Reduced-Order Zero-Forcing Beamforming vs Optimal Beamforming and Dirty Paper Coding and Massive MIMO Analysis

Optimal linear transmitter beamformers in multi-antenna multi-user systems are of the Minimum Mean Squared Error (MMSE) type (dual uplink MMSE receivers). MMSE designs make an optimal compromise between noise enhancement and interference suppression and reduce to matched filters at low SNR and zero-forcing at high SNR. We consider a realistic scenario of user channels of varying attenuation and constrain the beamformers to either zero-force or ignore each interference term. This leads to a reduced-order zero-forcing (RO-ZF) design in which the number of interference sources being zero-forced increases with SNR. We apply a simple large systems analysis (applicable to Massive MIMO) to determine the asymptotic performance of RO-ZF designs, determine the optimal ZF orders, and compare to optimal and ZF linear and Dirty Paper Coding (DPC) designs. RO-ZF designs lead to variable reductions of computational complexity and channel state information (CSI) requirements (esp. in future multi-cell extensions), both important considerations in Massive MIMO systems.