Restricted Domain Compressive Sensing for Antenna Metrology

Published

November 21, 2022

Author(s)

Marc Valdez, Alex Yuffa, Michael Wakin

Abstract

In this paper, we prove a compressive sensing guarantee for restricted measurement domains in spherical near-field to far-field transformations for antenna metrology. We achieve this by first defining Slepian functions on a measurement sub-domain $R$ of the rotation group $\sot$, the full domain of the linear inverse problem associated with spherical near-field to far-field transformations. Then, we transform the inverse problem from the measurement basis, the bounded orthonormal system of band-limited Wigner $D$-functions on $\sot$, to the Slepian functions in a way that preserves sparsity. We then partition the inverse problem into Slepian functions with large concentrations on $R$ and those with small concentrations on $R$ and treat the contribution of the latter part as additive noise. This process results in measurements being over a new bounded orthonormal system on the measurement sub-domain $R$ for which we prove compressive sensing guarantees. The restriction to Slepian functions with large concentrations on $R$ results in the compressive sensing guarantees giving the most accurate reconstructions when the measured signal has its energy concentrated on the measurement sub-domain $R$. We provide numerical examples of our method in comparison with other classical and compressive sensing approaches. In terms of reconstruction quality, we find that our method performs the best out of the compressive sensing approaches and at least as good as classical approaches but with a reduction in the number of measurements.

Citation

IEEE Transactions on Signal Processing

Volume

70

Pub Type

Journals

Download Paper

https://doi.org/10.1109/TSP.2022.3223848

Local Download

Keywords

Compressive Sensing, Antenna Metrology, Slepian Functions

Citation

Valdez, M. , Yuffa, A. and Wakin, M. (2022), Restricted Domain Compressive Sensing for Antenna Metrology, IEEE Transactions on Signal Processing, [online], https://doi.org/10.1109/TSP.2022.3223848, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=933415 (Accessed December 22, 2024)