Bayesian Estimation of a Gaussian source in Middleton's Class-A Impulsive Noise

The paper focuses on minimum mean square error (MMSE) Bayesian estimation for a Gaussian source impaired by additive Middleton's Class-A impulsive noise. In addition to the optimal Bayesian estimator, the paper considers also the soft-limiter and the blanker, which are two popular suboptimal estimators characterized by very low complexity. The MMSE-optimum thresholds for such suboptimal estimators are obtained by practical iterative algorithms with fast convergence. The paper derives also the optimal thresholds according to a maximum-SNR (MSNR) criterion, and establishes connections with the MMSE criterion. Furthermore, closed form analytic expressions are derived for the MSE and the SNR of all the suboptimal estimators, which perfectly match simulation results. Noteworthy, these results can be applied to characterize the receiving performance of any multicarrier system impaired by a Gaussian-mixture noise, such as asymmetric digital subscriber lines (ADSL) and power-line communications (PLC).Comment: 30 pages, 13 figures, part of this work has been submitted to IEEE Signal Processing Letter

Detection in non gaussian environment: various approaches and use of mixture models

Most of the signal processing methods, especially in detection/estimation theory, are based on a Gaussian noise probability density function (PDF). As real noises are not usually Gaussian, a good performance can not be obtained by assuming a Gaussian probability density. This paper can be viewed as a survey of some alternatives when the noise is known to be non-Gaussian, and even non-stationnary or imperfectly known . The emphasis is on a noise PDF modeled as a mixture, this PDF being sum of two or more elementary density functions. This representation, used in minimax robustness and adaptive methods, is particularly suitable for impulsive noise model and for the case of uncertainties on the noise PDF . Some applications in underwater acoustics are given.Les bruits réels ne suivent que rarement la loi gaussienne; de bonnes performances ne peuvent être obtenues qu'en s'affranchissant de l'hypothèse gaussienne. On expose quelques méthodes de prise en compte du décalage entre la loi réelle et la loi gaussienne. On insiste sur l'importance de la représentation de la loi du bruit par un modèle de mixture, la densité de probabilité étant la somme de deux ou plusieurs densités élémentaire

Utilisation de tests basés sur des statistiques d'ordre supérieur dans l'analyse de séries temporelles mesurées dans l'espace

Tests of hypotheses based on Higher Order Statistics (HOS) are reviewed in the particular context of the identification of nonlinear processes in space plasma. The time series under study are associated with the measurements of electric or/and magnetic field components, or/and counting rates of particles. The basic principles of HOS techniques are reviewed. A general and unified procedure is suggested in order to construct statistical tests: (1) for detecting a non-gaussian or transient signal in a gaussian (or non-gaussian) noise, (2) testing a stochastic time series for non-gaussianity (including non-linearity), (3) studying non-linear wave interactions by using the kth-order coherency function. Asymptotic theory of estimates of the kthorder spectra is implemented in a digital signal processing framework. The effectiveness of the signal detection algorithms is demonstrated through computer simulations. Examples of application on the analysis of satellite data are given.Des tests d'hypothèses basés sur des statistiques d'ordre supérieur sont revus dans le contexte particulier de l'identification de processus non-linéaires dans les plasmas spatiaux. Les séries temporelles étudiées sont associées à la mesure de composantes du champ électrique et/ou magnétique d'ondes ou de turbulences, et/ou de données particules. Les principes de base des statistiques d'ordre supérieur sont brièvement rappelés. Une procédure générale et unifiée est suggérée afin de construire des tests statistiques permettant: (1) de détecter des signaux non-gaussiens ou transitoires au sein d'un bruit gaussien (ou non-gaussien), (2) de tester si une série temporelle est associée ou non à un processus stochastique issu d'un processus non-linéaire, (3) d'étudier des interactions non-linéaires à plusieurs ondes par l'utilisation de la fonction de cohérence d'ordre k. La théorie asymptotique des estimés des spectres d'ordre k est mise en oeuvre dans le cas discret. L'efficacité des algorithmes de détection est démontrée par le biais de simulations numériques. Des exemples d'applications à des données satellites sont présentés

Multilevel Coding and Unequal Error Protection for Multiple-Access Communications and Ultra-Wideband Communications in the Presence of Interference.

Interference is one of the major factors that degrade the performance of a communication system. Various types of interference cause di Kerent impact on the system performance. In this thesis, we consider interference management at the physical layer. In order to enhance the performance, the receiver needs to have the knowledge about the interference. By exploiting the knowledge about interference, such as statistical properties, it can be suppressed to enhance the link quality. This thesis contains two main topics: multilevel coding (MLC) for unequal error protection (UEP) and receiver design for ultra-wideband (UWB) communications to suppress interference. Both topics deal with interference in di Kerent ways, and face di Kerent design challenges. MLC is a way to provide UEP for different streams of information with different levels of importance in a communication system. It combines coding and modulation schemes to optimize the system performance. The idea is to protect each bit in the modulation constellation point by an individual binary code. We designed and analyzed a DS-CDMA system with asymmetric PSK modulation and MLC using BCH codes in an AWGN channel. The analysis includes probability of bit error of the system, and the capacity and throughput of the MLC scheme combined with 8-PSK modulation. The results show that the MLC scheme can have a higher throughput than the regular coding scheme in the low SNR region in the AWGN channel. We also analyzed the performance of UWB communications in the presence of MAI and jamming interference. We considered a nonlinear interference suppression technique for impulse radio based UWB systems in the AWGN channel. The technique is based on the locally optimum Bayes detection (LOBD) algorithm, which utilizes the interference probability density function (PDF) for receiver design. This type of receiver has low complexity, and numerical results show that its performance asymptotically approaches that of the optimum receiver. Lastly, we discussed the implementation of the proposed receiver by adaptively monitor and update the interference PDF. The adaptive LOBD algorithm makes the proposed receiver implementation practical to deal with different types of interference.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75955/1/wangcw_1.pd