Essential characteristics of signal data can be captured by the autocovariance matrix, which, in stationary scenarios, is the Toeplitz Hermitian positive definite (HPD). In this article, several well-known Riemannian geometric structures of HPD matrix manifolds are applied to signal detection, including the affine invariant Riemannian metric, the log-Euclidean metric, and the Bures–Wasserstein (BW) metric, the last of which was recently extended to HPD manifolds. Riemannian gradient descent algorithms are proposed to solve the corresponding geometric means and medians, that play fundamental roles in the detection process. Simulations within the scenario using the ideal steering vector as the target signal provide compelling evidence that the BW detectors outperform the other geometric detectors as well as the conventional adaptive matched filter and adaptive normalized matched filter when observation data are limited. Further simulations demonstrate that the matrix-CFAR is robust in scenarios where the signal is mismatched. In addition to detection performances, robustness of the geometric detectors to outliers and computational complexity of the algorithms are analyzed.


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    Title :

    The Comparison of Riemannian Geometric Matrix-CFAR Signal Detectors


    Contributors:
    Ono, Yusuke (author) / Peng, Linyu (author)


    Publication date :

    2024-04-01


    Size :

    1884735 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



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