Performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. In this paper, we present a theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) for the class of beamformers based on generalized (i.e., not necessarily diagonal) loading of the covariance matrix in the presence of random steering vector errors. A closed-form expression for the SINR is derived that is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR

Covariance matrix estimation with heterogeneous samples

We consider the problem of estimating the covariance matrix Mp of an observation vector, using heterogeneous training samples, i.e., samples whose covariance matrices are not exactly Mp. More precisely, we assume that the training samples can be clustered into K groups, each one containing Lk, snapshots sharing the same covariance matrix Mk. Furthermore, a Bayesian approach is proposed in which the matrices Mk. are assumed to be random with some prior distribution. We consider two different assumptions for Mp. In a fully Bayesian framework, Mp is assumed to be random with a given prior distribution. Under this assumption, we derive the minimum mean-square error (MMSE) estimator of Mp which is implemented using a Gibbs-sampling strategy. Moreover, a simpler scheme based on a weighted sample covariance matrix (SCM) is also considered. The weights minimizing the mean square error (MSE) of the estimated covariance matrix are derived. Furthermore, we consider estimators based on colored or diagonal loading of the weighted SCM, and we determine theoretically the optimal level of loading. Finally, in order to relax the a priori assumptions about the covariance matrix Mp, the second part of the paper assumes that this matrix is deterministic and derives its maximum-likelihood estimator. Numerical simulations are presented to illustrate the performance of the different estimation schemes

Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters

We derive asymptotic expansions of the Kummer functions $M(a,b,z)$ and $U(a,b+1,z)$ for large positive values of $a$ and $b$, with $z$ fixed. For both functions we consider $b/a\le 1$ and $b/a\ge 1$, with special attention for the case $a\sim b$. We use a uniform method to handle all cases of these parameters.Comment: 17 pages, 2 figure

Comparison of adaptive radar algorithms : transformed SMI, eigencanceler, and SMI

Advanced airborne radars must perform target detection in the presence of interference and heavy clutter. In many applications, the practical usefulness of adaptive arrays is limited by their convergence rate. In this paper, we first analyze the performance of the SMI method. Then, two other methods, the transformed SMI and the eigencanceler, both based on the principle component inversion (PCI) technique, are described and analyzed by simulation. It is shown by simulation based comparison that the transformed SMI and the Eigencanceler outperform the SMI method. It is also shown that the transformed SMI and the eigencanceler has higher convergence rate in terms of output signal-to-noise ratio than the SMI, specially for short data record sizes. It is concluded that the transformed SMI and the eigencanceler are good alternatives to the SMI method when data set available is small

Analysis of the SNR Loss Distribution With Covariance Mismatched Training Samples

We analyze the distribution of the signal to noise ratio (SNR) loss at the output of an adaptive filter which is trained with samples that do not share the same covariance matrix as the samples for which the filter is foreseen. Our objective is to find an accurate approximation of the distribution of the SNR loss which has a similar form as in the case of no mismatch. We successively consider the case where the two covariance matrices satisfy the so-called generalized eigenrelation, and the case where they are arbitrary. In the former case, this amounts to approximate a central quadratic form in normal variables while the latter case entails approximating a non-central quadratic form in Student distributed variables. In order to obtain the approximate distribution, a Pearson type approach is advocated. A numerical study shows that this approximation is rather accurate, and enables one to assess in a straightforward manner the impact of covariance mismatch

Effects of estimated noise covariance matrix in optimal signal detection

There is loss of efficiency when an estimated noise covariance matrix is used in the place of the unknown true noise covariance matrix in the construction of the optimum filter for signal detection. In the case of detecting a single signal specified by a real or a complex vector, we investigate the extent of this loss by obtaining an exact confidence bound for the realized signal-to-noise ratio. We also give an estimate of this ratio which is useful in optimum selection of features. Some of these results are extended to the case of discrimination between a number of given signals

Estimation et détection en milieu non-homogène, application au traitement spatio-temporel adaptatif

Pour un radar aéroporté, la détection de cibles nécessite, de par la nature du fouillis de sol, la mise en place d'un filtre spatio-temporel adaptatif (STAP). Les détecteurs basés sur l'hypothèse d'un milieu homogène sont souvent mis à mal dans un environnement réel, où les caractéristiques du fouillis peuvent varier significativement en distance et en angle. Diverses stratégies existent pour contrer les effets délétères de l'hétérogénéité. La thèse propose d'approfondir deux de ces stratégies. Plus précisément, un nouveau modèle d'environnement est présenté dans un contexte Bayésien : il intègre à la fois une relation originale d'hétérogénéité et de la connaissance a priori. De nouveaux estimateurs de la matrice de covariance du bruit ainsi que de nouveaux détecteurs sont calculés à partir de ce modèle. Ils sont étudiés de manière théorique et par simulations numériques. Les résultats obtenus montrent que le modèle proposé permet d'intégrer de manière intelligente l'information a priori dans le processus de détection. ABSTRACT : Space-time adaptive processing is required in future airborne radar systems to improve the detection of targets embedded in clutter. Performance of detectors based on the assumption of a homogeneous environment can be severely degraded in practical applications. Indeed real world clutter can vary significantly in both angle and range. So far, different strategies have been proposed to overcome the deleterious effect of heterogeneity. This dissertation proposes to study two of these strategies. More precisely a new data model is introduced in a Bayesian framework ; it allows to incorporate both an original relation of heterogeneity and a priori knowledge. New estimation and detection schemes are derived according to the model ; their performances are also studied theoretically and through numerical simulations. Results show that the proposed model and algorithms allow to incorporate in an appropriate way a priori information in the detection schem

Procesamiento de señales e imágenes biomédicas para el estudio de la actividad cerebral

En esta tesis se estudian distintos aspectos que influyen en la calidad de la solución de los problemas directo e inverso de la electro/magnetoencefalografía, así como problemas de estimación relacionados a las imágenes de resonancia magnética por tensor de difusión. Se analizan los efectos de variaciones en el modelo de cabeza utilizado, en el posicionamiento de los electrodos y la modelización de la actividad cerebral de fondo. Se estudia también la influencia del ruido propio del sistema de adquisición en imágenes de tensor de difusión y mediciones derivadas de éste. Tales influencias se plasman en errores en la estimación de la conductividad eléctrica, necesaria para la adecuada modelización de la cabeza, así como en la estimación de la geometría estructural intracerebral, denominada tractografía.Facultad de Ingenierí