Mohamed Sahmoudi

Fast Iterative Maximum-Likelihood Algorithm (FIMLA) for Multipath Mitigation in the Next Generation of GNSS Receivers

In this paper, we efficiently solve the maximum likelihood (ML) time-delay estimation problem for GNSS signals in a multipath environment. Exploiting the GNSS signal model structure and the spreading code periodicity, we develop an efficient implementation of the Newton iterative likelihood maximization method by finding simple analytical expressions for the first and second derivatives of the likelihood function. The proposed fast iterative ML algorithm (FIMLA) for timedelay estimation, which uses the correlation function of the received signal with its local replica, is shown to be an attractive technique for mitigation of closely-spaced multipath arrivals. For the future modernized GPS and the European Galileo signals based on binary offset carrier (BOC) waveforms, the correlation function has multiple positive and negative peaks leading to potential tracking ambiguities. Instead of the standard crosscorrelation, we propose an implementation characterized by a different choice of the local replica so as to cancel the sub-carrier phase, thus eliminating ambiguities. The asymptotic performance of FIMLA is analyzed by deriving the corresponding Cramer-Rao bound (CRB). Representative simulation examples are included to illustrate the FIMLA is performance for delay estimations in the presence of multipath for both C/A code and BOC signals.

Robust tracking of weak GPS signals in multipath and jamming environments

In this paper, we address the problem global positioning system (GPS) signals tracking in low signal-to-noise ratio (SNR) and multipath plus interference environments using a two-step approach: a block-averaging pre-processing (BAP) which converts the zero-mean interferences to colored Gaussian noise and a maximum likelihood (ML) based algorithm combined with a whitening transform. We apply the recently proposed BAP technique to improve the SNR. For code tracking with multipath mitigation, we exploit the fact that during a period with no data bit edges, the propagation delay causes only a circular shift to the C/A code block. This allows the decomposition of the averaged data vector into a constant C/A code component plus an undesired signal component. An efficient temporal whitening transform is derived from the sample covariance matrix and applied to suppress strong colored interferers, rendering the ML estimation problem of the multipath parameters tractable. A computationally efficient procedure for solving the complex ML optimization problem is considered using a finite difference maximization technique. By estimating the multipath signals and subtracting their contributions in a sequential scheme, the code synchronization is achieved. The resulting robust ML (RML) tracking procedure is more efficient in mitigating multipath and non-Gaussian interferences. The performance of the developed RML receiver is evaluated through computer simulations to show its superiority over that of narrow correlator and MEDLL approach.

Blind separation of impulsive alpha-stable sources using minimum dispersion criterion

This letter introduces a novel blind source separation (BSS) approach for extracting impulsive signals from their observed mixtures. The impulsive signals are modeled as real-valued symmetric alpha-stable (S/spl alpha/S) processes characterized by infinite second- and higher-order moments. The proposed approach uses the minimum dispersion (MD) criterion as a measure of sparseness and independence of the data. A new whitening procedure by a normalized covariance matrix is introduced. We show that the proposed method is robust, so-named for the property of being insensitive to possible variations in the underlying form of sampling distribution. Algorithm derivation and simulation results are provided to illustrate the good performance of the proposed approach. The new method has been compared with three of the most popular BSS algorithms: JADE, EASI, and restricted quasi-maximum likelihood (RQML).

Acquisition of weak GNSS signals using a new block averaging pre-processing

In this paper, we introduce a new approach for the acquisition of weak GNSS signals. For the GPS L1 signal, we utilize the replication property of the C/A code within each data bit to introduce a block averaging pre-processing (BAP) approach for improving receiver robustness against undesired signals. A large number of weighted signal blocks is coherently accumulated and synchronously averaged to obtain a single block with improved signal power. We present several properties of the proposed GNSS signals enhancement technique and we analyze its robustness against noise and different classes of interferers. Thus, we develop a software defined acquisition procedure using the efficient FFT correlation approach. We propose two acquisition algorithms based on the BAP approach. The first scheme implements the parallel code phase search in finding the 2-D spectrum peak using circular cross-correlations. In the second scheme, we exploit the BAP for a fast acquisition performing the frequency estimation prior to the 1-D code-phase search.

Optimal Robust Beamforming for Interference and Multipath Mitigation in GNSS Arrays

In this paper, we introduce an optimal robust beamformer for detecting a desired signal in presence of noise, strong interferers of unknown directions-of-arrival (DOA), and multipath. The proposed approach achieves the highest possible signal-to-interference plus noise ratio (SINR) by optimally estimating the interference DOA, followed by a triply constrained robust Capon beamformer. More specifically, we maximize the SINR subject to nulling strong interferers and offer robustness against multipath and steering vector uncertainty. Unlike existing techniques, we examine explicitly the use of robust beamforming for multipath mitigation to enhance acquisition and tracking performance of GPS receivers.

Fast Iterative Maximum-Likelihood Algorithm (FIMLA) for Multipath Mitigation in Next Generation of GNSS Receivers

In this paper, we efficiently solve the maximum-likelihood (ML) time-delay estimation problem for GNSS signals in a multipath environment. Exploiting the GNSS signal model structure and the spreading code periodicity, we develop an efficient implementation of the Newton iterative likelihood- maximization method by finding simple analytical expressions for the first and second derivatives of the likelihood function. The proposed Fast Iterative ML Algorithm (FIMLA) for time- delay estimation is shown to be an attractive technique for mitigation of closely-spaced multipath for current GPS receivers as well as future modernized GPS and the European Galileo systems based on BOC signals. Simulation results show that FIMLA improves the performance of the ML synchronization algorithm in presence of multipath.

Blind Separation of Convolutive Mixtures using Nonstationarity and Fractional Lower Order Statistics (FLOS): Application to Audio Signals

In this paper, we introduce new time-varying fractional spectral matrices to exploit both the nonstationarity and heavy-tailed sources properties for blind separation of convolutive audio mixtures. We define these spectrum matrices, that are different for various delays, using fractional lower order statistics (FLOS) of data. Similar to the second order statistics (SOS) based approaches, we maximize the sources independence by jointly diagonalizing these fractional matrices spectrum of the reconstructed signals using a mutual information criterion. A set of experiments using audio signals and real impulse response of acoustic room are designed to verify the usefulness of the proposed method

Blind Separation of Heavy-Tailed Signals Using Normalized Statistics

This paper introduces a new approach for the blind separation (BS) of heavy tailed signals that can be modeled by real-valued symmetric α-stable (SαS) processes. As the second and higher order moments of the latter are infinite, we propose to use normalized statistics of the observation to achieve the BS of the sources. More precisely, we show that the considered normalized statistics are convergent (i.e., take finite values) and have the appropriate structure that allows for the use of standard BS techniques based on second and higher order cumulants.

A Maximum-Likelihood Synchronization Scheme for GPS Positioning in Multipath, Interference, and Weak Signal Environments

In this paper, a novel multipath parameters estimation approach for GPS receivers using the maximum likelihood (ML) principle is proposed. Exploiting the replication property of the GPS C/A code within each symbol, we develop a coherent preprocessing approach based on a sample mean model. This model employs long integration time that improves the SNR and enhances receiver robustness against interference and weak signal effects. It also allows a simplified expression for the likelihood function which facilitates the use of computationally efficient iterative techniques for solving the complex ML optimization problem. In the proposed approach, the ML estimator is iteratively computed using the fast and low-complexity SAGE (Space-Alternating Generalized Expectation Maximization) algorithm. The proposed scheme is a candidate for indoor GPS navigation, as demonstrated by computer simulations.

Improved Maximum-Likelihood Time Delay Estimation for GPS Positioning in Multipath, Interference and Low SNR Environments

In this paper, we propose a robust maximum like- lihood (RML) approach for delay and amplitude estimation of weak GPS signals in multipath and interference environments such as that encountered in indoor applications. First, to formu- late the problem we exploit the fact that during the acquisition period the propagation delay causes only a circular shift to the spreading C/A code vector. This allows the decomposition of the received data vector into a constant component plus an undesired signals component. Then, a sample mean model is developed using a moving average over long time durations to reduce the effect of undesired zero-mean signals to one of a colored Gaussian noise. The developed model has an anti- jam structure which relies on the exploitation of a temporal structure property of the GPS signal, namely the replication of the C/A-code. An efficient temporal whitening technique is derived from the sample covariance matrix and applied to suppress the colored noise effect. The ML time-delay estimation of the superimposed multipath parameters becomes tractable and results in an efficient algorithm by adopting a sequential procedure.