"Blind" Calibration and Toeplitz Covariance Matrix Estimation in Uniform Linear Arrays. Part I. Benchmark Analysis and Matrix-Free Techniques

TL;DR

This paper re-evaluates calibration and Toeplitz covariance matrix estimation for uniform linear arrays in high-frequency radar applications, emphasizing matrix-free techniques and benchmark analysis in an over-sampled regime.

Contribution

It introduces a benchmark analysis of blind calibration methods and explores matrix-free techniques leveraging array properties and recent mathematical theories.

Findings

Benchmark efficiency of blind calibration methods analyzed.

Techniques based on Toeplitz properties without matrix estimation evaluated.

Over-sampled array regimes exploited for improved calibration approaches.

Abstract

The problems of uniform linear array (with uniform mutual coupling) calibration and Toeplitz covariance matrix estimation are re-examined for application in the receive arrays of modern High Frequency Over-the-Horizon Radars (HF OTHR). Specifics of these arrays, operating predominantly in the "over-sampled" (d/$\lambda$ < 0.5) regime, are exploited along with the recent findings in the Toeplitz Inverse Eigenvalue problem (ToIEP), Random Matrix Theory, and the "Expected Likelihood" methodology developed earlier to advance the problem solution. In this paper we re-evaluate the benchmark efficiency of the "blind" calibration and analyze several techniques that are based on certain properties of the Toeplitz covariance matrix and "over-sampled" uniform antenna arrays, but do not require matrix estimation. In Part II we analyze the case of the unknown symmetric and Hermitian Toeplitz matrices and introduce techniques for joint antenna calibration and Toeplitz covariance matrix estimation.