Abstract
Hybrid beamforming (HB) using both analog precoding at RF and digital precoding is an effective solution to reduce the complexity and power consumption of massive MIMO systems. Extensive work has determined that HB can achieve the performance of the optimal precoder, assuming optimal antennas implementation, ideal environment, and full rank effective channel. However, depending on the implementation techniques adopted for the RF precoder and other system parameters, such as the number of active RF chains, the limited distance between antennas, and the geometric placement of both ends of wireless systems, the effective channel matrix could be rank deficient, which degrades the performance of the system. This paper provides a new and complete set of solutions for HB that approaches the performance of a fully digital beamformer in terms of MIMO multiplexing gains, by taking careful consideration of the matrix of the effective channel, appropriately selecting independent columns of the analog precoder, calculating the least squares solution for the digital precoder, and selecting its digital gain based on the selected columns of the RF precoder and the effective channel.