On Optimization of Joint Base Station Association and Power Control via Benders´ Decomposition

In multi-cell networks where mobile stations perceive different channel gains to different base stations (BS), it is critical to associate a mobile station with the proper BS to maintain good communication quality with limited bandwidth resources. Oftentimes, the already-challenging BS association problem is further complicated by the need of transmission power control, which is an essential component to manage co-channel interference in many wireless communications systems. Despite its importance, joint BS association and power control (BAPC) problem has remained largely open, mainly due to its non-convex nature that makes the global optimal solution difficult to obtain. In this paper, we propose a novel algorithm, referred to as BARN, to solve the joint BAPC problem efficiently and optimally in the sense that the number of mobile stations in service is maximized and the total transmission power is minimized in the same time. In particular, we first propose a single-stage formulation that captures the two objectives simultaneously. Then, the problem is transformed in a way that can be efficiently solved using the BARN algorithm that is derived from the standard Benders´ Decomposition. Finally, we derive a close-form analytical formula to characterize the effect of the termination criterion of the algorithm on the gap between the obtained solution and the optimal one. By carefully choosing the termination rule, the BARN algorithm can always converge to the global optimal solution.