In recent years there has been much interest in robustness issues in general and in robust signal processing schemes in particular. Robust schemes are useful in situations where imprecise a priori knowledge of input characteristics makes the sensitivity of performance to deviations from assumed conditions an important factor in the design of good signal processing schemes. In this survey we discuss the minimax approach for the design of robust methods for signal processing. This has proven to be a very useful approach because it leads to constructive procedures for designing robust schemes. Our emphasis is on the contributions which have been made in robust signal processing, although key results of other robust statistical procedures are also considered. Most of the results we survey have been obtained in the past fifteen years, although some interesting earlier ideas for minimax signal processing are also mentioned. This survey is organized into five main parts, which deal separately with robust linear filters for signal estimation, robust linear filters for signal detection and related applications, nonlinear methods for robust signal detection, nonlinear methods for robust estimation, and robust data quantization. The interrelationships among many of these results are also discussed in the survey.

Robust techniques for signal processing: A survey

A statistical processing method is considered for interference suppression in W-CDMA systems. The major first-order statistic of interference, namely, the pdf function is estimated by use of higher-order statistics (HOS) of the received samples. This estimate, in turn, leads to deriving the best non-linear processor of the samples for enhanced detection performance of the desired user. A mathematical model for the process is presented and the relative asymptotic efficiency of the detector with respect to the conventional linear detector is computed. Some numerical results are also provided to show the achievable enhancement by the proposed nonlinear processing as applied to UMTS-based receivers.

https://ieeexplore.ieee.org/iel5/6675/17952/00827597.pdf

Interference cancellation in W-CDMA cellular structures using statistical processing

The Middleton Class A narrow-band non-Gaussian noise model [9]-[12] is examined. It is shown that this noise model (which is known to fit closely a variety of non-Gaussian noises) can itself be closely approximated by a computationally much simpler noise model. It is then shown by numerical examples that, for the problem of locally optimum detection, the simplest form of this approximation yields nearly optimal (asymptotic) performance. The performance of other simple suboptimal threshold detectors in Class A noise is also examined. Finally, a useful relationship between the Class A model and the e-mixture model is developed.

Threshold Detection in Narrow-Band Non-Gaussian Noise

A type of iterative deconvolution that extracts the source waveform and reflectivity from a seismogram through the use of zero memory, non-linear estimators of reflection coefficient amplitnde is developed. Here, we present a theory for iterative deconvolution that is based upon the specification of a stochastic model describing reflectivity. The resulting parametric algorithm deconvolves the seismogram by forcing a filtered version of the seismogram to resemble an estimated reflection coefficient sequence. This latter time series is itself obtained from the filtered seismogram, and so a degree of iteration is required. Algorithms utilizing zero memory non-linearities (ZNLs) converge to a family of processes, which we call Bussgang, of which any colored Gaussian process and any independent process are members. The direction of convergence is controlled by the choice of ZNL used in the algorithm. Synthetic and real data show that, generally, five to ten iterations are required for acceptable deconvolutions.

Zero Memory Non-Linear DECONVOLUTION*

The discrete time detection of a known constant signal in white stationary Laplace noise is considered. Exact expressions describing the performance of both the Neyman-Pearson optimal detector and the suboptimal linear detector are presented. Also, graphs of the receiver operating characteristics are given. The actual performance of the Neyman-Pearson optimal detector is compared to that predicted by a Gaussian approximation to the distribution of the test statistic.

Detection in Laplace Noise

A first-order mixture noise density is considered as a model for impulsive noise channels It consists of a mixture of a small variance, probably Gaussian, background noise pdf and a large variance impulsive pdf Optimal nonlinear detector structures for known discretetime signals in such noise are derived Their large-sample performance compared to that of a linear detector is studied using asymptotic relative efficiency

J. Thomas

Papers

The Detection of Signals in Impulsive Noise Modeled as a Mixture Process