Spatial Multiplexing in the Single-Relay MIMO Channel

This work considers the problem of relaying spatially multiplexed signals between a source and a destination using a non-regenerative relay equipped with multiple antennas. In addition to the usual power amplification, the relay is assumed to process the received data vector before forwarding it to the destination. We present two linear filtering techniques that perform this processing in an optimal manner when channel state information (CSI) on the backward and forward channels is available at the relay. Firstly, we derive the relay filter that minimizes the pairwise error probability (PEP) assuming maximum-likelihood (ML) detection at the destination. Secondly, we simultaneously optimize the relay and destination filters in the mean-square error (MSE) sense. The proposed relaying techniques are shown to achieve error performance improvements, especially when the number of antennas at the relay is increased.