ADAPTIVE DECISION FEEDBACK TECHNIQUES FOR MULTIUSER DETECTION IN CDMA SYSTEMS

Abstract

To satisfy the ever-increasing demand for higher data rates, as well as to allow more number of users to simultaneously access a common channel using the entire frequency spectrum allocated for transmission, interest has peaked in the direct sequence code division multiple access (DS-CDMA) techniques. In DS-CDMA transmission, the multipara propagation through linear dispersive media introduces intersymbol interference (ISI), which results in the bit error rate (BER) performance degradation. In addition to ISI, the nonorthogonal properties of signature sequences and asynchronism (i.e., the random time offsets for the received signals of different users) lead to multiple access interference (MAI) along with additive white Gaussian noise (AWGN). The problem of MAI is not only due to the known intra-cell users, but also from the unknown inter-cell users. The unpredictable nature of MAI limits the capacity and performance of the multiuser system. Thus, even if the receiver thermal noise goes to zero, the error probability of the conventional receiver exhibits a non-zero floor because of MAI. Due to the propagation mechanism, the received signal from a user close to the base station can be stronger than the signal received from desired user located far from the base station. The near-far problem arises as the weaker signal can be overwhelmed by MAI. The multiuser detection (MUD) has become a topic of extensive research interest since 1986, when Verdu formulated an optimum MUD receiver based on the maximum likelihood sequence detection criterion. However the solution involves a joint Viterbi processor with exponential complexity in the number of users, which has motivated the design of suboptimum detectors with linear complexity. The decorrelating and minimum mean square error (MMSE) detectors are the most useful sub-optimum detectors. Though the decorrelating detector is near-far resistant, but it also enhances the background noise. The MMSE detector, which minimizes the mean square error between the actual and estimated data bits, provides greater ability to combat noise at the cost of reduction in the near-far resistance. However the difficulty in the estimation of covariance matrix of the timevarying received signals has given rise to the use of adaptive MMSE techniques, which directly processes the samples of received signal at the chip interval without the explicit knowledge of MAI, and can be implemented using the tapped delay line filter. The adaptive MMSE techniques are analogous to the adaptive equalization of dispersive channels by virtue of the analogy betweenMAI and ISI. For very large loads i.e., KIN» 70% (K = numberof strong users, and N = processing gain or signature sequence length), the substantial degradation in the performance of adaptive linear multiuser detector is observed. The adaptive non-linear MMSE techniques (decision feedback) are more affective than the linear techniques because latter is having only feedforward filter, whereas former is having feedforward as well as feedback filters to combat ISI. In the case of a multiuser system, ISI not only originates from the past symbols of desired user, but also from the past symbols ofinterfering users, which can be suppressed by using the non-linear adaptive decision feedback detectors (ADFDs). At high signal to noise ratios (SNR) and loads, the non-linear techniques outperform the linear multiuser detection techniques. However the ADFDs suffer due to the error propagation problem, which leads to degradation in the BER performance. "The requirements imposed on the CDMA systems in terms of capacity and flexibility necessitate the advanced signal processing solutions for the multiuser interference suppression and data detection in the presence of ISI, MAI and AWGN. In the presented work, adaptive decision feedback structures based on the MMSE criterion are considered to solve the problems inherited in both non-adaptive and linear multiuser detection techniques." Starting with the linear MMSE sub-optimum MUD, we focus on its probability of error performance analysis, and investigate the behavior of MAI in terms of the leakage coefficients. The MMSE linear multiuser detector considers MAI asymptotically Gaussian for a large number of users in the asynchronous DS-CDMA system. For this asymptotic condition, the MMSE detector outperforms the decorrelating detector only if the value of normalized cross-correlation (NCC) for any pair of signature sequence is less than or equal to the numerically derived upper bounded value. The available results in the literature have been derived for the two-user case. We have presented a general formula to calculate the upper bound on NCC for the arbitrary number of users under the near-far situation. The upper bound and optimum NCC ranges for 7>K>2 have been derived. We also propose the Chernoff bound on the error probability ofMMSE multiuser detector for Binomial as well as Gaussian distributed leakage coefficients. Its proof based on the Kullback-Leibler divergence theorem and study of the leakage coefficients for more than two users impose the stringent condition on SNR of the desired user for unbiased output of the linear MMSE MUD receiver. We have shown that the SNR of the desired user should be greater than the minimum bounded value, which depends on the number of users and NCC. The derived results depict that the MAI follows binomial distribution for a small number of users. For adaptive implementation of the linear MMSE detector and for the channel estimation, the least mean square (LMS) algorithm is normally used under the slowly timevarying multipath fading environment. However the Kalman filtering algorithm is used for the fast time-varying channel estimation, which increases the computational complexity of the receiver. Our motivation is to develop anovel two-step least mean square type adaptive algorithm, with low computational complexity 0[n], for the Markovian channel identification problem. In this work, we present amodified version ofthe two-step LMS-type adaptive algorithm motivated by the work of Gazor in [60]. We describe the nonstationary adaptation characteristics of this modified two-step least mean square (MG-LMS) algorithm for the system identification problem. It ensures stable behavior during convergence as well as improved tracking performance in the smoothly time-varying environments. The estimated weight increment vector is used for the prediction ofweight vector for the next iteration. The proposed modification includes the use of acontrol parameter to scale the estimated weight increment vector in addition to asmoothing parameter used in the two-step least mean square (G-LMS) algorithm, which controls the initial oscillatory behavior of the algorithm. The analysis focuses on the effects of these parameters on the lag-misadjustment in the tracking process. The mathematical analysis for a nonstationary case, where the plant coefficients are assumed to follow a first-order Markov process, shows that the MG-LMS algorithm contributes less lag-misadjustment than the conventional LMS and G-LMS algorithms. Further, the stability criterion imposes upper bound on the value of the control parameter. These derived analytical results are verified and demonstrated with simulation examples, which clearly show that the lag-misadjustment reduces with the increasing values of smoothing and control parameters under permissible limits. It also supersedes the NLMS algorithm in tracking by combating the lag noise, which consequently reduces the lagmisadjustment at the cost of slight increase in the gradient-misadjustment. At the optimum value of control parameter, the MG-LMS algorithm provides approximately 3dB performance advantage over the G-LMS algorithm. The G-LMS and MG-LMS are developed by exploiting the Kalman filtering algorithm. By combining the strategy used for MG-LMS and spread spectrum technique, we next present an adaptive decision feedback equalizer (ADFE) based multiuser receiver for the DSCDMA systems over the smoothly time-varying multipath fading channels using the reduced Kalman least mean square (RK-LMS) adaptive algorithm. The frequency-selective fading channel is modelled as a tapped delay line filter with smoothly time-varying Rayleigh distributed tap-coefficients, which are considered to be auto-regressive processes varying at in the data rate. The receiver uses an adaptive MMSE multiuser channel estimator to predict the coefficients of the tapped delay line filter. We consider first the design ofadaptive MMSE feedforward and feedback filters by using the estimated channel response. We next present the convergence characteristics and the tracking performance of the proposed multiuser channel estimator using the RK-LMS algorithm. Unlike the previously available Kalman filtering algorithm based approach, the incorporation ofthe RK-LMS algorithm reduces the computational complexity of the multiuser receiver. The computer simulation results are presented to show the substantial improvement in its tracking as well as BER performance over the conventional LMS algorithm based receiver. The simulation results depict that the performance ofthe proposed multiuser receiver is dependent on the channel estimation errors because the residual ISI adversely affects the BER performance. The increasing load and velocities of the mobile users deteriorates the performance of DS-CDMA system. The BER performance also degrades for a large number of multiparas because the SNR per path reduces, which results in high channel estimation errors. However for a small number of multipaths, the feedforward filter provides performance advantage by exploiting the multipath diversity. It may be inferred from the presented results that the proposed multiuser receiver proves to be robust against the nonstationarity introduced due to the channel variations, and is beneficial for the multiuser interference cancellation and data detection. Subsequently, we consider the mitigation oferror propagation effect in the decision feedback detection techniques. We present an ADFE with erasure algorithm (E-DFE) for the asynchronous DS-CDMA transmission using the LMS algorithm, which not only combats ISI and MAI but also reduces the effects of error propagation in the presence of Gaussian background noise. To reduce the possibility of feeding back the wrong decisions, the output of feedforward filter ofthe E-DFE is processed before it is fed back to the feedback filter. Specifically, the focus is on the performance ofE-DFE using the soft-slicer based on a novel erasure algorithm. In addition, the fully connected feedback filter ofE-DFE has been used to eliminate ISI due to other active users. We use the over-sampling technique to deal with the asynchronous reception of users. Comparison of the performance of conventional decision feedback equalizer and E-DFE over the slowly varying frequency-selective fading channel is presented to show the advantages ofE-DFE in terms ofthe reduced BER. Simulation results are also presented to demonstrate the substantial improvement in its performance under the near-far and high load situations. The receiver also proves to be effective against sudden changes in the SNR ofthe desired user. We next present a novel ADFD based on the parallel interference cancellation approach IV (ADFD-PIC) using the LMS algorithm for the DS-CDMA system, which is motivated by the previous work on P-DFD (parallel-) in [128]. It not only combats ISI and MAI, but also suppresses other-cell interference. The multiuser P-DFD uses the estimated covariance matrix of the received signal vector, but the ill-conditioned nature of the covariance matrix introduces numerical problems. In P-DFD, the tentative decisions of K users obtained from the linear MMSE receiver are used for the parallel interference cancellation. The tentative decisions may be unreliable due to the residual MAI, which leads to error propagation in the multistage detector. The erasure algorithm may be used to generate the time-variable partial cancellation factors depending on the soft-output of multiuser linear filter. The presented ADFD-PIC structure using the channel estimator and erasure algorithm based soft-slicer (ECADFD- PIC) offers performance improvement by mitigating the adverse effects of error propagation. The simulation results are presented to demonstrate the substantial improvement in the BER performance ofMMSE EC-ADFD-PIC over other multiuser detection techniques. Previously reported results depict that the P-DFD offers approximately 2dB gain relative to the MMSE MUD receiver. However, the presented EC-ADFD-PIC provides approximately 3dB performance advantage over the linear MMSE multiuser receiver under the smoothly time-varying multipath fading channel. The results also demonstrate that EC-ADFD-PIC may be used for the slow mobile users. The two-stage DFD using the S-DFD (successive-) and P-DFD in concatenation (S-PDFD) suffers due to the error propagation effect for a small number of users. In this work, we present a novel two-stage MMSE multiuser DFD for the DS-CDMA system working under the frequency-selective multipath fading environment. The first stage of the proposed cascaded structure is the noise-predictive successive DFD (NP-S-DFD), in which the active users are demodulated and detected successively using the conventional Bell Labs Layered Space-Time (BLAST) ordering criterion. The second stage includes an adaptive successive/parallel DFD (SP-DFD), which uses the tentative decisions obtained at the first stage for the multiuser interference cancellation and data detection. Therefore, the presented two-stage detector may be called the noise-predictive successive SP-DFD (NP-S-SP-DFD). The first user is detected using the linear MMSE transformation in NP-S-DFD, which may lead to the error propagation at successive stages due to the wrong detection of data symbol corresponding to the first user. However at the second stage of NP-S-SP-DFD, the first user is detected using the parallel interference cancellation approach, which leads to reduction in the bit error rate. Simulation results are presented to show the substantial improvement in the BER performance of NP-S-SP-DFD over the conventional single-stage S-, P-, NP-S-, and cascaded S-P-DFDs. The presented DFD provides performance improvement, when the order in which the users are detected is optimized according to the BLAST ordering based on MMSE criterion. However under the low SNR conditions, significant degradation in the BER performance ofNP-S-SP-DFD is observed due to the error propagation effect. On the other hand, its performance substantially improves under the high SNR conditions, and the presented results demonstrate that the NP-S-SP-DFD based on MMSE criterion outperforms the conventional single-stage and two-stage DFDs.