A novel technique for space-time singular value decomposition
John G. McWhirter · 2004
Summary form only given. Singular value decomposition (SVD) is a very important tool for narrowband sensor array signal processing. SVD decorrelates the signals received from an array of sensors by applying a unitary matrix of complex scalars which modify the signals in phase and amplitude. In the case of a broadband sensor array, the received signals cannot be described in terms of phase and amplitude, so instantaneous decorrelation using a unitary matrix is no longer sufficient to separate them. In the broadband case, it is necessary to decorrelate the signals over a suitable range of relative time delays. This process requires a matrix of suitably chosen filters which may be represented mathematically as a polynomial matrix. The SVD can be generalised to broadband sensor arrays by requiring the polynomial matrix to be paraunitary so that it preserves the total energy at every frequency. A novel technique can be used to compute the required paraunitary matrix and the resulting broadband SVD algorithm can be used to identify the signal subspace for broadband adaptive beamforming. It has potential application in many other areas including filterbanks for optimal data compaction, space-time adaptive processing and space-time coding for MIMO communication channels.