Joint Receive-Transmit Beamforming for Multi-Antenna Relaying Schemes

In this correspondence, we study the problem of joint receive and transmit beamforming for a wireless network consisting of a transmitter, a receiver, and a relay node. The relay node is equipped with multiple antennas while the transmitter and the receiver each uses only one antenna. Our communication scheme consists of two phases: first the transmitter sends the information symbols to the relay. In the second phase, the relay re-transmits a linearly transformed version of the vector of the signals received at its multiple antennas. We introduce the novel concept of general rank beamforming which can be applied to our communication scheme. In our general rank beamforming approach, the relay multiplies the vector of its received signals by a general-rank complex matrix and re-transmits each entry of the output vector on the corresponding antenna. Through maximizing the signal-to-noise ratio (SNR), we obtain a closed-form solution to the general rank beamforming problem. We also prove that for the case of statistically independent transmitter-relay (TR) and relay-receiver (RR) channels, the general rank beamforming approach results in a rank-one solution for the beamforming matrix regardless of the rank of the channel correlation matrices. Simulation results show that when applied to the case of statistically dependent TR and RR channels, our general rank beamforming technique outperforms the separable receive and transmit beamforming method by a significant margin.