1556 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 8, AUGUST 2001Multicell Uplink Spectral Efficiency of CodedDS-CDMA With Random SignaturesBenjamin M. Zaidel, Student Member, IEEE, Shlomo Shamai (Shitz), Fellow, IEEE, and Sergio Verdú, Fellow, IEEEAbstract—A simple multicell uplink communication model issuggested and analyzed for optimally coded randomly spreaddirect sequence code-division multiple access (DS-CDMA). Themodel adheres to Wyner’s (1994) infinite linear cell-array model,according to which only adjacent-cell interference is present, andcharacterized by a single parameter0 1. The discussionis confined to asymptotic analysis where both the number of usersand theprocessing gain goto infinity, while their ratio goesto somefinite constant. Single cell-site processing is assumed and fourmultiuser detection strategies are considered: the matched-filterdetector, “optimum” detection with adjacent-cell interferencetreated as Gaussian noise, the linear minimum mean square error(MMSE) detector, and a detector that performs MMSE-basedsuccessive interference cancellation for intracell users with linearMMSE processing of adjacent-cellinterference.Spectral efficiencyis evaluated under three power allocation policies: equal receivedpowers (for all users), equal rates, and a maximal spectral effi-ciency policy. Comparative results demonstrate how performanceis affected by the introduction of intercell interference, and what isthe penalty associated with the randomly spread coded DS-CDMAstrategy. Finally, the effect of intercell time-sharing protocols assuggested by Shamai and Wyner (1997) is also examined, and asignificant system performance enhancement is observed.Index Terms—Capacity, cellular communication, code-divisionmultiple access, multiuser detection, random signatures, spectralefficiency.I. INTRODUCTIONINFORMATION theoretic analyzes of direct sequencecode division multiple access (DS-CDMA) systems havegained much attention in recent years, as a result of the rapiddevelopment of commercial cellular systems employing thismulti-access strategy. Results for a single cell DS-CDMAsystem were recently presented in [1]–[4] (see also referencestherein). These works explicitly relate to CDMA systemswith random spreading sequences, and the limiting scenario isexamined, where both the number of users and the processinggain go to infinity, while their ratio goes to some finite constant.This ratio is commonly referred to as the “system load.”Manuscript received December 13, 2000; revised May 10, 2001. The work ofS. Shamai (Shitz) and S. Verdú was supported by the US-Israel Binational Sci-ence Foundation. The work of Sergio Verdú was supported also by the NationalScience Foundation under Grant NCR-0074277. This paper was presented inpart at the 37th Allerton Conference, Monticello, IL, September 1999, and atthe 21st IEEE Israel Conference, Tel-Aviv, Israel, April 2000.B. M. Zaidel and S. Shamai (Shitz) are with the Department of ElectricalEngineering, Technion—Israel Institute of Technology, Haifa 32000, Israel(e-mail: [email protected]; [email protected]).S. Verdú is with the Department of Electrical Engineering, Princeton Univer-sity, Princeton, NJ 08544 USA (e-mail: [email protected]).Publisher Item Identifier S 0733-8716(01)07223-7.The above asymptotic assumptions are particularly appealingsince in such case performance measures of interest, such asoutput signal-to-interference-plus-noise ratio (SINR) or spec-tral efficiency, converge to deterministic values, that can be an-alytically expressed. These performance measures are functionsof the empirical eigenvalue distribution of random matrices ofparticular structures, which is known to converge, when dimen-sions go to infinity, to some limiting distribution (determined inthe case considered here through its Stieltjes transform, see [5]and Appendix). In contrast, the problem becomes analyticallyintractable even for moderate finite system sizes (except forsome particular random matrix structures). Furthermore, pre-vious results indicate a rather fast convergence to the asymptoticlimits with system size, demonstrating the practical importanceof these limits. The reader is referredto [3], [6], and [7]for somenumerical examples and an analysis of the rate of convergence.Assuming equal received powers and nonfading channels,four multiuser detection strategies are compared and analyzedin [1], in terms of spectral efficiency. The authors examineoptimum decoding, the matched filter detector, the decorre-lating detector, and the linear minimum mean squared error(MMSE) detector. In addition to explicit analytical expressionsfor the spectral efficiencies of the four detection strategies,asymptotic analysis for cases in which the system load orgo to either zero or infinity is provided, and alsocomparison to the spectral efficiency without (the constraint of)spreading, and the spectral efficiency obtained with orthogonal(deterministic) spreading sequences. It should be noted herethat it is well known [8] that the optimum spectral efficiency(without spreading) can be achieved with orthogonal spreadingsequences when the system load equals unity. It is also known[9] that even when the system load is higher than unity, thereexist spreading codes that incur no loss in capacity relative tomulti-access with no spreading. The results obtained in [1]extend also to the case of homogeneous fading where each ofthe spreading sequences’ chips is assumed to be affected byindependent identically distributed (i.i.d.) fading coefficientswith unit variance. The impact of flat (nonhomogeneous)fading on the four multiuser detection strategies considered in[1] is analyzed in [2]. SINRs at the output of linear detectors(the matched-filter detector, the linear MMSE detector, and thedecorrelator) are presented in [3], and an extension of theseresults to fading channels with multi-antenna reception can befound in [10].In this paper, multicell systems are addressed using the at-tractive cellular model suggested by Wyner in [11]. This simplemodel allows for analytical tractability on the one hand, whilegivinginsight to practical systems on the other. Accordingly, the0733–8716/01$10.00 ©2001 IEEEZAIDEL et al.: MULTICELL UPLINK SPECTRAL EFFICIENCY OF CODED DS-CDMA 1557system’s cells compose an infinite linear array, where the re-ceived signal at each cell site is the sum of the signals receivedfrom intracell users,