Large-Scale Analysis of Linear Massive MIMO Precoders in the Presence of Phase Noise

We study the impact of phase noise on the downlink performance of a multi-user multiple-input multiple-output system, where the base station (BS) employs a large number of transmit antennas $M$. We consider a setup where the BS employs M_{\mr{osc}} free-running oscillators, and M/M_{\mr{osc}} antennas are connected to each oscillator. For this configuration, we analyze the impact of phase noise on the performance of regularized zero-forcing (RZF) precoding, when $M$ and the number of users $K$ are asymptotically large, while the ratio $M/K=\beta$ is fixed. We analytically show that the impact of phase noise on the signal-to-interference-plus-noise ratio (SINR) can be quantified as an effective reduction in the quality of the channel state information available at the BS when compared to a system without phase noise. As a consequence, we observe that as M_{\mr{osc}} increases, the SINR of the RZF precoder degrades as the interference power increases, and the desired signal power decreases. On the other hand, the variance of the random phase variations caused by the BS oscillators reduces with increasing M_{\mr{osc}}. Through simulations, we verify our analytical results, and study the performance of the RZF precoder for different phase noise and channel noise variances