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Game theoretic precoding strategy selection for MIMO relay networks

In this paper, we study joint source and relay precoding strategy selection for multiple-input multiple-output (MIMO) relay networks from a game theoretic approach. We appropriately formulate it as a potential game in which the rate is the common utility and also the potential function. This game is shown to possess at least one pure strategy Nash equilibrium (NE) and the optimal strategy profile which maximizes the rate constitutes a pure strategy NE. Then we design an iterative precoding strategy selection algorithm based on best response rule to achieve the NE. Finally, it is shown that our designed algorithm can achieve optimal or near optimal rate performance with much lower complexity compared to the exhaustive search algorithm and the random selection algorithm.