Large system error probability of multiuser decision feedback receivers

We consider interference rejection for code-division multiple-access (CDMA) channels using decision-feedback detectors. Performance of zero-forcing and the minimum mean square error (MMSE) multiuser decision-feedback detectors is studied, and the full and partial feedback approaches are investigated. We also derive the maximum-likelihood detector based on the white noise CDMA channel model. Comparison among the decision-feedback detectors, the two-stage receivers, the conventional detector, and the linear decorrelating detector is undertaken for a four-user bandwidth-efficient asynchronous CDMA channel. We find that the decision-feedback detectors compare favorably to other suboptimal methods and maintain good performance under diverse channel conditions. This conclusion is further strengthened by performance analysis of the decision-feedback detector for a two-user synchronous CDMA flat Rayleigh fading channel. >

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver; the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

A new and effective algorithm is proposed in this paper based on Gaussian Mixture Modeling (GMM) and Minimum Mean Square Error (MMSE) criterion for speech enhancement. GMM mean vectors are used to model the space span by the power spectra of the input noisy speech frames. No assumption is made on the nature or stationarity of the noise. No Voice Activity Detection (VAD) or any other means is used to estimate the input Signal to Noise Ratio (SNR). The mean vectors derived from mixture models of Power Spectral Densities (PSDs) of speech and different noise sources are used to form sets of over-determined system of equations, as many as noise source candidates, whose solutions lead to the MMSE estimations of speech and noise power spectra. These are then used for noise suppression by applying Wiener filtering carried out on overlapping frames. The input SNR is estimated and the nature of the noise involved is determined as by-products of the method used. Results are compared with those of two variants of a method based on approximate but explicit MMSE Bayesian estimation that show good results but suffer from long processing times. It is shown that, at the cost of a slight lower improvement in SNR and PESQ score, the new algorithm reduces the computation time to 1/30 which makes it suitable for practical applications.

A systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of K simultaneously transmitting users of a synchronous correlated waveform multiple-access (CWMA) channel with Gaussian noise. A new performance criterion called symmetric energy is defined which is a low-noise indicator of the joint error rate that at least one user is detected erroneously. Even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum-likelihood detector. A general class of decision feedback detectors (DFDs) is defined with O(K) implementational complexity per user. The symmetric energy of arbitrary DFD and bounds on their asymptotic effective energy (AEE) performance are obtained along with an exact bit-error rate and AEE analysis for the decorrelating DFD. The optimum DFD that maximizes symmetric energy is obtained. Each one of the K! optimum, decorrelating, and conventional DFDs, that correspond to the K! orders in which the users can be detected, are shown to outperform the linear optimum, decorrelating, and conventional detectors, respectively, in terms of symmetric energy. Moreover, algorithms are obtained for determining the choice of order of detection for the three DFDs which guarantee that they uniformly (user-wise) outperform their linear counterparts. In addition to optimality in symmetric energy, it is also shown that under certain conditions, the optimum DFD achieves the AEE performance of the exponentially complex maximum-likelihood detector for all users simultaneously. None of the results of this paper make the perfect feedback assumption. The implications of our work on power control for multiuser detection are also discussed.

The large-system performance of iterative multiuser decision-feedback detectors (DFDs) is studied for synchronous coded direct-sequence code-division multiple access. Both successive and parallel demodulation of users are considered. The filters are optimized according to the minimum mean-squared error criteria, assuming perfect feedback. We first consider Viterbi decoding with hard decision feedback, and compute union bounds on the large-system error rate. We then consider maximum a posteriori (MAP) decoding with soft decision feedback, and evaluate the error rate semianalytically by assuming the log-likelihood ratios computed by the MAP decoder are Gaussian random variables. Performance is studied numerically as a function of noise level, spectral efficiency, and code rate. Results show that soft decision feedback gives substantial gains relative to hard decision feedback. At moderate spectral efficiencies (users divided by bandwidth expansion less than 0.9), the iterative DFDs with soft decision feedback based on a posteriori probabilities can achieve near-single-user performance at an E/sub b//N/sub 0/ close to the large-system capacity bound.

In this paper, linear precoding (LP) algorithm has been studied to improve the bit error rate (BER) performance of large scale multiple input multiple output (MIMO) system. A new technique of enhancing the BER performance of linear precoding algorithm without complexity in hardware and mathematical calculations is proposed and it is used on a traditional LP algorithms like a Maximum Ratio Transmission (MRT), a Zero-Forcing (ZF), a Regularized Zero-Forcing (RZF), and a Minimum Mean Square Error (MMSE) for Millimeter wave MU-MIMO communication system. A new technique is also used to mitigate the BER gab problem between (ZF, MMSE) and (RZF, MMSE) linear precoding algorithms. The result shows that with using the new technique, the BER performance of modified LP significantly outperform their traditional LP by 10−5 when using 4 element of BS antenna, 10−6 when using 16 element of BS antenna and mitigate the BER gab problem at different signal to noise ratio (SNR).

Free space optical communication (FSO) is widely deployed to transmit high data rates for rapid communication traffic increase. Asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) modulation is a very efficient FSO communication technique in terms of transmitted optical power. However, its performance is limited by atmospheric turbulence. When the channel includes strong turbulence or is non-deterministic, the bit error rate (BER) increases. To reach optimal performance, the ACO-OFDM decoder needs to know accurate channel state information (CSI). We propose novel detection using different deep learning (DL) algorithms. Our DL models are compared with minimum mean square error (MMSE) detection methods in different turbulent channels and improve performance especially for non-stationary and non-deterministic channels. Our models yield performance very close to that of the MMSE estimator when the channel is characterized by weak or strong turbulence and is stationary. However, when the channel is non-stationary and variable, our DL model succeeds in improving the performance of the system and decreasing the signal to noise ratio (SNR) by more than 8 dB compared to that of the MMSE estimator, and it succeeds in recovering the received data without needing to know accurate CSI. Our DL decoders also show notable speed and energy efficiency improvement.

This work focuses on studying signal detection using three different equalization techniques, namely: Zero Forcing (ZF), Minimum Mean Square Error (MMSE) and Beam Forming (BF), for a 4×4 MIMO-system. Results show that ZF equalization is the simplest technique for signal detection, However, Beam Forming (BF) gives better Bit Error Rate (BER) performances at high Signal to Noise Ratio (SNR) values with some complexity in design. For more antennas at the base station, it is too complex to design the weight matrix for ZF, however, it is suitable for BF with the help of good quality digital signal processors. Performance of MIMO-system, with 8 antennas at the base station using BF equalization, is analysed to get BER values at different SNR. Results show a considerable improvement in BER for 8 antennas at the base station.

We present a method for exactly solving the optimization problem for a scenario of discrete rate adaptive modulation. The aim is to maximize the spectral efficiency based on the imperfect channel estimation condition, constant power and average bit error rate(BER) constraints for multilevel quadrature amplitude modulation MQAM over Rayleigh flat fading channels with band-limited feedback signal. Transmission rates are not assigned predetermined values before solving the optimization problem. We show that the general optimization solution entails constellation sizes shouldn't be very large. Our proposed method is an iterative algorithm during which two sets of transmission rates and classification regions for signal to noise ratio (SNR) are updated alternately. The joint solution is a special case of Vector Quantization solution with minimum average cost function. We consider the case where channel is estimated by Pilot Symbol Assisted Modulation (PSAM) and Minimum Mean Square Error (MMSE) criterion.

Multiple-input multiple-output (MIMO) systems can achieve high data-rate and high capacity transmission. In MIMO systems, the scheme that weight substreams based on minimum mean square error (MMSE) criterion at the transmitter using feedback channel state information (CSI) achieves good performance (denoted hereafter as MMSE precoder). However, if the optimum number of substreams is not selected based on CSI and methods for reducing the performance degradation due to feedback delay is not used, MMSE precoder cannot achieve the full performance possible. In this paper, we propose an MMSE precoder with mode selection for MIMO systems, which selects both the number of substreams and the modulation scheme for each substream to minimize the average BER at a fixed rate. We evaluate the BER of the proposed MMSE precoder with two methods for reducing performance degradation due to feedback delay, channel prediction and receive weight robust to feedback delay. We also evaluate the BER of the proposed MMSE precoder with the method that combines channel prediction with receive weight robust to feedback delay. Simulation results show that the BER of the proposed MMSE precoder is improved compared to that of the conventional MMSE precoder using the fixed number of substreams. We also show that the method that combines channel prediction with receive weight robust to feedback delay can achieve good BER even when the large feedback delay exists.

A multiuser decision-feedback detector (DFD) for direct-sequence code-division multiple-access (DS-CDMA) is proposed for fast-fading channels. The proposed modified minimum mean-squared error (MMSE)-DFD (termed precombining MMSE-DFD) is shown to be independent of the instantaneous channel coefficients. Hence, it can be adaptively implemented unlike the standard MMSE-DFD (termed postcombining MMSE-DFD), where it is known to break down in fast-fading channels due to the severe tracking problems. A two-stage MMSE-DFD is also derived which consists of two cascaded MMSE-DFDs, each performing parallel or successive interference cancellation prior to multipath combining. The performance of the various MMSE-DFDs is investigated and compared to the linear MMSE detector (i.e. no feedback) over different fading-channel models, using the Gaussian approximation. The numerical results show that, in all cases, the postcombining receivers perform significantly better than the corresponding precombining receivers. Finally, a simple adaptive implementation for the two-stage detector is derived based on the normalised least-mean-square (NLMS) algorithm. The performance of this two-stage receiver is examined using both the Gaussian approximation and Monte Carlo simulations.

Satellite communications are expected to collaborate with 5G techniques in the future. In this paper, a detector based on the minimum mean square error (MMSE) criterion is designed at the receiver of a LEO satellite system to cancel co-channel interference (CCI) in a predetermined order successively, which is called ordered successive interference cancellation (OSIC). In order to make the detector have stronger ability to mitigate interference, low density parity check (LDPC) coding and soft demodulation schemes are applied with the OSIC jointly to improve our proposed MMSE-OSIC detector's performance. In the simulation analysis, we present the bit error rate (BER) performance of our proposed detector in an AWGN channel. Numerical results show that compared to the results of the conventional detection in existing literatures, the MMSE-OSIC detector can reduce the BERs for fixed signal-to-noise ratio (SNR) values. It means our proposed detector can be employed at the receiver with high service availability and reliability guaranteed.

Adaptive channel equalisation is a signal processing technique to mitigate inter-symbol interference (ISI) in a time dispersive channel. To this end, the use of least mean squares (LMS) algorithm and its variants is widespread since they minimise the minimum mean squared error (MMSE) criteria by online stochastic gradient algorithms and they asymptotically tend to the optimal Weiner solution for linearly separable channels. The kernel least mean squares (KLMS) algorithm and its variants are based on the MMSE based algorithms for non-linear channels. However, as has been pointed out in the literature, the minimum bit/symbol error rate (MBER/MSER) criterion is a better choice for adapting an equaliser as compared to the traditional approaches based on MMSE criterion. In this paper, we propose a novel equaliser that is inspired from the recently proposed MSER adaptation by Gong et al. using the kernel trick for non-linear channel equalisation.

In this paper, the training sequence design for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems under the minimum mean square error (MMSE) criterion is addressed. The optimal training sequence for channel estimation in spatially correlated MIMO-OFDM systems was not known for an arbitrary signal-to-noise ratio (SNR). Only one class of training sequences was proposed in the literature in which the power allocation is given only for the extreme conditions of low and high SNRs. The current paper presents a necessary and sufficient condition for the optimal training sequence, and reformulates the training design problem as a convex optimization problem whose optimal solution is efficiently solved. In addition, tight upper bounds for MMSE and resulting low complexity iterative algorithms with the closed-form expression in iterations to find the optimum training sequence are derived. Simulation results confirm the superiority of the proposed design over the existing one in terms of both MSE estimation and BER performance. The proposed methods are also shown to be robust with respect to the spatial correlation mismatch at the transmitter.

Enhanced genetic algorithms (GA) applied in space-time block coded (STBC) multiuser detection (MUD) systems in Rayleigh flat-fading channels are reported in this paper. Firstly, an improved objective function, which is designed to help speed up the search for the optimal solution, is introduced. Secondly, a decorrelating detector (DD) and a minimum mean square error (MMSE) detector have been added to the GA STBC MUD receiver to create the seed chromosome in the initial population. This operation has improved the receiver performance further because some signal information has been intentionally embedded in the initial population. Simulation results show that the receiver employing the improved objective function and the DD or MMSE detector can converge faster with the same bit error rate (BER) performance than the receiver with the initial population chosen randomly. The total signal-to-noise ratio (SNR) improvement contributed by these two modifications can reach 4 dB. Hence the proposed GA receiver is a promising solution of the STBC MUD problem.