#### Technical Report USC-SIPI-309

“Cumulants and Subspace Techniques for Array Processing”

by Egemen Gönen

May 1997

Subspace-based techniques are developed for direction finding (DF), parameter estimation and blind separation of narrowband signals using antenna arrays. The conventional approach to solving these problems is to use the first- and second-order statistics of the measurements. In this work, the emphasis is on the advantages of using higher-order statistics (cumulants) in addition to first- and second order statistics. The techniques developed in this work rely on separating the signal and noise subspaces of a cumulant matrix which is formed in a different way for each of the above problems. The key idea is to realize that for each problem, a set of cumulants exists which yields a solution that is less-constrained and more practical than a comparable second-order statistics-based method.

First, a comprehensive survey of existing subspace-based (or, high resolution) DF techniques, including second- and higher-order statistics-based ones, is presented. Second, we address the problem of DF in coherent (or, completely correlated) signal environments which arise when multipath propagation and/or smart jammers are present. In this case, most subspace-based approaches fail. We develop a cumulant-based DF algorithm which works for coherent as well as independent signals. It is applicable to a larger set of arrays than the spatial smoothing method which was proposed as a cure to subspace-based approaches; and, more signals than sensors can be detected. Third, using the same approach, a blind beamformer is developed for multipath signals for which existing subspace-based beamformers tend to cancel the desired signal. Our beamformer combines coherent multipaths of the desired signal. It is applicable to arbitrary array configurations. Fourth, a beamspace VESPA is developed; it works with arbitrary beamspace transformations as opposed to its covariance-based counterpart, beamspace-ESPRIT. Using the beamspace approach, we also develop an iterative VESPA which works when the source cumulants and powers are highly different in which case VESPA fails for short data lengths. Last, an algorithm is developed for joint DF and polarization parameter estimation with uncalibrated arrays that are minimally-constrained in geometry. Conventional methods for this problem assume that the array manifold is obtained through array calibration.

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