Large System Analysis of Two-Stage Beamforming with Limited Feedback in FDD Massive MIMO Systems

Two-stage beamforming is a transmit strategy that uses two types of beamformers to reduce the feedback overhead of frequency-division-duplexing massive multiple-input multiple-output systems that are spatially correlated. In this paper, we present large system analysis of two-stage beamforming when a transmitter has limited channel information from feedback and when regularized-zero-forcing (RZF) is used as a second-stage beamformer. We consider two random-vector-quantization-based feedback schemes that can be respectively applied when users have perfect channel information or perfect effective channel information. For each feedback method, we analyze both expected signal-to-interference-plus-noise ratio (SINR) and expected rate loss and then characterize their bounds as a function of the number of feedback bits. From the characterization, we reveal that the sum rate of two-stage beamforming is very sensitive to the regularization parameter of RZF, especially when the number of feedback bits is limited. Motivated by this, we derive the optimal regularization parameter that maximizes the SINR of two-stage beamforming with limited feedback. Using simulations, we verify the tightness of the characterized bounds and quantify how the use of the optimal regularization parameter improves the sum rate of two-stage beamforming.