Analysis of the Optimal Feedback Rate for Limited Feedback-Based Block Diagonalization in Cellular MU-MIMO Systems

We examine a downlink cellular network utilizing multiple-antenna base stations (BSs) deployed via a homogeneous Poisson point process. Each BS serves multiple users concurrently using spatial division multiple access (SDMA), with each user equipped with multiple receive antennas. The downlink SDMA employs linear precoding, specifically block diagonalization (BD), with channel state information obtained through limited feedback to construct BD precoding matrices. We offer close approximations for the optimal feedback rate aimed at maximizing the net spectral efficiency, which quantifies the net data rate achieved through limited-feedback-based BD. To achieve this, we introduce a novel lower bound for the Laplace transform of multi-cell interference. This analytical result aids in deriving the optimal feedback rate and the corresponding maximum net spectral efficiency. In comparison to previous studies that assumed single-antenna users, limited-feedback-based BD, enhanced by optimized feedback rates, substantially improves net sum spectral efficiency in interference-limited cellular networks. This result is remarkable as it holds true even with a reduced feedback bit requirement per data stream.