Super-Resolution Harmonic Retrieval of Non-Circular Signals

TL;DR

This paper introduces a super-resolution harmonic retrieval method tailored for non-circular signals, leveraging structured covariance matrices and a low-rank Toeplitz-Hankel approach for improved estimation accuracy.

Contribution

It develops a novel low-rank Toeplitz-Hankel covariance reconstruction method for non-circular signals, enhancing harmonic retrieval accuracy without prior noise knowledge.

Findings

LRTHCR outperforms benchmark methods in estimation accuracy

Structured covariance matrices enable efficient harmonic retrieval

Proposed method is robust in practical noisy environments

Abstract

This paper proposes a super-resolution harmonic retrieval method for uncorrelated strictly non-circular signals, whose covariance and pseudo-covariance present Toeplitz and Hankel structures, respectively. Accordingly, the augmented covariance matrix constructed by the covariance and pseudo-covariance matrices is not only low rank but also jointly Toeplitz-Hankel structured. To efficiently exploit such a desired structure for high estimation accuracy, we develop a low-rank Toeplitz-Hankel covariance reconstruction (LRTHCR) solution employed over the augmented covariance matrix. Further, we design a fitting error constraint to flexibly implement the LRTHCR algorithm without knowing the noise statistics. In addition, performance analysis is provided for the proposed LRTHCR in practical settings. Simulation results reveal that the LRTHCR outperforms the benchmark methods in terms of lower estimation errors.