Blind source separation using a spatial fourth-order cumulant matrix-pencil

The research presented investigates the use of cumulants in conjunction with a spectral estimation technique of the signal subspace to perform the blind separation of statistically independent signals with low signal-to-noise ratios under a narrowband assumption. A new blind source separation (BSS) algorithm is developed that makes use of the generalized eigen analysis of a matrix pencil defined on two similar spatial fourth-order cumulant matrices. The algorithm works ín the presence of spatially and/or temporally correlated noise and, unlike most existing higher-order BSS techniques, is based on a spectral estimation technique rather than a closed loop optimization of a contrast function, for which the convergence is often problematic.; The dissertation makes several contributions to the area of blind source separation. These include: (1) Development of a robust blind source separation technique that is based on higher-order cumulant based principle component analysis that works at low signal-to-noise ratios in the presence of temporally and/or spatially correlated noise. (2) A novel definition of a spatial fourth-order cumulant matrix suited to blind source separation with non-equal gain and/or directional sensors. (3) The definition of a spatial fourth-order cumulant matrix-pencil using temporal information. (4) The concept of separation power efficiency (SPE) as a measure of the algorithm's performance. Two alternative definitions for the spatial fourth-order cumulant matrix that are found in the literature are also presented and used by the algorithm for comparison. Additionally, the research contributes the concept of wide sense equivalence between matrix-pencils to the field of matrix algebra.; The algorithm's performance is verified by computer simulation using realistic digital communications signals in white noise. Random mixing matrices are generated to ensure the algorithm's performance is independent of array geometry. The computer results are promising and show that the algorithm works well down to input signal-to-noise ratios of −6 dB, and using as few as 250 × 103 samples.