  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.
