Spatial Angular Pseudo-Derivative Searching: A Single Snapshot Super-resolution Sparse DOA Scheme with Potential for Practical Application

Accurate, high-resolution, and real-time DOA estimation is a cornerstone of environmental perception in automotive radar systems. While sparse signal recovery techniques offer super-resolution and high-precision estimation, their prohibitive computational complexity remains a primary bottleneck for practical deployment. This paper proposes a sparse DOA estimation scheme specifically tailored for the stringent requirements of automotive radar such as limited computational resources, restricted array apertures, and a single snapshot. By introducing the concept of the spatial angular pseudo-derivative and incorporating this property as a constraint into a standard L0-norm minimization problem, we formulate an objective function that more faithfully characterizes the physical properties of the DOA problem. The associated solver, designated as the SAPD search algorithm, naturally transforms the high-dimensional optimization task into an efficient grid-search scheme. The SAPD algorithm circumvents high-order matrix inversions and computationally intensive iterations. We provide an analysis of the computational complexity and convergence properties of the proposed algorithm. Extensive numerical simulations demonstrate that the SAPD method achieves a superior balance of real-time efficiency, high precision, and super-resolution, making it highly suitable for next-generation automotive radar applications.