Ramon F. Brcich

Detection of sources using bootstrap techniques

Source detection in array processing can be viewed as a test for equality of eigenvalues. Such a test is proposed, based on a multiple test procedure that considers all pairwise comparisons between eigenvalues. Using the bootstrap to estimate the null distributions of the test statistics results in a procedure with minimal assumptions on the nature of the signal. Simulations show that the proposed test is superior to information theoretic criteria such as the MDL, which are based on Gaussian signals and large sample sizes. Performance in most cases exceeds the more powerful sphericity test.

The stability test for symmetric alpha-stable distributions

Symmetric alpha-stable distributions are a popular statistical model for heavy-tailed phenomena encountered in communications, radar, biomedicine, and econometrics. The use of the symmetric alpha stable model is often supported by empirical evidence, where qualitative criteria are used to judge the fit, leading to subjective decisions. Objective decisions can only be made through quantitative statistical tests. Here, a goodness-of-fit hypothesis test for symmetric alpha-stable distributions is developed based on their unique stability property. Critical values for the test are found using both asymptotic theory and from bootstrap estimates. Experiments show that the stability test, using bootstrap estimates of the critical values, is better able to discriminate between symmetric alpha stable distributions and other heavy-tailed distributions than classical tests such as the Kolmogorov-Smirnov test.

Multiuser Detection in Heavy Tailed Noise

Abstract Zoubir, A. M., and Brcich, R. F., Multiuser Detection in Heavy Tailed Noise, Digital Signal Processing12 (2002) 262–273 We consider the problem of multiuser detection in impulsive noise channels. Multiuser detection methods have been shown to effectively combat multiple access interference in Gaussian noise, but are highly vulnerable to impulsive noise common in urban and indoor areas. Many multiuser detectors proposed for impulsive noise are based on a specific parametric noise model. While such a detector will perform well near the chosen model, performance is uncertain under larger deviations from the model. Robust detectors seek to minimize this loss, though they still rely on a static, albeit broader, model. We propose a nonparametric detector which makes minimal a priori assumptions on the noise model, requiring only a symmetric density. The detector is based on a nonparametric estimate of the noise density, obtained from the observations without the need for training data. Simulations show the nonparametric detector offers improved performance over existing methods when the noise is highly impulsive.

Robust estimation with parametric score function estimation

Robust estimation of signal parameters in the additive noise model has become an important problem. Its relevance can be attributed to the realisation that impulsive noise is present in communications channels. The approach to robust estimation taken here follows the M-estimation concept of robust statistics, except the score function is modeled as a linear combination of bases and is estimated from the observations. The asymptotic covariance of the M-estimates is derived and both the small and large sample performance is investigated. By imposing suitable constraints when estimating the score function small sample performance is improved with minimal large sample loss.

Suboptimal robust estimation using rank score functions

A parameter estimation scheme based on the adaptive modelling of the score function of M-estimators is presented. The weights of basis functions are estimated from the data to match the empirical distribution. The bases utilise rank based score functions to remove dependence on scale from the basis selection process. While determination of appropriate bases for a distribution is shown to be possible, the robustness and adaptivity of the scheme means good results may be achieved regardless.

Estimating the Parameters of the Multivariate Poisson Distribution Using the Composite Likelihood Concept

We address estimation for the multivariate Poisson distribution with second order correlation structure. Existing estimators such as maximum likelihood estimators are too computationally expensive whereas the moment estimator has low efficiency. The proposed estimator uses on the concept of composite likelihood and is, in terms of computational complexity and efficiency, in between a simple moment estimator and the complex maximum likelihood approach

Tolerance intervals for accuracy control of bootstrapped matched filters

We consider the problem of designing detectors using tolerance intervals. Signal detection based on tolerance intervals allows us to force the actual level of significance not to exceed the preset level with a given probability. The results presented in this letter demonstrate the accuracy with which these detectors can control the false-alarm rate when little is known about the noise distribution and only a small sample is available.

Adaptive ML signal detection in non-Gaussian channels

The problem of robust signal detection in non-Gaussian noise is revisited. In this paper, we look at some issues of robust estimators which have been discussed very little in previous works. Some robust estimators, which are adaptive in nature and asymptotically efficient, are introduced and some technical improvements are suggested. Performance of these robust estimators is given in a practical communication problem and their asymptotic properties are investigated when the parameter-to-observation ratio becomes large.

Detection of sources in array processing using the bootstrap

A hypothesis testing methodology for determining the number of narrowband sources impinging on an array is presented. Using multiple hypothesis tests the multiplicity of the smallest ordered eigenvalues of the sample correlation matrix and hence the number of sources, is determined. The finite sample null distributions of the test statistics are estimated using bootstrap resampling. By removing the assumption of Gaussianity and large sample size that the traditional MDL approach is based on, we are able to gain improvements in the small sample case or when there are deviations from Gaussianity.

Model selection for adaptive robust parameter estimation and its impact on multiuser detection

Robust parameter estimation in impulsive noise environments has become an important issue in wireless communications. In previous work, an adaptive robust estimator was developed which modelled the noise score function as a weighted sum of basis functions where the weights best fitted the empirical distribution. Here, this adaptive robust estimator is extended by using model selection to find a parsimonious set of basis functions to model the unknown noise distribution thereby improving small sample performance. It was found that the best model for small sample sizes is a single basis. Finally, we apply this procedure to robust multiuser detection in impulsive noise channels.