Mathematics Lecture: "A NOVEL TECHNIQUE FOR BROADBAND SINGULAR VALUE DECOMPOSITION"
Tuesday, March 23, 2003, Louis R. Weber Building, Room 202 at 4:00pm
Abstract:
The singular value decomposition (SVD) is a very important tool for narrowband adaptive sensor array processing. The SVD decorrelates the signals received from an array of sensors by applying a unitary matrix of complex scalars which serve to modify the signals in phase and amplitude. In broadband applications, or a situation where narrowband signals have been convolutively mixed, the received signals cannot be represented in terms of phase and amplitude. Instantaneous decorrelation using a unitary matrix is no longer sufficient to separate them. It is necessary to decorrelate the signals over a suitably chosen range of relative time delays. This process, referred to as strong decorrelation, requires a matrix of suitably chosen filters. Representing each filter (assumed to have finite impulse response) in terms of its z-transform, this takes the form of a polynomial matrix. The SVD may be generalized to broadband adaptive sensor arrays by requiring the polynomial matrix to be paraunitary so that it preserves the total energy at every frequency. In this talk, I will describe a novel technique for computing the required paraunitary matrix and show how the resulting broadband SVD algorithm can be used to identify the signal subspace for broadband adaptive beamforming.