An analytical framework for transmit beamforming with peak power constraint

Multi-antenna transmit beamforming is a well-adopted technique at base stations to reduce interference and improve communication quality. The radiation pattern in beamforming is determined by both the weights and configurations of antenna array. In base stations, orthogonal frequency-division multiplexing (OFDM) signals and multi-carrier wideband code division multiple access (WCDMA) signals exhibit high peak-to-average-power ratios (PAPRs), causing them to be susceptible to non-linear distortions of power amplifiers (PAs). The beam patterns may be impaired as well. Due to the beamforming weights, the transmitted signals on multiple chains can have different average and peak powers. In addition, the PAs on different chains can exhibit different non-linear characteristics. Therefore, multi-antenna transmit beamforming with non-linearity is more complicated than that for single chain transmission. In this paper, we will study transmit beamforming systems with peak power constraints by assuming that the PA follows a soft limiter model. We will establish a framework for analyzing clipping effects in transmit beamforming systems. Three metrics will be adopted to characterize the impairments: (i) the power gain pattern; (ii) the beamforming error pattern; and (iii) the signal-to-distortion power ratio (SDR) pattern. Both numerical derivations and simulations will be provided to assess the proposed metrics.