Phase noise is a topic of theoretical and practical interest in electronic circuits, as well as in other fields, such as optics. Although progress has been made in understanding the phenomenon, there still remain significant gaps, both in its fundamental theory and in numerical techniques for its characterization. In this paper, we develop a solid foundation for phase noise that is valid for any oscillator, regardless of operating mechanism. We establish novel results about the dynamics of stable nonlinear oscillators in the presence of perturbations, both deterministic and random. We obtain an exact nonlinear equation for phase error, which we solve without approximations for random perturbations. This leads us to a precise characterization of timing jitter and spectral dispersion, for computing of which we have developed efficient numerical methods. We demonstrate our techniques on a variety of practical electrical oscillators and obtain good matches with measurements, even at frequencies close to the carrier, where previous techniques break down. Our methods are more than three orders of magnitude faster than the brute-force Monte Carlo approach, which is the only previously available technique that can predict phase noise correctly.

Phase noise in oscillators: a unifying theory and numerical methods for characterization

Multicarrier modulation exhibits a significant sensitivity to the phase noise of the oscillator used for frequency down-conversion at the portable receiver. For this reason, it is important to evaluate the impact of the phase noise on the system performance. We present an accurate method to determine the error probability of an orthogonal frequency-division multiplexing (OFDM) system in the presence of phase noise. In particular, four modulation schemes are analyzed and their performances are compared.

On the effect of Wiener phase noise in OFDM systems

We provide an exact analysis of orthogonal frequency-division multiplexing (OFDM) performance in the presence of phase noise Unlike most methods which assume small phase noise, we examine the general case for any phase noise levels After deriving a closed-form expression for the signal-to-noise-plus-interference ratio (SINR), we exhibit the effects of phase noise by precisely expressing the OFDM system performance as a function of its critical parameters This helps in understanding the meaning of small phase noise and how it reflects on the proper parameters selection of a specific OFDM system In order to combat phase noise, we also provide in this paper a general phase-noise suppression scheme, which, by analytical and numerical results, proves to be quite effective in practice

OFDM systems in the presence of phase noise: consequences and solutions

In this paper, we study the ability of transmit diversity to provide diversity benefit to a receiver in a Rayleigh fading environment. With transmit diversity, multiple antennas transmit delayed versions of a signal to create frequency-selective fading at a single antenna at the receiver, which uses equalization to obtain diversity gain against fading. We use Monte Carlo simulation to study transmit diversity for the case of independent Rayleigh fading from each transmit antenna to the receive antenna and maximum likelihood sequence estimation for equalization at the receiver. Our results show that transmit diversity with M transmit antennas provides a diversity gain within 0.1 dB of that with M receive antennas for any number of antennas. Thus, we can obtain the same diversity benefit at the remotes and base stations using multiple base-station antennas only.

The diversity gain of transmit diversity in wireless systems with Rayleigh fading

Studies the ability of transmit diversity to provide diversity benefit to a receiver in a Rayleigh fading environment. With transmit diversity, multiple antennas transmit delayed versions of a signal to create frequency-selective fading at a single antenna at the receiver, which uses equalization to obtain diversity gain against fading. The author uses Monte Carlo simulation to study transmit diversity for the case of independent Rayleigh fading from each transmit antenna to the receive antenna and maximum likelihood sequence estimation for equalization at the receiver. Ther results show that transmit diversity with M transmit antennas provides a diversity gain within 0.1 dB of that with M receive antennas, for any number of antennas. Thus, one can obtain the same diversity benefit at the remotes and base stations using multiple base station antennas only. >

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The phase noise associated with single-mode semiconductor lasers must be accounted for in performance studies of lightwave communication systems. The standard phase noise model is a Brownian-motion stochastic process. Although many analyses of lightwave communication systems have been published, none, to the authors knowledge, has fully adhered to the standard model. The reason is that a proper characterization of filtered lightwave signal had not been achieved. Such a characterization, along with theoretical approaches to obtaining it, is detailed. The authors show, for example, how to generate probability density functions (PDFs) of the magnitude of a filtered laser tone (with special attention to the tail region) and how to analytically represent the characteristic function of the PDF in closed form in the small-phase-noise realm. With the characterization in place, the stage is now set for determining the bit-error rate performance of advanced detection techniques which seek to mitigate the phase noise impairment. >

Characterizing filtered light waves corrupted by phase noise

The main result is the finding of the minimum distance, d/sub min/, for m-ary signals over a class of partial responses of interest in the field of digital magnetic recording. A previously published set of results (see H.K. Thapar and A.M. Patel, 1987) on d/sub min/ for a related class of partial responses relevant to the coaxial cable channel is extended. A simple, powerful algorithm for finding d/sub min/ is employed. A secondary result is given in a table, which extends a previously published table (see G.J. Foschini, 1975), reporting a solution to the corresponding problem for coaxial cable partial responses. >

G. Vannucci

Papers

Characterizing filtered light waves corrupted by phase noise

The minimum distance for digital magnetic recording partial responses