Impulsive Interference Research Articles

Efficient identification of non-Gaussian mixtures

Non-Gaussian mixtures are commonly used as parametric models for impulsive interference superimposed on a Gaussian background. In this study, the problem of efficient batch and recursive estimation of the parameters of such mixtures via minimization of the Kullback-Leibler distance is considered. The maximum-likelihood estimator (MLE) provides the starting point for the development of these estimators. First, it is shown that the MLE yields consistent estimates of the parameters, despite the existence of multiple roots in the Kullback-Leibler distance function. Since direct implementation of the MLE is difficult, an alternative estimator, designed with the objective of maximizing the likelihood function, is proposed. A simulation study of the proposed estimator reveals that it performs very well in terms of attaining the Cramer-Rao lower bound. Stochastic approximation is also considered in this study. A modification to the standard recursion is presented, which greatly facilitates its implementation. Three initiating estimators are developed for these recursions: an iterative likelihood-based scheme, a batch estimator that uses a histogram of the data, and an iterative scheme that integrates the concept of complete data into the method-of-moments estimator. Upon initiating the modified stochastic approximation recursion with these estimators, it is seen that excellent estimates of the parameters can be obtained.

Angle/Doppler estimation in heavy-tailed clutter backgrounds

This work describes new methods on the modeling of the amplitude statistics of airborne radar clutter by means of alpha-stable distributions. We develop joint target angle and Doppler, maximum likelihood-based estimation techniques from radar measurements retrieved in the presence of impulsive uncorrelated noise modeled as an alpha-stable random process. We derive the Cramer-Rao bounds (CRBs) for the additive Cauchy interference scenario to assess the best case estimation accuracy which can be achieved. In addition, we introduce a new joint spatial- and Doppler-frequency high-resolution estimation technique based on the fractional lower order statistics of the measurements of a radar array. Simulation results demonstrate that the proposed methods can be of interest in the study of space-time adaptive processing (STAP) for airborne pulse Doppler radar arrays operating in impulsive interference environments.

Calculation of blanking probability for the sidelobe blanking for two interference statistical models

Impulsive interference might increase the number of false alarms in a surveillance radar. The sidelobe blanking (SLB) device, used in connection with the radar system, reduces the number of false alarms. This paper presents closed-form expressions of the probability (P/sub B/) of blanking an impulsive interference via an SLB device for two statistical models of pulsed interference, namely: (i) known amplitude and random phase and (ii) random amplitude and random phase. A closed-form expression of P/sub B/ is found for the interference model ii. Performance curves are presented and compared for the two interference models.

General ℒ/sup (p,q)/-metric estimator of arbitrary complex impulsive interference in linear systems

A general /spl Lscr//sup (p,q)/-metric p, q>0 on a probability space is defined, and the corresponding optimality criterion is derived. This criterion is applied to the problem of complex impulsive interference estimation in linear systems represented by scalar state-space equations. The closed-form expression of the a posteriori density of the state (interference) is computed recursively for both arbitrary i.i.d. state noise and any discrete-type measurement noise (multilevel complex signal). Optimal /spl Lscr//sup (p,q)/-metric interference estimators based on different values of p and q are developed. As a test, the proposed algorithms are applied to estimate highly impulsive state processes driven by noise with symmetric /spl alpha/-stable distribution.

The Linear Prediction Method of Fading Channel Estimation for the RakeReceiver with Impulsive Interference

Parameter estimation of the multipath and fading channel is investigated for the Rake combiner used in a CDMA system with coherent demodulation. A linear predictor is proposed to obtain a better estimation. Since the industrial interference environment is generally impulsive, a parallel LMS adaptive algorithm is proposed to reduce the impact of impulsive noise on predictor weights adjustment. Performance analysis and computer simulations are presented.

Data-adaptive algorithms for signal detection in sub-Gaussian impulsive interference

We address the problem of coherent detection of a signal embedded in heavy-tailed noise modeled as a sub-Gaussian, alpha-stable process. We assume that the signal is a complex-valued vector of length L, known only within a multiplicative constant, while the dependence structure of the noise, i.e. the underlying matrix of the sub-Gaussian process, is not known. We implement a generalized likelihood ratio detector that employs robust estimates of the unknown noise underlying matrix and the unknown signal strength. The performance of the proposed adaptive detector is compared with that of an adaptive matched filter that uses Gaussian estimates of the noise-underlying matrix and the signal strength and is found to be clearly superior. The proposed new algorithms are theoretically analyzed and illustrated in a Monte-Carlo simulation.

Fast estimation of the parameters of alpha-stable impulsive interference

We address the problem of estimation of the parameters of the recently proposed symmetric, alpha-stable model for impulsive interference. We propose new estimators based on asymptotic extreme value theory, order statistics, and fractional lower order moments, which can be computed fast and are, therefore, suitable for the design of real-time signal processing algorithms. The performance of the new estimators is theoretically evaluated, verified via Monte Carlo simulation, and compared with the performance of maximum-likelihood estimators.

Impulsive noise: A nontraditional approach

The problem of impulsive interference modeling is considered. The proposed approach is based on the representation of the interference as the discontinuous Markov process observed at the output of the generally nonlinear filter, excited by a Poisson-distributed train of δ-pulses with random or constant energy. The dependence of the probability density and correlation functions of the simulating process on the filter structure and on the excitation characteristics is investigated. Examples of the considered model synthesis are included. The concept suggested should prove useful in simulators of the interference in continuous communication channels and in synthesis of optimal signal processing algorithms in the impulsive environment.

A robust algorithm for adaptive FIR filtering and its performance analysis with additive contaminated-Gaussian noise

Abstruct- We introduce a steepest descent linear adaptive algorithm, the proportion-sign algorithm (PSA), lo make the least mean square (LMS) algorithm robust to impulsive interference occurring in the desired response. Its performance analysis is presented when the signals are from zero-mean jlointly stationary Gaussian processes and the additive noise to the (desired response is from a zero-mean stationary contaminated-Gaussian (CG) process which is usually used to represent impulsive interference. Since a special case of the PSA becomes the LMS algorithm, the analysis of the LMS is also obtained as a by-product. By adding a minimal amount of computational complexity, thie PSA improves to some degree the convergence speed over the LMS algorithm without overly degrading the steady-state error performance for Gaussian noise. In addition, since the first derivative of its cost function with respect to estimation error is bounded, it has the properties of robustness to impulsive interference occurring in the desired response while the LMS algorithm is vulnerable to it. Computer simulations are used to demonstrate the validity of our analysis and the robustness of the PSA compared with the LMS algorithm.

A fast response split-path median LMS algorithm

An adaptive median LMS algorithm based on a split FIR filter structure is presented. The algorithm has a better tracking capability and a faster convergence rate by means of reducing the eigenvalue spread of the input correlation matrix. The performance of the adaptive system is evaluated in a line enhancement application. It is found that the algorithm is effective in both the suppression of impulsive interference and preservation of edge details of the desired signal.

Fractional lower-order statistics-based ambiguity functions for differential delay Doppler estimation

The problem of estimation of differential-delay Doppler in an environment in which the signal of interest is embedded in highly impulsive interference is addressed. A signal model is formulated with wide applications in radar, sonar, communications and biomedicine and the construction of a new ambiguity function is proposed which is based on the recently-developed concepts of fractional, lower-order statistics and is, therefore, resistant to the presence of severe outliers in the observed time series. The performance of the proposed differential-delay Doppler estimators is theoretically analysed, verified via Monte Carlo simulation, and compared to the performance of traditional, second-order statistics-based estimators.

Effective adaptive antenna scheme for mobile communications

In electromagnetically crowded mobile communication systems, adaptive antennas employed at the base station often experience simultaneous reception of strong cochannel and impulsive interferers impinging into the main beam of the array along with the desired signal. This results in performance degradation of the angle of arrival estimation schemes in supplying the accurate look-direction information to the beamformer. In the Letter, a simple and effective adaptive antenna scheme is devised to prevent the desired signal cancellation in the optimal weight vector computation of the beamformer without resorting to the derivative or other higher order constraints in the angular region of interest.

Two-dimensional median least mean squares adaptive algorithm

A two-dimensional adaptive algorithm which resists impulsive interference is presented. The proposed two-dimensional median least mean squares (TDMLMS) algorithm is a gradient-based steepest descent algorithm and employs the sample median of the instantaneous gradients within a suitable window as a measure of the true gradient. The nonlinear action of the median filtering operation smooths the gradients and significantly enhances the adaptive process. Transferring from two- to one-dimensional operation shows that the TDMLMS is convergent, in the mean, to the optimum Wiener solution with some widely used assumptions. The TDMLMS is somewhat slower than the conventional two-dimensional LMS (TDLMS) when no impulsive interference is present. The vastly improved performance of the proposed TDMLMS over the TDLMS in an impulsive noise environment is demonstrated.

Maximum likelihood localization of sources in noise modeled as a stable process

This paper introduces a new class of robust beamformers which perform optimally over a wide range of non-Gaussian additive noise environments. The maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature. The analysis is based on the assumption that the additive noise can be modeled as a complex symmetric /spl alpha/-stable (S/spl alpha/S) process. Transform-based approximations of the likelihood estimation are used for the general S/spl alpha/S class of distributions while the exact probability density function is used for the Cauchy case. It is shown that the Cauchy beamformer greatly outperforms the Gaussian beamformer in a wide variety of non-Gaussian noise environments, and performs comparably to the Gaussian beamformer when the additive noise is Gaussian. The Cramer-Rao bound for the estimation error variance is derived for the Cauchy case, and the robustness of the S/spl alpha/S beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments.

Estimation of multilevel digital signals in the presence of arbitrary impulsive interference

We first study the a posteriori probability density function of the state of a discrete-time system given the measurement data. By applying the Bayesian law to the state and measurement equations of the stochastic system, the a posteriori density is obtained in closed-form and computed recursively for arbitrary i.i.d. state noise and any discrete-type measurement noise (or multilevel digital signal). Then, our effort concentrates on the estimation of impulsive noise which interferes the multilevel signal of interest. By considering the L/sup p/-metric performance criterion, where 0<p<2, the corresponding estimators are obtained. Using a new damping function scheme, the performance of the new estimators is improved even further. As an example, a highly impulsive state process driven by noise with symmetric /spl cap/-stable distribution is estimated and then removed from the measurement data; after that, the multilevel digital signal is recovered.<<ETX>>

Median least mean squares lattice ( MLMSL) adaptive filters

An efficient algorithm for updating the gradient adaptive lattice (GAL) filter, termed the median least mean squares lattice (MLMSL) adaptive filter, is presented. The update in the proposed algorithm is achieved by employing the sample median of the gradient estimates at each stage of the lattice instead of the instantaneous value as in conventional GAL. Two structures are considered: the first is the normal lattice while the second incorporates an additional FIR configuration. It is shown that the MLMSL performs similar to the GAL in the absence of impulsive interference, and outperforms the GAL in the presence of such interference. Simulations are provided to demonstrate the efficiency of the proposed MLMSL adaptive filters.

Performance analysis of the dual sign algorithm for additive contaminated-Gaussian noise

In the previous analysis of the dual sign algorithm (DSA), Gaussian signals were assumed. When the desired response contains additive impulsive interference, however, the analysis seems to be inadequate. In this article, a performance analysis of the DSA is considered when the signals are zero-mean stationary Gaussian, and the additive noise of the desired response is zero-mean stationary contaminated-Gaussian (CG). Through computer simulations, our analysis is validated. It is also shown that the DSA is less vulnerable to impulsive interference than the least-mean square (LMS) algorithm. >

CFAR integration processors in randomly arriving impulse interference

Time diversity transmission is often used to circumvent the high probability of a deep fade on a single transmission which may result in loss of the signal. One way to combat deep fades is to postdetection integrate the received observations from each range resolution cell. The false alarm rate of the postdetection integrator (PI) is extremely sensitive to randomly arriving impulse interference. Such interfering pulses may be unintentionally generated by nearby radars or intentionally generated by pulse jammers seeking to destroy the visibility of the radar. The binary integrator (PI) which uses an M-out-of-L decision rule is insensitive to at most M-1 interfering pulses. We consider the adaptive implementation of the PI and BI detectors for constant false alarm rate (CFAR) operation. We show that the CFAR BI detector when the AND (L-out-of-L) decision rule is used exhibits more robust false alarm control properties in the presence of impulse interference at the expense of severe detection loss when no interference is present. The CFAR adaptive PI (API) detector is proposed to alleviate this problem. The CFAR API detector implements an adaptive censoring algorithm which determines and censors with high probability the interference samples thereby achieving robust false alarm control in the presence of interference and optimum detection performance in the absence of interference. >

A multiple time scale modularized adaptive beamformer

This paper analyzes the cascaded equivalent form of the minimum variance distortionless response (MVDR) beamformer. A unique feature of the modularized MVDR (M/sup 2/VDR) beamformer is the ability to distribute adaptive degrees of freedom (DOF) among beamformer stages. This property of the M/sup 2/VDR beamformer allows DOF to be adapted over different time scales. As a consequence of the multiple stage decomposition adaptive beamformer weights appear in a form which suggest an apparent increase in the number of DOF. To properly analyze this ease an alternative interpretation of adaptive DOF is introduced to establish the equivalence between the MVDR beamformer and its cascaded realization. In the second part of this paper the distribution for the output power estimate of a P stage M/sup 2/VDR beamformer is derived. Analysis reveals the necessity of placing constraints on the adaptation time assigned to each beamformer stage. Simulation experiments are presented that demonstrate the applicability of the M/sup 2/VDR beamformer in resolving closely spaced sources under impulsive interference conditions. >

Performance characteristics of the median LMS adaptive filter

The median least-mean-square (MLMS) adaptive filter alleviates the problem of degradation of performance when inputs are corrupted by impulsive noise by protecting the filter coefficients from the impact of the impulses. MLMS is obtained from the least mean square (LMS) by applying a median operation to the raw gradient estimates of the mean-squared-error performance surface. The algorithm is analyzed for the class of independent and identically distributed inputs, establishing exponential convergence. The rate of convergence is shown to depend on order statistics of the input but shows little dependence on characteristics of the impulsive interference. Analysis of the steady-state performance indicates a significantly improved performance for MLMS compared to LMS. Analytic predictions for both convergence and steady-state behavior are supported by simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>