Spatiotemporal variability compatibility for angular resolving within radar beamwidth

Under the constraint of the classical diffraction limit, radar angular resolution is intrinsically bounded by both the antenna aperture and the signal wavelength, rendering the discrimination of targets within a single beam a persistent and difficult challenge in radar technology. In particular, there is a lack of a unified theory to explain their common physical foundation and mathematical essence, to measure their angular resolution potential, to optimize their implementation, and to guide the exploration of new approaches and systems. This paper proposes a spatiotemporal variability compatibility theory for angular resolving within radar beamwidth, revealing that its physical foundation lies in the compatibility between the spatial and temporal variations of electromagnetic waves. The mathematical essence involves the effective construction and solution of angular observation equations. Based on the product of spatial gradient entropy and temporal nearest distance sum, a method for measuring the spatiotemporal variability compatibility is proposed. Then, this paper analyzes the differences in angular resolution capabilities within radar beamwidth across different system architectures and their applicable scenarios. Additionally, verification and application examples are provided, demonstrating the use of this theory to innovate system architectures and achieve angular resolving within the radar beamwidth.