Version 1
: Received: 26 September 2024 / Approved: 26 September 2024 / Online: 27 September 2024 (11:36:03 CEST)
How to cite:
Selva, J. Detection and Estimation of Diffuse Signal Components Using the Periodogram. Preprints2024, 2024092159. https://doi.org/10.20944/preprints202409.2159.v1
Selva, J. Detection and Estimation of Diffuse Signal Components Using the Periodogram. Preprints 2024, 2024092159. https://doi.org/10.20944/preprints202409.2159.v1
Selva, J. Detection and Estimation of Diffuse Signal Components Using the Periodogram. Preprints2024, 2024092159. https://doi.org/10.20944/preprints202409.2159.v1
APA Style
Selva, J. (2024). Detection and Estimation of Diffuse Signal Components Using the Periodogram. Preprints. https://doi.org/10.20944/preprints202409.2159.v1
Chicago/Turabian Style
Selva, J. 2024 "Detection and Estimation of Diffuse Signal Components Using the Periodogram" Preprints. https://doi.org/10.20944/preprints202409.2159.v1
Abstract
A basic limitation of the periodogram as frequency estimator is that any of its significant peaks may be produced by a diffuse (or spread) frequency component instead of a pure one. Diffuse components are common in applications such as channel estimation in which a given periodogram peak reveals the presence of a complex multipath distribution (unresolvable propagation paths or diffuse scattering, for example). We present a method to detect the presence of a diffuse component in a given peak based on analyzing the projection of the data vector onto the span of the signature’s derivatives up to a given order. Fundamentally, a diffuse component is detected if the energy in the derivatives’ subspace is too high at the peak’s frequency, and its spread is estimated as the ratio between this last energy and the peak’s energy. The method is based on exploiting the signature’s Vandermonde structure through the properties of discrete Chebyshev polynomials. We also present an efficient numerical procedure for computing the data component in the derivatives’ span based on barycentric interpolation. The paper contains a numerical assessment of the proposed estimator and detector.
Keywords
Periodogram; beamformer; Maximum Likelihood estimation; diffuse components; discrete Chebyshev polynomials; frequency estimation; channel estimation
Subject
Engineering, Telecommunications
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
