On the Sum-Rate of MIMO Interference Channel

The problem of maximizing the sum-rate of a MIMO interference channel is investigated. Each receiver node is assumed to perform single user detection by treating interference from other users as Gaussian noise. It is assumed that all the users share a single frequency band and no pre-coding is performed over time. The sum-rate maximization in such a setup is a long-standing open problem due to its non-linear non-convex nature. The solution, to date, has only been approximated using the local optimization algorithms. In this paper, we couple the branch and bound strategy with the reformulation and linearization technique (BB/RLT) to develop a global optimization algorithm that finds a provably optimal solution. This problem is essentially an optimal power control problem over spatial channels and should not be confused with some recent developments such as Interference Alignment (IA) that typically require pre-coding over temporal, spectral or spatial dimensions. As a comparison with the state of the art, we compare the sum-rate achievable in the current system with the one predicted by IA and draw some interesting conclusions. It should be noted however, that even though the sum-rate achievable by IA can be predicted by assuming $N/2$ degrees of freedom in an $N$-user interference channel, the feasibility of IA over a limited number of signaling dimensions is an open problem.