Bornes de Cramer Rao de DOA pour signaux BPSK et QPSK en présence de bruit non uniforme

Cet article est consacré au calcul de la borne de Cramer-Rao (CRB) stochastique des directions d'arrivée (DOA) de signaux de modulation BPSK et QPSK en présence de bruit additif gaussien circulaire de matrice de covariance spatiale diagonale arbitraire. Une expression analytique de cette borne est donnée dans le cas d'une seule source grâce au découplage entre les paramètres puissance et les paramètres de phase de la matrice d'information de Fisher (FIM). Cette borne est comparée à diverses bornes dérivées selon diverses connaissances a priori. Ces résultats et comparaisons sont ensuite étendus au cas de deux sources indépendantes où des expressions analytiques de CRB sont obtenues pour des grandes valeurs de rapport signal sur bruit (SNR). Nous avons mis en évidence de grandes différences de comportement par rapport à la borne standard obtenue dans le cas de signaux gaussiens circulaires, démontrant ainsi l'intérêt des approches EM dans le cas de connaissances a priori sur la distribution discrète des sources

Performance limits of alphabet diversities for FIR SISO channel identification

10 pagesInternational audienceFinite Impulse Responses (FIR) of Single-Input Single-Output (SISO) channels can be blindly identified from second order statistics of transformed data, for instance when the channel is excited by Binary Phase Shift Keying (BPSK), Minimum Shift Keying (MSK) or Quadrature Phase Shift Keying (QPSK) inputs. Identifiability conditions are derived by considering that noncircularity induces diversity. Theoretical performance issues are addressed to evaluate the robustness of standard subspace-based estimators with respect to these identifiability conditions. Then benchmarks such as asymptotically minimum variance (AMV) bounds based on various statistics are presented. Some illustrative examples are eventually given where Monte Carlo experiments are compared to theoretical performances. These comparisons allow to quantify limits to the use of the alphabet diversities for the identification of FIR SISO channels, and to demonstrate the robustness of algorithms based on High-Order Statistics

Bornes de Cramer Rao déterministe et stochastique de DOA de signaux rectilignes non corrélés

Cet article est consacré au calcul des bornes de Cramer-Rao (CR) déterministe et stochastique des directions d'arrivée (DOA) sous la connaissance a priori de signaux non circulaires rectilignes non corrélés en présence de bruit additif gaussien circulaire de matrice de covariance spatiale arbitraire. Des expressions analytiques de ces deux bornes sont données permettant de préciser le rôle primordial des phases de non circularité où plusieurs propriétés sont démontrées. Inférieures aux bornes générales ne prenant pas en compte ces informations a priori, des exemples numériques montrent que les bornes de CR déterministes et stochastiques avec a priori sont très proches entre elles mais très faibles par rapport à la borne de CR stochastique qui ne tient pas compte de ces a priori

The Gaussian assumption in second-order estimation problems in digital communications

This paper deals with the goodness of the Gaussian assumption when designing second-order blind estimation methods in the context of digital communications. The low- and high-signal-to-noise ratio (SNR) asymptotic performance of the maximum likelihood estimator - derived assuming Gaussian transmitted symbols - is compared with the performance of the optimal second-order estimator, which exploits the actual distribution of the discrete constellation. The asymptotic study concludes that the Gaussian assumption leads to the optimal second-order solution if the SNR is very low or if the symbols belong to a multilevel constellation such as quadrature-amplitude modulation (QAM) or amplitude-phase-shift keying (APSK). On the other hand, the Gaussian assumption can yield important losses at high SNR if the transmitted symbols are drawn from a constant modulus constellation such as phase-shift keying (PSK) or continuous-phase modulations (CPM). These conclusions are illustrated for the problem of direction-of-arrival (DOA) estimation of multiple digitally-modulated signals.Peer ReviewedPostprint (published version

A Linear Subspace Approach to Burst Communication Signal Processing

This dissertation focuses on the topic of burst signal communications in a high interference environment. It derives new signal processing algorithms from a mathematical linear subspace approach instead of the common stationary or cyclostationary approach. The research developed new algorithms that have well-known optimality criteria associated with them. The investigation demonstrated a unique class of multisensor filters having a lower mean square error than all other known filters, a maximum likelihood time difference of arrival estimator that outperformed previously optimal estimators, and a signal presence detector having a selectivity unparalleled in burst interference environments. It was further shown that these improvements resulted in a greater ability to communicate, to locate electronic transmitters, and to mitigate the effects of a growing interference environment

Deterministic Cramer-Rao bound for strictly non-circular sources and analytical analysis of the achievable gains

Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. In this paper, as a benchmark for these NC methods, we derive the closed-form deterministic R-D NC Cramer-Rao bound (NC CRB) for the multi-dimensional parameter estimation of strictly non-circular (rectilinear) signal sources. Assuming a separable centro-symmetric R-D array, we show that in some special cases, the deterministic R-D NC CRB reduces to the existing deterministic R-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain for two sources. Our analysis is supported by extensive simulation results.Comment: submitted to IEEE Transactions on Signal Processing, 13 pages, 4 figure

Efficient and Robust Signal Detection Algorithms for the Communication Applications

Signal detection and estimation has been prevalent in signal processing and communications for many years. The relevant studies deal with the processing of information-bearing signals for the purpose of information extraction. Nevertheless, new robust and efficient signal detection and estimation techniques are still in demand since there emerge more and more practical applications which rely on them. In this dissertation work, we proposed several novel signal detection schemes for wireless communications applications, such as source localization algorithm, spectrum sensing method, and normality test. The associated theories and practice in robustness, computational complexity, and overall system performance evaluation are also provided

Channel estimation and signal enhancement for DS-CDMA systems

This dissertation focuses on topics of Bayesian-based multiuser detection, space-time (S-T) transceiver design, and S-T channel parameter estimation for direct-sequence code-division multiple-access (DS-CDMA) systems. Using the Bayesian framework, various linear and simplified nonlinear multiuser detectors are proposed, and their performances are analyzed. The simplified non-linear Bayesian solutions can bridge the performance gap between sub-optimal linear multiuser detectors and the optimum multiuser detector. To further improve the system capacity and performance, S-T transceiver design approaches with complexity constraint are investigated. Novel S-T receivers of low-complexity that jointly use the temporal code-signature and the spatial signature are proposed. Our solutions, which lead to generalized near-far resistant S-T RAKE receivers, achieve better interference suppression than the existing S-T RAKE receivers. From transmitter side, we also proposed a transmit diversity (TD) technique in combination with differential detection for the DS-CDMA systems. It is shown that the proposed S-T TD scheme in combination with minimum variance distortionless response transceiver (STTD+MVDR) is near-far resistant and outperforms the conventional STTD and matched filter based (STTD+MF) transceiver scheme. Obtaining channel state information (CSI) is instrumental to optimum S-T transceiver design in wireless systems. Another major focus of this dissertation is to estimate the S-T channel parameters. We proposed an asymptotic, joint maximum likelihood (ML) method of estimating multipath channel parameters for DS-CDMA systems. An iterative estimator is proposed to further simplify the computation. Analytical and simulation results show that the iterative estimation scheme is near-far resistant for both time delays and DOAs. And it reaches the corresponding CRBs after a few iterations

A Fresh Look at the Bayesian Bounds of the Weiss-Weinstein Family

International audienceMinimal bounds on the mean square error (MSE) are generally used in order to predict the best achievable performance of an estimator for a given observation model. In this paper, we are interested in the Bayesian bound of the Weiss–Weinstein family. Among this family, we have Bayesian Cramér-Rao bound, the Bobrovsky–MayerWolf–Zakaï bound, the Bayesian Bhattacharyya bound, the Bobrovsky–Zakaï bound, the Reuven–Messer bound, and the Weiss–Weinstein bound. We present a unification of all these minimal bounds based on a rewriting of the minimum mean square error estimator (MMSEE) and on a constrained optimization problem. With this approach, we obtain a useful theoretical framework to derive new Bayesian bounds. For that purpose, we propose two bounds. First, we propose a generalization of the Bayesian Bhattacharyya bound extending the works of Bobrovsky, Mayer–Wolf, and Zakaï. Second, we propose a bound based on the Bayesian Bhattacharyya bound and on the Reuven–Messer bound, representing a generalization of these bounds. The proposed bound is the Bayesian extension of the deterministic Abel bound and is found to be tighter than the Bayesian Bhattacharyya bound, the Reuven–Messer bound, the Bobrovsky–Zakaï bound, and the Bayesian Cramér–Rao bound. We propose some closed-form expressions of these bounds for a general Gaussian observation model with parameterized mean. In order to illustrate our results, we present simulation results in the context of a spectral analysis problem