Optimality of Diagonalization of Multicarrier Multi-Hop Linear Non-Regenerative MIMO Relays

In this paper, a multicarrier multi-hop multiple-input multiple-output (MIMO) relay system is investigated. A linear non-regenerative strategy is applied at each relay node. We show that for Schur-concave objective functions, the optimal source precoding matrix, the optimal relay amplifying matrices and the optimal receiving matrix jointly diagonalize the multicarrier multi-hop MIMO relay channel. And for Schur-convex objectives, such joint diagonalization along with a rotation of the source precoding matrix is also shown to be optimal. Using the optimal structure of the source and relay matrices, the multi-hop relay design problem boils down to the issue of power loading among the resulting parallel multi-hop single-input single-output (SISO) relay channels. This paper provides additional details of the multicarrier version of some of our recent results

Power Allocation in Two-Hop Amplify-and-Forward MIMO Relay Systems with QoS requirements

The problem of minimizing the total power consumption while satisfying different quality-of-service (QoS) requirements in a two-hop multiple-input multiple-output network with a single non-regenerative relay is considered. As shown by Y. Rong in [1], the optimal processing matrices for both linear and non-linear transceiver architectures lead to the diagonalization of the source-relay-destination channel so that the power minimization problem reduces to properly allocating the available power over the established links. Unfortunately, finding the solution of this problem is numerically difficult as it is not in a convex form. To overcome this difficulty, existing solutions rely on the computation of upper- and lower-bounds that are hard to obtain or require the relaxation of the QoS constraints. In this work, a novel approach is devised for both linear and non-linear transceiver architectures, which allows to closely approximate the solutions of the non-convex power allocation problems with those of convex ones easy to compute in closed-form by means of multi-step procedures of reduced complexity. Computer simulations are used to assess the performance of the proposed approach and to make comparisons with alternatives

Tomlinson Harashima precoding design for non-regenerative MIMO relay networks

In this paper we consider the design of minimum mean square error (MMSE) transceivers for non-regenerative multiple input multiple output (MIMO) relay systems. Our design utilises Tomlinson Harashima precoding (THP) at the source along with linear processors in each stage of the network. Assuming full channel state information (CSI) is available at each node in the network the various processors are jointly optimised to minimise the system arithmetic mean square error (MSE) whilst abiding by average power constraints at both the source and relay terminals in the network. Simulations show that the proposed schemes outperform existing methods in terms of bit error ratio (BER)

A Tutorial on the Optimization of Amplify-and-Forward MIMO Relay Systems

The remarkable promise of multiple-input multiple-output (MIMO) wireless channels has motivated an intense research activity to characterize the theoretical and practical issues associated with the design of transmit (source) and receive (destination) processing matrices under different operating conditions. This activity was primarily focused on point-to-point (single-hop) communications but more recently there has been an extensive work on two-hop or multi-hop settings in which single or multiple relays are used to deliver the information from the source to the destination. The aim of this tutorial is to provide an up-to-date overview of the fundamental results and practical implementation issues of designing amplify-and-forward MIMO relay systems

Transceiver design for non-regenerative MIMO relay systems with decision feedback detection

In this paper we consider the design of zero forcing (ZF) and minimum mean square error (MMSE) transceivers for non-regenerative multiple input multiple output (MIMO) relay networks. Our designs utilise linear processors at each stage of the network along with a decision feedback detection device at the receiver. Under the assumption of full channel state information (CSI) across the entire link the processors are jointly optimised to minimise the system arithmetic mean square error (MSE) whilst meeting average power constraints at both the source and the relay terminals. We compare the presented methods to linear designs available in the literature and show the advantages of the proposed transceivers through simulation results

Joint Source and Relay Optimization for Parallel MIMO Relay Networks

In this article, we study the optimal structure of the source precoding matrix and the relay amplifying matrices for multiple-input multiple-output (MIMO) relay communication systems with parallel relay nodes. Two types of receivers are considered at the destination node: (1) The linear minimal mean-squared error (MMSE) receiver; (2) The nonlinear decision feedback equalizer based on the minimal MSE criterion. We show that for both receiver schemes, the optimal source precoding matrix and the optimal relay amplifying matrices have a beamforming structure. Using such optimal structure, joint source and relay power loading algorithms are developed to minimize the MSE of the signal waveform estimation at the destination. Compared with existing algorithms for parallel MIMO relay networks, the proposed joint source and relay beamforming algorithms have significant improvement in the system bit-error-rate performance

On the design of amplify-and-forward MIMO-OFDM relay systems with QoS requirements specified as Schur-convex functions of the MSEs

In this paper, we focus on the design of linear and nonlinear architectures in amplify-and-forward multiple-input–multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) relay networks in which different types of services are supported. The goal is to jointly optimize the processing matrices to minimize the total power consumption while satisfying the quality-of-service (QoS) requirements of each service specified as Schur-convex functions of the mean square errors (MSEs) over all assigned subcarriers. It turns out that the optimal solution leads to the diagonalization of the source–relay–destination channel up to a unitary matrix, depending on the specific Schur-convex function

Maximum mutual information design for amplify-and-forward multi-hop MIMO relaying systems under channel uncertainties

Conference Theme: PHY and FundamentalsIn this paper, we investigate maximum mutual information design for multi-hop amplify-and-forward (AF) multiple-input multiple-out (MIMO) relaying systems with imperfect channel state information, i.e., Gaussian distributed channel estimation errors. The robust design is formulated as a matrix-variate optimization problem. Exploiting the elegant properties of Majorization theory and matrix-variate functions, the optimal structures of the forwarding matrices at the relays and precoding matrix at the source are derived. Based on the derived structures, a water-filling solution is proposed to solve the remaining unknown variables. © 2012 IEEE.published_or_final_versionThe 2012 IEEE Wireless Communications and Networking Conference (WCNC), Paris, France, 1-4 April 2012. In IEEE Wireless Communications and Networking Conference Proceedings, 2012, p. 781-78

Transceiver Optimization for MIMO Multi-Relay Systems Using Projected Gradient Approach

In this paper, we develop the optimal source precoding matrix and relay amplifying matrices for non-regenerative multiple-input multiple-output (MIMO) relay communication systems with parallel relay nodes using the projected gradient (PG) approach. We show that the optimal relay amplifyingmatrices have a beamforming structure. Exploiting the structure of relay matrices, an iterative joint source and relay matrices optimization algorithm is developed to minimize the mean-squared error (MSE) of the signal waveform estimation at the destination using the PG approach. The performance of the proposed algorithm is demonstrated through numerical simulations

A General Robust Linear Transceiver Design for Multi-Hop Amplify-and-Forward MIMO Relaying Systems

In this paper, linear transceiver design for multi-hop amplify-and-forward (AF) multiple-input multiple-out (MIMO) relaying systems with Gaussian distributed channel estimation errors is investigated. Commonly used transceiver design criteria including weighted mean-square-error (MSE) minimization, capacity maximization, worst-MSE/MAX-MSE minimization and weighted sum-rate maximization, are considered and unified into a single matrix-variate optimization problem. A general robust design algorithm is proposed to solve the unified problem. Specifically, by exploiting majorization theory and properties of matrix-variate functions, the optimal structure of the robust transceiver is derived when either the covariance matrix of channel estimation errors seen from the transmitter side or the corresponding covariance matrix seen from the receiver side is proportional to an identity matrix. Based on the optimal structure, the original transceiver design problems are reduced to much simpler problems with only scalar variables whose solutions are readily obtained by iterative water-filling algorithm. A number of existing transceiver design algorithms are found to be special cases of the proposed solution. The differences between our work and the existing related work are also discussed in detail. The performance advantages of the proposed robust designs are demonstrated by simulation results.Comment: 30 pages, 7 figures, Accepted by IEEE Transactions on Signal Processin