Global D.C. Optimization for Multi-User Interference Systems

The weighted sum capacity of a Gaussian interference system is a nonconvex function of transmit power allocation vector of all users in the system. This paper shows that, by representing its objective function as a difference of two convex functions (d.c.), the non-convex optimization problem can be converted into an equivalent d.c. global optimization problem, which can be solved efficiently by various developed d.c. algorithms. In particular, a modified prismatic branch -and-bound algorithm that only requires solving a sequence of linear programming sub-problems, is introduced to find the global optimum. Simulation results in wireless flat-fading channel show that the proposed global d.c. optimization formulation outperforms considerably the local optimization methods in terms of achievable ergodic sum-rate capacity.