Chirp-Based Aliasing Analysis of Arrays in the Spherical Wavefront Regime

TL;DR

This paper introduces a chirp-based interpretation of steering vectors in the spherical wavefront regime, analyzing aliasing effects in antenna arrays and providing geometric insights into their impact on the ambiguity function.

Contribution

It presents a novel chirp-based framework for understanding aliasing in spherical wavefront regimes, applicable to various array geometries and near-field conditions.

Findings

Aliasing effects degrade the ambiguity function in array processing.

The framework provides geometric insights into non-space-invariant aliasing mechanisms.

Applicable to circular and linear array structures in near-field scenarios.

Abstract

In antenna arrays, wave propagation modeling based on Euclidean principles is typically represented by steering vectors or signals. This paper provides a new, chirp-based, interpretation of steering vectors in the Spherical Wavefront Regime (SWR), establishing a relationship between the spatial spectrum of the received (resp. transmitted) signal and the geometry of the array and the source (resp. target). Leveraging the well-known sampling theorem, we analyze aliasing effects arising from spatial sampling with a finite number of antennas and understand how these effects degrade the Ambiguity Function (AF). Our framework provides geometric insight into these degradations, offering a deeper understanding of the non-space-invariant aliasing mechanisms in the SWR. The proposed approach is formulated for general antenna arrays and then instantiated to Circular Array and to Uniform Linear Array structures operating in Near Field conditions.