Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

TL;DR

This paper introduces a versatile power spectral density estimation method using multi-coset sampling that performs well for both sparse and nonsparse spectra, offering improved resolution and reduced computational complexity.

Contribution

It proposes a novel estimation technique combining compressed sensing and noncompressive methods for wide-sense stationary signals from sub-Nyquist samples.

Findings

Compressive estimates outperform noncompressive ones in resolution and sampling rate tradeoffs.

Noncompressive estimates are obtained via least squares solutions.

Compressive estimates can be computed using non-negative least squares, reducing computational overhead.

Abstract

This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed sensing (CS) when the power spectrum is sparse, but applies to sparse and nonsparse power spectra alike. The estimates are consistent piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. We show that compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. For suitable sampling patterns, noncompressive estimates are obtained as least squares solutions. Because of the non-negativity of power spectra, compressive estimates can be computed by seeking non-negative least squares solutions (provided appropriate sampling patterns exist) instead of using standard CS recovery algorithms. This flexibility suggests a reduction in computational overhead for systems estimating both sparse and nonsparse power spectra because one algorithm can be used to compute both compressive and noncompressive estimates.