Signal Recovery from Phaseless Measurements of Spherical Harmonics Expansion

Arya Bangun, Arash Behboodi, Rudolf Mathar

Abstract: In this work, we study the problem of recovering spherical harmonics coefficients from phaseless measurements and evaluate the empirical performance of several well-known algorithms. Apart from trivial ambiguities that arise naturally from the properties of spherical harmonics, we will show that when a specific class of equiangular sampling patterns is chosen to construct the measurement matrix, another ambiguity appears as well. Nevertheless, we will numerically show that recovery can be achieved by carefully choosing the appropriate sampling patterns. Furthermore, an application of this work in phaseless spherical near-field antenna measurements will be addressed.