IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 46, NO. 12, DECEMBER 1998 1693 Iterative Multiuser Detection for CDMA with FEC: Near-Single-User Performance Mark C. Reed, Student Member, IEEE , Christian B. Schlegel, Senior Member, IEEE, Paul D. Alexander, Member, IEEE, and John A. Asenstorfer, Member, IEEE Abstract—This paper introduces an iterative multiuser receiver for direct sequence code-division multiple access (DS-CDMA) with forward error control (FEC) coding. The receiver is derived from the maximum a posteriori (MAP) criterion for the joint received signal, but uses only single-user decoders. Iterations of the system are used to improve performance, with dramatic effects. Single-user turbo code decoders are utilized as the FEC system and a complexity study is presented. Simulation results show that the performance approaches single-user performance even for moderate signal-to-noise ratios. Index Terms— Code-division multiaccess, decoding, multiuser channels, random codes, turbo codes. I. INTRODUCTION W ITH THE standardization of direct spread code- division multiple access (DS-CDMA) for mobile communications [1], a number of vendors have introduced their products onto the world market. This has raised a lot of interest on the potential capabilities and capacity of this multiple-access technology [2]–[7]. In this paper we study the uplink, or the base-station (BS) receiver. In the design of these systems most are currently symbol-synchronous or quasisymbol-synchronous so that orthogonal codes can be utilized. When orthogonal codes are used the BS linear filter receivers perform well in detecting the signal sent by taking advantage of this orthogonality, which gives performance equal to single-user performance. In a true mobile wireless system, synchronization is difficult to maintain and needs tight closed-loop timing control between the BS and the mobile station (MS). If this timing control is not maintained then the orthogonal properties are lost and Paper approved by R. Kohno, the EDitor for Spread Spectrum Theory and Applications of the IEEE Communications Society. Manuscript received April 28, 1997; revised December 17, 1997 and April 28, 1998. This work was supported in part by Telstra Australia under Contract 700136 and by the Commonwealth of Australia under International S & T Grant 56. This paper was presented in part at the International Symposium on Personal, Indoor and Mobile Radio Communications, Helsinki, Finland, September 1997. M. C. Reed was with the Mobile Communications Research Center, University of South Australia, Mawson Lakes SA 5095, Australia. He is now with Ascom Systec AG, Technology Unit, Gewerbepark, CH-5506 Maegenwil, Switzerland. C. B. Schlegel is with the Department of Eletrical Engineering, University of Utah, Salt Lake City, UT 84112 USA (e-mail: schlegel@ee.utah.edu). P. D. Alexander is with the Centre for Wireless Communications, National University of Singapore, Singapore 117674 (e-mail: cwcpa@leonis.nus.edu. sg). J. A. Asenstorfer is with the Mobile Communications Research Center, Institute for Telecommunications Research, University of South Australia, Mawson Lakes SA 5095, Australia (e-mail: john@spri.levels.unisa.edu.au). Publisher Item Identifier S 0090-6778(98)09380-5. performance degrades severely. Multipath effects, common in mobile radio channels, also destroy this orthogonal property. If the codes are randomly selected, however, the performance of a synchronous system is on average the same as that of an asynchronous system. Work produced by Grant et al. [8] shows that the capacity penalty vanishes, for a large number of users, using randomly selected spreading codes, as the ratio between number of users and spreading length becomes large. Jana et al. [9] have shown a slightly different result; they showed that the upper bound of the normalized minimum distance for a trellis-coded multiuser CDMA system with nonorthogonal spreading is identical to that of the single-user case. This means that asymptotically, using nonorthogonal codes, or random codes, single-user performance should be possible. With such a receiver the performance under asynchronous con- ditions will be the same as that under synchronous conditions. We are therefore motivated to look for new multiuser receiver structures that use random codes to achieve near-single-user performance. A paper by Giallorenzi et al. [7] formulated the optimal multiuser sequence estimator for an asynchronous DS-CDMA system where each user employs convolutional error control coding. Giallorenzi et al. found that the complexity per infor- mation bit using the MLSE solution depends exponentially on the number of users in the system and the number of states in each user’s encoder. We propose to partition the receiver to reduce the complexity, without sacrificing performance. This paper therefore describes a partitioned trellis-based receiver with separate equalization and decoding. We develop a mul- tiuser receiver (or equalizer) from the maximum-a posteriori (MAP) criterion. The MAP criterion maximizes the probability of a correct bit decision and, hence, minimizes the probability of error [10, p. 245]. Recently, a new coding method, called turbo codes, was introduced [11]. This technique achieves reliable transmission while operating close to the Shannon limit. Turbo codes combine the concept of soft-in/soft-out decoding, iterative decoding, nonuniform random interleaving, and parallel con- catenated convolutional codes (PCCC). Further to this, pub- lished results by Benedetto and Montorsi [12] discuss serial concatenated convolutional codes (SCCC). Several authors have proposed using turbo codes for DS- CDMA systems [4], [5]. These papers discuss system im- plementations but show no performance results. The authors would like to note that since the submission of this paper several independent publications have shown similar results 0090–6778/98$10.00  1998 IEEE