Memetic Differential Evolution Assisted Minimum Bit Error Rate Detector for Multi-user MIMO System

The paper considers the problem of constructing adaptive minimum bit error rate (MBER) neural network equalisers for binary signalling. Motivated from a kernel density estimation of the bit error rate (BER) as a smooth function of training data, a stochastic gradient algorithm called the least bit error rate (LBER) is developed for adaptive nonlinear equalisers. This LBER algorithm is applied to adaptive training of a radial basis function (RBF) equaliser in a channel intersymbol interference (ISI) plus co-channel interference setting. A simulation study shows that the proposed algorithm has good convergence speed, and a small-size RBF equaliser trained by the LBER can closely approximate the performance of the optimal Bayesian equaliser. The results also demonstrate that the standard adaptive algorithm, the least mean square (LMS), performs poorly for neural network equalisers because the minimum mean square error (MMSE) is clearly suboptimal in the equalisation setting.

Precoding for multiple-input multiple-output (MIMO) spatial multiplexing generally requires high feedback overhead and/or high-complexity processing. Simultaneous reduction in transmitter complexity and feedback overhead is proposed by imposing a diagonal structural constraint to precoding, i.e., power allocation. Minimum bit-error rate (MBER) is employed as the optimization criterion, and an approximate MBER (AMBER) power-allocation algorithm is proposed for a variety of receivers, including zero-forcing (ZF), successive interference cancellation (SIC), and ordered SIC (OSIC). While previously proposed precoding schemes either require ZF equalization for MBER, or use a minimum mean-squared error (MMSE) criterion, we provide a unified MBER solution to power allocation for ZF, SIC, and OSIC receiver structures. Improved error-rate performance is shown both analytically and by simulation. Simulation results also indicate that SIC and OSIC with AMBER power allocation offer superior performance over previously proposed MBER precoding with ZF equalization, as well as over MMSE precoding/decoding. Performance under noisy channels and power feedback is analyzed. A modified AMBER algorithm that mitigates error propagation in interference cancellation is developed. Compared with existing precoding methods, the proposed schemes significantly reduce both transmit processing complexity and feedback overhead, and improve error-rate performance

The V-BLAST (Vertically — layered Bell Laboratories Layered Space-Time) algorithm is a multilayer symbol detection scheme. The proposed work focuses on V-BLAST technique with a Multiple Input Multiple output (MIMO) technology followed by receiver detection techniques like Zero forcing (ZF), Minimum Mean Square Error (MMSE) with back substitution SIC (Symbol Interference Cancellation). The proposed methodology adopts BPSK, QAM modulation methods. The numerical analysis is conducted using MATLAB. The performance improvement is also significant and Simulation results shows that V-BLAST achieves better Bit error rates.

Block data transmission is an efficient scheme to mitigate the inter-symbol interference (ISI) caused by dispersive channels. Recent research work attempt to obtain optimal designs of precoders given various linear and non-linear receivers. In this paper we focus on the systems with optimal precoder designs based on the minimization of bit error rate (BER) which is the more meaningful criterion in data communications. The linear receivers employed in these systems include zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Recently, block decision feedback equalization (DFE) has also been suggested to be used in the design of such block data transmission systems. We also revisit the jointly optimum designs of the precoder coupled with the DFE receivers. First we derive the block-data error rate for all of these different systems with their corresponding optimal precoders. Then we rank their performance accordingly. Simulation results are also obtained to verify our analysis. Later, we evaluate the computational complexity on the various systems and draw some conclusions on their relative merits. Finally, we derive the lower and upper bounds of bit error rate (BER) considering error propagation for systems employing nonlinear equalizers.

In recent years, multiple-input multiple-output (MIMO) systems, which use several transmit and receive antennas, have attracted much attention for high performance radio systems. In MIMO systems, the channel estimation is important to distinguish transmit signals from multiple transmit antennas. While the space-alternating generalized expectation-maximization (SAGE) algorithm is known to offer good channel estimation and data detection. We proposed earlier the minimum mean square error (MMSE)-based SAGE algorithm for MIMO systems where the MMSE estimation is used for channel estimation. We showed that the proposed MMSE-based SAGE algorithm can achieve the better bit error rate (BER) than the maximum likelihood (ML) detection with training symbols. The MMSE channel estimation needs the knowledge of the maximum Doppler frequency F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> for deriving the covariance matrix of the channel and the variance sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of additive white Gaussian noise (AWGN). Additionally, the computation of the MMSE channel estimation requires O(L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where L is the transmitted frame length. Thus, its computational complexity is high. In this paper, we propose a zero-forcing (ZF)-based SAGE algorithm for channel estimation and data detection in MIMO systems that does not need the knowledge of Fd and sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Since the computation of the proposed ZF-based SAGE algorithm requires O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) operations where N is the number of transmit antennas, its computational complexity is low. We show that the proposed ZF-based tracking SAGE algorithm with less computational complexity can achieve almost the same BER as that of the MMSE-based tracking SAGE algorithm

We considers the beamforming assisted multiple-antenna receiver for space-division multiple-access based multiuser systems that employ high-throughput quadrature amplitude modulation (QAM) signalling. The bit error ratio (BER) expression as the function of the beamformer's weight vector is derived, and the minimum BER (MBER) beamforming receiver is then obtained as the solution of the resulting optimisation problem that minimises the MBER criterion. A simplified conjugate gradient algorithm, which has previously demonstrated its effectiveness in solving the minimum symbol error ratio (MSER) optimisation problem, is employed to solve this MBER optimisation. For high-order QAM, although the bit decision is an inherently more complicated procedure than making a symbol decision, it turns out that the computational complexity of computing the MBER solution is similar to that of computing the MSER solution. As expected, our simulation results show that both the MBER and MSER systems achieve the same BER performance, and they significantly outperform the standard minimum mean squares error based solution.

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).

A novel genetic algorithm (GA) assisted minimum bit error rate (MBER) beamforming technique is introduced. The performance of the proposed GAs is characterised by the probability density function (PDF) and the mean value of the achievable bit error rate (BER) at the beamformer's output. The results are also compared to the theoretical bounds. It is shown that GAs are suitable for MBER beamforming and that a trade-off between the complexity of the GA and its robustness against system parameter variations can be found.

The conventional decision feedback equaliser (DFE) that employs a linear combination of channel observations and past decisions is considered. The design of this class of DFE is to construct a hyperplane that separates the different signal classes. It is well known that the popular minimum mean square error (MMSE) design is generally not the optimal minimum bit error rate (MBER) solution. A strategy is proposed for designing the DFE based on support vector machines (SVMs). The SVM design achieves asymptotically the MBER solution and is superior in performance to the usual MMSE solution. Unlike the exact MBER solution, this SVM solution can be computed very efficiently.

Adaptive beamforming for binary phase shift keying communication systems

A minimum bit error rate (MBER) multiuser detector designed for space division multiple access (SDMA) aided orthogonal frequency division multiplexing (OFDM) systems is proposed. It is shown that the MBER detector outperforms the minimum mean squared error (MMSE) detector, since the MBER detector directly minimises the BER, while the MMSE detector minimises the mean-squared error (MSE), which does not guarantee achieving the minimum BER. When supporting two users, the proposed MBER scheme substantially outperforms the classic MMSE arrangement in the investigated propagation scenario.

In the field of multiple input multiple output (MIMO) decoder, K-best has been well investigated because it guarantees an SNR-independent fixed-throughput with a performance close to the optimal maximum likelihood detection (MLD). However, the complexity of its expansion and sorting tasks is significantly affected by the constellation size W. In this paper, we propose an algorithm and hardware design of a 2D sorter-based K-best MIMO decoder whose complexity is negligibly affected by W. The main novelties of the algorithm are the following: (1) Direct expansion and parent node grouping ideas are proposed for reducing the expansion task’s complexity. (2) Two-dimensional (2D) sorter is proposed for simplifying the sorting task. The hardware design of the decoder supports up to 256-QAM modulation, which aims to apply into 4 × 4 MIMO 802.11n and 11ac systems. The paper shows that the proposed decoder outperforms the Bell Labs layered space-time (BLAST) minimum mean square error (MMSE) and lattice-reduction aided (LRA) MMSE, and is close to the full K-best in terms of bit error rate (BER) performance. The hardware design of the decoder is synthesized in application specific integrated circuit (ASIC) and compared with the previous works. As a result, it achieves the highest throughput (up to 2.7 Gbps), consumes the least power (56 mW), obtains the best hardware efficiency (15.2 Mbps/Kgate), and has the shortest latency (0.07 µs).

In this contribution, we consider the performance of multiple-input multiple-output (MIMO) code division multiple access (CDMA) system for digital image transmission over correlated Rayleigh fading channel. MIMO system employs multiple antennas both at the transmitter and receiver. In our work, we consider turbo coded system to investigate the performance of MIMO-CDMA system. We realize turbo code using parallel concatenated convolutional encoder and second convolutional encoder is preceded by random interleaver. Further the output of two convolutional encoder are punctured to get rate of ½. At the receiver, we employ iterative decoding algorithm to reduce the effect of multiple access interference (MAI) and Inter-Symbol-Interference (ISI) and median filters to reduce the effect of salt and pepper noise.. In particular, we evaluate the performance of coded MIMO-CDMA system using Zero forcing (ZF) - multi-user detection (MUD) and minimum mean square error (MMSE)-MUD detection technique to mitigate the effects of multi-stream interference (MSI). It is shown through the simulation study that our considered coded MIMO-CDMA system with MMSE algorithm achieves better picture quality with less signal-to-noise ratio (SNR) as compared to ZF MUD.

Limited feedback precoding (LFP) significantly improves multiple-input multiple-output (MIMO) spatial multiplexing link reliability with a small amount of feedback from the receiver back to the transmitter. One of the key problems linked to LFP is how to select an optimal precoder from a pre- determined unitary codebook. We find that the conventional precoder selection criteria are not applicable to the stream maximization transmission (SMT) mode with linear receivers, including zero forcing (ZF) and minimum mean square error (MMSE) decoders. To solve this issue, a novel singular value decomposition (SVD) based precoder selection criterion is proposed in this paper. This criterion features a unified structure for all the linear receivers such as ZF and MMSE decoders, and is shown by simulation to provide significant coding gains in various SMT systems. With the same complexity as the conventional one, the proposed criterion could find its applications in next generation systems employing SMT spatial multiplexing, significantly improving system performance with affordable feedback requirement.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.