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

Spectral Weighting Functions for Single-symbol Phase-noise Specifications in OFDM Systems

For the specification of phase-noise requirements for the front-end of a HiperLAN/2 system we investigated available literature on the subject. Literature differed in several aspects. One aspect is in the type of phase-noise used (Wiener phase-noise or small-angle phase noise). A Wiener phase-noise based analysis leads to contradictions with the type of analysis normally used in the solid state oscillator literature. However, a phase-noise spectrum with a Wiener phase-noise shape can be used provided that the small-angle approximation is satisfied. An other aspect is whether a Fourier Series or DFT based approach is used. The approaches use weighting functions to relate phase-noise power spectral densities to phase-noise power. The two types of analysis are presented in a unified fashion that allows easy comparison of the weighting functions involved. It can be shown that for practical purposes results are identical. Finally phase-noise specifications for the Hiper-LAN/2 case are presented

Performance of DPSK Signals with Quadratic Phase Noise

Nonlinear phase noise induced by the interaction of fiber Kerr effect and amplifier noises is a quadratic function of the electric field. When the dependence between the additive Gaussian noise and the quadratic phase noise is taking into account, the joint statistics of quadratic phase noise and additive Gaussian noise is derived analytically. When the error probability for differential phase-shift keying (DPSK) signals is evaluated, depending on the number of fiber spans, the signal-to-noise ratio (SNR) penalty is increased by up to 0.23 dB due to the dependence between the Gaussian noise and the quadratic phase noise.Comment: 15 pages, 2 figure

Noise-induced synchronization for phase turbulence

Phase turbulence is suppressed by applying common noise additively to the Kuramoto-Sivashinsky type equation, and the noise-induced phase synchronization is realized. The noise strength necessary for the suppression of phase turbulence is evaluated theoretically.Comment: 7 pages, 4 figure

Phase-noise limitations in continuous-variable quantum key distribution with homodyne detection

In continuous-variables quantum key distribution with coherent states, the advantage of performing the detection by using standard telecoms components is counterbalanced by the lack of a stable phase reference in homodyne detection due to the complexity of optical phase-locking circuits and to the unavoidable phase noise of lasers, which introduces a degradation on the achievable secure key rate. Pilot-assisted phase-noise estimation and postdetection compensation techniques are used to implement a protocol with coherent states where a local laser is employed and it is not locked to the received signal, but a postdetection phase correction is applied. Here the reduction of the secure key rate determined by the laser phase noise, for both individual and collective attacks, is analytically evaluated and a scheme of pilot-assisted phase estimation proposed, outlining the tradeoff in the system design between phase noise and spectral efficiency. The optimal modulation variance as a function of the phase-noise amount is derived

Constrained Phase Noise Estimation in OFDM Using Scattered Pilots Without Decision Feedback

In this paper, we consider an OFDM radio link corrupted by oscillator phase noise in the receiver, namely the problem of estimating and compensating for the impairment. To lessen the computational burden and delay incurred onto the receiver, we estimate phase noise using only scattered pilot subcarriers, i.e., no tentative symbol decisions are used in obtaining and improving the phase noise estimate. In particular, the phase noise estimation problem is posed as an unconstrained optimization problem whose minimizer suffers from the so-called amplitude and phase estimation error. These errors arise due to receiver noise, estimation from limited scattered pilot subcarriers and estimation using a dimensionality reduction model. It is empirically shown that, at high signal-to-noise-ratios, the phase estimation error is small. To reduce the amplitude estimation error, we restrict the minimizer to be drawn from the so-called phase noise geometry set when minimizing the cost function. The resulting optimization problem is a non-convex program. However, using the S-procedure for quadratic equalities, we show that the optimal solution can be obtained by solving the convex dual problem. We also consider a less complex heuristic scheme that achieves the same objective of restricting the minimizer to the phase noise geometry set. Through simulations, we demonstrate improved coded bit-error-rate and phase noise estimation error performance when enforcing the phase noise geometry. For example, at high signal-to-noise-ratios, the probability density function of the phase noise estimation error exhibits thinner tails which results in lower bit-error-rate

Quantum-enhanced phase estimation using optical spin squeezing

Quantum metrology enables estimation of optical phase shifts with precision beyond the shot-noise limit. One way to exceed this limit is to use squeezed states, where the quantum noise of one observable is reduced at the expense of increased quantum noise for its complementary partner. Because shot-noise limits the phase sensitivity of all classical states, reduced noise in the average value for the observable being measured allows for improved phase sensitivity. However, additional phase sensitivity can be achieved using phase estimation strategies that account for the full distribution of measurement outcomes. Here we experimentally investigate the phase sensitivity of a five-particle optical spin-squeezed state generated by photon subtraction from a parametric downconversion photon source. The Fisher information for all photon-number outcomes shows it is possible to obtain a quantum advantage of 1.58 compared to the shot-noise limit, even though due to experimental imperfection, the average noise for the relevant spin-observable does not achieve sub-shot-noise precision. Our demonstration implies improved performance of spin squeezing for applications to quantum metrology.Comment: 8 pages, 5 figure

Phase Noise Modeling of Opto-Mechanical Oscillators

We build upon and derive a precise far from carrier phase noise model for radiation pressure driven opto-mechanical oscillators and show that calculations based on our model accurately match published phase noise data for such oscillators. Furthermore, we derive insights based on the equations presented and calculate phase noise for an array of coupled disk resonators, showing that it is possible to achieve phase noise as low as -80 dBc/Hz at 1 kHz offset for a 54 MHz opto-mechanical oscillator