Power-law shot noise

The behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form, is explored. Expressions are obtained for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exhibits 1/f-type behavior over a substantial range of frequencies, so that the process serves as a source of 1/f^α shot noise for α in the range 0<α<2. For other parameters the amplitude probability density function is a Levy-stable random variable with dimension less than unity. This process then behaves as a fractal shot noise that does not converge to a Gaussian amplitude distribution as the driving rate increases without limit. Fractal shot noise is a stationary continuous-time process that is fundamentally different from fractional Brownian motion. Several physical processes that are well described by power-law noise in certain domains are considered: 1/f shot noise, Cherenkov radiation from a random stream of charged particles, diffusion of randomly injected concentration packets the electric field at the growing edge of a quantum wire, and the mass distribution of solid-particle aggregates     

Generalized Gaussian modeling of correlated signal sources

A generalized Gaussian model for correlated signal sources is introduced. The probability density function of a first-order autoregressive process driven by generalized Gaussian white noise is approximated by a generalized Gaussian probability density function. The interdependence between the correlation coefficient and the shape parameter of the first-order autoregressive process and the shape parameter of the driving noise is investigated. Application of the proposed method for modeling of probability density functions of transform and subband coefficients is considered     

An analytical method for linear combining with application to FFHNCFSK receivers

A method for obtaining the probability density function (PDF) and the cumulative density function (CDF) of sum-independent random variables is presented. The method is capable of determining the PDF and CDF of this sum for an input consisting of any combination of a signal tone, white Gaussian noise, and multiple interfering tones. It is based upon circularly symmetric function theory, Fourier-Bessel series, and Fourier series. To illustrate this method, applications are presented for a fast frequency-hopped noncoherent frequency-shift-keyed communications system. From the PDF and CDF of the received signal, performance values such as the error probability for demodulation, the probability of detection and false alarm for coarse-time synchronization and the mean and variance of timing-error estimates for fine-time synchronization are obtained     

一种有长拖尾特性的G-分布海杂波模型

针对雷达海杂波概率密度函数的长拖尾特征,在K一分布杂波模型基础上提出一种新的描述海杂波的长拖尾分布G-分布.该分布是由二元Raylei#独立积随机变量和广义x分布的随机变量进行级联而生成的三元独立积.使用Mel-lin变换方法得到G-分布概率密度函数的解析表达式.仿真结果表明G-分布的长拖尾特性比K-分布强.最后使用实验数据验证G-分布描述海杂波的有效性,并给出一种产生相关G-分布随机变量的方法,产生所需的相关随机变量.     

Stochastic differential equations: an approach to the generation ofcontinuous non-Gaussian processes

The generation of continuous random processes with jointly specified probability density and covariation functions is considered. The proposed approach is based on the interpretation of the simulated process as a stationary output of a nonlinear dynamic system, excited by white Gaussian noise and described by a system of a first-order stochastic differential equations (SDE). The authors explore how the statistical characteristics of the equation's solution depends on the form of its operator and on the intensity of the input noise. Some aspects of the approximate synthesis of stochastic differential equations and examples of their application to the generation of non-Gaussian continuous processes are considered. The approach should be useful in signal processing when it is necessary to translate the available a priori information on the real random process into the language of its Markov model as well as in simulation of continuous correlated processes with the known probability density function     

Symbol-to-symbol performance evaluation of densely populatedasynchronous DS-CDMA in Gaussian and impulsive noise environments: aFourier-Bessel series approach

This letter considers the well-established Poisson impulse noise model with a random amplitude area distributed according to the ϵ-mixture Gaussian probability density function. This model is used to develop fast converging truncated Fourier-Bessel (FB) series expressions, required to evaluate accurately the performance of a binary phase-shift keying (BPSK) modulation scheme as part of a densely populated asynchronous direct-sequence code-division multiple-access (A/DS-CDMA) configuration. The average error probability of the correlation receiver is easily and quickly obtained here, even for the case of a large number of users (K=100), unlike earlier attempts in this area in which the use of other analysis approaches (e.g., closed-form approach or Taylor series expansion approach) could not exceed the limit of K=2 and K=24 in an ϵ-mixture impulsive and/or Gaussian noise environment, respectively     

实时高精度雷达噪声信号产生方法与FPGA实现

针对各种典型分布的噪声信号在雷达系统半实物仿真和噪声雷达波形设计中的实际需求，基于Box-Muller算法提出了一种能够实时产生多种分布特性噪声的信号生成方法。首先使用线性反馈移位寄存器产生均匀分布随机序列，然后利用能够实现高精度、低延迟的坐标旋转数字算法(Coordinate Rotation Digital Computer,CORDIC)实现Box-Muller变换中复杂函数的快速计算，将均匀随机序列转换成高斯分布随机序列，最后利用高斯随机序列经过相关数学运算得到其他复杂分布的随机序列，在此基础上产生具有各种分布特性的噪声信号。基于Xilinx XC7VX415T 现场可编程门阵列(Field Programmable Gate Array,FPGA)芯片的实验结果表明，所提方法在保证小数位数据精度为20 b时，可实时产生速率为2.5 Gb/s的高精度随机数据序列，进而生成服从多种函数分布下的噪声信号。所提方法整体资源占用率较少，具有较强的实用性。     

Adaptive Iterative Detectors for Phase-Uncertain Channels via Variational Bounding

The problem of iterative detection/decoding of data symbols transmitted over an additive white Gaussian noise (AWGN) channel in the presence of phase uncertainty is addressed in this paper. By modelling the phase uncertainty either as an unknown deterministic variable/process or random variable/ process with a known a priori probability density function, a number of non-Bayesian and Bayesian detection algorithms with various amount of suboptimality have been proposed in the literature to solve the problem. In this paper, a new set of suboptimal iterative detection algorithms is obtained by utilizing the variational bounding technique. Especially, applying the generic variational Bayesian (VB) framework, efficient iterative joint estimation and detection/decoding schemes are derived for the constant phase model as well as for the dynamic phase model. In addition, the relation of the VB-based approach to the optimal noncoherent receiver as well as to the classical approach via the expectation-maximization (EM) algorithm is provided. Performance of the proposed detectors in the presence of a strong dynamic phase noise is compared to the performance of the existing detectors. Furthermore, an incremental scheduling of the VB (or EM) algorithm is shown to reduce the overall complexity of the receiver.     

Multitone jamming of FH/BFSK in Rician channels

A new bit error rate (BER) expression for a noncoherent frequency-hopped binary-frequency-shift-keying (FH/BFSK) receiver in Rician channels, subjected to independent multitone and wideband noise interference, is derived. Unlike previously published analyzes, we combine the signal and jammer multipath components, the additive white Gaussian noise (AWGN), and other wideband interference as a single Gaussian process. This method leads to a BER expression which consists of only a single rather than a triple integral requiring numerical computation. We also present a new derivation of the probability density function (PDF) of the ratio of two Rician random variables, used in a previously published approximate BER analysis     

A representation theorem and its applications to spherically-invariant random processes

Thenth-order characteristic functions (cf) of spherically-invariant random processes (sirp) with zero means are defined as cf, which are functions ofnth-order quadratic forms of arbitrary positive definite matricesp. Everynth-order spherically-invariant characteristic function (sicf) is represented as a weighted Lebesgue-Stieltjes integral transform of an arbitrary univariate probability distribution functionF(cdot)on[0,infty). Furthermore, everynth-order sicf has a corresponding spherically-invariant probability density (sipd). Then we show that everynth-order sicf (or sipd) is a random mixture of anth-order Gaussian cf [or probability density]. The randomization is performed onnu^2 rho, wherenuis a random variable (tv) specified by theF(cdot)function. Examples of sirp are given. Relations to previously known results are discussed. Various expectation properties of Gaussian random processes are valid for sirp. Related conditional expectation, mean-square estimation, semMndependence, martingale, and closure properties are given. Finally, the form of the unit threshold likelihood ratio receiver in the detection of a known deterministic signal in additive sirp noise is shown to be a correlation receiver or a matched filter. The associated false-alarm and detection probabilities are expressed in closed forms.     

A radar application of a modified Cramer-Rao bound: parameterestimation in non-Gaussian clutter

In this paper, we derive a lower bound on the error covariance matrix for any unbiased estimator of the parameters of a signal composed of a mixture of spherically invariant random processes (SIRPs). The proposed approach represents a special case of the global Cramer-Rao bound for hybrid random and deterministic parameters estimation, and it is particularly useful when the data, conditioned on a vector of unwanted random parameters (nuisance parameters) with a priori known probability density function, can be modeled as a Gaussian vector. The case of signal composed of a mixture of K-distributed clutter, Gaussian clutter, and thermal noise belongs to this set, and it is regarded as a realistic radar scenario. In the radar problem considered here, this bound can be numerically computed in closed-form, whereas the computation of the true (marginal) Cramer-Rao bound turns out to be infeasible. The performance of some practical estimators are compared with it for two study cases     

Multichannel detection for correlated non-Gaussian random processesbased on innovations

The paper addresses the problem of multichannel signal detection in additive correlated non-Gaussian noise using the innovations approach. Although this problem has been addressed extensively for the case of additive Gaussian noise, the corresponding problem for the non-Gaussian case has received limited attention. This is due to the fact that there is no unique specification for the joint probability density function (PDF) of N correlated non-Gaussian random variables. The authors overcome this problem by using the theory of spherically invariant random processes (SIRPs) and derive the innovations-based detector. It is found that the optimal estimators for obtaining the innovations, processes are linear and that the resulting detector is canonical for the class of PDFs arising from SIRPs. The authors also present a performance analysis of the innovations-based detector for the case of a K-distributed SIRP     

Performance of First-Order Digital Phase-Locked Loops in Mobile Radio Channels

The performance of a first-order digital phase-locked loop (DPLL) using nonuniform sampling is studied in the mobile radio environments. The mobile radio channel is characterized by introducing fast Rayleigh fading and random phase variation to the signal envelope and phase, respectively. The nonlinear stochastic difference equation describing the loop operation in fading environments is introduced. The joint probability density function (pdf) of the random variables of this equation is derived by transformation of random variables for fast Rayleigh fading channels. A closed-form expression for the transition probability of the ChapmanKolmogorov (C-K) equation is obtained for phase step plus noise input and for frequency step plus noise input. The probability density function of the steady-state phase error is obtained by solving the C-K equation numerically.     

Coding for radio channels

The conventional remedy to time and/or frequency variability of radio channels is diversity. Redundant coding is a kind of diversity, as each coded symbol can be recovered from other symbols. Only linear binary block codes are considered. Any binary random variable can be represented by its algebraic value,a real number whose sign indicates its most likely value and whose absolute value measures the probability of this value. The algebraic value of a received binary symbol is itself a random variable, whose distribution obeys a particular constraint. The algebraic value associated with the maximum likelihood decision on a binary symbol, given a set of independent received replicas of it, and that associated with the sum modulo 2 of binary random variables are also considered. The symbol-by-symbol decoding is then analysed in the case of threshold decoding, then in the general case. An approximate bound on the decoding error probability for additive Gaussian noise and coherent demodulation is used to assess the advantage of coding when unequalenergy symbols are received, according to a deterministic or a Rayleigh distribution. Simulation results are given for the Hamming (15,11) code. Coding affords a significant advantage provided the channel is good enough, while conventional diversity always provides gain.     

基于输入信号峭度的变步长LMS自适应谱线增强方法

提出了一种基于输入信号峭度的变步长LMS自适应谱线增强方法，该方法以输入信号的峭度为自变量，构造新的步长。该步长对高斯噪声或非高斯噪声均有一定免疫性，同时能快速收敛。最后用实测的水下目标辐射噪声数据和瑞利有色环境噪声进行了仿真，表明该方法有较强的谱线增强能力。     

CRLB for DOA Estimation in Gaussian and Non-Gaussian Mixed Environments

The determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of Direction-of-arrival (DOA) estimation is a very important issue. Several CRLBs on DOA estimation have been derived for Gaussian noise. However, a practical channel is affected by not only Gaussian background noise but also non-Gaussian noise such as impulsive interference. This paper derives the deterministic CRLB for Gaussian and non-Gaussian mixed environments. Since non-parametric kernel method is used to build the probability density function (PDF) of non-Gaussian noise, the CRLB derived is suitable for various noise distributions with or without symmetric PDF. The relationship between the CRLB for Gaussian noise and the proposed CRLB is also investigated. Theoretical analysis shows that the proposed CRLB provides a unified representation for both the cases of Gaussian and mixed environments. Computer simulations are included to verify the derived CRLB in different noise environments.     

Nonparametric trellis equalization in the presence of non-Gaussian interference

We consider the problem of trellis equalization of the intersymbol interference channel in the presence of thermal noise and cochannel interference (CCI). Conventional maximum-likelihood sequence estimation (MLSE) and maximum a posteriori probability (MAP) trellis equalizers treat the sum of noise and interference as additive white Gaussian noise, while CCI is generally a colored non-Gaussian process. We propose a novel nonparametric approach based on the estimation of the probability density function of the noise-plus-interference. Given the availability of a limited volume of data, the density is estimated by kernel-smoothing techniques. The use of a whitening filter in the presence of temporally colored disturbance is also addressed. Simulation results are provided for the global system for mobile communications (GSM), showing a significant performance improvement with respect to the equalizer based on the Gaussian assumption. Major advantages of the proposed strategy are its intrinsic robustness and general applicability to those cases where accurate modeling of the interference is difficult or a model is not available.     

强跟踪五阶CKF算法在初始对准中的应用

针对载体行进间初始对精对准过程易受有色噪声影响,造成对准精度高的问题,提出一种基于高阶球面-径向积分的强跟踪滤波方法,该算法基于里程计辅助下惯性系行进间精对准误差模型,将状态变量的自相关函数进行正交化运算,保证噪声信号的白化,并运用五阶球面-径向准则对于滤波过程中参数的后验概率密度函数进行近似数值计算。仿真实验表明,在方位角为大失准角的条件下,该算法可以有效地保证较高的滤波精度,并且在噪声未知的情况下,滤波器保证很好的鲁棒性。     

The Gaussian Mixture Probability Hypothesis Density Filter

A new recursive algorithm is proposed for jointly estimating the time-varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty, detection uncertainty, noise, and false alarms. The approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density (PHD) recursion to propagate the posterior intensity, which is a first-order statistic of the random finite set of targets, in time. At present, there is no closed-form solution to the PHD recursion. This paper shows that under linear, Gaussian assumptions on the target dynamics and birth process, the posterior intensity at any time step is a Gaussian mixture. More importantly, closed-form recursions for propagating the means, covariances, and weights of the constituent Gaussian components of the posterior intensity are derived. The proposed algorithm combines these recursions with a strategy for managing the number of Gaussian components to increase efficiency. This algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented Kalman filters.     

First and second passage times of Rayleigh processes (Corresp.)

The first and second passage times of a stationary Rayleigh processR(t,a)are discussed.R(t,a)represents the envelope of a stationary random process consisting of a sinusoidal signal of amplitude and frequencyf_{0}plus stationary Gaussian noise of unit variance having a narrow-band power spectral density which is symmetrical aboutf_{0}. Approximate integral equations are developed whose solutions yield approximate probability densities concerning the first and second passage times ofR(t,a). The resulting probability functions are presented in graphs for the case when the power spectral density of the noise is Gaussian. Related results concerning the approximate distribution function of the absolute minimum or absolute maximum ofR(t,a)in the closed interval[0,tau]are also presented. The exact probability densities are expressed in the form of an infinite series of multiple integrals.