Managing analog beams in mmWave networks

In this paper we consider multi-cell mmWave networks wherein each cell equipped with a large antenna array can employ an analog precoder (or a group of analog beams) to serve its associated users, while each such user can employ a single analog beam. A key problem over such a network is to determine the set of users that each cell should serve (a.k.a. user association), the group of beams it should employ, as well as their attributes such as how often and with how much power should each beam be used. This problem becomes harder since the choice of beam at any user is coupled to the cell it is assigned to and the latter's choice of beams. Moreover, practical considerations demand that each transmitting and receiving beam and their attributes be selected from finite codebooks. We develop novel solutions to this seemingly intractable problem. We adopt the generalized Quality-of-Service (QoS) Proportional Fairness (PF) network utility which can balance efficiency with fairness, and is particularly relevant for coverage constrained mmWave systems, since QoS constraints demand provisioning a minimum rate for each user. We prove that, remarkably, the user association problem under this QoS-PF utility can be formulated as a constrained submodular set function maximization problem. Consequently, it can be optimally solved (up to an additive constant) using distributed algorithms. We then propose a simple distributed algorithm to optimize the choice of beams and their attributes, and prove that it converges to a social equilibrium even in the presence a non-ideal communication channel between cells.