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. Both amplify-and-forward and decode-and-forward relaying strategies are considered. Given fixed power allocation to the channels, we show that channel pairing over multiple hops can be decomposed into independent pairing problems at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal, where each relay pairs its incoming and outgoing channels by their SNR order. For the joint optimization of channel pairing and power allocation under both total and individual power constraints, we show that the problem can be decomposed into two separate subproblems solved independently. This separation principle is established by observing the equivalence between sorting SNRs and sorting channel gains in the jointly optimal solution. It significantly reduces the computational complexity in finding the jointly optimal solution. The solution for optimizing power allocation is also provided. Numerical results are provided to demonstrate substantial performance gain of the jointly optimal solution over some suboptimal alternatives. It is also observed that more gain is obtained from optimal channel pairing than optimal power allocation through judiciously exploiting the variation among multiple channels. Impact of the variation of channel gain, the number of channels, and the number of hops on the performance gain is also studied through numerical examples.
This separation was also established in the general multi-hop case in REF , for both AF and DF relaying, and under either total power or individual power constraints.
Jointly Optimal Channel Pairing and Power Allocation for Multi-channel Multi-hop Relaying
IEEE Transactions on Signal Processing, vol. 59, pp.4998-5012, October 2011
Computer Science Mathematics