International audienceThis paper introduces the optimal widely linear (WL) minimum variance distorsionless response (MVDR) beamformer for the reception of an unknown signal of interest (SOI) corrupted by potentially second order (SO) noncircular background noise and interference. The SOI, whose waveform is unknown, is assumed to be SO noncircular with arbitrary noncircular properties. In the steady state and for SO noncircular SOI and/or interference, this new WL beamformer, that is derived from an original orthogonal decomposition, is shown to always improve the performance of both the well-known Capon's beamformer and a WL MVDR beamformer introduced recently in the literature. This optimal WL MVDR beamformer is first introduced and some of its performance are analyzed. Then, several adaptive implementations of this optimal WL beamformer are presente

This paper addresses subspace-based direction of arrival (DOA) estimation and its purpose is to complement previously available theoretical results generally obtained for specific algorithms. We focus on asymptotically (in the number of measurements) minimum variance (AMV) estimators based on estimates of orthogonal projectors obtained from singular value decompositions of sample covariance matrices in the general context of noncircular complex signals. After extending the standard AMV bound to statistics whose first covariance matrix of its asymptotic distribution is singular and deriving explicit expressions of this first covariance matrix associated with several projection-based statistics, we give closed-form expressions of AMV bounds based on estimates of different orthogonal projectors. This enable us to prove that these AMV bounds attain the stochastic Cramer-Rao bound (CRB) in the case of circular or noncircular Gaussian signals. r

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Abstract-Active research in blind single input multiple output (SIMO) channel identification has led to a variety of second-order statistics-based algorithms, particularly the subspace (SS) and the linear prediction (LP) approaches. The SS algorithm shows good performance when the channel output is corrupted by noise and available for a finite time duration. However, its performance is subject to exact knowledge of the channel order, which is not guaranteed by current order detection techniques. On the other hand, the linear prediction algorithm is sensitive to observation noise, whereas its robustness to channel order overestimation is not always verified when the channel statistics are estimated. We propose a new second-order statistics-based blind channel identification algorithm that is truly robust to channel order overestimation, i.e., it is able to accurately estimate the channel impulse response from a finite number of noisy channel measurements when the assumed order is arbitrarily greater than the exact channel order. Another interesting feature is that the identification performance can be enhanced by increasing a certain smoothing factor. Moreover, the proposed algorithm proves to clearly outperform the LP algorithm. These facts are justified theoretically and verified through simulations.Index Terms-Blind channel identification and equalization, order overestimation, second-order statistics algorithms.