Polynomial-time DC (POTDC) for sum-rate maximization in two-way AF MIMO relaying

The problem of sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying is considered. Mathematically, this problem is equivalent to the constrained maximization of the product of quadratic ratios that is a non-convex problem. Such problems appear also in many other applications. This problem can be further relaxed into a difference-of-convex functions (DC) programming problem, which is typically solved using the branch-and-bound method without polynomial-time complexity guarantees. We, however, develop a polynomial-time convex optimization-based algorithm for solving the corresponding DC programming problem named polynomial-time DC (POTDC). POTDC is based on a specific parameterization of the problem, semi-definite programming (SDP) relaxation, linearization, and iterations over a single parameter. The complexity of the problem solved at each iteration of the algorithm is equivalent to that of the SDP problem. The effectiveness of the proposed POTDC method for the sum-rate maximization in two-way AF MIMO relay systems is shown.