On the Equivalence of Hybrid Beamforming to Full Digital Zero Forcing in mmWave MIMO

Recently, Millimeter Wave (mmWave) systems have emerged as a potential solution for the spectrum secrecy problem suffered by current wireless technologies. However, practically implementing such systems is challenging as they suffer from high hardware complexity and power consumption. Therefore, analog beamforming is considered the most suitable approach for practical implementation of such systems, relaxing the hardware and power consumption requirements compared to full digital beamforming solution. Moreover, hybrid beamforming solutions emerged as an attractive solution that can capture the trade-off between digital and analog ones. In this paper we show mathematically that in pure Line of Sight (LoS) channels, using hybrid beamforming with Zero Forcing (ZF) at the baseband can achieve equivalent Spectral Efficiency (SE) compared to the full digital ZF precoding, with lower hardware complexity, and lower power consumption. Moreover, we validate the equivalence in SE performance between hybrid ZF and digital ZF by simulation results.