Space Time MUSIC: Consistent Signal Subspace Estimation for Wideband Sensor Arrays

Abstract

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 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.

A Review of Closed-Form Cramér-Rao Bounds for DOA Estimation in the Presence of Gaussian Noise Under a Unified Framework

“…which is a sufficient statistic for the wideband Gaussian problem [78]. Note that the spectral leakage inherent in the DFT might break the consistency of the established frequency bin model [57], so that the wideband CRB derived here is an approximation to the truth, but is of practical value since most algorithms regardR φ as the actual measured data [78].…”

“…Different from the narrowband scenario, for wideband signals, the phase difference between sensor pairs depends on not only the DOAs but also the signal frequencies. Mathematically, the array sampling process for wideband signals involves matrix convolution instead of direct multiplication [57]. In an effort to deal with this problem, the observation interval can be divided into nonoverlapping subintervals and then transformed into the frequency domain via the discrete Fourier transform (DFT) or a filter bank [58].…”

A Fourth-Order Cumulants Orthonormal Propagator Rooting Method Based on Toeplitz Approximation

“…Direction-of-arrival estimation based on antenna array is one of the important directions of research hotspot in array signal processing, which has wide prospects of application in military and civil fields such as wireless communications, radar, passive sonar, biomedicine and seismic exploration [1][2][3][4].…”

Atomic Norm-Based DOA Estimation with Dual-Polarized Radar

“…The most important super-resolution methods are subspace-based methods, including the multiple signal classification (MUSIC) method [10] and the estimating signal parameters via rotational invariance techniques (ESPRIT) method [11]. Since then, extension algorithms based on the MUSIC and ESPRIT methods have been proposed in more recent papers, such as the Root-MUSIC method [12], space-time MUSIC method [13], G-MUSIC method [14], higher-order ESPRIT and virtual ESPRIT [15], etc. In the subspace-based methods, the signal and noise subspaces are estimated from the covariance of received signals, so multiple measurements are needed to obtain the corresponding covariance matrix.…”