Bargaining over Fading Interference Channels

We consider the problem of bargaining over block fading interference channels, where interaction between players takes place over multiple channel realizations. Based on the assumption that the transmitters have conflicting objectives, we use axiomatic bargaining theory to derive optimal rate allocations in each block. In the setup under consideration, the Nash bargaining solution (NBS) is non-causal, i.e., cannot be implemented in a real-world system. We argue that the invariance axiom is superfluous when bargaining over a rate region. Without the invariance axiom, an equivalent solution follows from the maximization of a sum of utilities under minimum utility constraints. This alternative solution is also non-causal. We propose causal approximations to the optimal solutions. The sum utility solution allows for a more systematic approximation than the NBS. Thus, dropping the invariance axiom makes it possible to choose a solution which can be better approximated. We provide numerical results to illustrate the performance of the proposed solutions.