Joint Uplink Power Control, Beamforming and Bandwidth Allocation for Optimal QoS Assignment

This paper addresses the problem of joint resource allocation and QoS assignment in multi-cellular uplink of wireless data networks. We show how to jointly optimize three degrees of design freedom: transmit power, bandwidth allocation, and spatial diversity through antenna beamforming, in order to maximize the network-wide utility as a function of attained QoS. Many existing formulations of power control and antenna-beamforming can be viewed as special cases of this joint optimization. Our holistic framework leads to a quantitative understanding of the tradeoff among increasing power, partitioning the spectrum, and installing multiple antennas. The joint optimization is a globally coupled, non-convex problem. We solve it in several steps. First, we fix the bandwidth allocation and optimize transmit power across cells for a given beamforming vector. This extends naturally to the problem of jointly optimizing over receiver beamformer and transmit power, for which we develop a distributed algorithm that is proved to be convergent in general and globally optimal in the two user case, despite the non-convexity of this optimization. Next, the joint power-bandwidth optimization with fixed beamforming is shown to be a convex optimization, and we propose a distributed algorithm that computes the global optimum. Finally, an alternate maximization method is used to combine these two algorithms and shown to be convergent. Simulations show that the algorithm always converges to the jointly and globally optimal allocation, and demonstrate the tradeoff among power, bandwidth, and beamforming resources in maximizing network utility.