#### Technical Report USC-SIPI-327

“Array Signal Processing Using Higher-Order and Fractional Lower-Order Statistics”

by Tsung-Hsein Liu

December 1998

We apply higher-order statistics (HOS) and fractional lower-order statistics (FLOS) to different array signal processing scenarios. In Chapter 2, we solve the two-angle (azimuth and elevation) direction of arrival (DOA) estimation problem using fourth-order cumulants. This work extends the virtual-ESPRIT algorithm (VESPA) from one-angle (azimuth angle) to two angle DOA problems. In Chapter~3, we discuss the sensitivity of VESPA. We are only interested in how VESPA is influenced by the model errors. Our analyses are useful when the finite-sample effects are small.We follow a conventional sensitivity procedure to perform our analyses, and derive sensitivity formulas for all the model parameters and output quantities. In Chapter 4, we develop gradient-based target tracking using cumulants. The resulting subspace tracking algorithm has complexity of ${mathcal{O}}(M^2P)$, where $M$ is the number of array elements and $P$ is the number of signals. We combine the resulting subspace tracking algorithm with VESPA to track moving targets. In Chapter 5, we develop a cumulant-based preprocessing method that can be used with any data-matrix based algorithm to achieve rank and target tracking. We demonstrate the use of preprocessing with Rabideau's rank tracking algorithm for both rank and target tracking. The resulting tracking algorithm has computational complexity of ${mathcal{O}}(MP)$. In Chapter 6, we consider the scenario where the additive noise is alpha stable. We construct several classes of fractional lower-order moment (FLOM) based matrices that can be used with MUSIC to extract DOAs. We assume that the signals are circular. >From the simulation results, we conclude that the FLOM $p$ should be selected close to unity to yield best performance. In Chapter 7, we construct a class of FLOM-based matrices that can be used with ESPRIT to extract DOAs. The scenario in this chapter is very similar to that in Chapter 6, except that there are two identical subarrays available. Analyses and simulations reveal that the FLOM-based ESPRIT shares similar properties with FLOM-based MUSIC. In Chapter 8, we present our future research.

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