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A coalitional game is proposed for multicell multi-user downlink beamforming. Each base station intends to minimize its transmission power while aiming to attain a set of target signal-to-interference-plus-noise-ratio (SINR) for its users. To reduce power consumption, base stations have incentive to cooperate with other base stations to mitigate intercell interference. The coalitional game is introduced where base stations are allowed to forge partial cooperation rather than full cooperation. The partition form coalitional game is formulated with the consideration that beamformer design of a coalition depends on the coalition structure outside the considered coalition. We first formulate the beamformer design for a given coalition structure in which base stations in a coalition greedily minimize the total weighted transmit power without considering interference leakage to users in other coalitions. This can be considered as a non-cooperative game with each player as a distinct coalition. By introducing cost for cooperation, the coalition formation game is considered for the power minimization-based beamforming. A merge-regret-based sequential coalition formation algorithm has been developed that is capable of reaching a unique stable coalition structure. Finally, an &#x03B1;-Modification algorithm has been proposed to improve the performance of the coalition formation algorithm.

Coalitional Games for Downlink Multicell Beamforming