A constraint relaxation version of the interference leakage minimization algorithm in MIMO interference channels

This study explores the convergence property of the interference leakage minimization algorithm (ILMA) proposed by S. W. Peters and R. W. Heath Jr. Among the cooperative interference alignment (IA) schemes, we specialize the ILMA for its better feasibility in real applications than others. However, ILMA cannot converge to a global minimum because of its unitary constraints. As an iterative algorithm, no guarantee of global convergence means the tendency towards system instability. Up to the present, most efforts on cooperative IA are focused on pursuing high sum rate or low error floor. None of existing works looks into the convergence issue. In this paper, we explore the global convergence of ILMA. Specifically, we devise a constraint relaxation version of ILMA, named rILMA. Except that rILMA inherits the benefits from ILMA, mathematical proofs given in this paper also show that rILMA converges to a global minimum. This exploration directly results in the improvement of performance. Numerical simulations show that rILMA outperforms Max-SINR and ILMA in sum rate performance.