t) dt represents the K(2L + 1)-vector of matched fiter outputs, p = I s (t)p(t) dt represents the K(2L+1)-vector of matched fiter outputs for the piot portion of the received signa, and R = I s (t)s (t) dt represents the K(2L +1) K(2L +1) dimensiona user signature correation matrix. The brute-force soution to the probem of computing the jointy optimum symbo estimates requires the exhaustive computation of Ω(u) over the set of a 2 K(2L+1) hypotheses u U to find the maximum. IV. Reduced Compexity Optimum Detection In this section we take advantage of the structure of the IS 95 downink in order to propose an optimum detector that exhibits significanty ess compexity than the bruteforce approach. The intuitive idea behind the reduced compexity optimum detector is to use the fact that the K m + 1 synchronous user pus piot transmissions from base station m are mutuay orthogona at every symbo index if the propagation channe from the m th base station to the receiver is singe-path. This wi aow us to decoupe the decisions of one base station s users to achieve the desired compexity reduction whie retaining optimaity. This idea can aso be appied in the mutipath channe case but since users within a ce are no onger orthogona there wi be some oss of optimaity. Note that even if the orthogonaity between the users within a particuar ce is restored using the equaization techniques described in [3], [4], [5], [6], [7], [8], [9], [10], [11], the resuting matched fiter bank outputs wi contain noise terms that are correated across the users. Hence, the ideas described in this section may aso be appied to an IS 95 downink receiver with an equaizer front-end but there wi be some oss of optimaity. To deveop the reduced compexity optimum detector, we first observe that the signature correation matrix exhibits the structure R = s [1] (t) [ ]. s [1] (t) s [M] (t) dt = s [M] (t) I R [1,1]... R [1,M]..... R [M,1]... R [M,M] where R [m,m ] has dimension K m (2L +1) K m (2L + 1). The submatrices R [m,m ] have the

11 structure R [m,m ] = R [m,m ] L, L... R[m,m ] L,L..... R [m,m ] L, L... R [m,m ] L,L where R [m,m ], = s [m] I (t)s [m ] (t) dt = R [m,m]h,. At this point we require the propagation channes to be singe-path in order to proceed with the compexity reduction. This assumption, combined with the facts that 1. the IS 95 puse shaping fiters approximatey satisfy the Nyquist puse criterion and 2. each base station assigns orthonorma signature waveforms to the set of users in its ce, impies that the downink transmissions in each ce do not interfere with the other downink transmissions in the same ce and that the downink transmissions in each ce are received without any intersymbo interference. In this case, the IS 95 downink signature correation matrix exhibits two specia properties: 1. The ack of intersymbo interference impies that R [m,m], = 0 for. 2. The orthonorma signature sequences of a in-ce users of each base-station at symbo index impies that R [m,m], = I. The combination of these two properties impies that R [m,m] = I for m =1,...,M. Let H = A H RA and note that since R is a Hermitian matrix then H is aso Hermitian. Moreover, since A is diagona, H shares the same IS 95 structure properties as R except that H [m,m] = A [m,m]h A [m,m] (2) It turns out that this difference wi not matter in the maximization of Ω(u). Using our previousy deveoped notation, we can write Ω(u) = 2Re [ u A H (y p) ] u Hu. (3)

12 Since A is diagona and u is rea, we can isoate the symbos from the first 1 base station to write 2Re[u A H (y p)] = u [1] 2Re [ A [1]H (y [1] p [1] ) ] + ū 2Re [ Ā H (ȳ p) ] (4) where vectors with an overbar are (K K 1 )(2L +1) 1 dimensiona with eements from a base stations except m = 1 and matrices with an overbar are (K K 1 )(2L +1) (K K 1 )(2L + 1) dimensiona with corresponding eements. The quadratic term in (3) may be rewritten as M M u Hu = u [m] H [m,m ] u [m ]. m=1 m =1 The binary nature of u and (2) impy that u [m] H [m,m] u [m] = 1 A [m,m]h A [m,m] 1 = α m where α m is a rea positive constant that does not depend on u. Denotingα = M m=1 α m, wecanthenwrite u Hu = α + M m=1 m m u [m] H [m,m ] u [m ]. As before, we isoate the symbos from the first base station to write u Hu = α + M u [m] H [m,1] u [1] + m=2 M u [1] H [1,m] u [m] + m=2 M m=2 m m m 1 u [m] H [m,m ] u [m ]. } {{ } G(ū) Since H is a Hermitian matrix then H [m,1]h = H [1,m] and we can write u Hu = α + M u [1] 2Re (H [1,m] u [m] )+G(ū). (5) m=2 1 In order to achieve the maximum compexity reduction we assume without oss of generaity that K 1 = max m K m.

13 Finay, we pug (4) and (5) back into (3) and coect terms to write [ Ω(u) =u [1] 2Re A [1]H (y [1] p [1] ) ] M H [1,m] u [m] m=2 } {{ } F (ū) + ū 2Re [ Ā H (ȳ p) ] α G(ū). (6) Observe that, for any ū B K K 1, (6) is maximized when u [1] reduced compexity optimum detector needs ony to compute =sgn(f (ū)). Hence, the ˆ bopt = arg max ū B K K 1 Ω ( [sgn(f (ū)), ū ] ) (7) from which the vector of optimum symbo estimates can be written directy as [ ( )) ] ˆb OPT = sgn F (ˆ bopt, ˆ b OPT. Note that, in contrast to the brute-force optimum detector, (7) ony requires the computation of Ω(u) over a set of 2 (K K 1)(2L+1) hypotheses in order to find the maximum. For a ce system with two or three significant base stations, this compexity reduction can be significant. This prior anaysis can aso be easiy appied to the synchronous CDMA case where the brute-force optimum detector requires the evauation of Ω(u) for 2 K hypotheses. In this case, the reduced compexity optimum detector requires the evauation of Ω(u) for 2 K K 1 hypotheses. V. Group Parae Interference Canceation Detection In this section, we examine the properties of the reduced compexity optimum detector in order to deveop a ow-compexity suboptimum detector caed the Group Parae Interference Canceation (GPIC) detector. Like the reduced compexity optimum detector, the GPIC detector aso expoits the orthogonaity of the in-ce user transmissions in the IS 95 downink. In the foowing deveopment, we consider an approach simiar to that described in [21] where a conditiona maximum ikeihood detector was deveoped by reaxing the maximum ikeihood criterion for a set of undesired symbos. Suppose temporariy that the IS 95

14 downink receiver has perfect knowedge of ˆ bopt, the jointy optimum symbo estimate of the users symbos in ces 2,...,M. Inthiscase,weshowedinSectionIVthatˆb [1] = sgn(f (ˆ bopt )) is the jointy optimum estimate of the users symbos in ce 1. Unfortunatey, reaistic receivers do not have access to the jointy optimum out-of-ce symbo estimates in genera, but we are compeed to ask the foowing question: What if the receiver formed some ow-compexity estimate ˆ b of b and we et ˆb[1] =sgn(f (ˆ b))? In fact, consider the owest compexity estimate of b: conventiona matched fiter estimates where ˆ bmf = sgn(re(āh ȳ)). Then ˆb [1] = sgn(f (ˆ bmf )) ( [ = sgn Re A [1]H (y [1] p [1] ) but since H [1,m] = A [1]H R [1,m] A [m] then { ( ˆb [1] = sgn Re [A [1]H (y [1] p [1] ) m=2 M m=2 H [1,m]ˆb[m] MF ]) )]} M R [1,m] A [m]ˆb[m] MF. (8) It is evident from this ast expression that a detector using (8) forms decisions by subtracting the estimated out-of-ce cochanne interference from the matched fiter inputs (minus the known piot terms) corresponding to the users in ce 1. When this operation is performed on a of the base stations it is caed parae interference canceation (first caed mutistage detection in [22]) and, since the interference canceation is performed over groups of users, we coin the name Group Parae Interference Canceation for this detector. We can extend this idea to write the foowing expression for the GPIC detector of base station m as { ( ˆb [m] = sgn Re [A [m]h (y [m] p [m] ) )]} R [m,m ] A [m ]ˆb[m ] MF m m where ˆb [m ] MF ]H =sgn(re(ā[m y [m ] )). Assembing the symbo estimates into a K(2L +1) vector containing a of the users bits in the muti-ce system, we can write a a simpe expression for the GPIC detector as ˆb GPIC = ˆb [1]. ˆb [M] { ])} =sgn Re (A [(y H p)+(i R)Aˆb MF.

15 We note that athough it is certainy possibe to perform GPIC detection in batch where a K(2L+1) symbos are first estimated with the conventiona matched fiter detector and stored prior to cacuation of the GPIC symbo estimates, it is aso possibe to impement the GPIC detector with a decision deay proportiona to K. VI. Simuation Resuts In this section we compare the performance of the optimum, GPIC, and conventiona matched fiter detectors via simuation. We examine a scenario where a nonsubscribing downink receiver (e.g. an eavesdropper) is istening to IS 95 downink transmissions in the simpe ceuar system shown in Figure 3 with B = 2 base stations and K 1 =2and K 2 = 2 users in each ce. The subscribing users in the system are represented by circes and our downink receiver is represented by a square with an antenna symbo. We evauate the quaity of reception at the receiver from both base stations as the receiver moves on the dashed ine from point a to point b. R b a Fig. 3. Simpe two base station IS 95 ceuar system with ces of radius R and centered base stations. The propagation channes between the base stations and the eavesdropping receiver are assumed to be singe-path with random received phases uniformy distributed in [0, 2π). Asynchronism offsets between the base station transmissions are aso assumed to be uniformy distributed. User powers, phases and deays are assumed to be time invariant over the duration of the receiver s observation. We assume the user positions to be uniformy

16 distributed within the ce. This assumption combined with IS 95 downink power contro impies that the user ampitudes observed at the eavesdropper are aso random. The distribution of the user ampitudes is derived in the Appendix under simiar path-oss modeing assumptions as the upink study in [23], [24]. Figure 4 shows the bit error rate of the optimum (denoted as OPT ), GPIC, and conventiona matched fiter (denoted by MF ) detectors for a user in the first ce 2 averaged over the user positions, deays, phases, ampitudes, and PN-codes. The singe-user error probabiity (denoted as SU ) is aso shown for comparison. Note that, in this simuation, the distance to the desired base station is fixed and the out-of-ce cochanne interference is decreasing as we move the eavesdropper toward position b and away from base station 2. Figure 5 shows the resuts of the same simuation for a user in the second ce In this case the eavesdropper is moving away from the desired base station and remaining at a fixed distance from the interfering base station Mean BER for a user in ce Mean BER for a user in ce MF OPT GPIC SU 10 3 MF OPT GPIC SU Distance from base station 2 Figure 4: Averaged bit error rate for a downink transmissions in ce Distance from base station 2 Figure 5: Averaged bit error rate for a downink transmissions in ce 2. Figure 4 shows that the conventiona matched fiter detector performs we when the eavesdropper is istening to a downink transmission from base station 1 in a position distant from base station 2. However, because of its near-far susceptibiity, the matched fiter detector performs poory when the eavesdropper attempts to extract weak downink transmissions from strong out-of-ce cochanne interference. Figures 4 and 5 show that 2 The first ce denotes the ce on the eft of Figure 3 and the second ce denotes the ce on the right of Figure 3.

17 the GPIC detector does not suffer from this probem and actuay exhibits performance indistinguishabe from the optimum detector in these exampes. These resuts suggest that the GPIC detector may offer near-optimum eavesdropping performance over a wide range of out-of-ce cochanne interference powers with the most benefit in severe out-of-ce cochanne interference environments. VII. On-Air Data This section compares the performance of the GPIC and conventiona matched fiter detectors on one snapshot of on-air measured data 3 from an active IS 95 ceuar system. One 45.6ms snapshot of IS 95 downink measured data was gathered with an omnidirectiona antenna. The received waveform was samped at twice the chip rate to yied a data fie with sampes corresponding to 875 (coded) symbo periods. The resuts of a base station piot survey on this data are shown in Figure Piot correation magnitude (db) Piot PN offset x 10 4 Fig. 6. Base station piot survey for IS 95 on-air data. 3 The authors woud ike to thank Rich Gooch, Mariam Motamed, and David Chou of Appied Signa Technoogies, Sunnyvae, CA, for providing us with this data and aso for their assistance in testing the agorithms deveoped in this paper.

18 Throughout this section, base station 1 denotes the base station with the strongest piot as seen at PN-offset in Figure 6. Base station 2 denotes the second strongest base station at PN-offset The powers of each active Wash channe at the output of their respective matched fiter detector, for both base station 1 and base station 2, are given in Tabes I and II. It can be seen that the power of the piot (Wash channe 0) from base station 1 is approximatey 11dB higher than the piot from base station 2, hence our receiver is positioned cose to base station 1 and reativey distant from base station 2. The remaining base stations seen in Figure 6 are ignored in the foowing deveopment for carity. Wash Channe % of BS1 transmit power % of tota received power Tota TABLE I Base station 1 active Wash channes. A. Conventiona Matched Fiter Detection In this section we quaitativey examine the soft outputs of the conventiona matched fiter detector for base stations 1 and 2. The matched fiters are obtained by estimating the impuse response of the combined propagation channe and puse shaping fiters via piot correation and convoving this impuse response with the appropriate combined Wash and PN-codes for each active user in the system. Athough Rake detection is not used, the matched fiter detector considered in this section automaticay incudes coherent mutipath combining since it incorporates the estimated impuse response of the propagation channe. Figure 7 shows a histogram of the matched fiter outputs for the active Wash channes

19 Wash Channe % of BS2 transmit power % of tota received power Tota TABLE II Base station 2 active Wash channes. of base station 1. Figure 7 ceary shows that the eye is open for a of the active channes and impies that one coud expect that these users decoded symbos woud have very ow probabiity of error. In addition to the strong piot channe at Wash code 0, there is a strong paging channe at Wash code 1, a reativey weak sync channe at Wash code 32, and two traffic channes of disparate power at Wash codes 12 and 63. Quaitativey, matched fiter detection appears to be adequate for downink reception of this base station. Figure 8 shows a histogram of the matched fiter outputs for the active Wash channes of base station 2. Figure 8 ceary shows that, unike the transmissions from base station 1, a of the channes from base station 2 are highy corrupted by interference (incuding outof-ce cochanne interference from base station 1, other base stations, and unstructured noise sources). The eye is cosed for a Wash channes, impying that subsequent channe decoding may be unreiabe.

20 pdf Matched Fiter Output Wash Channe pdf Matched Fiter Output Wash Channe Figure 7: Histograms of MF outputs by Figure 8: Histograms of MF outputs by Wash channe for base station 1. Wash channe for base station 2. B. GPIC Detection In this section we quaitativey examine the soft outputs of the GPIC detector for base stations 1 and 2. The matched fiter outputs generated in the prior subsection are passed through a hard decision device and then respread by the combined impuse response of the appropriate Wash codes, PN-codes, and estimated puse-shaping and propagation channe impuse responses. The waveforms are then scaed and rotated according to each user s estimated ampitude and phase. Figure 9 shows the histogram of the matched fiter outputs by Wash channe of base station 1 after subtraction of the estimated interference from base station 2. There is itte noticeabe change from the resuts in Figure 7 since the out-of-ce cochanne interference from base station 2 is very weak with respect to the transmission of base station 1 and interference canceation has itte effect. Figure 10 shows the histogram of the matched fiter outputs by Wash channe of base station 2 after subtraction of the estimated interference from base station 1. The performance improvement is significant with respect to the conventiona matched fiter resuts in Figure 8. Channes 1 and 20 appear to be much ceaner and channes 32 and 34 are beginning to exhibit troughs in the midde of their histograms indicating improved detection quaity. The piot channe is aso significanty ceaner.

21 pdf Wash Channe Matched Fiter Output Figure 9: Histograms of GPIC outputs by Wash channe for base station 1. pdf Wash Channe Matched Fiter Output Figure 10: Histograms of GPIC outputs by Wash channe for base station 2. The resuts in this section agree with the simuation resuts in Section VI and suggest that the GPIC detector may not offer much performance improvement when detecting strong signas in the presence of weak out-of-ce cochanne interference. On the other hand, comparison of Figures 8 and 10 show that significant performance improvements are possibe for a downink receiver attempting to extract weak signas from strong outof-ce cochanne interference. VIII. Concusions In this paper we investigated noninear mutiuser detection for improving the performance of IS 95 downink reception. We used the orthogonaity of the in-ce users of the IS 95 downink to deveop a reduced compexity optimum detector with exponentiay ower compexity than the brute-force optimum detector under the assumption that the propagation channes between the base stations and the receiver were singe-path. Examination of the properties of the reduced compexity optimum detector ed to the deveopment of the suboptimum, ow-compexity GPIC detector. The GPIC detector does not require any form of subspace tracking, matrix inversions, or exhaustive searches for goba maxima. Simuations and experiments with on-air IS 95 downink data showed that the GPIC detector offers the greatest performance improvements when detecting weak desired signas in the presence of strong out-of-ce cochanne interference. Athough this scenario woud be unusua for a subscribing user in an IS 95 ceuar system, a nonsubscribing

22 user such as an eavesdropper may derive the greatest benefit from GPIC detection. Our resuts aso suggest that subscribing users that use GPIC detection can achieve an acceptabe quaity of service with ess base station transmit power which resuts in ess induced cochanne interference on out-of-ce users in the system. Appendix: Received Power Distribution In this appendix, we derive the received user power distribution for transmissions to users in the m th ce observed by a receiver positioned at a deterministic distance d (m) (0, ) from the m th base station. We impose the foowing assumptions: Each base station is ocated in the center of its circuar ce of radius R. Each user s position is uniformy distributed in their ce and is independent of other user positions. The k th user s distance from base station m is denoted by d (m,k) (0,R]. Perfect power contro is maintained between each base station and its users such that the power received is identica for a users within the ce. The ratio of received to transmitted power obeys a simpe path oss mode 1/d 2λ where d is the distance separating the transmitter and receiver, and λ is the path oss exponent. The circuar shape of each ce and the users uniformy random positions impy that the cumuative distribution function of the (m, k) th user s distance from the m th base station, denoted as d (m,k), is equa to the ratio of the area of 2 circes, (x/r) 2 x [0,R], F d (m,k)(x) =P (d (m,k) x) = 0 otherwise. The pdf of d (m,k) foows directy as f d (m,k)(x) = x F d (m,k)(x) = 2x/R 2 x [0,R], 0 otherwise. IS 95 downink power contro eads to random reaizations for the user ampitudes observed at a deterministicay positioned receiver. The received power ratio (deterministicay positioned receiver to randomy positioned user) may be expressed as Ψ= Π(m) Π (m,k) = Π(m) /Π t = (d(m,k) ) 2λ Π (m,k) /Π t (d (m) ) 2λ

23 where Π (m),π (m,k),andπ t denote the power of the m th base station observed at the eavesdropper, the power of the m th base station observed at the (m, k) th user, and the power transmitted by the m th base station, respectivey. To find the cumuative distribution of Ψ, we note that F Ψ (x) =P (Ψ x) =P ((d (m,k) ) 2λ /(d (m) ) 2λ x) =F d (m,k)(d (m) x 1/2λ ) hence (d (m) /R) 2 x 1/λ x [0, (d (m) /R) 2λ ], F Ψ (x) = 0 otherwise and the pdf of Ψ foows directy as λ 1 (d (m) /R) 2 x (1 λ)/λ x [0, (d (m) /R) 2λ ], f Ψ (x) = 0 otherwise. This pdf is used to generate the random ampitude reaizations used for the simuation resuts in Section VI. References [1] Teecommunications Industry Association, Mobie Station Base Station Compatibiity Standard for Dua- Mode Wideband Spread Spectrum Ceuar Systems IS 95A. Washington, DC: TIA/EIA, [2] R. Kohno, R. Meidan, and L. Mistein, Spread spectrum access methods for wireess communications, IEEE Communications Magazine, vo. 33, pp , January [3] A. Kein, Data detection agorithms speciay designed for the downink of CDMA mobie radio systems, in 1997 IEEE 47th Vehicuar Technoogy Conference: Technoogy in Motion, vo. 1, (Phoenix, AZ), pp , May 4-7, [4] I. Ghauri and D. Sock, Linear receivers for the DS-CDMA downink expoiting orthogonaity of spreading sequences, in Conference Record of the Thirty-Second Asiomar Conference on Signas, Systems, and Computers, vo. 1, (Pacific Grove, CA), pp , November 1-4, [5] C. Frank and E. Visotsky, Adaptive interference suppression for direct-sequence CDMA systems with ong spreading codes, in Proceedings of the 36th Annua Aerton Conference on Communications, Contro and Computing, (Monticeo, IL), pp , September 23-25, [6] S. Werner and J. Lieberg, Downink channe decorreation in CDMA systems with ong codes, in 1999 IEEE 49th Vehicuar Techoogy Conference. Moving Into a New Mienium., vo. 2, (Houston, TX), pp , May 16-20, [7] K. Hooi, M. Latva-aho, and M. Juntti, Linear chip equaization in WCDMA downink receivers, in 1999 Finnish Signa Processing Symposium, vo. 1, (Ouu, Finand), pp. 1 5, May 31, [8] K. Hooi, M. Latva-aho, and M. Juntti, Mutipe access interference suppression with inear chip equaizers in WCDMA downink receivers, in Proceedings of the IEEE Goba Teecommunications Conference Gobecomm 99, vo. 1A, (Rio de Janeiro, Brazi), pp , December

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