Coalition formation in MISO interference channels

We consider a multi-link multiple-input single-output interference channel. A link in this setting is noncooperative if its transmission does not take into account the interference it generates at other links. Noncooperative operation of the links is generally not efficient. To improve this situation, we study link cooperation via coalitional games. In coalitional games, a player has an incentive to cooperate with other players if this improves his payoff. We model the setting as a game in coalitional form without transferable utility. The players (links) in a coalition either perform zero forcing transmission or Wiener filter precoding to each other. Necessary and sufficient conditions, in terms of a lower signal-to-noise ratio (SNR) threshold, are provided under which all players have the incentive to cooperate and form a grand coalition. In addition, we provide sufficient conditions under which all players have no incentive to cooperate. In this case, the SNR has to be below a specified SNR threshold. Hence, there exists an SNR range in which the links would profit in forming subcoalitions. Therefore, we turn our attention to coalition formation games between the links. We utilize a coalition formation algorithm, called merge-and-split, to determine stable user grouping. Numerical results show that while in the low SNR regime noncooperation is efficient with single-player coalitions, in the high SNR regime all users benefit in forming a grand coalition. Coalition formation shows its significance in the mid SNR regime where subset user cooperation provides joint performance gains.