Rayleigh Noise Research Articles

Extended MLSE receiver for the frequency-flat, fast-fading channel

This paper develops a maximum likelihood sequence estimation (MLSE) receiver for the frequency-flat, fast-fading channel corrupted by additive Gaussian noise when linear modulations (M-ASK, M-PSK, and M-QAM) are employed. This paper extends Ungerboeck's derivation of the extended MLSE receiver for the purely frequency-selective channel to the time-selective channel. Although the new receiver's structure and metric assume ideal channel state information (CSI) at the receiver, the receiver structure can be used wherever high-quality CSI is available. The receiver is maximum likelihood for a variety of channels, including Ricean, Rayleigh, lognormal, and additive white Gaussian noise (AWGN) channels. Bounds on the receiver's bit error rate (BER) are deduced for ideal and pilot tone CSI for fast Rayleigh fading. A crude lower bound is developed on the BER of predictor-based receivers for the same channel. This paper offers insight into matched filtering and receiver processing for the fast-fading channel and shows how pilot symbols and tones should be exploited.

Exactly solvable models of nonlinear dynamical systems driven by colored Ornstein-Uhlenbeck and Rayleigh noise

Exact solutions of the stationary Kolmogorov-Fokker-Planck equations corresponding to a certain class of nonlinear dynamical systems of first order driven parametrically (multiplicatively) by colored Markov Ornstein-Uhlenbeck and Rayleigh noise are obtained. The influence of asymmetric fluctuations on the form of the stationary distributions is discussed. Phase diagrams are constructed for some examples, and phase transitions induced by colored Rayleigh noise are noted.

Amplitude discrimination of sinusoids and narrow-band noise with Rayleigh properties.

The ability of human observers to discriminate differences in the amplitude of sinusoids and narrow-band noises was measured by the rating method of detection theory. Although each sinusoid (always 1000 Hz) was presented at a fixed amplitude, its amplitude on any trial was drawn from one of two Rayleigh probability distributions that differed in mean amplitude: a signal distribution and a noise distribution. Similarly, the amplitudes of the narrow-band noises were distributed as the Rayleigh distribution by virtue of the reciprocal relation between their bandwidth (100 Hz centered on 1000 Hz) and duration (10 msec). The obtained psychometric functions showing the area under the ROC as a function of signal-to-noise ratio were similar for both kinds of signals and were displaced, on average, about 4 dB from an ideal observer's function. The slopes of the obtained functions were similar to those of an ideal observer using 1 degree of freedom--half the number available in Rayleigh noise.

Crosstalk penalities due to coherent Rayleigh noise in bidirectional optical communication systems

The statistical properties, i.e. power spectral densities and probability density functions, of the noise due to Rayleigh backscattered light and due to interference of backscattered and reflected light are derived from the autocorrelation function of the optical source field. The crosstalk penalties due to Rayleigh backscattering in single- and double-source bidirectional systems are calculated. It is shown that it is possible to realize a bidirectional system with commercially available connectors in which Rayleigh backscattering is the dominant crosstalk contribution. The measured crosstalk penalties and bit-error probabilities in a double-source bidirectional system confirm the theoretical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Power penalties due to multiple Rayleigh backscattering in coherent transmission systems using in-line optical amplifiers

The power penalties due to double Rayleigh backscattering are calculated for coherent lightwave systems with optical in-line amplifiers. It is shown that coherent systems are less sensitive to Rayleigh noise than high-speed direct-detection systems. For PSK heterodyne systems, the maximum gain of in-line amplifiers that can be achieved without optical isolation is limited to about 25 dB. >

A model for target detection with over-the-horizon radar

The effects of including Faraday rotation and multipath on the probability of detecting low-flying, distant, fluctuating and nonfluctuating targets immersed in Rayleigh noise plus clutter are studied. The effect of ionospheric fluctuations is also considered. It is found that both multipath and Faraday rotation strongly influence the detection statistics, with the effect being greatest for linearly polarized targets and less marked for symmetric targets.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Observation of coherent Rayleigh noise in single-source bidirectional optical fiber systems

The authors report noise in a directional optical fiber system that they believe arises from the interference of the signal light with the Rayleigh backscattered light. This noise, called coherent Rayleigh noise (CRN), is the dominant noise source in this system. The interference provides a mechanism for translation of laser phase fluctuations into receiver photocurrent fluctuations. A number of noise reduction schemes are proposed. The authors demonstrate that CRN can be reduced, but not eliminated, by providing a small drive current modulation signal to the source laser to broaden its linewidth. Systems using this single-source-bidirectional architecture must take this noise source into account.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Single-laser high-selectivity bidirectional transmission system for local-area-network applications

Bidirectional transmission at 90Mbit/s over 30 km of fibre using a single laser source is demonstrated. At the subscriber end, a narrowband resonant optical amplifier serves not only as amplifier, but also as detector, modulator and optical filter. The coherent Rayleigh noise, encountered in previous single-laser bidirectional systems, is eliminated by using a subcarrier modulation scheme. The demonstrated capacity is more than an order of magnitude improvement over similar systems.

Transfer Functions for Partially Coherent SAR Systems

An impulse response function and a transfer function of use for partially coherent systems are presented. Partially coherent systems are those that transform a complex amplitude input to an output intensity and are encountered in many guises including optical systems, radiometers, scatterometers, astronomical radars, and synthetic aperture radar. (In the fully coherent or noncoherent limits, linear analysis and the associated system descriptions are well known in terms of amplitude or modulation transfer functions, respectively.) Properties are derived herein for partially coherent systems that describe performance dependence on system phase and amplitude match to input signal characteristics and to system and signal partial coherence. Such systems are shown to be energy conservative in the event of coherence variations. Output spectral properties that describe the dependence of multiplicative Rayleigh noise (speckle) on input signal coherence, system coherence, and phase match are presented. Unlike linear systems, partially coherent systems require both (1) the impulse response and (2) a quantitative measure of scene/system coherence to adequately describe their performance. The general formulation of this paper is applied to synthetic aperture radar (SAR) imaging systems to derive closed-form results of importance for that discipline. It is shown that the mean output from a SAR for a random distributed scene input is not dependent on system focus, system coherence, or scene coherence, whereas imagery of scene detail is dependent on these same parameters. The speckle spectrum is a function of system coherence, but not a function of scene coherence or system focus.

Intensity discrimination of Rayleigh noise.

A human observer is less effective at auditory intensity discrimination when the signal is a wide-band noise than when it is a pure (sinusoidal) tone. An experiment in intensity discrimination of Rayleigh noise shows that amplitude uncertainty seems to govern the discrimination. The empirical psychometric function is found to be only slightly displaced from the performance of an ideal energy detector.