Abstract-Oscillator phase noise (PN) is one of the major problems that affect the performance of communication systems. In this paper, a direct connection between oscillator measurements, in terms of measured single-side band PN spectrum, and the optimal communication system performance, in terms of the resulting error vector magnitude (EVM) due to PN, is mathematically derived and analyzed. First, a statistical model of the PN, considering the effect of white and colored noise sources, is derived. Then, we utilize this model to derive the modified Bayesian Cramér-Rao bound on PN estimation, and use it to find an EVM bound for the system performance. Based on our analysis, it is found that the influence from different noise regions strongly depends on the communication bandwidth, i.e., the symbol rate. For high symbol rate communication systems, cumulative PN that appears near carrier is of relatively low importance compared to the white PN far from carrier. Our results also show that 1/f 3 noise is more predictable compared to 1/f 2 noise and in a fair comparison it affects the performance less.

In this paper, we address the classical problem of maximum-likelihood (ML) detection of data in the presence of random phase noise. We consider a system, where the random phase noise affecting the received signal is first compensated by a tracker/estimator. Then the phase error and its statistics are used for deriving the ML detector. Specifically, we derive an ML detector based on a Gaussian assumption for the phase error probability density function (PDF). Further without making any assumptions on the phase error PDF, we show that the actual ML detector can be reformulated as a weighted sum of central moments of the phase error PDF. We present a simple approximation of this new ML rule assuming that the phase error distribution is unknown. The ML detectors derived are also the aposteriori probabilities of the transmitted symbols, and are referred to as soft metrics. Then, using the detector developed based on Gaussian phase error assumption, we derive the symbol error probability (SEP) performance and error floor analytically for arbitrary constellations. Finally we compare SEP performance of the various detectors/metrics in this work and those from literature for different signal constellations, phase noise scenarios and SNR values.

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 Mosc free-running oscillators, and M/Mosc 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 = β is fixed. We analytically show that the impact of phase noise on the signal-to-interference-plusnoise 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 Mosc 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 Mosc. Through simulations, we verify our analytical results, and study the performance of the RZF precoder for different phase noise and channel noise variances.

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 Mosc freerunning oscillators, and M/Mosc antennas are connected to each oscillator. For this configuration, we analyze the impact of phase noise on the performance of the zero-forcing (ZF), regularized ZF, and matched filter (MF) precoders when M and the number of users K are asymptotically large, while the ratio M/K = β 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 Mosc 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 Mosc. Through MonteCarlo 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 β 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 β is large and the signal-to-noise ratio at the users is low.Index Terms -Massive MIMO, linear precoding, phase noise, broadcast channel, random matrix theory, multi-user MIMO.

Abstract-In multiple antenna systems, phase noise due to instabilities of the radio-frequency (RF) oscillators, acts differently depending on whether the RF circuitries connected to each antenna are driven by separate (independent) local oscillators (SLO) or by a common local oscillator (CLO). In this paper, we investigate the high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for both the CLO and the SLO configurations.Our results show that the first-order term in the high-SNR capacity expansion is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to 0.5 ln(ρ), where ρ stands for the SNR. On the contrary, the second-order term, which we refer to as phasenoise number, turns out to be scenario-dependent. For the SIMO case, the SLO configuration provides a diversity gain, resulting in a larger phase-noise number than for the CLO configuration. For the case of Wiener phase noise, a diversity gain of at least 0.5 ln(M ) can be achieved, where M is the number of receive antennas. For the MISO, the CLO configuration yields a higher phase-noise number than the SLO configuration. This is because with the CLO configuration one can obtain a coherent-combining gain through maximum ratio transmission (a.k.a. conjugate beamforming). This gain is unattainable with the SLO configuration.