Compressive Joint Angular-Frequency Power Spectrum Estimation

TL;DR

This paper presents a novel compressive method for joint estimation of power spectrum in frequency and direction of arrival, enabling sub-Nyquist sampling and accurate source localization without sparsity assumptions.

Contribution

It introduces a compressive approach that reconstructs the 2D power spectrum matrix from sub-Nyquist samples, allowing estimation of more sources than sensors without sparsity constraints.

Findings

Accurate power spectrum reconstruction from sub-Nyquist samples.

Ability to estimate more sources than sensors.

Theoretical guarantees under full column rank condition.

Abstract

We introduce a new compressive power spectrum estimation approach in both frequency and direction of arrival (DOA). Wide-sense stationary signals produced by multiple uncorrelated sources are compressed in both the time and spatial domain where the latter compression is implemented by activating only some of the antennas in the underlying uniform linear array (ULA).We sample the received signal at every active antenna at sub-Nyquist rate, compute both the temporal and spatial correlation functions between the sub-Nyquist rate samples, and apply least squares to reconstruct the full-blown two-dimensional power spectrum matrix where the rows and columns correspond to the frequencies and the angles, respectively. This is possible under the full column rank condition of the system matrices and without applying any sparsity constraint on the signal statistics. Further, we can estimate the DOAs of the sources by locating the peaks of the angular power spectrum. We can theoretically estimate the frequency bands and the DOAs of more uncorrelated sources than active sensors using sub-Nyquist sampling.