Detection and Estimation of Diffuse Signal Components Using the Periodogram

Area of Science:

• Signal Processing
• Spectral Analysis
• Communications Engineering

Background:

• Periodogram analysis limitations in distinguishing pure vs. diffuse frequency components.
• Diffuse components are prevalent in channel estimation due to multipath propagation and scattering.
• Existing methods struggle to accurately identify and quantify diffuse frequency characteristics.

Purpose of the Study:

• To develop a method for detecting diffuse frequency components within periodogram peaks.
• To estimate the spread of detected diffuse components.
• To improve the accuracy of frequency estimation in the presence of complex signal distributions.

Main Methods:

• Analyzing the projection of the data vector onto the span of the signature's derivatives.
• Utilizing the Vandermonde structure of the signature and properties of discrete Chebyshev polynomials.
• Employing an efficient numerical procedure based on barycentric interpolation for computation.

Main Results:

• A novel detector for diffuse frequency components based on energy in the derivatives' subspace.
• An estimator for the spread of diffuse components, defined as the ratio of energies.
• Numerical assessment demonstrating the effectiveness of the proposed estimator and detector.

Conclusions:

• The proposed method effectively detects and quantifies diffuse frequency components, overcoming periodogram limitations.
• Exploiting signature derivatives and Chebyshev polynomials offers a robust approach to spectral analysis.
• The method provides significant improvements for applications like channel estimation requiring precise frequency identification.