A two time scale approach for coordinated multi-point transmission and reception over practical backhaul

We consider the problem of maximizing a given utility over heterogeneous wireless networks (HetNets) that have a practical (non ideal) backhaul. Such a backhaul is characterized by high latency and possibly limited capacity, which necessitates the use of semi-static schemes for resource management. The management in these semi-static schemes is done at two time scale s over a coordination unit within the HetNet, that comprises of a set of transmission points (TPs) and a set of users. In this paper we consider one such promising semi-static resource management scheme in which the group of beam vectors that each TP in the coordination unit should employ and the set of users that it should serve is decided at a coarse time scale in a centralized manner, while the fine time scale per-slot scheduling is done in a distributed fashion with each TP using its assigned beam group (precoder) to serve its associated set of users. We propose an optimal two time scale policy for this scheme that guarantees a long-term optimality with respect to the given utility. However, this policy involves repeatedly solving a joint precoder set assignment and user association problem, which we prove is strongly NP-hard. Consequently, we develop an approximation algorithm for the latter optimization problem and also prove that the two time scale policy that employs this approximation algorithm also yields an approximate long-term optimality with respect to the given utility. Finally, we also incorporate another practically relevant constraint which demands that the per-slot scheduling policy of each TP remain unaltered.