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

Distributed closed-loop EO-STBC for a time-varying relay channel based on kalman tracking

This paper considers distributed closed-loop extended orthogonal space-time block coding (EO-STBC) for amplify-forward relaying over time-varying channels. In between periodically injected pilot symbols for training, the smooth variation of the fading channel coefficients is exploited by Kalman tracking. We show in this paper that the joint variation of both relay channels still motivates the use of a higher-order auto-regressive model for the a priori prediction step within a decision-feedback system, compared to a first-order standard Kalman model. Simulations results compare these two case and highlight the benefits of the proposed higher-order Kalman filter, which offer joint decoding and tracking

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

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

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

Broadband angle of arrival estimation using polynomial matrix decompositions

This thesis is concerned with the problem of broadband angle of arrival (AoA) estimation for sensor arrays. There is a rich theory of narrowband solutions to the AoA problem, which typically involves the covariance matrix of the received data and matrix factorisations such as the eigenvalue decomposition (EVD) to reach optimality in various senses. For broadband arrays, such as found in sonar, acoustics or other applications where signals do not fulfil the narrowband assumption, working with phase shifts between different signals - as sufficient in the narrowband case - does not suffice and explicit lags need to be taken into account. The required space-time covariance matrix of the data now has a lag dimension, and classical solutions such as those based on the EVD are no longer directly applicable. There are a number of existing broadband AoA techniques, which are reviewed in this thesis. These include independent frequency bin processors, where the broadband problem is split into several narrowband ones, thus loosing coherence across bins. Coherent signal subspace methods effectively apply a pre-steering by focussing matrices in the assumed directions of existing sources, and sum the narrowband covariance matrices coherently. Subsequently, classical narrowband methods can be applied. A recent auto-focussing approach dispenses with the requirement of knowing the approximate direction of sources, and calculates the focussing matrices on a data-dependent fashion. A recent parametric covariance matrix approach for broadband AoA estimation is also reviewed, and it is shown that this can only detect a single - the strongest - source. Based on a polynomial EVD (PEVD) factorisation of polynomial matrices such as created by a space-time covariance matrix emerging from a broadband problem, this thesis proposes an extension of the powerful high-resolution but narrowband multiple signal classification (MUSIC) algorithm. While narrowband MUSIC is based on an EVD to identify signal and noise subspaces, the PEVD can extract polynomial subspaces. This also requires the definition of broadband steering vectors, which are used in the proposed polynomial MUSIC (P-MUSIC) method to scan the noise-only subspace. Two different P-MUSIC versions are proposed here: a spatio-spectral P-MUSIC (SSP-MUSIC) is capable to resolve sources with respect to the AoA and frequency range, and a spatial P-MUSIC (SP-MUSIC) extracts the AoA alone. Broadband steering vectors are proposed as polynomial vectors containing fractional delay filters. For the implementation, a number of methods are reviewed and compared, including windowed sinc functions and Farrow structures. All these techniques show degraded performance as the frequency approaches half of the sampling rate. Therefore, this dissertation also proposes a highly accurate fractional delay filter implementation based on undecimated filter banks, whereby the subband signals are modulated to lower frequency ranges, where individual fractional delay filters can operate with high accuracy. For the implementation of P-MUSIC, we demonstrate that the broadband steering vector accuracy is important. We also apply different iterative PEVD algorithms belonging to the families of second order sequential best rotation (SBR2) and sequential matrix diagonalisation (SMD) algorithms. We demonstrate the SMD familly, which offers a better diagonalisation of the space-time covariance matrix, is also capable of providing a more accurate subspace decomposition than SBR2. This is evidenced by a higher resolution that can be achieved if SP-MUSIC and SSP-MUSIC are based on SMD rather than SBR2. The thesis concludes with an extensive set of simulations for both toy problems and realistic scenarios. This is to explain and highlight the operation of the P-MUSIC algorithms, but also compares their performance to other state-of-the-art broadband AoA methods. For the closest competitor, the auto-focussing approach, an analysis in a polynomial matrix framework is provided, which highlights similarities and differences to P-MUSIC. The simulations indicate that PMUSIC is a powerful and robust extension of MUSIC to the broadband case.This thesis is concerned with the problem of broadband angle of arrival (AoA) estimation for sensor arrays. There is a rich theory of narrowband solutions to the AoA problem, which typically involves the covariance matrix of the received data and matrix factorisations such as the eigenvalue decomposition (EVD) to reach optimality in various senses. For broadband arrays, such as found in sonar, acoustics or other applications where signals do not fulfil the narrowband assumption, working with phase shifts between different signals - as sufficient in the narrowband case - does not suffice and explicit lags need to be taken into account. The required space-time covariance matrix of the data now has a lag dimension, and classical solutions such as those based on the EVD are no longer directly applicable. There are a number of existing broadband AoA techniques, which are reviewed in this thesis. These include independent frequency bin processors, where the broadband problem is split into several narrowband ones, thus loosing coherence across bins. Coherent signal subspace methods effectively apply a pre-steering by focussing matrices in the assumed directions of existing sources, and sum the narrowband covariance matrices coherently. Subsequently, classical narrowband methods can be applied. A recent auto-focussing approach dispenses with the requirement of knowing the approximate direction of sources, and calculates the focussing matrices on a data-dependent fashion. A recent parametric covariance matrix approach for broadband AoA estimation is also reviewed, and it is shown that this can only detect a single - the strongest - source. Based on a polynomial EVD (PEVD) factorisation of polynomial matrices such as created by a space-time covariance matrix emerging from a broadband problem, this thesis proposes an extension of the powerful high-resolution but narrowband multiple signal classification (MUSIC) algorithm. While narrowband MUSIC is based on an EVD to identify signal and noise subspaces, the PEVD can extract polynomial subspaces. This also requires the definition of broadband steering vectors, which are used in the proposed polynomial MUSIC (P-MUSIC) method to scan the noise-only subspace. Two different P-MUSIC versions are proposed here: a spatio-spectral P-MUSIC (SSP-MUSIC) is capable to resolve sources with respect to the AoA and frequency range, and a spatial P-MUSIC (SP-MUSIC) extracts the AoA alone. Broadband steering vectors are proposed as polynomial vectors containing fractional delay filters. For the implementation, a number of methods are reviewed and compared, including windowed sinc functions and Farrow structures. All these techniques show degraded performance as the frequency approaches half of the sampling rate. Therefore, this dissertation also proposes a highly accurate fractional delay filter implementation based on undecimated filter banks, whereby the subband signals are modulated to lower frequency ranges, where individual fractional delay filters can operate with high accuracy. For the implementation of P-MUSIC, we demonstrate that the broadband steering vector accuracy is important. We also apply different iterative PEVD algorithms belonging to the families of second order sequential best rotation (SBR2) and sequential matrix diagonalisation (SMD) algorithms. We demonstrate the SMD familly, which offers a better diagonalisation of the space-time covariance matrix, is also capable of providing a more accurate subspace decomposition than SBR2. This is evidenced by a higher resolution that can be achieved if SP-MUSIC and SSP-MUSIC are based on SMD rather than SBR2. The thesis concludes with an extensive set of simulations for both toy problems and realistic scenarios. This is to explain and highlight the operation of the P-MUSIC algorithms, but also compares their performance to other state-of-the-art broadband AoA methods. For the closest competitor, the auto-focussing approach, an analysis in a polynomial matrix framework is provided, which highlights similarities and differences to P-MUSIC. The simulations indicate that PMUSIC is a powerful and robust extension of MUSIC to the broadband case

An extension of the MUSIC algorithm to broadband scenarios using polynomial eigenvalue decomposition

The multiple signal classification (MUSIC) algorithm for direction of arrival estimation is defined for narrowband scenarios. In this paper, a generalisation to the broadband case is presented, based on a description of broadband systems by polynomial space-time covariance matrices. A polynomial eigenvalue decomposition is used to determine the noiseonly subspace of the this matrix, which can be scanned by appropriately defined broadband steering vectors. Two broadband MUSIC algorithm versions are presented, which resolve either angle of arrival alone or in combination with the frequency range over which sources are active. Initial results for these approaches are presented and demonstrate a significant benefit over independent frequency bin processing using narrowband MUSIC

Angle of Arrival Estimation for Broadband Signals: A Comparison

This paper reviews and compares three different linear algebraic signal subspace techniques for angle of arrival estimation. These include a polynomial matrix approach to multiple signal classification (MUSIC), a parameterised spatial covariance matrix approach, and an auto-focussing based version of coherent signal subspace estimation applied to MUSIC. These approaches are expressed in the framework of polynomial space-time covariance matrices and their polynomial eigenvalue decomposition, thus highlighting their commonalities and differences. Simulation results comparing the accuracy of these broadband angle of arrival estimation methods are presented