Oscillator phase noise: a tutorial

Linear time-invariant (LTI) phase noise theories provide important qualitative design insights but are limited in their quantitative predictive power. Part of the difficulty is that device noise undergoes multiple frequency translations to become oscillator phase noise. A quantitative understanding of this process requires abandoning the principle of time invariance assumed in most older theories of phase noise. Fortunately, the noise-to-phase transfer function of oscillators is still linear, despite the existence of the nonlinearities necessary for amplitude stabilization. In addition to providing a quantitative reconciliation between theory and measurement, the time-varying phase noise model presented in this tutorial identifies the importance of symmetry in suppressing the upconversion of 1/f noise into close-in phase noise, and provides an explicit appreciation of cyclostationary effects and AM-PM conversion. These insights allow a reinterpretation of why the Colpitts oscillator exhibits good performance, and suggest new oscillator topologies. Tuned LC and ring oscillator circuit examples are presented to reinforce the theoretical considerations developed. Simulation issues and the accommodation of amplitude noise are considered in appendixes

Virtual damping and Einstein relation in oscillators

This paper presents a new physical theory of oscillator phase noise. Built around the concept of phase diffusion, this work bridges the fundamental physics of noise and existing oscillator phase-noise theories. The virtual damping of an ensemble of oscillators is introduced as a measure of phase noise. The explanation of linewidth compression through virtual damping provides a unified view of resonators and oscillators. The direct correspondence between phase noise and the Einstein relation is demonstrated, which reveals the underlying physics of phase noise. The validity of the new approach is confirmed by consistent experimental agreement

Self-Interference Cancellation Using Time-Domain Phase Noise Estimation in OFDM Full-Duplex Systems

In full-duplex systems, oscillator phase noise (PN) problem is considered the bottleneck challenge that may face the self-interference cancellation (SIC) stage especially when orthogonal frequency division multiplexing (OFDM) transmission scheme is deployed. Phase noise degrades the SIC performance significantly, if not mitigated before or during the SIC technique. The presence of the oscillator phase noise has different impacts on the transmitted data symbol like common phase error (CPE) and inter-carrier interference (ICI). However, phase noise can be estimated and mitigated digitally in either time or frequency domain. Through this work, we propose a novel and simple time domain self-interference (SI) phase noise estimation and mitigation technique. The proposed algorithm is inspired from Wiener filtering in time domain. Simulation results show that the proposed algorithm has a superior performance than the already-existing time-domain or frequency domain PN mitigation solutions with a noticeable reduction in the computational complexity

Frequency Precision of Oscillators Based on High-Q Resonators

We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the stochastic oscillator dynamics onto a slow time scale corresponding physically to the long relaxation time of the resonator. We derive general expressions for the phase drift generated by noise sources in the electronic feedback loop of the oscillator. These are mixed with the signal through the nonlinear amplifier, which makes them {cyclostationary}. We also consider noise sources acting directly on the resonator. The expressions allow us to investigate reducing the oscillator phase noise thereby improving the frequency precision using resonator nonlinearity by tuning to special operating points. We illustrate the approach giving explicit results for a phenomenological amplifier model. We also propose a scheme for measuring the slow feedback noise generated by the feedback components in an open-loop driven configuration in experiment or using circuit simulators, which enables the calculation of the closed-loop oscillator phase noise in practical systems

Calculation of the Performance of Communication Systems from Measured Oscillator Phase Noise

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 Cramer-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.Comment: Accepted in IEEE Transactions on Circuits and Systems-I: Regular Paper

Local Oscillator Phase Noise Impact on M-ary Modulation Schemes

This paper presents the impact of a local oscillator phase noise on digital modulation schemes based on bit error rate and error vector magnitude. The adopted methodology enables base band metrics estimation which is dependent of a specific communication standard. A generic local oscillator phase noise model is presented to evaluate the impact of different phase noise values on error vector magnitude and bit error rate. For a phase noise of -65dBc @ 1kHz the error vector magnitude changes from 7% to 12.8%. Increasing the modulation order leads to bit error rate increment for the same phase noise value.publishersversionpublishe

Oscillator Phase Noise and Small-Scale Channel Fading in Higher Frequency Bands

This paper investigates the effect of oscillator phase noise and channel variations due to fading on the performance of communication systems at frequency bands higher than 10GHz. Phase noise and channel models are reviewed and technology-dependent bounds on the phase noise quality of radio oscillators are presented. Our study shows that, in general, both channel variations and phase noise can have severe effects on the system performance at high frequencies. Importantly, their relative severity depends on the application scenario and system parameters such as center frequency and bandwidth. Channel variations are seen to be more severe than phase noise when the relative velocity between the transmitter and receiver is high. On the other hand, performance degradation due to phase noise can be more severe when the center frequency is increased and the bandwidth is kept a constant, or when oscillators based on low power CMOS technology are used, as opposed to high power GaN HEMT based oscillators.Comment: IEEE Global Telecommun. Conf. (GLOBECOM), Austin, TX, Dec. 201

Uplink Performance of Time-Reversal MRC in Massive MIMO Systems Subject to Phase Noise

Multi-user multiple-input multiple-output (MU-MIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chains and severely degrades the performance of communication systems. We study the effect of oscillator phase noise in frequency-selective Massive MIMO systems with imperfect channel state information (CSI). In particular, we consider two distinct operation modes, namely when the phase noise processes at the $M$ BS antennas are identical (synchronous operation) and when they are independent (non-synchronous operation). We analyze a linear and low-complexity time-reversal maximum-ratio combining (TR-MRC) reception strategy. For both operation modes we derive a lower bound on the sum-capacity and we compare their performance. Based on the derived achievable sum-rates, we show that with the proposed receive processing an $O(\sqrt{M})$ array gain is achievable. Due to the phase noise drift the estimated effective channel becomes progressively outdated. Therefore, phase noise effectively limits the length of the interval used for data transmission and the number of scheduled users. The derived achievable rates provide insights into the optimum choice of the data interval length and the number of scheduled users.Comment: 13 pages, 6 figures, 2 tables, IEEE Transactions on Wireless Communications (accepted