Maximizing System Capacity in a Sub-Symbol based DS-CDMA Multiuser Detector Z. A. Uzmi, M. J. Narasimha {uzmi, sim}@nova.Stanford.EDU Electrical Engineering Department Stanford University, Stanford, CA. USA Abstract- A sub-symbol based multiuser detector for DS- CDMA systems was proposed in [1]. This paper addresses the optimization of such detectors to maximize the system capacity. It is shown that the maximum number of simultaneous users supported in a DS-CDMA system using sub-symbol scheme can be increased by the proper selection of certain thresholds delineated in [1], and by imposing moderate synchronization requirements on the transmitters. It is also shown that, in a moderately synchronized environment, performing decorrelation with only one sub-symbol is enough for accommodating a fairly large number of users, if the system signal to noise ratio (SNR) is medium to high. It has been verified through simulations that the maximum number of simultaneous users depends on the degree of synchronism and is approximately given by the number of chips in the longest sub- symbol. I. INTRODUCTION CDMA is the preferred air interface technology for third generation wireless systems that are currently undergoing the standardization process. It has been shown previously that the capacity of CDMA systems is limited by multiple access interference (MAI) and not by thermal noise [2]. Currently deployed commercial CDMA systems regard MAI as an additive noise and perform detection of each user independently. This limits the maximum number of users that can be simultaneously supported due to the deterioration of the bit error rate (BER). A number of researchers have addressed multiuser detection schemes for CDMA systems in the last two decades to improve the system capacity. The main reason that these schemes are not used in practical systems is because of their stringent processing requirements. Multiuser detection schemes are specified as optional [3] even in the proposals for the third generation wireless systems. The complexity of the optimal multiuser detector (MUD) [4] increases exponentially with the number of users. Hence, several low-complexity sub-optimal schemes have been proposed and evaluated in the literature [5], [6]. The MUD schemes researched so far can be broadly classified into linear schemes and interference cancellation (IC) methods. Linear schemes require more computation but are robust against near-far resistance. Therefore, we focus on these schemes in this paper. In particular, we present results for schemes that are based on zero forcing (ZF) linear multiuser detection. ZF MUD schemes have lower complexity, as they do not require channel gain estimates. The first linear ZF multiuser detection scheme was proposed in [7] for a synchronous CDMA system. Unfortunately, commercial cellular systems do not have synchronous uplinks since users transmit from random locations at random instants of time. Even if the users time their transmission such that the line-of-sight arrivals are aligned at the base station, the multipath rays render the system asynchronous. Thus it is necessary to consider asynchronous multiuser detection schemes in a practical situation. For asynchronous systems, the MUD proposed in [8] is difficult to implement as its complexity depends on the product of the number of users and the number of symbols in the whole duration of transmission. Several linear MUD schemes for asynchronous systems have since been proposed and analyzed. A survey of such schemes can be found in [9], [10] and the references therein. All these schemes are based on full symbol correlation detection at the base station. More recently, techniques that consider sub-symbols for partial correlations have been proposed [1]. This paper focuses on fine tuning the sub-symbol technique and maximizing the number of simultaneous users for the combining algorithms presented in [11]. We assume that moderate synchronism can be achieved by issuing downlink commands to the users to adjust their transmission instants. Section 2 briefly describes the system model considered in the sub-symbol scheme. In Section 3, we discuss the algorithms for sub-symbol combining and promote the idea that for a large number of users, one long sub-symbol is better than using several small sub-symbols. Simulation and analytic results and guidelines on choosing the optimum thresholds for the algorithms used in the sub-symbol scheme are presented in Section 4. II. SYSTEM MODEL AND SUB-SYMBOL SCHEME The baseband model of a CDMA uplink with single-user matched-filter (SUMF) receiver is depicted in Fig. 1 for u N users. The user data signals before spreading are denoted as ) ( , ), ( ), ( 2 1 t d t d t d u N K . These are multiplied by the spreading codes ) ( , ), ( ), ( 2 1 t K t K t K u N K before transmission. The signal received at the base station is the sum of individual signals from each user modified by the respective channels, and the additive white gaussian noise. Succinctly, the received signal is given by: