A linear precoding strategy based on particle swarm optimization in multicell cooperative transmission

Multiple input multiple output (MIMO) symbol detection problem belongs to non-deterministic polynomial acceptable hard combinatorial optimization (CO) class. One of the key trials in design of MIMO scheme is to develop a low complexity detection algorithm without much compromise in performance. Detection approaches proposed in the literature can be split into non-linear and linear algorithms. Vertical Bell-Labs Layered Space Time (V-BLAST) and Sphere Decoder (SD) are non-linear methods used for extracting transmitted data; whereas, Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) detections are comparatively in complex and effectual linear techniques. In this work, the heuristic 1-Opt local search method used for solving computationally hard combinatorial optimization problems is applied to the ZF and MMSE detection algorithms. First, simple MIMO decoding using ZF and MMSE is accomplished to find the estimated symbol then the transmitted symbol is calculated using the heuristic 1-opt approach by means of the estimated symbol. Simulation results demonstrate that 1-opt search when applied to the ZF and MMSE displays better bit error rate (BER) performance than the simple ZF and MMSE detectors. It is also verified through simulations that the proposed 1-Opt based detectors display better BER performance as compared to the complex nonlinear VBLAST and SD at considerably reduced complexity. Hence, the proposed detectors are appropriate for effective hardware implementations.

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.

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

Most existing quasi-orthogonal space time Block coding (QO-STBC) schemes have been developed relying on the assumption that the channel is at or remains static during the length of the code word symbol periods to achieve an optimal antenna diversity gain. However, in time-selective fading channels, this assumption does not hold and causes intertransmit-antenna-interferences (ITAI). Therefore, the simple pairwise maximum likelihood decoding scheme is not sufficient to recover original transmitted signals at the receiver side. To avoid the interferences, we have analyzed several signal detection schemes, namely zero forcing (ZF), two-step zero forcing (TS-ZF), minimum mean square error (MMSE), zero forcing - interference cancelation - decision feedback equalizer (ZF-IC-DFE) and minimum mean square error - interference cancelation { decision feedback equalizer (MMSE-IC-DFE). We have proposed two efficient iterative signal detection schemes, namely zero forcing - iterative interference cancelation - zero forcing { decision feedback equalization (ZF-IIC-ZF-DFE) and minimum mean square error - parallel interference cancelation - zero forcing – decision feedback equalization (MMSE-IIC-ZF-DFE). The simulation results show that these two proposed detection schemes significantly outperform all conventional methods for QOSTBC system over time selective channel.

This study concentrates on the investigation of signal detection by using Zero Forcing (ZF), Minimum Mean Square Error (MMSE) and Beam Forming (BF), for a MIMO and massive MIMO system. Outcomes show that ZF is the modest method for signal detection, though BF gives better Bit Error Rate (BER) performance with some constraints in implementation, but MMSE implementation complexity is reduced by avoiding the matrix inversion in the receiver while sustaining the optimal performance as compared to other conventional methods. For several antennas at the base location, it is too difficult to implement the weight matrix for ZF, still, it is appropriate for BF with the benefit of decent digital signal algorithms. Performance of MIMO and massive MIMO using equalisation is investigated to get the throughput of the system (BER vs. SNR). Results indicate a significant improvement in BER for 16x16 as compared to 4x4, 8x1 and 8x8 antennas at the base station. The other parameters like capacity and Signal Interference Noise Ratio (SINR) are likewise examined for massive MIMO system.

ABSTRACTThis article presents a field programmable gate array design and implementation of particle swarm optimisation (PSO) algorithm for multiple input multiple output (MIMO) detection systems. Although, the simulations results prove that the maximum likelihood (ML) detector presents better performances than the other detectors like zero forcing (ZF) and minimum mean square error (MMSE), but with MIMO systems this algorithm has a high computational complexity. To minimise this effect, we apply a new type of cost function and give an efficient calculation algorithm. We propose a PSO approach based on signal transmitted vector from, and . The simulation result shows the effectiveness of the proposed algorithm in terms of achieving better bit error rate performance compared to ZF and MMSE with low complexity. This algorithm has been developed to reduce the ML detector complexity.

In wireless channels, Non-Gaussian noise is one of the most common noise models that is observed. This type of noise has a severe impact on wireless systems with linear and multiuser detection devices. In this paper, We study the performance of zero forcing (ZF) and minimum mean square error (MMSE) ZF detection methods in Impulsive multi-cell MIMO channels. We start by showing the Bit Error Rate performance in non-Gaussian channels for ZF Detection, then we extend the derivations for MMSE ZF system. We clearly show the lower and upper bound derivations and verify it through simulations. The sum rate analysis for this case is also examined. Finally, we address the ZF matrix inversion complexity problem, and propose a simple ZF algorithm that does not necessitate the matrix inversion. We then investigate the convergence of such a detector and look at the Symbol Error rate SER performance through simulation again.

The application of equalization schemes to Single Carrier (SC) modulation techniques has made them a valuable alternative to Orthogonal Frequency Division Multiplexing (OFDM). Equalization schemes mitigate Inter Symbol Interference (ISI) caused by multipath fading which degrades the performance of modulation schemes. In this paper we study Zero Forcing, Minimum Mean Square Error and Decision Feedback equalization schemes and compare their Bit Error rate (BER) performance with Maximum likelihood sequence estimation (MLSE) based Matched Filter Bound (MFB), also called as optimum filter. Simulations in Matlab show that BER performance of Decision Feedback Equalizer (DFE) is better than Zero Forcing Equalizer (ZFE) and Minimum Mean Square Error (MMSE) equalizer and is comparable to the performance of MFB with DFE having very low complexity as compared to MLSE based MFB.

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).

The problem of blind adaptive equalization of underwater single-input multiple-output (SIMO) acoustic channels was analyzed by using the linear prediction method. Minimum mean square error (MMSE) blind equalizers with arbitrary delay were described on a basis of channel identification. Two methods for calculating linear MMSE equalizers were proposed. One was based on full channel identification and realized using RLS adaptive algorithms, and the other was based on the zero-delay MMSE equalizer and realized using LMS and RLS adaptive algorithms, respectively. Performance of the three proposed algorithms and comparison with two existing zero-forcing (ZF) equalization algorithms were investigated by simulations utilizing two underwater acoustic channels. The results show that the proposed algorithms are robust enough to channel order mismatch. They have almost the same performance as the corresponding ZF algorithms under a high signal-to-noise (SNR) ratio and better performance under a low SNR.

In this paper, we studied the bit error rate (BER) for zero forcing (ZF) and minimum mean square error (MMSE) detection methods in spatially multiplexed multi-input-multi-output (SM-MIMO) systems over nakagami-m flat fading channels using binary phase shift keying (BPSK), quadrature phase shift keying (QPSK) and 16-ary phase shift keying (16-PSK) modulations. The coefficients of nakagami-m channel matrix has been generated from the gamma random variables (RVs). The analysis assumes that MIMO channels are limited by the Gaussian noise and receiver has complete knowledge of these channels. The results for spatially multiplexed MIMO system with two inputs two outputs with ZF and MMSE receivers for different values of fading parameter ‘m’ and scale parameter ‘Ω’ are illustrated using BER plots. Performance comparison of SM-MIMO system and single-input-multiple-output (SIMO) system is also presented in the results. Eye diagrams for received symbols after ZF and MMSE are also shown separately using 4-ary quadrature amplitude modulation (4-QAM).

&lt;span&gt;Massive multi-input–multi-output (MIMO) systems are crucial to maximizing energy efficiency (EE) and battery-saving technology. Achieving EE without sacrificing the quality of service (QoS) is increasingly important for mobile devices. We first derive the data rate through zero forcing (ZF) and three linear precodings: maximum ratio transmission (MRT), zero forcing (ZF), and minimum mean square error (MMSE). Performance EE can be achieved when all available antennas are used and when taking account of the consumption circuit power ignored because of high transmit power. The aim of this work is to demonstrate how to obtain maximum EE while minimizing power consumed, which achieves a high data rate by deriving the optimal number of antennas in the downlink massive MIMO system. This system includes not only the transmitted power but also the fundamental operation circuit power at the transmitter signal. Maximized EE depends on the optimal number of antennas and determines the number of active users that should be scheduled in each cell. We conclude that the linear precoding technique MMSE achieves the maximum EE more than ZF and MRT&lt;/span&gt;&lt;em&gt;&lt;/em&gt;&lt;span&gt;because the MMSE is able to make the massive MIMO system less sensitive to SNR at an increased number of antennas&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;

Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can provide a better bit error rate (BER) performance than rake combining. However, the residual inter-chip interference (ICI) is produced after MMSE-FDE and degrades the BER performance. Recently, we showed that frequency-domain ICI cancellation can bring the BER performance close to the theoretical lower bound. To further improve the BER performance, transmit antenna diversity technique is effective. Cyclic delay transmit diversity (CDTD) can increase the number of equivalent paths and hence achieve a large frequency diversity gain. Space-time transmit diversity (STTD) can obtain antenna diversity gain due to the space-time coding and achieve a better BER performance than CDTD. In this paper, we point out that the performance difference between CDTD and STTD is mainly due to the residual ICI. We theoretically show that the introduction of ICI cancellation into DS-CDMA/MMSE-FDE gives almost the same BER performance for CDTD and STTD. This is confirmed by computer simulation.

Mobile WiMAX is a broadband wireless solution that enables convergence of mobile and fixed broadband network through a common wide area broadband radio access technology and flexible network architecture. The aim of this paper is the performance evaluation of 802.16e system using different channel equalizers at the receiver module for different communication and modulation technique for different bandwidth. We analyze the Symbol Error Rate (SER) of the wireless communication channel (SUI -3 channel with AWGN) for using zero-force (ZF) and Minimum Mean Square Error (MMSE) equalizers at FFT size 256, 512 and 1024, respectively for BPSK, QPSK, 16-QAM and 64-QAM modulation. The simulation includes symbol error rate versus signal to noise ratio performance predictions. In our simulation we use deterministic random number generator (RNG) algorithm to generate the random input value. It is concluded that the performance of the MMSE equalizer is comparable to or slightly better than the ZF equalizer. Key words: Fast Fourier Transform (FFT), Symbol Error Rate (SER), zero force, Minimum Mean Square Error (MMSE), bit error rate.

In this paper, we propose a simple method which may enhance the performance of zero-forcing (ZF) or lattice reduction (LR) algorithm in multiple input multiple output (MIMO) detection. As we know MIMO communication systems increase the spectral efficiency and data reliability. Designing detector for such systems that have low complexity and performance near to optimum have attracted much of attention. Optimum detection due to its complexity is not applicable. Famous suboptimal algorithms are ZF, Minimum Mean Square Error (MMSE) and LR. ZF and MMSE are known as linear detectors although are very simple, their performance are far from optimum. LR technique were proposed to improve the linear detector performances. In this paper we propose a method that can improve the performances of the linear detectors as well as LR. This method is applied to the output of the above mentioned MIMO detection algorithm (ZF, MMSE and LR) and employing this point as the initial lattice point and search the neighboring point for better metric in the lattice. Simulation results confirm the reduction of the bit error rate by this algorithm.