Discrete Sum Rate Maximization for MISO Interference Broadcast Channels: Convex Approximations and Efficient Algorithms

This paper considers the discrete sum rate maximization (DSRM) problem for beamformer optimization in multi-input single-output interference broadcast channels. In this problem, the achievable rates of the receivers are restricted to be taken from a set of finite discrete rate values, and such constraints arise from practical limitations with the modulation and coding schemes. Many existing studies consider sum rate maximization without the discrete rate constraints, and that may result in performance loss. In this paper, the DSRM problem is tackled via a convex approximation approach. Due to the discrete rate constraints, DSRM is a mixed-integer program. The idea of the proposed approach is to reformulate DSRM as a continuous, but still nonconvex, optimization problem. Then, appropriate convex approximations are applied. The advantage of the proposed approach is that the resulting approximate problems can be easily decomposed from a first-order optimization viewpoint. Utilizing this special feature, low-complexity and decentralized algorithms based on projected gradient are derived. Numerical results are used to show the efficiencies of the proposed algorithms in a multicell coordinated beamforming scenario. Also, this paper provides a proof for the convergence guarantee of one decentralized optimization strategy, namely, inexact maximum block improvement.