Matched direction detectors and estimators for array processing with subspace steering vector uncertainties

In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the steering vector but, on the other hand, some knowledge about the steering vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Cramer-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations

Asymptotic Karlin-Rubin's Theorem with Application to Signal Detection in a Subspace Cone

International audienc

Robustness Analysis of the Matched Filter Detector Through Utilizing Sinusoidal Wave Sampling

This thesis performs a quantitative study, derived from the Neyman-Pearson framework, on the robustness of the matched filter detector corrupted by zero mean, independent and identically distributed white Gaussian noise. The variance of the noise is assumed to be imperfectly known, but some knowledge about a nominal value is presumed. We utilized slope as a unit to quantify the robustness for different signal strengths, nominals, and sample sizes. Following to this, a weighting method is applied to the slope range of interest, the so called tolerable range, as to analyze the likelihood of these extreme slopes to occur. A ratio of the first and last quarter section of the tolerable range have been taken in order to obtain the likelihood ratio for the low slopes to occur. We finalized our analysis by developing a method that quantifies confidence as a measure of robustness. Both weighted and non-weighted procedures were applied over the tolerable range, where the weighted procedure puts greater emphasis on values near the nominal. The quantitative analysis results show the detector to be non-robust and deliver poor performance for low signal-to-noise ratios. For moderate signal strengths, the detector performs rather well if the nominal and sample size are chosen wisely. The detector has great performance and robustness for high signal-to-noise ratios. This even remains true when only a few samples are taken or when the practitioner is uncertain about the nominal chosen

Contribution des filtres LPTV et des techniques d'interpolation au tatouage numérique

Les Changements d'Horloge Périodiques (PCC) et les filtres Linéaires Variant Périodiquement dans le Temps (LPTV) sont utilisés dans le domaine des télécommunications multi-utilisateurs. Dans cette thèse, nous montrons que, dans l'ensemble des techniques de tatouage par étalement de spectre, ils peuvent se substituer à la modulation par code pseudo-aléatoire. Les modules de décodage optimal, de resynchronisation, de pré-annulation des interférences et de quantification de la transformée d'étalement s'appliquent également aux PCC et aux filtres LPTV. Pour le modèle de signaux stationnaires blancs gaussiens, ces techniques présentent des performances identiques à l'étalement à Séquence Directe (DS) classique. Cependant, nous montrons que, dans le cas d'un signal corrélé localement, la luminance d'une image naturelle notamment, la périodicité des PCC et des filtres LPTV associée à un parcours d'image de type Peano-Hilbert conduit à de meilleures performances. Les filtres LPTV sont en outre un outil plus puissant qu'une simple modulation DS. Nous les utilisons pour effectuer un masquage spectral simultanément à l'étalement, ainsi qu'un rejet des interférences de l'image dans le domaine spectral. Cette dernière technique possède de très bonnes performances au décodage. Le second axe de cette thèse est l'étude des liens entre interpolation et tatouage numérique. Nous soulignons d'abord le rôle de l'interpolation dans les attaques sur la robustesse du tatouage. Nous construisons ensuite des techniques de tatouage bénéficiant des propriétés perceptuelles de l'interpolation. La première consiste en des masques perceptuels utilisant le bruit d'interpolation. Dans la seconde, un schéma de tatouage informé est construit autour de l'interpolation. Cet algorithme, qu'on peut relier aux techniques de catégorisation aléatoire, utilise des règles d'insertion et de décodage originales, incluant un masquage perceptuel intrinsèque. Outre ces bonnes propriétés perceptuelles, il présente un rejet des interférences de l'hôte et une robustesse à diverses attaques telles que les transformations valumétriques. Son niveau de sécurité est évalué à l'aide d'algorithmes d'attaque pratiques. ABSTRACT : Periodic Clock Changes (PCC) and Linear Periodically Time Varying (LPTV) filters have previously been applied to multi-user telecommunications in the Signal and Communications group of IRIT laboratory. In this thesis, we show that in each digital watermarking scheme involving spread-spectrum, they can be substituted to modulation by a pseudo-noise. The additional steps of optimal decoding, resynchronization, pre-cancellation of interference and quantization of a spread transform apply also to PCCs and LPTV filters. For white Gaussian stationary signals, these techniques offer similar performance as classical Direct Sequence (DS) spreading. However we show that, in the case of locally correlated signals such as image luminance, the periodicity of PCCs and LPTV filters associated to a Peano-Hilbert scan leads to better performance. Moreover, LPTV filters are a more powerful tool than simple DS modulation. We use LPTV filters to conduct spectrum masking simultaneous to spreading, as well as image interference cancellation in the spectral domain. The latter technique offers good decoding performance. The second axis of this thesis is the study of the links between interpolation and digital watermarking.We stress the role of interpolation in attacks on the watermark.We propose then watermarking techniques that benefit from interpolation perceptual properties. The first technique consists in constructing perceptualmasks proportional to an interpolation error. In the second technique, an informed watermarking scheme derives form interpolation. This scheme exhibits good perceptual properties, host-interference rejection and robustness to various attacks such as valumetric transforms. Its security level is assessed by ad hoc practical attack algorithms