On the Energy Efficiency of MIMO Hybrid Beamforming for Millimeter Wave Systems with Nonlinear Power Amplifiers

Multiple-input multiple-output (MIMO) millimeter wave (mmWave) systems are vulnerable to hardware impairments due to operating at high frequencies and employing a large number of radio- frequency (RF) hardware components. In particular, nonlinear power amplifiers (PAs) employed at the transmitter distort the signal when operated close to saturation due to energy efficiency considerations. In this paper, we study the performance of a MIMO mmWave hybrid beamforming scheme in the presence of nonlinear PAs. First, we develop a statistical model for the transmitted signal in such systems and show that the spatial direction of the inband distortion is shaped by the beamforming filter. This suggests that even in the large antenna regime, where narrow beams can be steered toward the receiver, the impact of nonlinear PAs should not be ignored. Then, by employing a realistic power consumption model for the PAs, we investigate the trade-off between spectral and energy efficiency in such systems. Our results show that increasing the transmit power level when the number of transmit antennas grows large can be counter-effective in terms of energy efficiency. Furthermore, using numerical simulation, we show that when the transmit power is large, analog beamforming leads to higher spectral and energy efficiency compared to digital and hybrid beamforming schemes.