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

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

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