Block diagonalization precoding game in a multiuser multicell system

This paper characterizes the multicell precoding game where block-diagonalization (BD)-based precoding is utilized on a per-cell basis for downlink transmissions. Sharing the same frequency band, the base-station (BS) at each cell wishes to maximize the sum-rate for its connected mobile-stations (MS) with BD precoding. In this context, the paper considers a strategic non-cooperative game (SNG), where each BS greedily determines its precoding strategy in a distributed manner, based on the knowledge of the inter-cell interference (ICI) at its connected MSs. Via the game-theory framework, the existence and uniqueness of a Nash Equilibrium (NE) of this multicell game are subsequently studied. It is shown that there always exists at least one pure NE in the game, whereas the uniqueness of the NE is guaranteed under a certain condition on the ICI. The paper also characterizes the multicell precoding game where BD-Dirty Paper Coding (BD-DPC) is utilized at each BS on a per-cell basis. Simulation results then confirm our analysis on the NE´s uniqueness in the BD and BD-DPC multicell precoding games.