Wideband Large-Array Processing and Sparse Design for Angle Imaging

Abstract

This paper shows that wideband large-array processing can recover a large number of angle pixels with far fewer antenna elements. The key advantage of wideband signaling is that different frequencies induce different virtual arrays, whose union forms a virtual array with a substantially increased number of effective virtual elements. Thus, a sparse physical array can support far more spatial samples than physical antennas. Motivated by this capability, we study the recovery of angular responses across the full field of view $[-90^\circ, 90^\circ)$, discretized according to the improved angular resolution, and refer to this sensing regime as angle imaging. However, the resulting virtual array is inherently irregular, clustered, and does not automatically guarantee stable recovery. To address this challenge, we introduce a coverage criterion that estimates the number of stably recoverable angle pixels, without computationally intensive singular-value-based conditioning tests over candidate image dimensions. For systems satisfying this criterion, we theoretically establish deterministic condition-number bounds that characterize stable angle imaging. Building on this criterion, we derive non-uniform sparse array designs that minimize the number of physical antennas while maintaining recovery over the full field of view. Simulation results show that the proposed criterion provides practical guidance for stable system design, and that the resulting sparse arrays can recover substantially more angle pixels than the number of physical antennas, with representative designs supporting over ten times as many angle pixels as physical antennas.