Bayesian Signal Subspace Estimation with Compound Gaussian Sources

International audienceIn this paper, we consider the problem of low dimensional signal subspace estimation in a Bayesian con- text. We focus on compound Gaussian signals embedded in white Gaussian noise, which is a realistic modeling for various array processing applications. Following the Bayesian framework, we derive two algorithms to compute the maximum a posteriori (MAP) estimator and the so-called minimum mean square distance (MMSD) estimator, which minimizes the average natural distance between the true range space of interest and its estimate. Such approaches have shown their interests for signal subspace esti- mation in the small sample support and/or low signal to noise ratio contexts. As a byproduct, we also introduce a generalized version of the complex Bingham Langevin distribution in order to model the prior on the subspace orthonormal basis. Finally, numerical simulations illustrate the performance of the proposed algorithms

Three-Way Tensor Decompositions: A Generalized Minimum Noise Subspace Based Approach

Tensor decomposition has recently become a popular method of multi-dimensional data analysis in various applications. The main interest in tensor decomposition is for dimensionality reduction, approximation or subspace purposes. However, the emergence of “big data” now gives rise to increased computational complexity for performing tensor decomposition. In this paper, motivated by the advantages of the generalized minimum noise subspace (GMNS) method, recently proposed for array processing, we proposed two algorithms for principal subspace analysis (PSA) and two algorithms for tensor decomposition using parallel factor analysis (PARAFAC) and higher-order singular value decomposition (HOSVD). The proposed decomposition algorithms can preserve several desired properties of PARAFAC and HOSVD while substantially reducing the computational complexity. Performance comparisons of PSA and tensor decomposition of our proposed algorithms against the state-of-the-art ones were studied via numerical experiments. Experimental results indicated that the proposed algorithms are of practical values

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels

In this paper, we establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive multiple-input multiple-output MIMO systems employing single-carrier (SC) modulation in time division duplex (TDD) mode by exploiting the joint angle-delay domain channel sparsity in millimeter (mm) wave frequencies. First, based on a generic subspace projection taking the joint angle-delay power profile and user-grouping into account, the reduced rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived for spatially correlated wideband MIMO channels. Second, the statistical pre-beamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction problem and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. Finally, a spatio-temporal domain correlator type reduced rank channel estimator, as an approximation of the RR-MMSE estimate, is obtained by carrying out least square (LS) estimation in a proper reduced dimensional beamspace. It is observed that the proposed techniques show remarkable robustness to the pilot interference (or contamination) with a significant reduction in pilot overhead