The subject here is generalized (i.e., non-Gaussian) noise models, and specifically their first-order probability density functions (PDFs). Attention is focused primarily on the author's canonical statistical-physical Class A and Class B models. In particular, Class A noise describes the type of electromagnetic interference (EMI) often encountered in telecommunication applications, where this ambient noise is largely due to other, "intelligent" telecommunication operations. On the other hand, ambient Class B noise usually represents man-made or natural "nonintelligent"-i.e., nonmessage-bearing noise-and is highly impulsive. Class A noise is not an /spl alpha/-stable process, nor is it reducible to such, except in the limiting Gaussian cases of high-density noise (by the central limit theorem). Class B noise is also asymptotically normal (before model approximation). Under rather broad conditions, principally governed by the source propagation and distribution scenarios, the PDF of Class B noise alone (no Gaussian component) can usually be approximated by (1) a symmetric Gaussian /spl alpha/-stable (S/spl alpha/S) model in the case of narrowband reception, or when the PDF /spl omega//sub 1/(/spl alpha/) of the amplitude is symmetric; and (2) a nonsymmetric /spl alpha/-stable (NS/spl alpha/S) model (no Gaussian component) can be constructed in broadband regimes. New results here include: (i) counting functional methods for constructing the general qth-order characteristic functions (CFs) of Class A and Class B noise, from which (all) moments and (in principle), the PDFs follow; (ii) the first-order CFs, PDFs, and cumulative probabilities (APDs) of nonsymmetric broadband Class B noise, extended to include additive Gauss noise (AGN); (iii) proof of the existence of all moments in the basic Class A and Class B models; (iv) the key physical role of AGN and the fact that AGN removes /spl alpha/-stability; (v) the explicit roles of the propagation and distribution scenarios; and (vi) extension to noise fields. Although telecommunication applications are emphasized, Class A and Class B noise models apply selectively, but equally well, to other physical regimes, e.g., underwater acoustics and EM (radar, optics, etc.). Supportive empirical data are included.

Non-Gaussian noise models in signal processing for telecommunications: new methods an results for class A and class B noise models

In studying the performance of coded communications over memoryless channels (with or without fading), the results are given as upper bounds on the average bit error probability (BEP). In principle, there are three different approaches to arriving at these bounds, all of which employ obtaining the so-called pairwise error probability , or the probability of choosing one symbol sequence over another for a given pair of possible transmitted symbol sequences, followed by a weighted summation over all pairwise events. In this chapter, we will focus on the results obtained from the third approach since these provide the tightest upper bounds on the true performance. The first emphasis will be placed on evaluating the pairwise error probability with and without CSI, following which we shall discuss how the results of these evaluations can be used via the transfer bound approach to evaluate average BEP of coded modulation transmitted over the fading channel.

Coded Communication over Fading Channels

(1963). Statistical Inference for Markov Processes. Technometrics: Vol. 5, No. 3, pp. 413-415.

Statistical Inference for Markov Processes

The paper considers interference in a wireless communication network caused by users that share the same propagation medium. Under the assumption that the interfering users are spatially Poisson distributed and under a power-law propagation loss function, it has been shown in the past that the interference instantaneous amplitude at the receiver is /spl alpha/-stable distributed. Past work has not considered the second-order statistics of the interference and has relied on the assumption that interference samples are independent. In this paper, we provide analytic expressions for the interference second-order statistics and show that depending on the properties of the users' holding times, the interference can be correlated. We provide conditions under which the interference becomes m-dependent, /spl phi/-mixing, or long-range dependent. Finally, we present some implications of our theoretical findings on signal detection.

Co-channel interference modeling and analysis in a Poisson field of interferers in wireless communications

This paper reviews how to construct sets of random numbers with particular amplitude distributions and correlations among values. These constructions support both high-fidelity Monte Carlo simulation and analytic design studies. A variety of constructions is presented to free engineering models from "white or normal" limitations embodied in many current simulations. The methods support constructions of conventional stationary and normally distributed processes, nonstationary, nonnormal signal and interference waveforms, nonhomogeneous random scenes, nonhomogeneous volumetric clutter realizations, and snapshots of randomly evolving, nonhomogeneous scenes. Each case will have specified amplitude statistics, e.g., normal, log-normal, uniform, Weibull, or discrete amplitude statistics; and selected correlation, e.g., white, pink, or patchy statistics, clouds. or speckles. Sets of random numbers with correlation, nonstationarities, various tails for the amplitude distributions, and multimodal distributions can be constructed. The paper emphasizes aspects of probability theory necessary to engineering modeling. >

Constructions of particular random processes

In this article we propose the use of the so-called Fisher-Snedecor $\mathcal {F}$ -distribution to model atmospheric turbulence-induced fading in free space optical communication systems. The proposed model is a two-parameter distribution, defined as the ratio of two independent gamma random variables. In this context, the proposed model is based on a doubly stochastic theory of turbulence-induced fading, assuming that small-scale irradiance variations of the propagating wave, modeled by a gamma distribution, are a subject to large-scale irradiance fluctuations, modeled by an inverse gamma distribution. It is shown that the $\mathcal {F}$ -distribution yields at least as good, or even a better fit to experimental and computer simulation data as compared to the well known gamma-gamma distribution. Also, important statistical measures such as cumulative distribution function (CDF) and moment generating function (MGF) are mathematically simpler than those of the gamma-gamma distribution. Motivated by these facts, the performance of single-input—multiple output (SIMO) and multiple-input—multiple output (MIMO) systems operating in the presence of $\mathcal {F}$ turbulence is assessed. The proposed analysis is substantiated by numerically evaluated results and Monte Carlo simulations.

The Fischer–Snedecor $\mathcal {F}$ -Distribution Model for Turbulence-Induced Fading in Free-Space Optical Systems

Secrecy capacity is a fundamental information-theoretic performance metric to predict the maximum data rate of reliable communication, while the intended message is not revealed to the eavesdropper. Motivated by this consideration in this paper, a unified communication-theoretic framework for the analysis of the probability of nonzero secrecy capacity, the secrecy outage probability, and the secrecy capacity of multiple-antenna systems over fading channels is proposed. Specifically, a powerful frequency-domain approach is first developed in which the integrals involved in the evaluation of the probability of nonzero secrecy capacity and secrecy outage probability are transformed into the frequency domain, by employing Parseval’s theorem. A generic approach for the evaluation of the asymptotic secrecy outage probability at high signal-to-noise ratio (SNR) region is also introduced, thus providing useful insight as to the parameters affecting the secrecy performance. Finally, a unified numerical approach for computing the average secrecy capacity of multiple-antenna systems under arbitrary fading environments is developed. The proposed framework is general enough to accommodate any well-known multiantenna transmission technique and fading model. Finally, the secrecy performance of several multiple-antenna system setups is assessed, in the presence of generalized fading conditions and arbitrary antenna correlation, while various numerical and computer simulation results are shown and compared to substantiate the proposed mathematical analysis.

Physical Layer Security for Multiple-Antenna Systems: A Unified Approach

Soft computing techniques are used, in this paper, to model and solve the inverse problem of a thin, circular, loop antenna that radiates in free space The electromagnetic field intensity serves as the input to the inverse model, whereas the antenna radius is the output Three different architectures, based on artificial neural networks (ANNs), are implemented and various training algorithms are tested in order to obtain the optimum performance The effect of the size of the training data set and the number of the observers on the accuracy of the results are investigated Specific information for the selection of the appropriate ANN architecture is provided, depending on the constraints imposed by various parameters of the problem Extensive numerical tests indicate that the results predicted by the proposed models are in excellent agreement with the theoretical data obtained from the existing analytical solutions of the forward problem

Neural Network Modeling for the Solution of the Inverse Loop Antenna Radiation Problem

The purpose of this paper is to extend the recent formulation of locally optimum Bayes (LOB) detection in nonadditive non-Gaussian noise with independent sampling to the case where dependence between the noise samples is modeled via an ergodic first-order Markov discrete-time process. Moreover, unlike previous related work, numerical results are provided which are based on an empirically derived second-order transition density, the marginal PDF of which is Middleton's (1993) Class A noise, an experimentally verifiable and widely applicable non-Gaussian model. Canonical, in signal waveform and noise statistics, asymptotically and LOB detectors in both coherent and incoherent modes are derived and their statistics are computed under both "signal present" and "signal absent" hypotheses. Performance measures are thus obtained together with the correlation gain G/sup (M.P.)/, which is used for systems comparison. Explicit forms for the transition density and and the nonlinearities involved, as well as numerical values of the noise indices, are calculated from a generalized observation model containing multiplicative and additive Markov noise components. It is shown that significant performance gains over the case with independent sampling can be achieved, depending upon the degree of correlation between the noise samples.

Locally optimum Bayes detection in nonadditive first-order Markov noise

Detection algorithms that are locally optimum Bayes, and also asymptotically optimum, are developed for both coherent and incoherent signaling for arbitrary interference and signal waveforms when the dependence in the noise samples is represented by a moving-average model. This leads to receiver structures, which are prewhitened versions of the locally optimum detectors in the independent case. A probability-of-error expression (in the ideal-observer symmetric case), the processing gain, and the minimum-detectable signal are derived in both cases. These demonstrate, by means of an expression comparing performance between this and the independent case, that for the same large sample size (n>>1), an improvement in performance is always achieved when the noise samples are dependent, without any additional complexity in receiver structure. >

A.M. Maras

Papers

The Fischer–Snedecor $\mathcal {F}$ -Distribution Model for Turbulence-Induced Fading in Free-Space Optical Systems

Physical Layer Security for Multiple-Antenna Systems: A Unified Approach

Neural Network Modeling for the Solution of the Inverse Loop Antenna Radiation Problem

Locally optimum Bayes detection in nonadditive first-order Markov noise

Locally optimum detection in moving average non-Gaussian noise