A Worst-Case Robust MMSE Transceiver Design for Nonregenerative MIMO Relaying

In this paper, we consider interference multiple-input multiple-output (MIMO) relay systems where multiple pairs of transmitters–receivers simultaneously communicate through a single relay node and where all nodes are equipped with multiple antennas. We propose a new iterative algorithm to jointly optimize the relay precoding matrix and the receiver matrices of such a system based on the minimum sum mean-squared error (MSE) criterion. The optimal structure of the relay precoding matrix is developed to decrease the computational complexity of transceiver optimization. Simulation results demonstrate that the proposed transceiver optimization algorithm has a better MSE and bit-error-rate (BER) performance and a faster convergence rate than existing works.

Based on the knowledge of instantaneous channel state information (CSI), the optimal source and relay pre-coding matrices have been developed recently for multiple-input multiple-output (MIMO) relay communication systems. However, in real communication systems, the instantaneous CSI is unknown and needs to be estimated at the destination node. In this paper, we propose a superimposed channel training method for MIMO relay communication systems. It is shown that to minimize the mean-squared error (MSE) of channel estimation, the optimal training sequence at each node matches the eigenvector matrix of the transmitter correlation matrix of the forward MIMO channel. Then we optimize the power allocation among different streams of the training sequence at the source node and the relay node. Simulation results show that the proposed algorithm leads to a smaller MSE of channel estimation compared with the conventional MIMO relay channel estimation algorithm.

In this paper, we investigate the impact of the outdated Channel State Information (CSI) and the Co-Channel Interference (CCI) on the performance of Transmit Antenna Selection with Selective Combining (TAS/SC) in a dual-hop amplify-and-forward (AF) Multiple-Input Multiple-Output (MIMO) relay network. We derive the exact closed-form and asymptotic expressions for the outage probability in the cases of perfect and outdated CSI, respectively. The simulation results match the theoretical analysis well. The findings suggest that the outdated CSI and CCI have significant impacts on the outage probability of an AF MIMO relay system with TAS/SC.

In this work, we propose a minimum mean squared error (MMSE) robust base station (BS) precoding strategy based on switched relaying (SR) processing and limited transmission of side information for interference suppression in the downlink of multiuser multiple-input multiple-output (MIMO) relay systems. The BS and the MIMO relay station (RS) are both equipped with a codebook of interleaving matrices. For a given channel state information (CSI) the selection function at the BS chooses the optimum interleaving matrix from the codebook based on two optimization criteria to design the robust precoder. Prior to the payload transmission the BS sends the index corresponding to the selected interleaving matrix to the RS, where the best interleaving matrix is selected to build the optimum relay processing matrix. The entries of the codebook are randomly generated unitary matrices. Simulation results show that the performance of the proposed techniques is significantly better than prior art in the case of imperfect CSI.

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.

The authors investigate quantisation and feedback of channel state information in a multiuser (MU) multiple-input multiple-output (MIMO) system. Each user may receive multiple data streams. The authors design minimises the sum mean squared error (SMSE) while accounting for the imperfections in channel state information (CSI) at the transmitter. This study makes three contributions: first, the authors provide an end-to-end SMSE transceiver design that incorporates receiver combining, feedback policy and transmit precoder design with channel uncertainty. This enables the proposed transceiver to outperform the previously derived limited feedback MU linear transceivers. Second, the authors remove dimensionality constraints on the MIMO system, for the scenario with multiple data streams per user, using a combination of maximum expected signal combining and minimum MSE receiver. This makes each user's feedback independent of the others and the resulting feedback overhead scales linearly with the number of data streams instead of the number of receiving antennas. Finally, the authors analyse the SMSE of the proposed algorithm at high signal-to-noise ratio (SNR) and large number of transmit antennas. As an aside, the authors show analytically why the bit error rate, in the high SNR regime, increases if quantisation error is ignored.

Power optimization for maximum channel capacity in MIMO relay system

Traditional receiver algorithms developed for multiple-input multiple-output (MIMO) wireless communication systems are based on the assumption that the channel state information (CSI) is perfectly known at the receiver. However, in real environments the exact CSI is unavailable. In this paper, we address the problem of robustness of multiuser space-time block coded MIMO systems against imperfect CSI and develop a simple linear receiver which guarantees robustness against CSI errors with a certain selected probability. The proposed receiver is formulated via a probability-constrained optimization problem which is further relaxed using Chebyshev inequality to a much simpler second-order cone programming (SOCP) problem. Simulations demonstrate that the proposed receiver has a moderate performance degradation as compared to the exact solution to the original probability-constrained optimization problem, while offering much simpler implementation.

Optimal linear minimum mean square error (MMSE) transceiver design techniques are proposed for Bayesian learning (BL)-based sparse parameter vector estimation in a multiple-input multiple-output (MIMO) wireless sensor network (WSN). Our proposed transceiver designs rely on majorization theory and hyperparameter estimates obtained from the BL module for minimizing the mean square error (MSE) of parameter estimation at the fusion center (FC). The linear transceiver design framework is initially proposed for the general scenario with arbitrary SNR sensor observations, followed by a special case with high-SNR sensor observations scenario. Our analysis also incorporates the channel correlation. The MMSE channel estimates are determined for the sensors (SNs), followed by a robust transceiver design procedure that is resilient to the channel state information (CSI) uncertainty arising due to the channel estimation error, an aberration that is unavoidable in practical implementations. Our simulation results demonstrate the improved performance of the proposed BL framework and optimal MMSE transceiver design in sparse parameter estimation relyingon realistic imperfect channel estimates over the benchmarks.

This chapter is attempted to provide a survey of the advanced concepts and related issues involved in Multiple Input Multiple Output (MIMO) systems. MIMO system technology has been considered as a really significant foundation on which to build the next and future generations of wireless networks. The chapter addresses advanced MIMO techniques such as polarization diversity and antenna selection. We gradually provide an overview of the MIMO features from basic to more advanced topics. The first sections of this chapter start by introducing the key aspects of theMIMO theory. TheMIMO systemmodel is first presented in a genericway. Then, we proceed to describe diversity schemes used in MIMO systems. MIMO technology could exploit several diversity techniques beyond the spatial diversity. These techniques essentially cover frequency diversity, time diversity and polarization diversity. We further provide the reader with a geometrically based models for MIMO systems. The virtue of this channel modeling is to adopt realisticmethods for modeling the spatio-temporal channel statistics from a physical wave-propagation viewpoint. Two classes for MIMO channel modeling will be described. These models involve the Geometry-based Stochastic ChannelModels (GSCM) and the Stochastic channel models. Besides the listedMIMO channel models already described, we derive and discuss capacity formulas for transmission over MIMO systems. The achieved MIMO capacities highlight the potential of spatial diversity for improving the spectral efficiency of MIMO channels. When Channel State Information (CSI) is available at both ends of the transmission link, the MIMO system capacity is optimally derived by using adaptive power allocation based on water-filling technique. The chapter continues by examining the combining techniques for multiple antenna systems. Combining techniques are motivated for MIMO systems since they enable the signal to noise ratio (SNR) maximization at the combiner output. The fundamental combing techniques are the Maximal Ratio Combining (MRC), the Selection Combining (SC) and the Equal Gain Combining(EGC). Once the combining techniques are analyzed, the reader is introduced to the beamforming processing as an optimal strategy for combining. The use of multiple antennas significantly improves the channel spectral efficiency. Nevertheless, this induces higher system complexity of the communication system and the communication system performance is effected due to correlation between antennas that need to be deployed at the same terminal. As such, the antenna selection algorithm for MIMO systems is presented. To elaborate on this point, we introduce Space time coding techniques for MIMO systems and we evaluate by simulation the performance of the communication system. Next, we emphasis on multi polarization techniques for MIMO systems. As a background, we presume that the reader has a thorough understanding of antenna theory. We recall the basic antenna theory and concepts that are used throughout the rest of the chapter. We rigorously introduce the 3D channel model over the Non-Line of Sight (NLOS) propagation channel for MIMO system with polarized antennas. We treat the depolarization phenomena and we study its effect on MIMO system capacity. The last section of the chapter provides a scenario for collaborative sensor nodes performing distributed MIMO system model which is devoted to sensor node localization in Wireless Sensor Networks. The localization algorithm is based on beamforming processing and was tested by simulation. Our chapter provides the reader by simulation examples for almost all the topics that have been treated for MIMO system development and key issues affecting achieved performance.

The authors propose a full-duplex relay (FDR) based on a block diagonalisation (BD) method in multiple-input multiple-output (MIMO) relay channels. The BD method is employed to suppress the self-interference in MIMO FDR as well as to transmit multiple data streams to multiple users at the same time. The authors also derive the optimal power allocation strategy for MIMO FDR operation. Numerical results show that the use of the proposed FDR with BD can provide enhanced system performance compared with the FDR with zero-forcing beamforming.

Multiple transmit antennas can be employed in a downlink channel to serve multiple users under the assumption of perfect channel state information (CSI) of all users at the base station. In practice, however, the channel knowledge available at the base station is not perfect. For instance, in case of a time division duplex (TDD) system, the transmit CSI is the estimated uplink channel. On the other hand, in a frequency division duplex (FDD) system, feedback from the users is required to obtain transmit CSI. In this case, we assume the transmit CSI consists of a quantized version of the normalized estimated channel vector and the statistics of the channel norm of each user. In this work we consider the transceiver design of the downlink of a multiuser MISO system based on the minimum mean square error (MMSE) criterion with imperfect CSI as discussed above.

This letter proposes a robust joint linear precoding scheme based on the minimum mean squared error (MMSE) criterion for amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay broadcast systems with limited feedback, where only the quantized channel direction information (CDI) of the forward channel is available for the base station (BS) and the relay station (RS). The proposed scheme employs an iterative algorithm which alternately optimizes the BS and RS precoders to jointly minimize the expected MSE conditioned on the quantized CDI.

Interference alignment (IA) is a multi-user wireless communication strategy that enables several transmitters simultaneous communicate with their paired receivers without interfering each other. IA is a multiplexing gain optimal strategy at the expense of requiring the global channel state information (CSI) at the transmitters. Most previous works assume the availability of perfect CSI which is not possible in practice. The performance of IA algorithms based on perfect CSI drop dramatically in circumstance where CSI errors exist. In this paper we propose a robust minimum mean square error (MMSE) IA algorithm with imperfect CSI. Based on a Gaussian statistic channel error model, we give the mean square error objective function with per transmitter power constraint. The objective function is not joint convex in precoders and decoders, but convex in precoders with fixed decoders and vice versa. We convert the problem to two convex sub problems and iteratively find the solutions. Numerical results are presented to validate the effectiveness of proposed algorithm when CSI errors exist.

This letter investigates the spectrum sharing between a multiple-input single-output (MISO) secure communication system and a multiple-input multiple-output (MIMO) radar system in the presence of one suspicious eavesdropper. We harness the detrimental radar interference, which traditionally impairs communication systems, as a strategic mechanism to jam the eavesdropper, thereby substantially enhancing the performance of secure communication. In particular, by considering the imperfect channel state information (CSI) for the user and eavesdropper, we present a robust joint design for the radar waveform and communication beamforming vector at the two systems, with the objective of maximizing the worst-case secrecy rate at the user, while ensuring the detection performance of the radar system. To tackle this challenging problem, we propose a two-layer robust cooperative algorithm based on the Charnes-Cooper transformation and the Cauchy-Schwarz inequality. Simulation results reveal the trade-off between secrecy rate and detection probability and highlight the pivotal role of such robust designs in facilitating secure coexistence systems.