  In a heterogeneous wireless cellular network, each user may be covered by
multiple access points such as macro/pico/relay/femto base stations (BS). An
effective approach to maximize the sum utility (e.g., system throughput) in
such a network is to jointly optimize users' linear procoders as well as their
base station associations. In this paper we first show that this joint
optimization problem is NP-hard and thus is difficult to solve to global
optimality. To find a locally optimal solution, we formulate the problem as a
noncooperative game in which the users and the BSs both act as players. We
introduce a set of new utility functions for the players and show that every
Nash equilibrium (NE) of the resulting game is a stationary solution of the
original sum utility maximization problem. Moreover, we develop a best-response
type algorithm that allows the players to distributedly reach a NE of the game.
Simulation results show that the proposed distributed algorithm can effectively
relieve local BS congestion and simultaneously achieve high throughput and load
balancing in a heterogeneous network.
