An distributed deflation algorithm for joint admission control and beamforming in multi-user max-min fairness networks

Consider a network consisting of one multi-antenna base station (BS) and multiple single-antenna users. With a lot of users awaiting service, the network tends to be congested and the quality of service (QoS) degrades remarkably. This promotes the research on user admission control; i.e., to guarantee QoS, the network serves only a subset of users and rejects the rest. In this paper, we consider a max-min fairness (MMF) problem based on joint admission control and beamforming. In particular, by jointly optimizing the admissible users and the transmit beamformers, we maximize the minimum signal-to-interference-plus-noise-ratio (SINR) of admissible users, such that high QoS and fairness can be guaranteed for them. This problem is essentially NP-hard, and hence we develop a low-complexity iterative deflation algorithm to obtain some efficient approximate solution. In each iteration, we improve the users' SINRs and drop the user with the lowest SINR-to-power ratio, until the given user number is achieved. To facilitate the algorithm implementation, especially in large-scale networks, we further employ the alternating direction method of multipliers (ADMM) to perform per-user optimization. Finally, an efficient distributed algorithm is developed, with each step being solved in closed form.