Joint Network Optimization and Downlink Beamforming for CoMP Transmissions Using Mixed Integer Conic Programming

Coordinated multipoint (CoMP) transmission is a promising technique to mitigate intercell interference and to increase system throughput in single-frequency reuse networks. Despite the remarkable benefits, the associated operational costs for exchanging user data and control information between multiple cooperating base stations (BSs) limit practical applications of CoMP processing. To facilitate wide usage of CoMP transmission, we consider in this paper the problem of joint network optimization and downlink beamforming (JNOB), with the objective to minimize the overall BS power consumption (including the operational costs of CoMP transmission) while guaranteeing the quality-of-service (QoS) requirements of the mobile stations (MSs). We address this problem using a mixed integer second-order cone program (MI-SOCP) framework and develop an extended MI-SOCP formulation that admits tighter continuous relaxations, which is essential for reducing the computational complexity of the branch-and-cut (BnC) method. Analytic studies of the MI-SOCP formulations are carried out. Based on the analyses, we introduce efficient customizing strategies to further speed up the BnC algorithm through generating tight lower bounds of the minimum total BS power consumptions. For practical applications, we develop polynomial-time inflation and deflation procedures to compute high-quality solutions of the JNOB problem. Numerical results show that the inflation and deflation procedures yield total BS power consumptions that are close to the lower bounds, e. g., exceeding the lower bounds by about 12.9% and 9.0%, respectively, for a network with 13 BSs and 25 MSs. Simulation results also show that minimizing the total BS power consumption results in sparse network topologies and reduced operational overhead in CoMP transmission and that some of the BSs are switched off when possible.