Showing papers on "Complex normal distribution published in 2001"
TL;DR: In this article, it was shown that the likelihood ratio statistic based on the Kullback-Leibler information criterion of the null hypothesis that a random sample is drawn from a k 0 -component normal mixture distribution against the alternative hypothesis that the sample was drawn from an k 1 -component normalized mixture distribution is asymptotically distributed as a weighted sum of independent chi-squared random variables with one degree of freedom, under general regularity conditions.
Abstract: We demonstrate that, under a theorem proposed by Vuong, the likelihood ratio statistic based on the Kullback-Leibler information criterion of the null hypothesis that a random sample is drawn from a k 0 -component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k 1 -component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi-squared random variables with one degree of freedom, under general regularity conditions. We report simulation studies of two cases where we are testing a single normal versus a two-component normal mixture and a two-component normal mixture versus a three-component normal mixture. An empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution.
3,531 citations
TL;DR: A simple closed-form approximation for the distribution of the peak-to-average power ratio (PAPR) in strictly band-limited orthogonal frequency-division multiplexing (OFDM) signals is developed, based on the level-crossing rate analysis.
Abstract: The distribution of the peak-to-average power ratio (PAPR) in strictly band-limited orthogonal frequency-division multiplexing (OFDM) signals is studied. Assuming that the base-band OFDM signal is characterized as a band-limited complex Gaussian process, we first attempt to derive the exact distribution of the PAPR in the band-limited OFDM signals. Since this distribution cannot be expressed in a closed form, we further develop a simple closed-form approximation, based on the level-crossing rate analysis. Comparisons of the proposed distributions with those obtained by computer simulations show good agreement and convergence with an increase in the number of subcarriers.
658 citations
25 Nov 2001
TL;DR: A formula for the characteristic function of the maximum output signal-to-noise ratio (SNR) is derived and a closed-form expression of the symbol error probability (SEP) for coherent binary keying is obtained.
Abstract: We analyze the error performance of a wireless communication system employing transmit-receive diversity in Rayleigh fading. By focussing on the complex Gaussian statistics of the independent and identically distributed entries of the channel matrix, we derive a formula for the characteristic function (cf) of the maximum output signal-to-noise ratio (SNR). We use this cf to obtain a closed-form expression of the symbol error probability (SEP) for coherent binary keying. An approximate expression for the SEP when the average SNR per branch is large is also obtained. The method can be easily extended to obtain the SEP of M-ary modulation schemes.
193 citations
09 Dec 2001
TL;DR: An efficient analytical Monte Carlo method is proposed for generating daily changes using a multivariate mixture of normal distributions with arbitrary covariance matrix for modeling of daily changes in market variables with fatter-than-normal tails and skewness.
Abstract: The mixture of normal distributions provides a useful extension of the normal distribution for modeling of daily changes in market variables with fatter-than-normal tails and skewness. An efficient analytical Monte Carlo method is proposed for generating daily changes using a multivariate mixture of normal distributions with arbitrary covariance matrix. The main purpose of this method is to transform (linearly) a multivariate normal with an input covariance matrix into the desired multivariate mixture of normal distributions. This input covariance matrix can be derived analytically. Any linear combination of mixtures of normal distributions can be shown to be a mixture of normal distributions.
37 citations
TL;DR: A non-iterative method based on using forward–backward linear prediction and the notion of extended order modeling is proposed, which can be used to specify initial values in any standard minimization algorithm to obtain the least-squares estimators.
32 citations
TL;DR: A thresholding function is defined that significantly decreases the probability of error for binary and multiple hypothesis testing problems for the exponential class of populations and special attention is paid to the complex Gaussian model with zero mean and unknown variances.
Abstract: Often recognition systems must be designed with a relatively small amount of training data. Plug-in test statistics suffer from large estimation errors, often causing the performance to degrade as the measurement vector dimension increases. Choosing a better test statistic or applying a method of dimensionality reduction are two possible solutions to this problem. In this paper, we consider a recognition problem where the data for each population are assumed to have the same parametric distribution but differ in their unknown parameters. The collected vectors of data as well as their components are assumed to be independent. The system is designed to implement a plug-in log-likelihood ratio test with maximum-likelihood (ML) estimates of the unknown parameters instead of the true parameters. Because a small amount of data is available to estimate the parameters, the performance of such a system is strongly degraded relative to the performance with known parameters. To improve the performance of the system we define a thresholding function that, when incorporated into the plug-in log-likelihood ratio, significantly decreases the probability of error for binary and multiple hypothesis testing problems for the exponential class of populations. We analyze the modified test statistic and present the results of Monte Carlo simulation. Special attention is paid to the complex Gaussian model with zero mean and unknown variances.
26 citations
07 Oct 2001
TL;DR: New exact closed-form expressions for the outage probability of cellular systems (without diversity reception) in which the desired user follows a Rician distribution whereas the interferers are subject to correlated Rayleigh fading.
Abstract: This paper presents new exact closed-form expressions for the outage probability of cellular systems (without diversity reception) in which the desired user follows a Rician distribution whereas the interferers are subject to correlated Rayleigh fading. It then capitalizes on a numerical technique by D. Raphaeli (see IEEE Trans. Inf. Theory, vol.42, p.1002-7, 1996) dealing with the accurate evaluation of the cumulative distribution function of quadratic forms in complex Gaussian random variables to solve for the outage probability in the more general case of arbitrary fading statistics, average fading powers, diversity branches correlation, and/or correlation between the interferers. In some scenarios, the numerical approach reduces to finite-sum closed-form expressions.
12 citations
01 May 2001
TL;DR: In this paper, an expression for the optimum non-Gaussian radar detector is derived from the SIRP model (spherically invariant random process) clutter and a Pade approximation of the characteristic function.
Abstract: An expression for the optimum non-Gaussian radar detector is derived from the non-Gaussian SIRP model (spherically invariant random process) clutter and a Pade approximation of the characteristic function of the SIRP. The SIRP model is used to perform coherent detection and to modelize the non-Gaussian clutter as a complex Gaussian process whose variance is itself a positive random variable (r.v.). The probability density function (PDF) of the variance characterizes the statistics of the STEP and after performing a Pade approximation of this PDF from reference clutter cells we derive the so-railed Pade estimated optimum (radar) detector (PEOD) without any knowledge about the statistics of the clutter. We evaluate PEOD performance for an unknown target signal embedded in K-distributed clutter and compare it with optimum detector performance (optimum in particular clutter statistics such as Optimum K Detector - OKD - in K-distributed clutter).
5 citations
TL;DR: In this article, a definition of complex stable random variables is presented which includes earlier definitions as special cases, and the class of stable random variable is characterized and the exact conditions under which a sum of independent stable variable is again stable are also found.
4 citations
01 Nov 2001
TL;DR: From the statistics of the channel matrix and the propagation vectors of the interferers, a closed-form expression for the probability density function (p.d.f.) of the maximum output SINR is derived that can be used to obtain the symbol error probability for various digital modulation schemes.
Abstract: We consider a K-transmit dual-receive diversity communication system employing K antennas for transmission and two antennas for reception. The desired signal is corrupted by N interfering sources apart from additive white Gaussian noise. The channel is Rayleigh fading. As a result, the channel matrix for the desired signal and the propagation vectors of the interferers have zero-mean complex Gaussian entries; the entries are assumed to be independent and identically distributed. The complex receive weight vector used for combining the received signals is chosen so as to maximize the output signal-to-interference-plus-noise ratio (SINR). From the statistics of the channel matrix and the propagation vectors of the interferers, we derive a closed-form expression for the probability density function (p.d.f.) of the maximum output SINR. This p.d.f. can be used to obtain the symbol error probability for various digital modulation schemes.
3 citations
TL;DR: In this article, the number of components and the mixing ratios are preserved on each marginal density through the transformation of a k-dimensional finite normal mixture. And under the assumption of a K-dimensional FNM, a one-dimensional random variable with a FNM of the true number of component and mixing ratios is constructed.
Abstract: We give a transformation such that, for a k-dimensional finite normal mixture, the number of components and the mixing ratios are preserved on each marginal density through the transformation. Furthermore, under the only assumption of a kdimensional finite normal mixture, we construct a one-dimensional random variable with a finite normal mixture of the true number of components and the true mixing ratios.
07 May 2001
TL;DR: It is shown that this estimator for polynomial frequency modulated signals in the presence of multiplicative and additive complex Gaussian processes is unbiased and an analytic expression of its asymptotic variance is derived.
Abstract: We propose the peak of the polynomial Wigner-Ville distribution as an instantaneous frequency estimator for polynomial frequency modulated signals in the presence of multiplicative and additive complex Gaussian processes. We show that this estimator is unbiased and we derive an analytic expression of its asymptotic variance. Simulation results, based on Monte-Carlo realisations, are presented in order to show the validity of the theoretical derivations.
11 Jun 2001
TL;DR: The distribution of zeros of mobile channels is investigated and the results obtained are applied to the channel models standardized for the GSM (Global System for Mobile Communications)/EDGE (Enhanced Data Rates for GSM Evolution) system.
Abstract: In this paper, the distribution of zeros of mobile channels is investigated and the results obtained are applied to the channel models standardized for the GSM (Global System for Mobile Communications)/EDGE (Enhanced Data Rates for GSM Evolution) system. The taps of the discrete-time overall impulse response can be modeled as correlated complex Gaussian random variables with zero or nonzero mean, where the correlations depend on the transmit filter, the power delay profile of the channel, and the receiver input filter. For calculation of the density of zeros of the overall transfer function results from the mathematical literature on the zeros of random polynomials are used. From this density two cumulative distributions which are relevant for the design of suboptimum receivers for intersymbol interference (ISI) channels are derived for the case of uncorrelated taps with exponential distribution of the tap variances. Finally, practical equalizer design rules for the GSM/EDGE system are deduced from the calculated statistical distributions.
TL;DR: A statistical view of radar imaging in which target reflectances are realizations of an underlying random process, which is zero-mean complex Gaussian for diffuse targets and an implementation which exploits Strassen's recursive strategy for matrix multiplication and inversion is presented.
Abstract: We explore a statistical view of radar imaging in which target reflectances are realizations of an underlying random process. For diffuse targets, this process is zero-mean complex Gaussian. The data consists of a realization of this process, observed through a linear transformation, and corrupted by additive noise. Image formation corresponds to estimating the elements of a diagonal covariance matrix. In general, maximum-likelihood estimates of these parameters cannot be computed in closed form. Snyder, O'Sullivan, and Miller proposed an expectation-maximization algorithm for computing these estimates iteratively. Straightforward implementations of the algorithm involve multiplication and inversion operations on extremely large matrices, which makes them computationally prohibitive. We present an implementation which exploits Strassen's recursive strategy for matrix multiplication and inversion, which may make the algorithm feasible for image sizes of interest in high-resolution radar applications.