Resource Allocation for Wireless Networks: A Distributed Optimization Approach

We consider the multi-cell joint power control and scheduling problem in cellular wireless networks as a weighted sum-rate maximization problem. This formulation is very general and applies to a wide range of applications and QoS requirements. The problem is inherently hard due to objectiveu0027s non-convexity and the knapsack-like constraints. Moreover, practical system requires a distributed operation. We applied an existing algorithm proposed by Scutari et al. in distributed optimization literature to our problem. The algorithm performs local optimization followed by consensus update repeatedly. However, it is not fully applicable to our problem, as it requires all decision variables to be maintained at every base station (BS), which is impractical for large-scale networks; also, it relies on the Lipschitz continuity of the objective functionu0027s gradient, which does not hold here. We exploited the nature of our objective function, and proposed a localized version of the algorithm. Furthermore, we relaxed the requirements of Lipschitz continuity with the proximal approximation. Convergence to local optimal solutions was proved under some conditions. Future work includes proving the above results from a stochastic approximation perspective, and investigating non-linear consensus schemes to speed up the convergence.