Rotating ULA-Enabled Computed Tomography for Efficient 3D Spatial Power Spectrum Synthesis: Architecture and Principled Orientation Design

This paper proposes an efficient three-dimensional (3D) spatial power spectrum synthesis method by rotating a uniform linear array (ULA) about its center in 3D space. Inspired by classical computed tomography (CT), the ULA performs analog receive combining at each rotation angle to produce a partial coherent sum. By collecting such sums over multiple rotations, the full 3D spectrum can be synthesized online via a single radio-frequency (RF) chain, without explicitly acquiring per-antenna signals. Depending on whether the overall coherent sum is accessible, the synthesis is obtained through either a minimum operation over partial spectrum images or joint synthesis after accumulating all coherent sums. Compared with fixed uniform planar array (UPA)-based combining and dense single movable-antenna (MA) sampling for 3D cubic virtual arrays, the proposed scheme achieves full-space 3D coverage with substantially reduced sampling and movement overhead while maintaining uniformly high angular resolution. Its sampling geometry and sequential orientation design also support pipelined analog beamforming, reducing practical hardware cost. To design rotation orientations in a principled manner without prior environmental information, we aim to maximize the expected worst-case projected separation between multi-path component (MPC) pairs. A secondary criterion then minimizes the worst-case projective correlation among orientation axes to reduce orientation redundancy. Accordingly, we optimize orientation sets for different numbers of orientations under isotropic-matrix and unit-norm constraints, using a multistart smooth minimax algorithm. Numerical results show that the optimized orientations uniformly span 3D space and reconstruct full-space 3D spectra close to the dense 3D cubic reference using only a fraction of spatial samples.