Xijing Guo

A CANDECOMP/PARAFAC Perspective on Uniqueness of DOA Estimation Using a Vector Sensor Array

We address the uniqueness problem in estimating the directions-of-arrival (DOAs) of multiple narrowband and fully polarized signals impinging on a passive sensor array composed of identical vector sensors. The data recorded on such an array present the so-called “multiple invariances,” which can be linked to the CANDECOMP/PARAFAC (CP) model. CP refers to a family of low-rank decompositions of three-way or higher way (mutidimensional) data arrays, where each dimension is termed as a “mode.” A sufficient condition is derived for uniqueness of the CP decomposition of a three-way (three mode) array in the particular case where one of the three loading matrices, each associated to one mode, involved in the decomposition has full column rank. Based on this, upper bounds on the maximal number of identifiable DOAs are deduced for the two typical cases, i.e., the general case of uncorrelated or partially correlated sources and the case where the sources are coherent.

Uni-mode and Partial Uniqueness Conditions for CANDECOMP/PARAFAC of Three-Way Arrays with Linearly Dependent Loadings

In this paper, three sufficient conditions are derived for the three-way CANDECOMP/PARAFAC (CP) model, which ensure uniqueness in one of the three modes (“uni-mode-uniqueness”). Based on these conditions, a partial uniqueness condition is proposed which allows collinear loadings in only one mode. We prove that if there is uniqueness in one mode, then the initial CP model can be uniquely decomposed in a sum of lower-rank tensors for which identifiability can be independently assessed. This condition is simpler and easier to check than other similar conditions existing in the specialized literature. These theoretical results are illustrated by numerical examples.

Approximate joint diagonalization by nonorthogonal nonparametric Jacobi transformations

We propose a novel algorithm for the problem of nonorthogonal joint diagonalization of a set of structured matrices based on successive Jacobi-like transformations. Though the elementary transformation matrices we use are not optimal in the sense of the global criterion, they are ensured to be nonsingular, and can be computed in closed form. The algorithm is efficient in virtue of its low computational complexity and fast convergence. The performance of the new algorithm is compared in simulations to the similar algorithms of the recent literature.

Identifiability of the parafac model for polarized source mixture on a vector sensor array

By means of the parallel factor (PARAFAC) decomposition, we present a novel method working on a vector-sensor array for blind separation of polarized sources in virtue of their distinct spatial and temporal signatures. Identifiability is studied, and explicit constraints on the sources are derived to ensure the data model identifiable. We show, by numerical simulations, that the estimation performance can approach that of non-blind estimation by optimally designing the source polarizations.

Low-frequency beamforming for a miniaturized aperture three-by-three uniform rectangular array of acoustic vector sensors.

This paper proposes a mode domain beamforming method for a 3 × 3 uniform rectangular array of two-dimensional (2D) acoustic vector sensors with inter-sensor spacing much smaller than the wavelengths in the working frequency band. The acoustic modes are extracted from the particle velocity observations in light of the source-sink pictures of the Taylors series multipoles [Wikswo and Swinney, J. Appl. Phys. 56(11), 3039-3049 (1984)]. Then, similar to other mode domain methods, the modes are synthesized to obtain the desired beam pattern. The proposed method is limited to the cases where five is the maximum order of the modes for pattern synthesis, meaning that the directivity index in the 2D isotropic noise case can reach up to 10.4 dB. The proposed method has been validated by field experiments.

The effect of polarization separation on the performance of Candecomp/Parafac-based vector sensor array processing

Abstract In this paper we generalize the polarization separation measure introduced by Compton (1981) [2] for collocated sources, to the case of two sources with distinct DOAs recorded on a vector sensor array. We give a geometrical interpretation of this new measure and show that this polarization separation becomes essential for source estimation accuracy when the angular separation is insufficient.

An upper bound for the directivity index of superdirective acoustic vector sensor arrays

Approximate analytical expressions of the white noise gain (WNG) for two superdirective acoustic vector sensor arrays are provided, which disclose the strong dependence of the tradeoff between the WNG and the directivity index (DI) on the highest order of the modes for the pattern synthesis. The considered arrays are a uniform linear array and a uniform circular array. A condition on the WNG that ensures a high array gain in the two-dimensional homogeneous and isotropic noise field is deduced. Using this condition, an upper bound on the highest order of the modes for the pattern synthesis can be derived, and hence the maximum DI can be determined. The presented results are not strictly limited to the two array geometries considered herein, and can be extended to other superdirective acoustic array designs.

Vector Sensor Array Processing for Polarized Sources Using a Quadrilinear Representation of the Data Covariance

Array processing techniques aim principally at estimating source Directions Of Arrivals (DOA’s) based on the observations recorded on a sensor array. The vector-sensor technology allows the use of polarization as an additional parameter, leading to vector sensor array processing. In electromagnetics, a vector sensor is composed of six spatially collocated but orthogonally polarized antennas, measuring all six components (three for the electric and three for the magnetic fields) of the incident wave. The benefits of considering source polarization in signal estimation were illustrated in Burgess and Van Veen (1994); Le Bihan et al. (2007); Li (1993); Miron et al. (2006); Nehorai and Paldi (1994); Rahamim et al. (2003); Weiss and Friedlander (1993a); Wong and Zoltowski (1997) for diverse signal processing problems. Most of these algorithms are based on bilinear polarized source mixture models which suffers from identifiability problems. This means that, without any additional constraint, the steering vectors of the sources (and implicitly their DOA’s) cannot be uniquely determined by matrix factorization. The identifiability issues involved in vector sensor applications are investigated in Ho et al. (1995); Hochwald and Nehorai (1996); Tan et al. (1996a;b).

Second-order cone programming with probabilistic regularization for robust adaptive beamforming

Probabilistic regularization (PR) is introduced to make superdirective array beamforming robust against sensor characteristic mismatches. The objective is to enlarge the directivity while ensuring robustness with high probability. The PR problem is solved via the second-order cone programming where the regularization parameter is chosen through a statistical analysis of the system perturbations, based on Monte Carlo simulations. Experiments are carried out on a miniaturized 3 × 3 uniform rectangular array without calibration. The results show that for this particular array, the PR method is robust to sensor mismatches and achieves a higher level of directivity compared with other robust adaptive beamforming approaches.