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12 pages; International audience; The classical higher order MUSIC-like methods based on a simultaneous search for all Directions Of Arrival (DOA's) show i) a capacity for processing underdetermined mixtures of sources, ii) a high robustness with respect to both a Gaussian noise with unknown spatial coherence and modeling errors, and iii) a better resolution than algorithms based on second order statistics. However, these methods have some limits: for a finite number of samples, they show poor performance for sources exhibiting quasi-collinear DOA's. In order to overcome this drawback, two new sequential MUSIC-like algorithms are proposed in this paper, namely the 2q-D-MUSIC and the 2q-RAP-MUSIC (q>1) algorithms. These methods are based on a sequential optimization of proposed generalized noise and signal 2q-MUSIC metrics, respectively. That allows us to learn and then to take into account the level of correlation between sources. A comparative study, both in terms of performance and numerical complexity, is performed showing the interest of the proposed techniques when some sources are angularly close. Eventually, an upper bound of the maximum number of sources which can be processed by the 2q-MUSIC-like techniques is given for all q. This improves recent work on the 2q-th order virtual arrays.

12 pages , in one part by the ANR DECOTES Contract (), in second part by the mv-EMD Contract() and in third part by; International audience; A new family of cumulant-based algorithms is proposed in order to blindly identify potentially underdetermined mixtures of statistically independent sources. These algorithms perform a joint canonical decomposition (CAND) of several higher order cumulants through a CAND of a three-way array with special symmetries. These techniques are studied in terms of identifiability, performance and numerical complexity. From a signal processing viewpoint, the proposed methods are shown i) to have a better estimation resolution and ii) to be able to process more sources than the other classical cumulant-based techniques. Second, from a numerical analysis viewpoint, we deal with the convergence speed of several procedures for three-way array decomposition, such as the ACDC scheme. We also show how to accelerate the iterative CAND algorithms by using differently the symmetries of the considered three-way array. Next, from a multilinear algebra viewpoint the paper aims at giving some insights on the uniqueness of a joint CAND of several Hermitian multiway arrays compared to the CAND of only one array. This allows us, as a result, to extend the concept of virtual array (VA) to the case of combination of several VAs.