Fundamentals, Techniques and Algorithms for Processing Multichannel Broadband Data

Lead Research Organisation: University of Strathclyde
Department Name: Electronic and Electrical Engineering

Abstract

In many information technology problems data that is drawn from several sensors is generally collected in a two-dimensional array or 'matrix'. Linear algebraic techniques for the factorisation or decomposition of such a matrix, in particular the eigenvalue (EVD) and singular value decompositions (SVD), form a classic set of tools that enable optimum solutions (usually in the least squares sense), but assume that the data is narrowband i.e. a tone. However in most applications, data extends over a bandwidth of one or more octaves, such as found for wireless, wireline and underwater communications; audio involving multiple microphones or stereo/3d-sound fields; sonar; or multi-sensor biomedical problems. In these cases, the data must be considered broadband, and the EVD and SVD are suboptimal at best.
Over the past decade, polynomial matrix methods have emerged as an elegant way to formulate and solve such broadband multi-sensor problems, but there is a lack of theoretical foundation. Moreover, though the general approach has proven itself capable of providing a step change for some applications, algorithms are often computationally very demanding. Based on recent findings and discussions between the engineering and mathematics communities, this project aims tol (i) explore theoretical foundations of the existence and uniqueness of such decompositions, (ii) derive iterative algorithms based on a very different and hopefully vastly cost-reduced approach, and (iii) demonstrate how these results can solve an elusive problem in separating a mixture of sources blindly, i.e. without explicit knowledge of the sources, with an application for enhancing the performance of hearing aids.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R512205/1 01/10/2017 30/09/2021
2092479 Studentship EP/R512205/1 01/10/2017 30/09/2021 Connor Delaosa
 
Description Through extension of the previous work done in the field of broadband array signal processing, work in to how we can successfully estimate a 'space-time covariance matrix' has been done. From our first publication we can determine the bounds at which eigenvalues and eigenvectors (extracted from our space-time cov. matrix) can be changed/perturbed whilst estimated from a finite amount of data. Following from this, we can keep on this theme to extend the work in to determining meaningful statistics for these estimates and using these statistics for further applications in this field.
Exploitation Route The outcomes of the funding can be taken forward by others by applying the theory given in the papers as well as the ideas given to develop an understanding in to how practical system might suffer from estimation from finite data and whether or not their results are accurate enough.
Sectors Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Education,Healthcare

URL https://pureportal.strath.ac.uk/en/persons/connor-delaosa/publications/