Multiple-input Multiple-output Relay Research Articles

Cognitive Radio Channel with Cooperative Multi-Antenna Secondary Systems

Recently, a cooperative cognitive radio network (CCRN) and multiple-input multiple-output (MIMO) cognitive radio (CR) network have been proposed and investigated individually as promising paradigms for CR networks. Herein, we consider applying the MIMO techniques to a CCRN in order to achieve increased spectral efficiency. Assuming that the system comprises a single-input single-output (SISO) primary user (PU) pair and a multi-input single-output (MISO) secondary user (SU) pair, we propose jointly optimizing the beamforming vector and power allocation for the SU transmitter in order to maximize the rate for the SU while meeting the rate requirement for the PU. As the problem is nontrivial, we circumvent it using the uplink and downlink duality and equality of the left and right eigenvalues. Further, we introduce an iterative algorithm with a proof of convergence. From the numerical results, the proposed algorithm converges in a small number of iterations and outperforms the zero-forcing (ZF) beamforming algorithm while providing an upper bound for the CCRN-MIMO performance. Furthermore, the application of the proposed algorithm is not limited to CCRN-MIMO; it can also be extended to the conventional relay MIMO and/or MU-MIMO with a quality-of-service (QoS) requirement.

Joint Optimization of Source Precoding and Relay Beamforming in Wireless MIMO Relay Networks

This paper considers joint linear processing at multi-antenna sources and one multiple-input multiple-output (MIMO) relay station for both one-way and two-way relay-assisted wireless communications. The one-way relaying is applicable in the scenario of downlink transmission by a multi-antenna base station to multiple single-antenna users with the help of one MIMO relay. In such a scenario, the objective of join linear processing is to maximize the information throughput to users. The design problem is equivalently formulated as the maximization of the worst signal-to-interference-plus-noise ratio (SINR) among all users subject to various transmission power constraints. Such a program of nonconvex objective minimization under nonconvex constraints is transformed to a canonical d.c. (difference of convex functions/sets) program of d.c. function optimization under convex constraints through nonconvex duality with zero duality gap. An efficient iterative algorithm is then applied to solve this canonical d.c program. For the scenario of using one MIMO relay to assist two sources exchanging their information in two-way relying manner, the joint linear processing aims at either minimizing the maximum mean square error (MSE) or maximizing the total information throughput of the two sources. By applying tractable optimization for the linear minimum MSE estimator and d.c. programming, an iterative algorithm is developed to solve these two optimization problems. Extensive simulation results demonstrate that the proposed methods substantially outperform previously-known joint optimization methods.

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

Transceiver designs have been a key issue in guaranteeing the performance of multiple-input multiple-output (MIMO) relay systems, which are, however, often subject to imperfect channel state information (CSI). In this paper, we aim to design a robust MIMO transceiver for nonregenerative MIMO relay systems against imperfect CSI from a worst-case robust perspective. Specifically, we formulate the robust transceiver design, under the minimum mean-squared error (MMSE) criterion, as a minimax problem. Then, by decomposing the minimax problem into two subproblems with respect to the relay precoder and destination equalizer, respectively, we show that the optimal solution to each subproblem has a favorable channel-diagonalizing structure under some mild conditions. Based on this finding, we transform the two complex-matrix subproblems into their equivalent scalar forms, both of which are proven to be convex and can be efficiently solved by our proposed methods. We further propose an alternating algorithm to jointly optimize the precoder and equalizer that only requires scalar operations. Finally, the effectiveness of the proposed robust design is verified by simulation results.

Low-Complexity Detection Scheme for Cooperative MIMO Systems with Decode-and-Forward Relays

In this paper, we study low-complexity detection schemes for cooperative multiple-input multiple-output (MIMO) systems with decode-and-forward (DF) relays. In fixed DF protocols, the error propagation effect that limits the diversity gain can be overcome by using joint maximum-likelihood (JML) detection, but its complexity increases exponentially with the number of streams and modulation orders. To develop a low-complexity detection scheme, we first extend the cooperative maximum-ratio combining (C-MRC) scheme to MIMO relay networks, and then investigate the diversity order of the system. We show that C-MRC achieves full diversity gain for orthogonal space-time code, but its diversity gain is limited when the deployed space-time code is non-orthogonal. To address this problem, we propose an effective detection scheme that is applicable to arbitrary space-time codes. On the basis of pairwise error probability approximation, max-log approximation, and the Chernoff bound, we construct an equivalent point-to-point MIMO signal model, and then apply tree-search detection techniques. Compared to JML, the proposed detection scheme significantly reduces the detection complexity while preserving diversity gain. Moreover, it can be readily extended to complex-field network-coding systems whose performance is superior to that of Galois-field network-coding systems. Analysis and simulation results confirm the efficiency of the proposed scheme.

Performance Analysis of Multi-Source Multi-Relay with Multiple Antennas Cooperative Networks with Best Relay Selection

In this paper we analyze the system performance of multi-source multi-relay with multiple antennas cooperative networks. We present an amplify and forward (AF) multiple-input multiple-output relay scenario, where finite number of sources communicate with single destination via multiple relay access points equipped with finite number of antennas. In this network a relay selection scheme is adopted, where the best relay is chosen using the instantaneous channel state information (CSI). Maximal ration combiner (MRC) and maximal ratio transmitter (MRT) are used at the relay to obtain maximum achievable received signal-to-noise ratio (SNR). We derive closed-form and analytical bound expressions for the outage probability and symbol error rate (SER) with joint multiple-sources and cooperative diversity. Further high SNR asymptotic analysis on the outage probability and average SER are performed to characterize the diversity gain. Then, the analytical expressions are validated with Monte Carlo simulations. The results reveal that the diversity gain is determined by the number of the sources, the number of access points in the system and the number of the antennas in each access point. ©2014 Engineering and Technology Publishing.

Performance Analysis of OSTBC Relaying in AF MIMO Relay System with Imperfect CSI

In this paper, the transmission of orthogonal space–time block codes (OSTBCs) in amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay networks, with imperfect channel state information (CSI), is considered. Individual channel estimation and time-efficient cascaded (for estimating the product of channel matrices) channel estimation protocols are used for estimating the channel matrices required for decoding of OSTBC data at the destination. We derive tight approximations for the moment-generating function (m.g.f.) of the received signal-to-noise ratio at the destination node with imperfect CSI, by ignoring higher order noise terms, in Rayleigh fading. Using the derived m.g.f. expression, we obtain the analytical symbol error rate (SER) of the AF MIMO relay system for general OSTBCs with $M$ -ary phase-shift keying constellation. The diversity order of the MIMO OSTBC relay system is also derived for some special cases by using the SER expression.

A Unified Approach to Optimal Transceiver Design for Non-Regenerative MIMO Relaying

We propose a unified approach to transceiver optimization for nonregenerative multiple-input–multiple-output (MIMO) relay networks. This approach leads to new transceiver designs and reduces algorithmic complexity with adaptive implementations. First, we formulate a generic system model that accommodates various network topologies by imposing structural constraints on the source precoder, the relaying matrix, and the destination equalizer. Based on the minimum-mean-square-error (MMSE) criterion, we derive the optimal relaying matrix as a function of the other two matrices, thereby freeing the optimization problem from this matrix and its associated power constraint with no loss of optimality. Subsequently, we study how to optimize either the precoder or the equalizer under different structural constraints and propose an alternating algorithm for the joint design. When optimizing the equalizer, the optimum from the previous transmission block is chosen as the initial search point to speed up convergence and, hence, to reduce computational complexity. The proposed framework is further explained and numerically validated within the context of different system configurations.

Performance Analysis of Hop-by-Hop Beamforming and Combining in DF MIMO Relay System over Nakagami-m Fading Channels

In this paper, we study hop-by-hop beamforming and combining in a decode-and-forward (DF) multiple-input multiple-output (MIMO) relay network, with two antennas at each node, over Nakagami-m fading channels. We derive a closed-form expression of the approximate average bit error rate of the considered cooperative scheme with M-ary phase shift keying constellation. In addition, analytical outage probability and diversity order of the considered DF MIMO relay system are also obtained.

Transceiver Design for SC-FDE Based MIMO Relay Systems

In this paper, we propose a joint transceiver design for single-carrier frequency-domain equalization (SC-FDE) based multiple-input multiple-output (MIMO) relay systems. To this end, we first derive the optimal minimum mean-squared error linear and decision-feedback frequency-domain equalization filters at the destination along with the corresponding error covariance matrices at the output of the equalizer. Subsequently, we formulate the source and relay precoding matrix design problem as the minimization of a family of Schur-convex and Schur-concave functions of the mean-squared errors at the output of the equalizer under separate power constraints for the source and the relay. By exploiting properties of the error covariance matrix and results from majorization theory, we derive the optimal structures of the source and relay precoding matrices, which allows us to transform the matrix optimization problem into a scalar power optimization problem. Adopting a high signal-to-noise ratio approximation for the objective function, we obtain the global optimal solution for the power allocation variables. We illustrate the excellent performance of the proposed system and compare it to that of conventional orthogonal frequency-division multiplexing MIMO relay systems based on computer simulations.

MIMO Two-Way Compress-and-Forward Relaying with Approximate Joint Eigen-Decomposition

While compress-and-forward (CF) is one of the basic relay protocols in cooperative transmission, little is known about the optimal design of CF in multiple-input multiple-output (MIMO) two-way relay channels (TWRC). An intuitive method is to compress each element of the superimposed signal vector during the multiple-access (MAC) phase independently and with identical compression noise variance. In this paper, we introduce an improved compression method. The key idea is to apply approximate joint diagonalization (AJD) to realize simultaneous eigen-decomposition of the two channel matrices in the MAC phase of two-way relaying in an approximate manner. After that, a novel covariance matrix design of the compression noise vector is derived for sum-rate maximization. Numerical results show that the proposed CF design can improve the spectral efficiency, especially when the relay node is close to any of the two source nodes instead of in the midpoint.

Selection Beamforming and Combining in Decode-and-Forward MIMO Relay Networks

In this paper, decode-and-forward (DF) based cooperation in a multiple antenna based wireless communication system is studied. In particular, we address the problem of beamforming and combining in a DF multiple-input multiple-output (MIMO) relay network with transmission path selection. A maximum eigenvalue based criterion is used for selection of best transmission path between source and destination nodes. We derive the average bit error rate of the considered cooperative scheme for binary phase shift keying constellation over Rayleigh fading channels. In addition, analytical diversity order of the beamforming and combining based DF MIMO relay system is obtained, for some special cases.

Channel Training Algorithms for Two-Way MIMO Relay Systems

Two-way relay systems are known to be capable of providing higher spectral efficiency compared with conventional one-way relay systems. However, the channel estimation problem for two-way relay systems is more complicated than that of one-way relay systems. In this paper, we propose and compare two channel estimation algorithms, namely the superimposed channel training scheme and the two-stage channel estimation algorithm, for two-way multiple-input multiple-output (MIMO) relay communication systems, where the individual channel state information (CSI) for the first-hop and second-hop links is estimated. For both algorithms, we derive the optimal structure of the source and relay training sequences which minimize the mean-squared error (MSE) of channel estimation. In the superimposed channel training scheme, the power allocation between the source and relay training sequences is optimized. For the two-stage channel estimation algorithm, we optimize the power allocation at the relay node between two stages to improve the performance of the algorithm. Numerical examples are shown to demonstrate and compare the performance of the proposed channel training algorithms.

Performance analysis of multiple-input multiple-output relay networks based impulse radio ultra-wideband

In this paper, we study the performance of time hopping pulse position modulation for impulse radio ultra-wideband. We consider relay network applying decode-and-forward protocol. The channels between nodes adopt the IEEE 802.15.4a norms. The bit error rate performance is analyzed considering the effect of interference. Our results show significant improvement due to the diversity gain provided by the relay nodes. However, the performance is limited when multiple access interference MAI is present. To combat the MAI effect and further improve the detection reliability, we propose to use antenna selection at the relay. The relay receiver is assumed to be equipped with multiple antennas, and only the best antenna is selected. This is shown to improve the performance in the presence of MAI and improve the diversity gain.Copyright © 2013 John Wiley & Sons, Ltd.

Beamforming and Combining in Two-Way AF MIMO Relay Networks

In this letter, we propose a beamforming and combining scheme for a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network. An approximate expression for the symbol error rate of the scheme in Rayleigh fading for M-ary phase-shift keying is obtained based on the moment generating function of the instantaneous received signal-to-noise ratio. The diversity order is also analytically derived. It is shown by simulations that the proposed scheme outperforms existing schemes for beamforming and combining in two-way AF MIMO relay systems. We also discuss beamforming and combining in a two-way AF MIMO relay system with estimated channel gains.

Transmitter‐receiver and relay optimisation for spectrum sharing multiple‐input and multiple‐output peer‐to‐peer users

The authors investigate a spectrum sharing peer-to-peer relay network where multiple source nodes with multiple antennas communicate with their desired destination nodes with multiple antennas through a multiple-input and multiple-output (MIMO) relay. The authors establish the duality between uplink and downlink peer-to-peer MIMO channels with any number of antennas at each node and demonstrate mean square error (MSE) of a downlink peer-to-peer network can be achieved in a virtual uplink network with the same total network transmission power constraint. By applying this result, the authors develop an iterative algorithm to optimise the source, relay and receiver processing matrices such that the weighted MSE of the retrieved signal at the receivers is minimised. The simulation results demonstrate satisfactory performance of the proposed algorithm.

THP Transceiver Design for MIMO Relaying with Direct Link and Partial CSI

In this letter we consider Tomlinson Harashima precoding (THP) for multiple-input multiple-output (MIMO) relay systems with a direct link between the source and destination. It is assumed that the destination can acquire full channel state information (CSI) of all channels, whereas the source and relay have full CSI of the source-relay channel but only acquire statistical knowledge of the source-destination and relay-destination channels. Simulation results demonstrate that, for high signal to noise ratio (SNR) in the relay-destination link, the performance of the proposed design approaches that of non-linear transceivers utilising full CSI.

Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks

For the non-regenerative multiple-input multiple-output (MIMO) cognitive multi-relay network, we propose an optimal relay selection and beamforming scheme which maximizes the capacity of the secondary user by selecting the best cognitive MIMO relay subject to the transmit power constraints at the relays and the interference power constraints at the primary users. In our proposed scheme, the relay selection and beamforming optimization problem is solved separately by employing convex semidefinite programming (SDP) through rank-one relaxation and Charnes-Cooper transformation. It is shown that our proposed scheme achieves higher average capacity than the convectional relay beamforming schemes and relay selection schemes.

Joint signal‐to‐noise ratio‐based transceiver design for amplify‐and‐forward multiple‐input multiple‐output relay systems

In this study, the authors address the problem of transceiver design in an amplify-and-forward multiple-input multiple-output relay system with full or partial channel state information (CSI), where linear processing is applied to maximise the average received signal-to-noise ratio (SNR) at source, relay and destination, respectively. This joint design problem is a non-convex optimisation problem, so the authors convert it into a scalar problem and derive the optimal unitary decoder under average power constraint. The precoder at source and relay can be obtained by employing generalised Rayleigh quotient method. Specifically, two CSI assumptions are considered: (i) the authors first derive the precoder and decoder with full CSI; (ii) assumimg the statistical independence between the channel estimated value and channel estimation errors, the problem with partial CSI can be solved as the same way as full CSI case. Numerical results show a great improvement on the average received SNR by applying the proposed scheme. On the other hand, the authors also illustrate the impact on received SNR arose by the channel estimation errors.

End-to-end channel capacity of MAC-PHY cross-layer multiple-hop MIMO relay system with outdated CSI

For high end-to-end channel capacity, the amplify-and-forward scheme multiple-hop multiple-input multiple-output relay system is considered. The distance between each transceiver and the transmit power of each relay are optimized to prevent some relays from being the bottleneck and guarantee high end-to-end channel capacity. According to the proposed transmission environment coefficient, the path loss can be described in a new way, and then the distance of multiple-hop relay system can be optimized more simply than the original one. However, when the system has no control on media access control (MAC) layer, performance of the system deteriorates because of the presence of interference signal. Thus, the specific transmission protocol on the MAC layer for multiple-hop system is proposed to reduce the power of interference signal and to obtain high end-to-end channel capacity. According to the proposed transmission protocol on the MAC layer, the system indicates the trade-off between the end-to-end channel capacity and the delay time. The end-to-end channel capacity of the outdated channel state information system is also analyzed.

Joint source and relay design for two-hop amplify-and-forward relay networks with QoS constraints

Abstract In this paper, we consider the joint design of source precoding matrix and the relay precoding matrix in a two-hop multiple-input multiple-output relay network. The goal is to find a pair of matrices in order to minimize the power consumption and at the same time meet pre-selected quality of service constraints that are defined as the mean square error of each data stream. Using majorization theory, we simplify the matrix-valued optimization problem into a scalar-valued one. We then propose a lower bound and an upper bound of the original problem, both in convex forms. Specifically, the latter is solved by a multi-level water-filling algorithm that is much efficient than directly applying the interior point method. Numerical examples corroborate the proposed studies and also demonstrate the tightness of both bounds to the original problem.