The Effect of Spatial Correlation on the Capacity of Multi-Input Multi-Output Broadcast Channels with Partial Side Information

This report considers the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO Gaussian broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users n, we analyze the scaling laws of the sum-rate for the dirty paper coding and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large n, the sum rate is equal to M log log n +M log P M + o(1) where M is the number of transmit antennas, P is the average signal to noise ratio, and o(1) refers to terms that go to zero as n → ∞. When the channel exhibits some spatial correlation with a covariance matrix R (non-singular with Tr(R) = M), we prove that the sum rate of dirty paper coding is M log log n +M log P M + log det(R) + o(1). We further show that the sum-rate of various beamforming schemes achieves M log log n +M log P M +M log c + o(1) where c ≤ 1 depends on the type of beamforming. We can in fact compute c for random beamforming proposed in [26] and more generally, for random beamforming with precoding in which beams are pre-multiplied by a fixed matrix. In the second part of the report, we introduce various precoding matrices to reduce the hit that results from correlation. We obtain the optimum precoding matrix and various suboptimal precoding matrices. Our theoretical results are confirmed in both parts by simulations.