IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 2, FEBRUARY 2001 329 A Spatial-Temporal Decorrelating Receiver for CDMA Systems with Base-Station Antenna Arrays Ruifeng Wang, Member, IEEE, and Steven D. Blostein, Senior Member, IEEE Abstract—We investigate multiuser signal detection with a base-station antenna array for a synchronous DS-CDMA uplink using nonorthogonal codes in Rayleigh fading channels. We have developed a new formulation for a spatial-temporal decorrelating detector using the maximum-likelihood criteria. The detector is shown to be near–far resistant. We propose to implement the spatial-temporal decorrelating receiver iteratively by applying the space-alternating generalized expectation-maximization (SAGE) algorithm. Simulation results show that the SAGE-based decorrelating receiver significantly outperforms the conventional single-user receiver and with performance close to that of a spatial-temporal decorrelating receiver with known channel pa- rameters. We have observed that adding base-station antennas can actually improve convergence of the proposed iterative receiver. Index Terms—Antenna arrays, code-division multiple access, signal detection multiple-access communication. I. INTRODUCTION D IRECT-SEQUENCE code-division multiple-access (DS-CDMA) systems use spreading codes to distinguish different mobile users. Because of the relative time delays among the active mobile users, DS-CDMA systems suffer from cochannel interference, which results in the near–far problem [1]. For a synchronous system, the near–far problem is due to the nonorthogonal spreading codes. However, the near–far problem is not inherent to CDMA systems, but due to the con- ventional single-user receiver which models the interference from other users as noise. By jointly detecting all the users’ signals, optimum multiuser signal detection for DS-CDMA systems is near–far resistant and can achieve significant per- formance improvement over that of conventional single-user detection [2]. Because of the computational complexity of optimum multiuser detection, several suboptimum multiuser signal detectors have been proposed [1], [3]–[5] for additive white Gaussian noise (AWGN) channels. In [6], multiuser signal detection is extended to fading channels. Since multiuser signal detection is near–far resistant, precise power control is not needed. Paper approved by G. E. Corazza, the Editor for Spread Spectrum of the IEEE Communications Society. Manuscript received December 15, 1998; revised De- cember 24, 2000. This paper was presented in part at the International Confer- ence on Communications (ICC), Vancouver, BC, Canada, 1999. R. Wang is with Wireless Local Technologies Group, AT&T Wireless Ser- vices, Redmond, WA 98073-9759, USA. S. D. Blostein is with the Department of Electrical and Computer En- gineering, Queen’s University, Kingston, ON K7L 3N6, Canada (e-mail: sdb@ee.queensu.ca). This work was supported by the Canadian Institute for Telecommunications Research under the NCE program of the Government of Canada. This paper was presented in part at ICC’99, Vancouver, BC, 1999. Publisher Item Identifier S 0090-6778(01)01304-6. Multiple-access interference can also be reduced using array signal processing. By digital beamforming, a base-station antenna array can be used to improve CDMA communication system capacity and coverage (see [7] and references herein). Combined beamformer-RAKE single-user receivers have been proposed for multipath channels in [8] and [9], respectively. In [10], adaptive antenna array processing and interference cancellation approaches using the least mean squared (LMS) algorithm are analyzed and the convergence is found to be very slow, requiring several hundred training bits. The problem of integrating antenna array beamforming and multiuser signal detection is proposed for AWGN channels in [11], but channel estimation has not been addressed. In order to detect information symbols reliably, we have to estimate channel and antenna array response vectors. Feder and Weinstein apply the expectation-maximization (EM) algorithm to parameter estimation of superimposed signals [12]. Bit se- quence detection with joint random parameter estimation using the EM algorithm is studied for single-user systems in [13]. Re- cently, applications of the EM algorithm to DS-CDMA systems have been proposed for signal detection [14], channel estima- tion [15] and joint channel estimation, and signal detection [16]. The space-alternating generalized EM (SAGE) algorithm has been developed to accelerate the convergence of the EM algo- rithm [17]. Applications of the SAGE algorithm in multiuser CDMA channels can be found in [14] for single antenna and known channels, in [18] for antenna array channel parameter estimation, and in [19] for joint parameter estimation and signal detection based on the discrete wavelet transform for a single antenna system. In this paper, we investigate the integration of spatial signal processing with multiuser signal detection for synchronous DS-CDMA systems with nonorthogonal spreading codes over asynchronous multipath fading channels. We note that that a -user asynchronous system can be modeled as a synchronous system with users [1], where is the number of bits in each transmitted block. The synchronous problem formulation simplifies the derivation and analysis of the new algorithm and the results can be generalized to higher complexity asyn- chronous multipath systems [20]. This paper is organized as follows. The discrete-time system model is developed in Section II. In Section III, we derive a spatial-temporal decorrelator using the maximum-likelihood criteria and analyze its asymptotic efficiency. An iterative spatial-temporal decorrelating receiver is proposed in Sec- tion IV by applying the SAGE algorithm to jointly estimate channel array response vectors and detect information symbol sequences. The bit-error rate (BER) and Cramér–Rao lower 0090–6778/01$10.00 © 2001 IEEE