A Convergent version of the max SINR algorithm for the MIMO interference channel

The problem of designing linear transmit signaling strategies for the multiple input, multiple output (MIMO) interference channel is considered. For this problem, the best known iterative solution, in terms of maximizing signal to interference plus noise ratio (SINR) at the receivers, is the Max SINR algorithm. However, there is no proof that the Max SINR algorithm converges. In this paper, a modification to the Max SINR algorithm is proposed, in which a power control step is used to make a metric similar to the sum rate increase monotonically with each iteration, thus making the modified Max SINR algorithm convergent. It is further shown that with successive interference cancellation (SIC), the metric that the modified Max SINR algorithm optimizes is exactly the sum rate. Finally, simulations are used to demonstrate that the performance of the modified Max SINR algorithm, unlike other convergent alternatives, is nearly identical to that of the original Max SINR algorithm.