Radiation Pattern Recovery from Tilted Orbital Sampling Measurements via Sparse Spherical Harmonic Expansion

This paper proposes a reconstruction framework for estimating the far-field (FF) radiation patterns of large, heavy, or non-rotatable wireless-enabled systems. The method combines a tilted orbital sampling (ToS) strategy with sparse spherical harmonic (SH) expansion, compressed sensing (CS), and convex optimization (CO), thereby linking a mechanically constrained acquisition scheme with a mathematically efficient recovery process. The purpose of this integration is not only to reduce the number of measurements but also to retrieve the radiation information most relevant to Internet of Things (IoT) devices and bulky equipment that cannot be easily rotated within anechoic chambers. The framework is validated on two representative cases: a canonical half-wave dipole and a commercial Wi-Fi-enabled device. In the latter and more challenging case, accurate reconstruction is achieved with fewer than 30 SH coefficients and using less than 20% of the measurements required by a conventional full-sphere scan, with the normalized root-mean-square error remaining below 5%. Although inaccessible angular regions may be partially uncharacterized, such directions are of minor relevance for the intended operational coverage. The resulting SH-based representation can be seamlessly integrated into ray-tracing propagation simulators and electromagnetic optimization workflows, enabling efficient and application-oriented OTA characterization under realistic chamber constraints.