Non-Iterative Blind Calibration of Nested Arrays with Asymptotically Optimal Weighting

TL;DR

This paper introduces a non-iterative, optimal-weighting blind calibration method for 2-level nested arrays, improving accuracy and efficiency over existing techniques, and extends to higher-level arrays.

Contribution

It demonstrates that least-squares can be effectively used for blind calibration of nested arrays, providing an optimal weighting scheme and surpassing current methods in accuracy and efficiency.

Findings

LS approach works for 2-level nested arrays despite previous claims

The method achieves higher calibration accuracy

It is computationally more efficient than existing methods

Abstract

Blind calibration of sensors arrays (without using calibration signals) is an important, yet challenging problem in array processing. While many methods have been proposed for "classical" array structures, such as uniform linear arrays, not as many are found in the context of the more "modern" sparse arrays. In this paper, we present a novel blind calibration method for $2$-level nested arrays. Specifically, and despite recent contradicting claims in the literature, we show that the Least-Squares (LS) approach can in fact be used for this purpose with such arrays. Moreover, the LS approach gives rise to optimally-weighted LS joint estimation of the sensors' gains and phases offsets, which leads to more accurate calibration, and in turn, to higher accuracy in subsequent estimation tasks (e.g., direction-of-arrival). Our method, which can be extended to $K$-level arrays ($K>2$), is superior to the current state of the art both in terms of accuracy and computational efficiency, as we demonstrate in simulation.