MPOE Prefiltering with Statistical Channel Model for DS-CDMA Systems G. Kannan, Mohit Garg † , S. N. Merchant and U. B. Desai SPANN Laboratory, Department of Electrical Engineering Indian Institute of Technology-Bombay, Mumbai, India-400076 Email: {gkannan, merchant, ubdesai}@ee.iitb.ac.in, † mohitgarg@gmail.com Abstract— In order to reduce the complexity of the mobile receiver, we develop a linear precoding filter based only on the statistical knowledge of the channel. Moreover, the proposed prefilter (precoder) is based on minimizing the probability of error in downlink multiuser transmission. We investigate two approaches for the proposed algorithm. In the first approach we consider a common FIR precoding filter for all users, and jointly minimize the probability of error of all users. In the second approach, we assume separate precoders for each user which are obtained by minimizing the probability of error for the respective user. In order to fully utilize the knowledge available at the trans- mitter, in both the approaches, the filter weights are computed conditioned on the transmitted bit vector sequence. This also makes the computation of the optimal prefilter coefficients linear in the number of users. We compare the results of the proposed approach, with results based on assuming complete knowledge of the channel. Simulation results clearly show that precoders based only on the statistical knowledge of channel, do provide acceptable BERs. Moreover, individual precoders provide better BER as compared to joint precoders. I. I NTRODUCTION In this paper, we explore a prefiltering scheme at the base station transmitter which allows considerably simplified receiver structure in downlink transmission. Prefilter design is simple when the transmitter has complete channel knowledge. Unfortunately, in practice it is highly improbable to have full channel knowledge. Even in Time Division Duplex (TDD) sys- tems, in fast fading channel conditions, it is extremely difficult to keep track of the channel variations with time. In this paper, we explore the approach of working only with first order and second order statistics of the channel at the transmitter and op- timizing the transmitter precoding filter. The basic assumption is that the statistics of the channel change at a much slower rate than the channel itself and hence it may be reasonable to assume that tracking the channel statistics will be easier to implement in practical systems. Our approach becomes more attractive because the channel statistics for the most commonly used channels in wireless mobile communications have been well studied and standard models are available for the same [1]-[2]. We consider two approaches for prefiltering: the first one considers the common prefilter for all users as shown in Fig. 1. In the second approach, we consider a system which has an individual prefilter for each user as shown in Fig. 2. The standard single user receiver (conventional matched filter detector) is used in both of our models. Minimum Mean Squared Error (MMSE) has been traditionally used as the optimization criterion for precoder/detector design in many wireless systems. We believe since symbols are of significance in digital communications, optimum prefilter design should be based on minimizing the probability of symbol error at the receiver. We refer to this as Minimum Probability of Error (MPOE) prefilter [3]-[4]. Usually MPOE optimization tends to be computationally expensive, but as we assume ample computational resources at the base station, using MPOE instead of MMSE as the optimization criterion can be justified. Moreover, by conditioning the filter weights on the transmitted bits, one can design an MPOE precoder with linear complexity [3]-[4]. The rest of the paper is organized as follows: Section II briefly describes the related work. System model is introduced in Section III. MPOE and MMSE based joint prefilters are derived in Section IV. Individual prefilterings with MPOE and MMSE optimizations are discussed in Section V. Simulation results and discussions are provided in Section VI. Finally some concluding remarks are given in Section VII. II. RELATED WORK Significant research has been carried out in the area of prefiltering over the last few years. However almost all of it has been directed towards the design of MMSE based prefilters; moreover most of the approaches assume complete knowledge of the forward channel [5]-[8]. MPOE optimization method was proposed by Dua et.al. in [3]-[4] and later extended to de- cision feedback detector in [9]. Furthermore in [3]-[4], a linear computational complexity receiver with respect to number of users, was proposed. In [3]-[4] it was established that MPOE optimization has better performance than MMSE optimization. Independently, Minimum Bit Error Rate (MBER) optimization for decision feedback equalizer receiver was proposed in [10]. In [11], Ding et. al. proposed a MBER precoder and in [12] Palomar et. al. derived a transceiver based on MBER method for Zero-Forcing (ZF) equalizer at the receiver. These systems require a complex receiver model with complete channel knowledge and precoder knowledge. Georgoulis et. al. in [7] and Reynolds et. al. in [8] have used a simple matched filter receiver by considering a channel model with ISI, but the optimization criterion is MMSE. MPOE based prefiltering by considering a general channel model (MAI+ISI) and simple matched filter receiver was first proposed in [13]. All the above papers assume complete channel knowledge. 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