# Phase Noise in Communication Systems--Modeling, Compensation, and Performance Analysis

[Doktorsavhandling]

The continuous increase in demand for higher data rates due to applications with massive number of users motivates the design of faster and more spectrum efficient communication systems. In theory, the current communication systems must be able to operate close to Shannon capacity bounds. However, real systems perform below capacity limits, mainly because of considering too idealistic or simplistic assumptions on the imperfections such as channel estimation errors or hardware impairments.

Oscillator phase noise is one of the hardware impairments that is becoming a limiting factor in high data rate digital communication systems. Phase noise severely limits the performance of systems that employ dense constellations. Moreover, the level of phase noise (at a given off-set frequency) increases with carrier frequency, which means that the problem of phase noise may be worse in systems with high carrier frequencies.

The focus of this thesis is on: i) finding accurate statistical models of phase noise, ii) designing efficient algorithms to mitigate the effect of this phenomenon, iii) analyzing the Shannon capacity of the single and multiple-antenna communication systems affected by phase noise.

First, a new statistical model of phase noise valid for free-running and phase-locked-loop-stabilized oscillators is provided. The new model incorporates white and colored noise sources inside the oscillator circuitry. The new model is used in order to connect the performance of phase-noise affected communication systems, in terms of error-vector-magnitude, with oscillator phase-noise measurements. The results can be used by hardware and frequency generator designers to better understand the impairing effects of phase noise on the system performance and optimize their design criteria respectively.

Second, the proposed phase-noise model is employed for estimation of phase noise generated from white and colored noise sources. A soft-input maximum a posteriori phase noise estimator and a modified soft-input extended Kalman smoother are proposed. The performance of the proposed algorithms is compared against that of those studied in the literature, in terms of mean square error of phase noise estimation, and symbol error rate of the considered communication system. The comparisons show that considerable performance gains can be achieved by designing estimators that employ correct knowledge of the phase-noise statistics. The performance improvement is more significant in low-SNR or low-pilot density scenarios.

Finally, the capacity of single and multiple antenna communication systems affected by phase noise is investigated. For the SISO Wiener phase-noise channel, upper and lower bounds on the capacity are obtained, which are tight for a wide range of SNR values. In addition, a family of input distributions, which result in a tight lower bound are introduced. The high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for two different oscillator configurations is investigated. The provided analysis shows that driving antennas at the base station by separate (independent) local oscillators is beneficial for the SIMO channel compared to driving all the antennas with a common oscillator. In contrast, larger gains are achieved for the MISO channel when a common oscillator is employed.

**Nyckelord: **Oscillator phase noise, free-running oscillator, phase-locked loop, colored phase noise, phase noise model, Bayesian Cramér-Rao bound, maximum a posteriori estimator, extended Kalman filter/smoother, mean square error, channel capacity, Wiener process, capacity achieving distribution, multiple antennas, distributed oscillators.

Denna post skapades 2015-10-15. Senast ändrad 2015-11-24.

CPL Pubid: 224284