Chrysostomos L. Nikias

Signal processing with higher-order spectra

The strengths and limitations of correlation-based signal processing methods are discussed. The definitions, properties, and computation of higher-order statistics and spectra, with emphasis on the bispectrum and trispectrum are presented. Parametric and nonparametric expressions for polyspectra of linear and nonlinear processes are described. The applications of higher-order spectra in signal processing are discussed.<<ETX>>

Higher-order spectral analysis

Absltacl The purpose of this keynote lecture of the Signal Analysis Track is U) present the motivation behind he use of higher-order spectra (HOS) in signal processing as well as the definitions, properties, and biomedica1 signal processing applications of higher-order spectra. This lecture will also emphasize the state of science of the higher-order spectra field, especially as it applies to non-stadonary signal analysis.

Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process

Impulsive noise bursts in communication systems are traditionally handled by incorporating in the receiver a limiter which clips the received signal before integration. An empirical justification for this procedure is that it generally causes the signal-to-noise ratio to increase. Recently, very accurate models of impulsive noise were presented, based on the theory of symmetric /spl alpha/-stable probability density functions. We examine the performance of optimum receivers, designed to detect signals embedded in impulsive noise which is modeled as an infinite variance symmetric /spl alpha/-stable process, and compare it against the performance of several suboptimum receivers. As a measure of receiver performance, we compute an asymptotic expression for the probability of error for each receiver and compare it to the probability of error calculated by extensive Monte-Carlo simulation. >

Blind equalization using a tricepstrum-based algorithm

An adaptive blind equalization method is introduced for nonminimum phase communication channels. The method estimates the inverse channel impulse response, by using the complex cepstrum of the fourth-order cumulants (tricepstrum) of the synchronously sampled received signal. As such, the proposed adaptive method depends only on the statistics of the received sequence, and is capable of reconstructing separately both the minimum and maximum phase response of the channel. It is demonstrated, by means of extensive simulations, that the proposed tricepstrum-based equalization scheme performs well and outperforms other existing blind equalizers, at the expense of higher computational complexity. >

EVAM: an eigenvector-based algorithm for multichannel blind deconvolution of input colored signals

A new algorithm is proposed for the deconvolution of an unknown, possibly colored, Gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions. More specifically, not only the root (pole and zero) locations but also the orders of the channel transfer functions are unknown. It is assumed that the channel orders may be overestimated. The proposed algorithm estimates the orders and root locations of the channel transfer functions, therefore it can also be used in multichannel system identification problems. The input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal, hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones. Several experimental results indicate improvement compared to the existing methods in the literature. >

The complex cepstrum of higher order cumulants and nonminimum phase system identification

A computationally efficient identification procedure is proposed for a nonGaussian white-noise-driven linear, time-invariant, nonminimum phase system. The method is based on the idea of computing the complex cepstrum of higher order cumulants of the system output. In particular, the differential cepstrum parameters of the nonminimum phase impulse response are estimated directly from higher-order cumulants by least-squares solution or two-dimensional FFT operations. The method reconstructs the minimum-phase and maximum-phase impulse response components separately. It is flexible enough to be applied on autoregressive (AR), moving average (MA), or ARMA system without a priori knowledge of the type of the system. Benchmark simulation examples demonstrate the effectiveness of the method even with short length data records. >

Parameter estimation and blind channel identification in impulsive signal environments

New methods for parameter estimation and blind channel identification in impulsive signal environments are presented, where the signals/noise are modeled as symmetric /spl alpha/-stable (S/spl alpha/S) processes. First, we present methods for estimating the parameters (characteristic exponent /spl alpha/ and dispersion /spl gamma/) of a S/spl alpha/S distribution from a time series. The fractional lower order moments, with both positive and negative orders, and their applications to signal processing are introduced. Then we present a new algorithm for blind channel identification using the output fractional lower order moments, and the /spl alpha/-Spectrum, a new spectral representation for impulsive signals, is introduced. From the /spl alpha/-Spectrum, we establish the blind identifiability conditions of any FIR channel (mixed-phase, unknown order) with i.i.d. S/spl alpha/S (/spl alpha/>1) input. As a byproduct, a simple algorithm for recovering the phase of any type of a signal from the magnitude of its z-transform is presented. The novelty of our paper is in parameter estimation and blind identification of the FIR channel based on fractional lower order moments of its output data. Monte Carlo simulations clearly demonstrate the performance of the new methods.

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.

The robust covariation-based MUSIC (ROC-MUSIC) algorithm for bearing estimation in impulsive noise environments

This paper presents a new subspace-based method for bearing estimation in the presence of impulsive noise which can be modeled as a complex symmetric alpha-stable (S/spl alpha/S) process. We define the covariation matrix of the array sensor outputs and show that eigendecomposition-based methods, such as the MUSIC algorithm, can be applied to the sample covariation matrix to extract the bearing information from the measurements. A consistent estimator for the marginals of the covariation matrix is presented and its asymptotic performance is studied. The improved performance of the proposed source localization method in the presence of a wide range of impulsive noise environments is demonstrated via Monte Carlo experiments.

Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics

New methods for time delay estimation and joint estimation of time delay and frequency delay in the presence of impulsive noise are introduced. First, degradation of the conventional approaches based on second-order statistics is shown both theoretically and experimentally. Then, a new class of robust algorithms are developed using the theory of alpha-stable distributions, including the fractional lower order covariance (FLOC) method, which is formulated for the time delay estimation problem and the fractional lower order ambiguity function (FLOAF), which is defined for the joint estimation of time delay and frequency delay. It is shown that these new methods are robust for both Gaussian and non-Gaussian impulsive noise environments. The improved performance is clearly demonstrated through detailed analysis and comprehensive simulations with computer-generated data as well as actual radar and sonar clutter data.