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This paper addresses the estimation of multipath channels with long impulse response at low signal-to-noise ratio (SNR). The channel sparseness impulse response is modeled by means of a Bernoulli-Gaussian process. Then, the optimization of the resulting posterior distribution resorts to Monte Carlo Markov chain (MCMC) simulation techniques. Special attention is devoted to noise correlation involved by matched filtering: Taking this correlation into account in the algorithm derivation leads to significantly improved performance for both amplitude and time-delay estimation. The method is also extended to cope with Doppler frequency offsets. In particular, simultaneous paths with different Doppler offsets can be estimated. Cramér-Rao lower bounds (CRLBs) are derived and presented together with simulation results. [ABSTRACT FROM AUTHOR]

Estimating the number of sources impinging on an array of sensors is a well-known and well-investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is known to be a consistent estimator, robust against deviations from the Gaussian assumption, and nonrobust against deviations from the point source and/or temporally or spatially white additive noise assumptions. Over the years, several alternative estimation algorithms have been proposed and tested. Usually, these algorithms are shown, using computer simulations, to have improved performance over the MDL estimator and to be robust against deviations from the assumed spatial model. Nevertheless, these robust algorithms have high computational complexity, requiring several multidimensional searches. In this paper, which is motivated by real-life problems, a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken. An MDL-type estimator that is robust against deviation from assumption of equal noise level across the array is studied. The consistency of this estimator, even when deviations from the equal noise level assumption occur, is proven. A novel low-complexity implementation method avoiding the need for multidimensional searches is presented as well, making this estimator a favorable choice for practical applications. [ABSTRACT FROM AUTHOR]

In almost all analyzes of the least mean-square (LMS) finite impulse response (FIR) adaptive algorithm, it is assumed that the length of the adaptive filter is equal to that of the unknown system impulse response. However, in many practical situations, a deficient length adaptive filter, whose length is less than that of the unknown system, is employed, and analysis results for the sufficient length LMS algorithm are not necessarily applicable to the deficient length case. Therefore, there is an essential need to accurately quantify the behavior of the LMS algorithm for realistic situations where the length of the adaptive filter is deficient. In this paper, we present a performance analysis for the deficient length LMS adaptive algorithm for correlated Gaussian input data and using the common independence assumption. Exact expressions that completely characterize the transient and steady-state means square performances of the algorithm are developed, which lead to new insights into the statistical behavior of the deficient length LMS algorithm. Simulation experiments illustrate the accuracy of the theoretical results in predicting the convergence behavior of the algorithm. [ABSTRACT FROM AUTHOR]