RBG Matching Based Optimal Relay Selection and Subchannel Allocation

Relay selection has been shown to be a practical and effective way to achieve cooperative diversity. In wide-band OFDM cooperative communication systems with multiple source and destination nodes, however, the best relay selection and subchannel allocation has not been studied in a systematic way. In this paper, a random combinatorial optimization approach, referred to as the random bipartite graph based maximum matching (RBG matching), will be proposed to solve this problem. By applying the method of Euler beta function and generalized hypergeometric function, we will first derive a new closed-form outage probability for the best relay selection in the decode-and-forward (DF) scheme. Based on this result and the properties of the maximum matching on RBG, the outage probability and diversity-multiplexing tradeoff of the proposed RBG matching method will also be derived. As a result, we will demonstrate that the outage probability and the cooperative and frequency diversity-multiplexing tradeoff of the RBG matching method for cooperative communication systems with multiple source-destination pairs is the same as that of relay systems with only one source and one destination. Besides, the proposed algorithm for maximum matching also enjoys a sublinear computation complexity O(N^2/3), where N is the number of subchannels. Simulation results will illustrate the potential of the proposed RBG matching method, and also verify the theoretical derivations.