On linear processing for dual-hop multi-channel relaying

In this paper, we consider the amplified-and-forward relaying in a multichannel system with linear processing capability at the relay. We propose an analytical approach to study the linear processing performance with an aim to maximize the end-to-end achievable rate, assuming equal power amplification at the relay. For the class of permutation matrices as the special case of linear processing, the problem reduces to finding the optimal channel pairing scheme that maps incoming channels to outgoing channels at the relay. The proposed unified approach allows us to obtain the corresponding optimal permutation for channel pairing, for either relaying with or without the direct path available. Particular to the case when the direct path is available, such optimal pairing strategy has not been shown before. We further demonstrate that the so obtained optimal permutation is in fact also optimal among all unitary matrices for achievable rate maximization, thus, establishing the optimality of channel pairing approach among unitary linear processing schemes. Simulation results are presented to demonstrate the achievable gain of optimal channel pairing compared with non-optimal linear processing and non-pairing.