Grab-n-Pull: An Optimization Framework for Fairness-Achieving Networks

In this paper, we present an optimization framework for designing precoding (a.k.a. beamforming) signals that are instrumental in achieving a fair user performance through the networks. The precoding design problem in such scenarios can typically be formulated as a non-convex max-min fractional quadratic program. Using a penalized version of the original design problem, we derive a simplified quadratic reformulation of the problem in terms of the signal (to be designed). Each iteration of the proposed design framework consists of a combination of power method-like iterations and the Gram-Schmidt process, and as a result, enjoys a low computational cost. Moreover, the suggested approach can handle various types of signal constraints such as total-power, per-antenna power, unimodularity, or discrete-phase requirements—an advantage which is not shared by other existing approaches in the literature.