Sampling and Reconstructing Angular Domains with Uniform Arrays

The surge of massive antenna arrays in wireless networks required to adopt analog and hybrid array solutions, where antenna elements are not driven by a radio front end each. In such solutions the phase shifters' network connecting the antennas and the few front ends compresses the angular information, that the array could extract if a full digital solution were possible. In analog/hybrid arrays, each front end uses its phase shifters to focus on a specific angle in order to maximize the beamforming gain, requiring to sample the angular domain. While different heuristics have been proposed in the past to define which angles are to be sampled, to the best of the authors' knowledge, no formal solutions were given. In this work, we define (i) how many and (ii) which angles must be sampled with uniform linear and rectangular arrays, defining (iii) how to perform a loss-less reconstruction of the array's angular response, as if infinite angular acquisitions were available. Our proposed ensemble of techniques does not rely on any angular sparsity assumption, making it a general solution to scan the angular domain. It can therefore be applied not only to channel estimation, but also to imaging techniques, making it a candidate for future integrated sensing and communications (ISAC). Numerical evaluations validate our proposal, providing clear advantages versus state of the art baselines both in terms of angular reconstruction performance and computational complexity.