Competition versus cooperation on the MISO interference channel

We consider the problem of coordinating two competing multiple-antenna wireless systems (operators) that operate in the same spectral band. We formulate a rate region which is achievable by scalar coding followed by power allocation and beamforming. We show that all interesting points on the Pareto boundary correspond to transmit strategies where both systems use the maximum available power. We then argue that there is a fundamental need for base station cooperation when performing spectrum sharing with multiple transmit antennas. More precisely, we show that if the systems do not cooperate, there is a unique Nash equilibrium which is inefficient in the sense that the achievable rate is bounded by a constant, regardless of the available transmit power. An extension of this result to the case where the receivers use successive interference cancellation (SIC) is also provided. Next we model the problem of agreeing on beamforming vectors as a non-transferable utility (NTU) cooperative game-theoretic problem, with the two operators as players. Specifically we compute numerically the Nash bargaining solution, which is a likely resolution of the resource conflict assuming that the players are rational. Numerical experiments indicate that selfish but cooperating operators may achieve a performance which is close to the maximum-sum-rate bound.