  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 $M_{\mathrm{osc}}$ free-running oscillators, and
$M/M_{\mathrm{osc}}$ antennas are connected to each oscillator. For this
configuration, we analyze the impact of phase noise on the performance of the
regularized zero-forcing (RZF), 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 $M_{\mathrm{osc}}$ increases,
the SINR performance of all considered precoders degrades. On the other hand,
the variance of the random phase variations caused by the BS oscillators
reduces with increasing $M_{\mathrm{osc}}$. Through Monte-Carlo simulations, we
verify our analytical results, and compare the performance of the precoders for
different phase noise and channel noise variances. For all considered
precoders, we show that when $\beta$ is small, the performance of the setup
where all BS antennas are connected to a single oscillator is superior to that
of the setup where each BS antenna has its own oscillator. However, the
opposite is true when $\beta$ is large and the signal-to-noise ratio at the
users is low.
