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

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

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

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

Measuring Smoothness of Trigonometric Interpolation Through Incomplete Sample Points

In this paper we present a metric to assess the smoothness of a trigonometric interpolation through an in-complete set of sample points. We measure smoothness as the power of a particular derivative of a 2π-periodic Dirichlet interpolant through some sample points. We show that we do not need to explicitly complete the sample set or perform the interpolation, but can simply work with the available sample points, under the assumption that any missing points are chosen to minimise the metric, and present a simple and robust approach to the computation of this metric. We assess the accuracy and computational complexity of this approach, and compare it to benchmarks.This work was in parts supported by the Engineering and Physical Sciences Research Council (EPSRC) Grant number EP/S000631/1 and the MOD University Defence Research Collaboration in Signal Processing

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Finite element solution of solidification process in 2-D Cartesian and axisymmetric geometries is investigated. The use of finite element may result in spurious increase of temperature in the field and the selection of the mushy zone range when used as a numerical tool along with the selection of the mesh size results in large errors in the predicted solidification time. The approach works best for problems where the mushy zone range is finite and the thermal conductivities of both phases are high.M.S. - Master of Scienc

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