Optimal Channel Pairing and Power Allocation for Multi-channel Multi-hop Relay Networks

We study the problem of channel pairing and power allocation in a multi-channel, multi-hop relay network to enhance the end-to-end data rate. OFDM-based relays are used as an illustrative example, and the amplify-and-forward and decode-and-forward relaying strategies are considered. Given fixed power allocation to the OFDM subcarriers, we observe that a sorted-SNR subcarrier pairing strategy is data-rate optimal, where each relay pairs its incoming and outgoing subcarriers by their SNR order. For the joint optimization of subcarrier pairing and power allocation, we show that it is optimal to separately consider the two subproblems, for both individual and total power constraints. This separation principle significantly reduces the computational complexity in finding the jointly optimal solution. We further establish the equivalence between sorting SNRs and sorting channel gains in the jointly optimal solution, which allows simple implementation of optimal subcarrier pairing at the relays. Simulation results are presented to demonstrate the performance gain of the jointly optimal solution over some suboptimal alternatives.