First-order statistics of a non-Rayleigh fading signal and its detection

The first-order statistics of the vecter sum of a complex Gaussian variable and N complex exponentials with constant amplitudes but random independent phases are used to model a non-Rayleigh fading signal. Envelope detection, optimal for detecting Rayleigh (N = 0) and Rician (N = 1) signals, is also shown to be optimal for the considered non-Rayleigh signals in additive white Gaussian noise. However, the signal-to-noise ratio required to detect the latter signal for N = 2 may be substantially higher than for the former cases. Possible applications of this fading model to studies of multipath fading, non-Rayleigh sea echoes, microwave or laser radar detection and tracking are discussed.     

Estimation of environmental factors for the inverse Gaussian distribution

Two definitions of environmental factors for the inverse Gaussian distribution are proposed here. From the second definition the upper and lower confidence limits of the inverse Gaussian environmental factor are derived by a classical method. Based on the first definition the Bayes limits of the inverse Gaussian environmental factor are also given using non-informative reference prior as well as the natural conjugate prior. An application example is provided.     

SAR amplitude probability density function estimation based on a generalized Gaussian model.

In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena.     

On the joint statistics of amplitude and phase of a signal withco-channel interference

The joint probability density function (pdf) of the resultant amplitude and phase of a signal in presence of cochannel interference is given. The marginal pdf of the amplitude variable is evaluated. This joint pdf can be used to evaluate the receiver performance in presence of interfering signals     

CSCC for mean of an inverse Gaussian distribution under type I censoring

In this paper Cumulative Sum Control Chart (CSCC) have been constructed for the mean of Inverse Gaussian distributed life test data. The parameters of the V-mask have been determined and finally the expression for the Average Run Length has been derived and illustrated numerically.     

Angle and time of arrival statistics for the Gaussian scatterdensity model

Starting from a Gaussian distribution of scatterers around a mobile station, expressions are provided for the probability density function (PDF) in the angle of arrival, the power azimuth spectrum, the PDF in the time of arrival, and the time delay spectrum, all as seen from a base station. Expressions are also provided for some of the quantities of practical interest such as the root-mean-square (RMS) angular spread, the RMS delay spread, and the spatial cross-correlation function. Results for the Gaussian scatter density model are compared with those for the circular scattering model and the elliptical scattering model as well as with experimental results available for outdoor and indoor environments. Comparison is shown for the PDFs as well as for the power spectra in angle and delay. It is shown that the present model, in contrast to the previous models, produces results that closely agree with experimental results. With an appropriate choice of the standard deviation of the scattering region, the Gaussian density model can be made suitable both for environments with very small angular spreads as well as those with very large angular spreads. Consequently, the results provided in the paper are applicable to both macrocellular as well as picocellular environments     

逆伽马纹理复合高斯杂波参数的贝叶斯估计方法

复合高斯杂波(CGC)在拟合高分辨力、低掠射角海杂波中已得到广泛应用,带有逆伽马纹理的CGC的强度分布为广义帕累托(GP)分布。在实际雷达工作场景中,由于观测区域内海杂波的非平稳非均匀特性,导致独立同分布杂波样本的获取十分困难。提出一种广义帕累托分布参数的贝叶斯估计方法,通过在线更新数据的先验信息,获取小样本情形下GP分布参数。仿真实验证明,该方法能够在样本数量较小的情况下,对GP数据实现较为精确的参数估计。     

The approximation of a Poisson distribution by a Gaussian distribution

This letter describes a modified Gaussian approximation to a Poisson distribution which, unlike the usual Gaussian approximation, gives good agreement on the tails of the distribution. It is therefore useful in error-rate calculations where the usual Gaussian approximation often is not.     

On efficacy of Rayleigh‐inverse Gaussian distribution over K‐distribution for wireless fading channels

For studying performance characteristics of radio channels, the knowledge about the probability density function (pdf) of fading–shadowing effects is essential. K‐distribution corresponding to Rayleigh–gamma distribution (RGD) is widely used to approximate a more realistic Rayleigh–lognormal distribution (RLD) which does not have a closed form expression. A new composite Rayleigh‐inverse Gaussian distribution (RIGD), an alternative to K‐distribution, is analyzed with regards to its suitability and effectiveness in radio channels. Detailed investigations are made to study the performance characteristics of RIGD and K‐distribution (RGD) in terms of Kullback–Leibler (KL) measure of divergence. Based on these investigations, it is found that RIGD is better suited for capturing fading–shadowing aspects of radio channels instead of K‐distribution. Copyright © 2006 John Wiley & Sons, Ltd.     

Gaussian distribution model for gate-to-channel capacitance for carbon nanotube field-effect transistor

ABSTRACT

In this paper, a carbon nanotube (CNT) field-effect transistor gate-to-channel capacitance Gaussian distribution model is proposed. The proposed model is based on the assumption of random placement of CNTs within the channel region, in lieu of the traditional uniform distribution exhibited in the literature. The proposed model is inspired from the fact that the nanotubes in the central region along the channel that are more closely packed together yield a lower capacitance value over those that are widely spaced towards the edges. The Gaussian model as presented in this paper offers more accuracy to simulation results, where simulation results reveal that this model provides more practical answers for gate-to-channel capacitance, with higher percentages of improvement regarding energy consumption by the transistor. Moreover, the effects of several parameters such as type of material, tube diameter and the tube–gate distance have been evaluated using the proposed model.     

Ground-wave attenuation function for a Gaussian modulated carrier signal

The time-harmonic theory of ground-wave propagation is generalised to the time domain for a Gaussian modulated carrier signal. The model is a vertical electric dipole located on a flat imperfectly conducting earth. It is shown that the radiated field is characterised by a modified Sommerfeld-type attenuation function with a time-dependent `numerical distance?.     

Prediction method for the rain attenuation statistics based on a global rainfall-rate distribution model

A method for the prediction of the rain attenuation statistics is proposed, based on a global rainfall rate distribution model. This method also employs the spatial autocorrelation function to describe the inhomogeneity of the rainfall medium. A comparison with a prediction method recently proposed by the International Radio Consultative Committee and an other recent model is made, which shows that our model provides better results.     

Maximum likelihood predictive densities for the inverse Gaussian distribution with applications to reliability and lifetime predictions

Maximum likelihood predictive densities (MLPD) for the inverse Gaussian distribution are derived for the cases of one or both parameters unknown. They are then applied to obtain estimators of the reliability function and prediction or shortest prediction intervals for a future observation. Comparisons with the existing likelihood or frequentist methods show that the MLPD estimators of reliability gives smaller bias and smaller MSE for a wide range of population values, and that the MLPD prediction intervals are shorter while preserving the correct coverage probability. The shortest MLPD prediction intervals further sharpen the above equitailed MLPD intervals in terms of interval lengths.     

A note on constructing the confidence bounds of the failure rate for the inverse Gaussian distribution

In this paper, a Bonferroni confidence interval for the failure rate of the inverse Gaussian distribution is derived. It can be solved by formulating the problem as a nonlinear programming. A numerical example on repair time data is provided to illustrate the procedure.     

Noise and signal estimation in magnitude MRI and Rician distributed images: a LMMSE approach

A new method for noise filtering in images that follow a Rician model-with particular attention to magnetic resonance imaging-is proposed. To that end, we have derived a (novel) closed-form solution of the linear minimum mean square error (LMMSE) estimator for this distribution. Additionally, a set of methods that automatically estimate the noise power are developed. These methods use information of the sample distribution of local statistics of the image, such as the local variance, the local mean, and the local mean square value. Accordingly, the dynamic estimation of noise leads to a recursive version of the LMMSE, which shows a good performance in both noise cleaning and feature preservation. This paper also includes the derivation of the probability density function of several local sample statistics for the Rayleigh and Rician model, upon which the estimators are built.     

Error Probability Evaluation for Systems Employing Differential Detection in a Rician Fast Fading Environment and Gaussian Noise

A method is presented for determining the error probability of a receiver using differential detection in the presence of Gaussian noise and fast Rician fading. Equations for the covariances of the fading component are derived, which include the effect of IF filter distortion. It is shown that these equations may be readily evaluated numerically. A simple formula for the error probability is derived for systems using BPSK and a matched filter receiver. An example of the error probability is given using this receiver. Also given is an example of a system using MSK with a practical IF filter. Different spectral shapes and bandwidths for the fading process are investigated for this example and their effect on the error probability is determined.     

A new simple model for land mobile satellite channels: first- and second-order statistics

We propose a new shadowed Rice (1948) model for land mobile satellite channels. In this model, the amplitude of the line-of-sight is characterized by the Nakagami distribution. The major advantage of the model is that it leads to closed-form and mathematically-tractable expressions for the fundamental channel statistics such as the envelope probability density function, moment generating function of the instantaneous power, and the level crossing rate. The model is very convenient for analytical and numerical performance prediction of complicated narrowband and wideband land mobile satellite systems, with different types of uncoded/coded modulations, with or without diversity. Comparison of the first- and the second-order statistics of the proposed model with different sets of published channel data demonstrates the flexibility of the new model in characterizing a variety of channel conditions and propagation mechanisms over satellite links. Interestingly, the proposed model provides a similar fit to the experimental data as the well-accepted Loo's (1985) model but with significantly less computational burden.