Comparative study for broadband direction of arrival estimation techniques

This paper reviews and compares three different linear algebraic signal subspace techniques for broadband direction of arrival estimation --- (i) the coherent signal subspace approach, (ii) eigenanalysis of the parameterised spatial correlation matrix, and (iii) a polynomial version of the multiple signal classification algorithm. Simulation results comparing the accuracy of these methods are presented

Broadband angle of arrival estimation methods in a polynomial matrix decomposition framework

A large family of broadband angle of arrival estimation algorithms are based on the coherent signal subspace (CSS) method, whereby focussing matrices appropriately align covariance matrices across narrowband frequency bins. In this paper, we analyse an auto-focussing approach in the framework of polynomial covariance matrix decompositions, leading to comparisons to two recently proposed polynomial multiple signal classification (MUSIC) algorithms. The analysis is complemented with numerical simulations

Impact of fast-converging PEVD algorithms on broadband AoA estimation

Polynomial matrix eigenvalue decomposition (PEVD) algorithms have been shown to enable a solution to the broadband angle of arrival (AoA) estimation problem. A parahermitian cross-spectral density (CSD) matrix can be generated from samples gathered by multiple array elements. The application of the PEVD to this CSD matrix leads to a paraunitary matrix which can be used within the spatio-spectral polynomial multiple signal classification (SSP-MUSIC) AoA estimation algorithm. Here, we demonstrate that the recent low-complexity divide-and-conquer sequential matrix diagonalisation (DC-SMD) algorithm, when paired with SSP-MUSIC, is able to provide superior AoA estimation versus traditional PEVD methods for the same algorithm execution time. We also provide results that quantify the performance trade-offs that DC-SMD offers for various algorithm parameters, and show that algorithm convergence speed can be increased at the expense of increased decomposition error and poorer AoA estimation performance

Polynomial subspace decomposition for broadband angle of arrival estimation

In this paper we study the impact of polynomial or broadband subspace decompositions on any subsequent processing, which here uses the example of a broadband angle of arrival estimation technique using a recently proposed polynomial MUSIC (P-MUSIC) algorithm. The subspace decompositions are performed by iterative polynomial EVDs, which differ in their approximations to diagonalise and spectrally majorise s apce-time covariance matrix.We here show that a better diagonalisation has a significant impact on the accuracy of defining broadband signal and noise subspaces, demonstrated by a much higher accuracy of the P-MUSIC spectrum

Relevance of polynomial matrix decompositions to broadband blind signal separation

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polynomial matrix terminology such as parahermitian and paraunitary matrices, strong decorrelation and spectral majorization, the PEVD and its theoretical foundations will be briefly outlined. The paper then focuses on the applicability of the PEVD and broadband subspace techniques — enabled by the diagonalization and spectral majorization capabilities of PEVD algorithms—to define broadband BSS solutions that generalise well-known narrowband techniques based on the EVD. This is achieved through the analysis of new results from three exemplar broadband BSS applications — underwater acoustics, radar clutter suppression, and domain-weighted broadband beamforming — and their comparison with classical broadband methods

Enhancing polynomial MUSIC algorithm for coherent broadband sources through spatial smoothing

Direction of arrival algorithms which exploit the eigenstructure of the spatial covariance matrix (such as MUSIC) encounter difficulties in the presence of strongly correlated sources. Since the broadband polynomial MUSIC is an extension of the narrowband version, it is unsurprising that the same issues arise. In this paper, we extend the spatial smoothing technique to broadband scenarios via spatially averaging polynomial spacetime covariance matrices. This is shown to restore the rank of the polynomial source covariance matrix. In the application of the polynomial MUSIC algorithm, the spatially smoothed spacetime covariance matrix greatly enhances the direction of arrival estimate in the presence of strongly correlated sources. Simulation results are described shows the performance improvement gained using the new approach compared to the conventional non-smoothed method

Filter bank based fractional delay filter implementation for widely accurate broadband steering vectors

Applications such as broadband angle of arrival estimation require the implementation of accurate broadband steering vectors, which generally rely on fractional delay filter designs. These designs commonly exhibit a rapidly decreasing performance as the Nyquist rate is approached. To overcome this, we propose a filter bank based approach, where standard fractional delay filters operate on a series of frequency-shifted oversampled subband signals, such that they appear in the filter's lowpass region. Simulations demonstrate the appeal of this approach

Analysing the performance of divide-and-conquer sequential matrix diagonalisation for large broadband sensor arrays

A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is an extension of the ordinary EVD to polynomial matrices and will diagonalise a parahermitian matrix using paraunitary operations. Inspired by recent work towards a low complexity divide-and-conquer PEVD algorithm, this paper analyses the performance of this algorithm - named divide-and-conquer sequential matrix diagonalisation (DC-SMD) - for applications involving broadband sensor arrays of various dimensionalities. We demonstrate that by using the DC-SMD algorithm instead of a traditional alternative, PEVD complexity and execution time can be significantly reduced. This reduction is shown to be especially impactful for broadband multichannel problems involving large arrays

Shortening of paraunitary matrices obtained by polynomial eigenvalue decomposition algorithms

This paper extends the analysis of the recently introduced row-shift corrected truncation method for paraunitary matrices to those produced by the state-of-the-art sequential matrix diagonalisation (SMD) family of polynomial eigenvalue decomposition (PEVD) algorithms. The row-shift corrected truncation method utilises the ambiguity in the paraunitary matrices to reduce their order. The results presented in this paper compare the effect a simple change in PEVD method can have on the performance of the paraunitary truncation. In the case of the SMD algorithm the benefits of the new approach are reduced compared to what has been seen before however there is still a reduction in both reconstruction error and paraunitary matrix order

Implementation of accurate broadband steering vectors for broadband angle of arrival estimation

Motivated by accurate broadband steering vector requirements for applications such as broadband angle of arrival estimation, we review fractional delay filter designs. A common feature across these are their rapidly decreasing performance as the Nyquist rate is approached. We propose a filter bank based approach, which operates standard fractional delay filters on a series of frequency-shifted subband signals, such that they appear in the filters’ lowpass region. We demonstrate the appeal of this approach in simulations