The reflection method with a change of sign in problems of the quality analysis of signal detection

The reflection method with a change of sign, initially used as a technique for solving the first boundary value problem of the heat conduction equation, has been extended for allowing us to elucidate the solution of earlier known problems of the quality analysis of signal detection algorithms using the tool of Markov processes and also to derive an expression for the probability of finding the absolute maximum of the normal stationary Markov process in the negative half-plane of values. A comparative analysis with a similar probability was performed for the root-mean-square differentiable process.     

Algorithm characteristics for detection of signals of unknown energy

The paper presents a strict expression for quality indices of asymptotically optimal algorithms for detection of signals with unknown energy. The expression is based on distribution of the absolute maximum of the nonstationary process differentiable in the mean square representation. The solution for signal with unkhown amplitude received earlier is a particular case of the obtained result.     

Distribution of absolute maximum of Gaussian Markov’s stationery process

The absolute maximum of Gaussian Markov’s stationary process is obtained by means of solution of the Fokker-Planck-Kolmogorov equation with method of variables division. It is shown, known results are special cases of obtained solution. The probability of process location in one of half-plane of its values is specified.     

Error-probability bounds for continuous-time decision problems

The evaluation of error-probability bounds for binary detection problems involving continuons-time stochastic processes as signals is considered. These bounds are of interest because, in even the simplest detection problems, the computation of the exact probabilities of error is usually mathematically intractable. The method used consists of applying some results from martingale theory to detection and estimation problems. Only discontinuous observations that contain the rate process associated with a counting process are considered. The problem addressed is to evaluate Chernoff bounds on error probabilities for the likelihood-ratio test. The solution procedure consists of a measure transformation technique that makes it possible to obtain an expression for the Chernoff bound in terms of an expectation of a multiplicative functional of the conditional mean signal (rate process) estimates. If the processes involved are Markov, it is then possible to represent the above expression as a solution to a partial differential equation that is derived from the backward equation of Kolmogorov. The above procedure is repeated when the optimal estimates are replaced by suboptimal estimates. Examples are given to illustrate the technique.     

Distribution of time intervals determining the first instant when a stationary process reaches the set level

This paper describes a method of determining the rigorous analytical expression for the distribution of time instants when a stationary process differentiable in the root-mean-square sense attains threshold for the first time. It has been shown that this expression is a solution of the partial integral-differential equation corroborating earlier results.     

Nonlinear Analysis of Correlative Tracking Systems Using Renewal Process Theory

A new method is presented which describes the behavior of an(N + 1)th-order tacking system in which the nonlinearity is either periodic [phase-locked loop (PLL) type] or a nonperiodic [delay-locked loop (DLL) type]. The cycle slipping of such systems is modeled by means of renewal Markov processes. A fundamental relation between the probability density function (pdf) of the single process and the renewal process is derived which holds in the transient as well as in the stationary state. Based on this relation it is shown that the stationary pdf, the mean time between two cycle slips, and the average number of cycles to the right (left) can be obtained by solving a single Fokker-Planck equation of the renewal process. The method is applied to the special case of a PLL and compared with the so-called periodic-extension (PE) approach. It is shown that the pdf obtained via the renewal-process approach can be reduced to agree with the PE solution for the first-order loop in the steady state only. The reasoning and its implications are discussed. In fact, it is shown that the approach based upon renewal-process theory yields more information about the system's behavior than does the PE solution.     

LMS algorithms for tracking slow Markov chains with applications to hidden Markov estimation and adaptive multiuser detection

This paper analyzes the tracking properties of the least mean squares (LMS) algorithm when the underlying parameter evolves according to a finite-state Markov chain with infrequent jumps. First, using perturbed Liapunov function methods, mean-square error estimates are obtained for the tracking error. Then using recent results on two-time-scale Markov chains, mean ordinary differential equation and diffusion approximation results are obtained. It is shown that a sequence of the centered tracking errors converges to an ordinary differential equation. Moreover, a suitably scaled sequence of the tracking errors converges weakly to a diffusion process. It is also shown that iterate averaging of the tracking algorithm results in optimal asymptotic convergence rate in an appropriate sense. Two application examples, analysis of the performance of an adaptive multiuser detection algorithm in a direct-sequence code-division multiple-access (DS/CDMA) system, and tracking analysis of the state of a hidden Markov model (HMM) with infrequent jumps, are presented.     

On the Theory of Randomly Misaligned Beam Waveguides

A straightforward method for the determination of the expected attenuation in misaligned beam waveguides is presented. It applies to confocal guides and assumes that the misalignment consists of random displacements of the lenses in directions perpendicular to the beam axis. Reiterative fields, as they are present in perfectly aligned beam waveguides, do not exist in misaligned guides. However, it can be shown that there are beams whose expected field distribution is repeated from lens to lens. These "statistical modes" are determined by the eigenfunctions of a homogeneous integral equation of the second kind. The corresponding eigenvalues determine the expected attenuation per iteration. The absolute squares of the eigenvalues yield an upper bound for the expected power loss per iteration. The integral equation is solved for small mean square displacements of the lenses by a perturbation method. For infiitely extended lenses, the equation can be solved in closed form. In both cases the expected attenuation of the lower-order statistical modes has been calculated; the results are shown as function of the mean square displacement of the lenses.     

Performance of Voice/Data Integration on a TDM System

Data queueing is of primary concern in a voice/data integrated TDM system. The data queueing model is represented in the discrete-time domain with multiple servers and voice is given a higher priority than data. The data arrival process is assumed to be Poisson and the voice arrival process is characterized by a Markov chain. The correlation coefficient of the number of on voice calls between consecutive frames is used to measure the correlation behavior of the voice process. While the generating function approach may be used to analyze the queueing process, it involves the evaluation of a large number of boundary terms. On the assumption that the voice traffic consists ofNi.i.d. two-state Markov chains, we derive a simple expression for the mean queue size as a function of two variables in the form of the traffic departure processes. The results clearly reveal a significant influence of the correlation coefficient on the data queueing process. Then, an approximate analysis based on the departure processes is introduced. The numerical and simulation results indicate that this approximate approach yields reasonably accurate results.     

一种全解耦的Volterra自适应滤波器

本文研究了Volterra自适应滤波的解耦问题.通过对Volterra滤波器的伪线性组合结构的提出和分析,得到了一个新的关于均方误差MSE的表达式,并将Volterra自适应滤波问题描述为一个约束优化问题,从而导出了满足最小均方误差(MMSE)指标的具有分块对角型输入相关矩阵的全解耦Volterra标准方程,据此设计了一种全解耦的Volterra自适应滤波器,给出了滤波器权向量的自适应修正公式.仿真结果验证了本文方法的有效性.     

Optimal nonlinear filtering for independent increment processes--Part II

The main result obtained in Part I [1]--which is contained in Theorem1of Part I--is generalized and extended in several ways. First, a new basic stochastic integro-partial differential equation for the conditional probability density function for the state of a nonlinear dynamic system with disturbance noise given noisy nonlinear measurements of the state is derived under the less restrictive assumption that the disturbance noise is an arbitrary independent increment process with an infinitely divisible distribution, and the measurement noise is a Gaussian independent increment process with an infinitely divisible distribution. It is then shown that, under proper restrictions, this basic equation reduces to either the Fokker-Planck equation for diffusion processes or the Kolmogorov-Feller equation for jump processes. Also, it is shown that this basic equation contains the earlier results of Kushner [2] and Wonhamt [3] as special cases. Next, it is shown how the result represented by this basic equation can be easily extended to include the case where the disturbance noise is a Markov process of the type initially assumed for the state of the dynamic system. Finally, it is shown that, in contrast to results obtained by Bryson and Johansen [4] and Cox [5] for the linear, Gaussian case, it is not generally possible to extend the result represented by this basic equation to include either the case where the measurement noise is a Markov process of the type initially assumed for the state of the dynamic system, or the case where the covariance matrix of the Gaussian measurement noise is singular. However, some incomplete results indicating when such extensions might be possible are given.     

On the second derivative of a Gaussian process envelope

We explore some dynamic characteristics of the envelope of a bandpass Gaussian process, which are of interest in wireless fading channels. Specifically, we show that unlike the first derivative, the second derivative of the envelope, which appears in a number of applications, does not exist in the traditional mean square sense. However, we prove that the envelope is twice differentiable almost everywhere (with probability one) if the power spectrum of the bandpass Gaussian process satisfies a certain condition. We also derive an integral form for the probability density function (PDF) of the second derivative of the envelope, assuming an arbitrary power spectrum     

Use of support vector regression and numerically predicted cloudiness to forecast power output of a photovoltaic power plant in Kitakyushu,Japan

The development of a methodology to forecast accurately the power produced by photovoltaic systems can be an important tool for the dissemination and integration of such systems on the public electricity grids. Thus, the objective of this study was to forecast the power production of a 1‐MW photovoltaic power plant in Kitakyushu, Japan, using a new methodology based on support vector machines and on the use of several numerically predicted weather variables, including cloudiness. Hourly forecasts of the power produced for 1 year were carried out. Moreover, the effect of the use of numerically predicted cloudiness on the quality of the forecasts was also investigated. The forecasts of power production obtained with the proposed methodology had a root mean square error of 0.0948 MW h and a mean absolute error of 0.058 MW h. It was also found that the forecast and measured values of power production had a good level of correlation varying from 0.8 to 0.88 according to the season of the year. Finally, the use of numerically predicted cloudiness had an important role in the accuracy of the forecasts, and when cloudiness was not used, the root mean square error of the forecasts increased more than 32%, and the mean absolute error increased more than 42%. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance analysis of a random packet selection policy formulticast switching

This paper studies a random packet selection policy for multicast switching. An input packet generates a fixed number of primary copies plus a random number of secondary copies. Assuming a constant number of contending packets during a slot, the system is modeled as a discrete time birth process. A difference equation describing the dynamics of this process is derived, the solution of which gives a closed form expression for the distribution of the number of packets chosen. Then this result is extended to the steady state distribution through a Markov chain analysis. It is shown that the old packets have larger fanout than the fresh packets and the copy distribution of the mixed packets is determined. The packet and copy throughput taking into account the old packets have been obtained. We determined the mean packet delay as well as an upperbound for packet loss probabilities for finite buffer sizes. The asymptotic distribution of the number of packets is also given for large switch sizes under saturation by applying results from the renewal theory. Finally, simulations are done to determine the performance of the switch under mixed (unicast plus multicast) traffic     

有色噪声的扩散过程模型

研究使用基于随机微分方程的扩散过程模型产生有色噪声.首先给出Markov扩散过程的平稳分布,该分布给出了扩散过程模型中的漂移系数、扩散系数和有色噪声概率密度分布之间的关系;选择扩散过程模型中的扩散系数为x的一次幂,其系数决定了所生成噪声的相关特性;数值算法使用Milstein高阶法.以三元独立积构造的G-分布雷达杂波为例进行仿真分析,验证所提出方法的准确性和有效性.     

Time delay estimation between two phase shifted signals via generalized cross-correlation methods

This paper examines the generalized cross correlation (GCC) method for estimating time delay between two phase shifted replicas of a common signal which are embedded in additive noise. The analysis applies for widesense jointly stationary narrow-band signal and noise and is independent of signal, noise, and phase distributions. The paper derives expressions for the estimation error, specifically bias and mean square error (MSE), by starting with the cross correlation method and then extending the results to the GCC method. Assuming symmetric spectra signals, we derive two optimal weigth functions (OWF) that minimize the above MSE. With the first OWF the maximum of the absolute value of the GCC function has to be found; this is identical to the Wax maximum likelihood (ML) method where Gaussian signals possessing uniformly distributed phase were assumed. With the second OWF the zero of the absolute value of the GCC function has to be found. For signals possessing non-symmetric spectra (e.g. single side band modulated signals) the OWF can be obtained numerically, by minimizing the MSE, e.g. by using variational techniques. Using the cross correlation method we derive a simplified expression for the MSE, which is to be used instead of a previously published result.     

Characterization of stationary processes differentiable in mean square (Corresp.)

Recently Mazo and Salz proved that if{ Y(t), t in T }is a stationary random process with mean-square derivative{ dot{Y}(t), t in T }, then the conditional expectation ofdot{Y} (t)givenY(t)is zero almost everywhere with respect to the distribution ofY(t). We extend this property and obtain a characterization of stationary processes differentiable in mean square.     

Quantization error in regular grids: triangular pixels

Quantization of the image plane into pixels results in the loss of the true location of features within pixels and introduces an error in any quantity computed from feature positions in the image. We derive closed-form, analytic expressions for the error distribution function, the mean absolute error (MAE), and the mean square error (MSE) due to triangular tessellation, for differentiable functions of an arbitrary number of independently quantized points, using a linear approximation of the function. These quantities are essential in examining the intrinsic sensitivity of image processing algorithms. Square and hexagonal pixels were treated in previous papers. An interesting result is that for all possible cases 0.99相似文献   

Modeling Effects of Random Rough Interface on Power Absorption Between Dielectric and Conductive Medium in 3-D Problem

We study the effects of a random rough surface on the power absorption between a dielectric and conductive medium in a 3-D configuration where the surface height varies in both horizontal directions. The analytic small perturbation method of second order and numerical T-matrix method are used. The absorption depends on the root mean square height, correlation length, and correlation function of the random rough surface. A closed-form expression of power absorption enhancement factor is obtained from small perturbation method of second order. Results show that the T-matrix method agrees with the small perturbation method for rough surfaces with a small slope. We further compare the 3-D results to the previous 2-D results and show significant difference. The power absorption enhancement factor exhibits saturation for the Gaussian correlation function, but not for the exponential correlation function     

A Novel Convergence Accelerator for the LMS Adaptive Filter

Due to its ease of implementation, the least mean square (LMS) algorithm is one of the most well-known algorithms for mobile communication systems. However, the main limitation of this approach is its relatively slow convergence rate. This paper proposes a booster using the Markov chain concept to speed up the convergence rate of LMS algorithms. The nature of Markov chains makes it possible to exploit past information in the updating process. According to the central limit theorem, the transition matrix has a smaller variance than that of the weight itself. As a result, the weight transition matrix converges faster than the weight itself. Therefore, the proposed Markov-chain based booster is able to track variations in signal characteristics and simultaneously accelerate the rate of convergence for LMS algorithms. Simulation results show that the Markov-chain based booster allows an LMS algorithm to effectively increase the convergence rate and further approach the Wiener solution. This approach also markedly reduces the mean square error while improving the convergence rate.