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Analog network coding is a promising technique which can greatly improve the transmission efficiency of wireless communications. In two-way relay systems with multiple subchannels, multiple user pairs and multiple relays, however, the optimal joint relay selection and subchannel allocation problem has not been studied in a systematic way. In this paper, a random combinatorial optimization approach, referred to as the Weighted Random Bipartite Graph (WRBG) based Minimum Weighted Matching (MWM) method, will be proposed to solve this problem. By analyzing the properties of the MWM on WRBG, the authors shall derive the outage probability and diversity-multiplexing tradeoff of each user after relay selection and channel allocation.
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