IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 46, NO. 11, NOVEMBER 1998 2953 Probabilistic Algorithms for Blind Adaptive Multiuser Detection Carles Ant´ on-Haro, Student Member, IEEE, Jos´ e A. R. Fonollosa, Member, IEEE, Zoran Zvonar, and Javier R. Fonollosa, Senior Member, IEEE Abstract—In this paper, two probabilistic adaptive algorithms for jointly detecting active users in a DS-CDMA system are reported. The first one, which is based on the theory of hidden Markov models (HMM’s) and the Baum–Wech (BW) algorithm, is proposed within the CDMA scenario and compared with the second one, which is a previously developed Viterbi-based algorithm. Both techniques are completely blind in the sense that no knowledge of the signatures, channel state information, or training sequences is required for any user. Once convergence has been achieved, an estimate of the signature of each user convolved with its physical channel response (CR) and estimated data sequences are provided. This CR estimate can be used to switch to any decision-directed (DD) adaptation scheme. Perfor- mance of the algorithms is verified via simulations as well as on experimental data obtained in an underwater acoustics (UWA) environment. In both cases, performance is found to be highly satisfactory, showing the near–far resistance of the analyzed algorithms. I. INTRODUCTION R ECENTLY, multiuser detection in CDMA systems has received increasing attention [1]. In order to successfully decode the users in a CDMA system, the most important issue to be solved, apart from the multipath propagation problem, is the presence of multiple access interference (MAI). Two approaches can be followed in CDMA scenario: We can apply joint detection (JD) techniques [2], [3] or, otherwise, try to eliminate MAI explicitly (interference cancellation) [4]. In any case, the receiver should know (or should be able to acquire) one or more parameters from the following [5], [6]: 1) the signature waveforms of the desired user; 2) the signature waveforms of the interfering users; 3) the timing (bit-epoch and carrier phase) of the desired user; 4) the timing (bit-epochs and carrier phases) of the inter- fering users; 5) the received amplitudes of the interfering users relative to the amplitude of the desired user. Manuscript received August 28, 1996; revised March 19, 1998. This work was supported in part by the National Plan of Spain, CICYT, under Grants TIC98-0703, TIC98-0412, and TIC96-0500-C10-01, and the Generalitat de Catalunya, CIRIT, under Grant 1996SGR-00096. The associate editor coordinating the review of this paper and approving it for publication was Dr. Petar M. Djuric. C. Ant´ on-Haro, J. A. R. Fonollosa, and J. R. Fonollosa are with the Department of Signal Theory and Communications, Universitat Polit` ecnica de Catalunya, Barcelona, Spain (e-mail: carles@gps.tsc.upc.es; adrian@gps.tsc.upc.es; fono@gps.tsc.upc.es). Z. Zvonar is with the Communications Division, Analog Devices, Wilmington MA 01887-1024 USA (e-mail: Zoran.Zvonar@analog.com). Publisher Item Identifier S 1053-587X(98)07805-2. The conventional receiver neglects the presence of other users requiring only the knowledge of 1) and 3) but, in exchange, it is severely limited by the near-far problem. On the other hand, the optimum detector [3] attains the best performance by making use of all the aforementioned information and at the expense of exponential computational complexity in the number of users. Among other low-complexity multiuser receivers, we will consider the decorrelating [2] and the MMSE detectors [7] to show how different levels of knowledge of the parameters can be necessary at the receiver. The former requires knowledge of 1) to 4) to achieve optimum near–far resistance and avoids exponential complexity. The latter is more suited for adaptive implementation on the basis of mean square error (MSE) minimization [1]. In that case, previous knowledge of 2), 4), and 5) can be circumvented by making use of 6) training sequences. In all cases, external information must be supplied for proper operation of the multiuser algorithms. In the adaptive versions, such information, in the form of training sequences, must be sent not only during the startup period but also after sudden changes in the channel response (CR) or when a new active user appears. An interesting method to detect the latter cir- cumstance is addressed in [8]. The need to retransmit training sequences may be cumbersome in multiuser communications so that, in recent years, a large effort has been made in developing blind algorithms that perform CR acquisition and data detection without such information. In other words, only the channel output can be used to obtain estimates on the input data and the CR. In general, blind equalization/estimation methods can be classified in four families [9]: 1. Bussgang-type algorithms [9]–[11]; 2. polyspectra and cumulant-based algorithms [9], [12]; 3. cyclostationary statistics-based algorithms [13]–[15]; 4. probabilistic algorithms [16]–[19]. The algorithms presented and compared in this paper, belong to the fourth group. Probabilistic algorithms lead to joint channel estimation and data detection, often on a basis of a maximum likelihood (ML) criterion. These methods exhibit higher computational complexity, but they outperform the other approaches since they make better use of all the known statistical information about the input signal and, in general, require less symbols to obtain an accurate channel estimate. The proposed algorithms are absolutely blind in the sense that no knowledge of 1) to 6) is required for proper operation. The Viterbi-based algorithm was introduced in [19] to perform jointly blind channel estimation and sequence detection in a 1053–587X/98$10.00  1998 IEEE