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Interlacing of Non-Uniform Doppler Waveforms and Metric Space Geometry of Negative Curvature

Interlacing of Non-Uniform Doppler Waveforms and Metric Space Geometry of Negative Curvature

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In this chapter an advanced Doppler processing technique has been proposed, based on covariance matrix CFAR, that is itself based on an innovative mathematical tool (information geometry and geometry of Bruhat-Tits metric space) that provides explicit equations for computing: the robust distance between covariance matrices, the geometric mean of two covariance matrices, and Karcher's barycenter of N covariance matrices.Use of metric space and negative curvature space in place of normed and flat space to manipulate Hermitian positive definite covariance matrices could drastically improve the performance of classical signal processing algorithms, and improve the robustness of Doppler processing for sparse Doppler waveforms (based on regular non-uniform Doppler bursts).

Inspec keywords: covariance matrices; radar signal processing; Hermitian matrices; Doppler radar; waveform analysis; sparse matrices

Other keywords: nonuniform Doppler waveforms interlacing; metric space; relax time; sparse Doppler waveforms; Karcher barycenter; multifunction radar time budget; Doppler processing robustness; Bruhat-Tits metric space; covariance matrix; classical signal processing algorithms; innovative mathematical tool; regular nonuniform waveforms; CFAR; metric space geometry; negative curvature space; Hermitian positive definite covariance; geometric mean

Subjects: Radar equipment, systems and applications; Signal processing and detection; Algebra; Mathematical analysis

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