Asymptotic Analysis of Downlink Multi-cell Systems with Partial CSIT

We analyze the downlink of multiple input multiple output (MIMO) multicell systems in the presence of intercell interference (ICI), under different transmit channel state information (CSI) assumptions. We assume, for the first scenario, that the Base Stations (BSs) have only the statistical CSI of all the channels. For the second scenario, we assume that the BSs have perfect CSI of their User Terminals(UTs) but only the statistical CSI of channels of the interfering BSs. We consider the following receiver structures at the UTs a) Optimal Decoding b) Minimum Mean Square (MMSE) receiver. We derive analytical expressions to compute the optimal number of streams each BS must use in order to maximize the total spectral efficiency of the system. We perform our analysis in the large dimensional regime (assuming the number of antennas on the BSs and UTs approaching infinity, at the same rate) using results from random matrix theory (RMT). However, the asymptotic results provide close approximation in the finite dimensional scenario. Remarkably, in the asymptotic regime, the optimization parameters depend only on the channel statistics and not on the instantaneous CSI, thus enabling a decentralized resource allocation policy in a multicell scenario. Our results show that in an interference limited regime, it is optimal for the BSs to use only a small subset of its streams to maximize the total spectral efficiency of the system.