General-Rank Beamforming for Multi-Antenna Relaying Schemes

Abstract

We consider a wireless network consisting of a singleantenna transmitter, a single-antenna receiver, and a multi-antenna relay node. For such a network, we introduce the novel approach of general rank beamforming. In this approach, the relay multiplies the vector of its received signals by a general-rank complex matrix to obtain a new vector. Each entry of this new vector is then transmitted on one of the antennas available at the relay. We show that maximizing the receiver SNR subject to total relay power constraint yields a closedform solution for the beamforming matrix. We also prove that if the channel coefficients from the transmitter to the relay antennas and those from the relay antennas to the receiver are statistically independent, the general rank beamforming approach results in a rank-one solution for the beamforming matrix.

Robust General Rank Precoding Design for Amplify-and-Forward Relay Network

“…The CRBF scheme performs worse than all other methods in this case as the there is no cooperation in signal processing among multiple antennas at relay, i.e., W is constrained to be diagonal only. In perfect CSI, with independent fading in f and g, rank 1 solution that gives maximal ratio combining (MRC) on source side and transmit beamforming on destination side is proved to be optimal [14].…”

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

“…It has been proven in [24]- [26], [31]- [33] that the optimal precoding structure in one-way relaying is to first parallelize the channels between the source and the relay, as well as between the relay and the destination using singular value decomposition (SVD) and then match the eigen-channels in the two hops. Taking the transmission of single data stream in a one-way relay system for example as considered in [34] and [35], the idea of channel matching is as follows. The source should use the dominant right singular vector of the channel in the first hop as beamformer to transmit its signal.…”

“…Motivated by the findings in [24]- [26], [31]- [35], we aim to design A 1 , A 2 and A r so as to simultaneously parallelize the bidirectional links in the MIMO two-way relay system. In the following, we introduce a heuristic channel parallelization method for bidirectional communications by using two joint channel decomposition methods, namely, generalized singular value decomposition (GSVD) for the MAC phase and SVD for the BC phase.…”