On Design of Collaborative Beamforming for Two-Way Relay Networks

We consider a two-way relay network, where two source nodes, S1 and S2, exchange information through a cluster of relay nodes. The relay nodes receive the sum signal from S1 and S2 in the first time slot. In the second time slot, each relay node multiplies its received signal by a complex coefficient and retransmits the signal to the two source nodes, which leads to a collaborative two-way beamforming system. By applying the principle of analog network coding, each receiver at S1 and S2 cancels the "self-interference" in the received signal from the relay cluster and decodes the message. This paper studies the 2-dimensional achievable rate region for such a two-way relay network with collaborative beamforming. With different assumptions of channel reciprocity between the source-relay and relay-source channels, the achievable rate region is characterized under two setups. First, with reciprocal channels, we investigate the achievable rate regions when the relay cluster is subject to a sum-power constraint or individual-power constraints. We show that the optimal beamforming vectors obtained from solving the weighted sum inverse-SNR minimization (WSISMin) problems are sufficient to characterize the corresponding achievable rate region. Furthermore, we derive the closed form solutions for those optimal beamforming vectors and consequently propose the partially distributed algorithms to implement the optimal beamforming, where each relay node only needs the local channel information and one global parameter. Second, with the non-reciprocal channels, the achievable rate regions are also characterized for both the sum-power constraint case and the individual-power constraint case. Although no closed-form solutions are available under this setup, we present efficient numerical algorithms.Comment: new version of the previously posted, single column double spacing, 24 page

A Modified Levenberg-Marquardt Method for the Bidirectional Relay Channel

This paper presents an optimization approach for a system consisting of multiple bidirectional links over a two-way amplify-and-forward relay. It is desired to improve the fairness of the system. All user pairs exchange information over one relay station with multiple antennas. Due to the joint transmission to all users, the users are subject to mutual interference. A mitigation of the interference can be achieved by max-min fair precoding optimization where the relay is subject to a sum power constraint. The resulting optimization problem is non-convex. This paper proposes a novel iterative and low complexity approach based on a modified Levenberg-Marquardt method to find near optimal solutions. The presented method finds solutions close to the standard convex-solver based relaxation approach.Comment: submitted to IEEE Transactions on Vehicular Technology We corrected small mistakes in the proof of Lemma 2 and Proposition

How to Understand LMMSE Transceiver Design for MIMO Systems From Quadratic Matrix Programming

In this paper, a unified linear minimum mean-square-error (LMMSE) transceiver design framework is investigated, which is suitable for a wide range of wireless systems. The unified design is based on an elegant and powerful mathematical programming technology termed as quadratic matrix programming (QMP). Based on QMP it can be observed that for different wireless systems, there are certain common characteristics which can be exploited to design LMMSE transceivers e.g., the quadratic forms. It is also discovered that evolving from a point-to-point MIMO system to various advanced wireless systems such as multi-cell coordinated systems, multi-user MIMO systems, MIMO cognitive radio systems, amplify-and-forward MIMO relaying systems and so on, the quadratic nature is always kept and the LMMSE transceiver designs can always be carried out via iteratively solving a number of QMP problems. A comprehensive framework on how to solve QMP problems is also given. The work presented in this paper is likely to be the first shoot for the transceiver design for the future ever-changing wireless systems.Comment: 31 pages, 4 figures, Accepted by IET Communication

Throughput Analysis and Optimization of Wireless-Powered Multiple Antenna Full-Duplex Relay Systems

We consider a full-duplex (FD) decode-and-forward system in which the time-switching protocol is employed by the multi-antenna relay to receive energy from the source and transmit information to the destination. The instantaneous throughput is maximized by optimizing receive and transmit beamformers at the relay and the time-split parameter. We study both optimum and suboptimum schemes. The reformulated problem in the optimum scheme achieves closed-form solutions in terms of transmit beamformer for some scenarios. In other scenarios, the optimization problem is formulated as a semi-definite relaxation problem and a rank-one optimum solution is always guaranteed. In the suboptimum schemes, the beamformers are obtained using maximum ratio combining, zero-forcing, and maximum ratio transmission. When beamformers have closed-form solutions, the achievable instantaneous and delay-constrained throughput are analytically characterized. Our results reveal that, beamforming increases both the energy harvesting and loop interference suppression capabilities at the FD relay. Moreover, simulation results demonstrate that the choice of the linear processing scheme as well as the time-split plays a critical role in determining the FD gains.Comment: Accepted for publication in IEEE Transactions on Communication

Joint Source and Relay Precoding Designs for MIMO Two-Way Relaying Based on MSE Criterion

Properly designed precoders can significantly improve the spectral efficiency of multiple-input multiple-output (MIMO) relay systems. In this paper, we investigate joint source and relay precoding design based on the mean-square-error (MSE) criterion in MIMO two-way relay systems, where two multi-antenna source nodes exchange information via a multi-antenna amplify-and-forward relay node. This problem is non-convex and its optimal solution remains unsolved. Aiming to find an efficient way to solve the problem, we first decouple the primal problem into three tractable sub-problems, and then propose an iterative precoding design algorithm based on alternating optimization. The solution to each sub-problem is optimal and unique, thus the convergence of the iterative algorithm is guaranteed. Secondly, we propose a structured precoding design to lower the computational complexity. The proposed precoding structure is able to parallelize the channels in the multiple access (MAC) phase and broadcast (BC) phase. It thus reduces the precoding design to a simple power allocation problem. Lastly, for the special case where only a single data stream is transmitted from each source node, we present a source-antenna-selection (SAS) based precoding design algorithm. This algorithm selects only one antenna for transmission from each source and thus requires lower signalling overhead. Comprehensive simulation is conducted to evaluate the effectiveness of all the proposed precoding designs.Comment: 32 pages, 10 figure