Power inversion (PI) is a known adaptive beamforming algorithm that is widely used in wireless communication systems for anti-jamming purposes. The PI algorithm is typically implemented in a digital domain, which requires the radio-frequency signals to be down-converted into base-band signals, and then sampled by ADCs. In practice, the down-conversion circuit will introduce phase noises into the base-band signals, which may degrade the performance of the algorithm. At present, the impacts of phase noise on the PI algorithm have not been studied, according to the open literature, which is, however, important for practical design. Therefore, in this paper, we present a theoretical analysis on the impacts, provide a new mathematical model of the PI algorithm, and offer a closed-form formula of the interference cancellation ratio (ICR) to quantify the relations between the algorithm performance and the phase noise level, as well as the number of auxiliary antennas. We find that the ICR in decibel decreases logarithmically linearly with the phase noise variance. In addition, the ICR improves with an increasing number of auxiliary antennas, but the increment is upper-bounded. The above findings are verified with both simulated and measured phase noise data.
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