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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 sub-channel 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, the authors will first derive a new closed-form outage probability for the best relay selection in the Decode-and-Forward (DF) scheme.
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