Sum-Rate-Optimal Precoding for Multi-Cell Large-Scale MIMO Uplink Based on Statistical CSI

We investigate the sum-rate-optimal precoding for the uplink of the multi-cell large-scale MIMO systems. Specifically, we focus on transmitter precoder design based only on the statistical channel state information (CSI). We first consider the partial cooperation system, where only the CSI is shared among cells, and its base station (BS) decodes its in-cell users by treating out-cell signals as colored Gaussian noise. We derive the ergodic sum rate and its deterministic approximation for the regime where both the number of total user antennas and the number of BS antennas are large. We obtain the necessary conditions to maximize the deterministic approximation of the sum rate under the transmit power constraint, based on which a gradient search algorithm is proposed to find the local optimal precoders. Furthermore, a super cell system is also considered, where users from all cells are jointly decoded. The deterministic approximation to the sum rate and optimal precoder design for such systems are given. Numerical experiments show that the proposed precoders achieve significant performance gains over systems with no precoding. Compared with the existing precoding methods that require perfect CSI, the proposed precoders achieve similar sum rates and require only the statistical CSI.