Equal-rate QR decomposition based on MMSE technique for multi-user MIMO precoding

In this paper, we design a zero-forcing (ZF) Tomlinson-Harashima precoding (THP) and a minimum mean square error (MMSE) THP for multiuser MIMO relay system with direct link. Based on these precoding structures, we propose the optimal combining weights of the ZF THP and the MMSE THP in half duplex relay system, and the sub-optimal weights of MMSE THP to reduce feedback channel state information (CSI). Through the Monte Carlo simulation, we verify that the optimal weights combining method outperforms the constant weights combining method. In addition, we confirm that the performance of the sub-optimal weights combining method is close to the optimal method, while reducing the feedback CSI simultaneously.

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.

Foschini quantified the large capacity of the multiple-input multiple-output (MIMO) wireless channel and showed how this capacity could be achieved using a layered and coded space-time architecture. Unfortunately, his proposed diagonal Bell Laboratories Space-Time (D-BLAST) detection algorithm has proved awkward to implement. Attention has instead focused on the simpler vertically-layered architecture. The well-known vertical MIMO detectors, such as zero forcing (ZF), minimum mean squared error (MMSE), maximum likelihood (ML), vertical BLAST (V-BLAST), and several versions of sphere decoding (SD), offer different trade-offs between computational complexity and performance. V-BLAST offers intermediate, but clearly suboptimal performance that has a computational complexity that grows linearly in the number of transmitted layers and in the size M of the symbol constellation. Fouladi Fard, Alimohammad and Cockburn recently proposed a parallel V-BLAST algorithm, which we call F-BLAST, that offers performance that approaches that of optimal ML at the cost of performing V-BLAST in parallel for all M possible values of the symbol in the layer with the weakest expected signal-to-noise ratio. Here we revisit the performance of F-BLAST and show how the degree of parallelism can be reduced while maintaining performance that greatly exceeds that of V-BLAST. The data parallel structure of the new detection algorithms, and their simpler control structure compared to SD, should offer implementation advantages.

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

A wireless multiple-input multiple-output (MIMO) communications transceiver is a promising candidate for next generation wireless systems. It can enhance the capacity and reliability of the communication link. MIMO is enabled by the presence of multiple transmitting antennas and multiple receiving antennas in the communication link. The benefits of MIMO communication are obtained through a combination of antenna arrays, signal processing, and coding algorithms, which adapt the link to the changing channel. In this critical review paper, a propagation-oriented viewpoint is adopted to discuss wireless MIMO. We give an overview of current research areas and discuss some open problems.

Precoding is a technique which exploits transmission diversity by weighting the information stream, i.e. the transmitter sends the coded information to the receiver to achieve pre-knowledge of the channel. Visible light communication (VLC) channels inherently exhibit frequency-selective and multi-path fading effects that result in intersymbol interference (ISI) and thus reduces the data rate. To this end, optical multiple input multiple output (MIMO) can provide spatial diversity and thus achieve a high data rate. Inspired by these facts, we investigate different precoding and equalization schemes for $2 \times 2$ MIMO for the vehicle to vehicle (V2V-VLC) system. In this work, we consider three detection schemes, Zero Forcing (ZF), Maximum likelihood (ML), and Minimum Mean Squared Error (MMSE). Also, we consider flickering/dimming control and the nature of outdoor VLC channel as a frequency selective channel. Moreover, we investigate a transceiver considering perfect CSI based on different detection algorithms. Simulation results of the investigated transceiver demonstrate improvements in Bit Error Rate (BER) and Mean Squared Error (MSE) for the MMSE scheme.

Tomlinson Harashima Precoding (THP) for Multi-User Multiple Input Multiple Output (MU-MIMO) system has been proposed as an effective way to achieve near capacity to the theoretical limit in MU-MIMO channels. In order to achieve better performance, other THP methods such as minimum mean square error (MMSE) THP and lattice reduction aided (LRA) THP are proposed. Those methods outperform the conventional THP, however, the computational complexity also increases. In this paper, we propose a modified THP by new approach using square root with less increase of computational complexity. Computer simulation shows that proposed method can achieve better trade-off between bit error rate and computational complexity than MMSE THP and LRA THP.

In this paper, we consider an algorithm of detecting a signal with quadrature amplitude modulation (QAM) in a multiple inputs and multiple outputs (MIMO) communication system. The algorithm consists of two steps: soft-decision decoder using Kalman filtering and hard-decision decoder using criterion of the minimum distance between soft decision vectors and possible information symbols at each receiving antenna. The Kalman filter estimates symbols at the i-th time point during K iterations. The comparison of the noise immunity of QAM signal reception was performed using the Zero Forcing equalizer, the minimum mean square error (MMSE) algorithm, and the recurrent Kalman filtering. Signal processing takes place under conditions of Rayleigh fading multipath channel with Doppler spectrum spreading. Two cases were considered: the channel matrix is known precisely and the second when it is estimated by the least squares method (LS) using a first-order polynomial approximation for the elements of the channel matrix. The channel matrix contains not only signal distortions due to the multipath channel, but also distortions of the direct conversion receiver, such as amplitude and phase imbalance between signal in-phase and quadrature components, frequency offset due to non-ideal detection algorithm, as well as direct current offset (DC offset). In addition, the computational complexity of the detector based on the Kalman filtering is analyzed.

Conventional MIMO systems typically use full digital processing for optimal performance while it requires an independent radio frequency (RF) chain for each antenna, which is not feasible for large-scale antenna arrays due to the high cost, high-power consumption and high complexity of RF chain components in high frequencies. Fortunately, in recent years, the Hybrid beamforming has been proposed as an efficient and auspicious technique for the practical implementation of millimeter-Wave (mmWave) multiple-input multiple-output (MIMO) wireless systems. In this paper we propose a novel HBF (Hybrid beamforming) algorithm and simulate the sum rate of the proposed approach, then compare it with other algorithms in the sum rates. Specifically, the HBF algorithm as well as the maximizing minimum phase difference algorithm are based on the MMSE (Minimum Mean Square Error). For the full-digital beamforming and the beam steering, the ZF (zero forcing) criterion is employed. Simulations demonstrate that the performance of the proposed algorithm is similar to the full digital algorithm, and its robustness is confirmed by comparisons with other existing algorithms under the same channel model.

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.

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).

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.

3GPP (3rd Generation Partnership Project) LTE (Long Term Evolution) Advanced standards are currently under way, where 4×4 MIMO (Multiple Input Multiple Output) scheme is the minimum structure. One of the best solutions to support the maximum data rate transmission is to adopt a MIMO scheme, especially spatial multiplexing mode, which means that each antenna port can transmit separate data. To realize this algorithm, the main issue is to cancel interferences added to each antenna port, and therefore, the algorithm at the receiver should have good performances. In the aspect of implementation, MMSE (Minimum Mean Square Error) detection algorithm is a reasonable method considering both complexity and performance. Furthermore, an iterative receiver (IR) algorithm can also be applied to this system. An IR algorithm has a tradeoff between complexity and performance. In this paper, we designed a reasonable and implementable MIMO receiver structure and showed performance for 3GPP LTE Advanced system, and verified that hard decoded bits, PIC-MMSE (Parallel Interference Cancellation - MMSE) and 1-iteration PIC are enough to meet the required SNR using the implemented test-bed system.

We present an interesting and powerful new framework connecting the achievable sum rate of multiple-input multiple-output (MIMO) wireless systems employing linear minimum mean-squared error (MMSE) receivers, and the ergodic MIMO mutual information. This allows the vast literature on ergodic MIMO mutual information to be directly applied to the analysis of MMSE receivers. As an example, the framework is particularized to spatially-correlated Rayleigh fading to yield new exact closed-form expressions for the achievable sum rate, as well as simplified expressions for high and low signal to noise ratios.