A Hardware-Efficient Adaptive PDE Framework for FPGA-Based Single-Snapshot DOA Estimation

Abstract

Direction-of-arrival (DOA) estimation is a fundamental task in smart antenna systems, radar, wireless communications, and sensing applications. However, conventional subspace-based methods exhibit degraded performance under single-snapshot and low signal-to-noise ratio (SNR) conditions due to unreliable covariance estimation and increased sensitivity to noise. This paper proposes a hardware-efficient Adaptive Partial Differential Equation (PDE) framework for FPGA-based single-snapshot DOA estimation. The proposed approach initially reconstructs the covariance matrix from the received single-snapshot data and computes a structured covariance matrix to preserve the spatial correlation among antenna elements. Unlike conventional fixed-weight covariance reconstruction techniques, an adaptive weighting coefficient is determined from the covariance reconstruction error using the Frobenius norm, enabling dynamic fusion of the sample and structured covariance matrices. Furthermore, a PDE-inspired diffusion regularization term is incorporated into the reconstructed covariance matrix to suppress noise while preserving the underlying signal subspace, thereby improving eigenvalue separation and estimation stability. The enhanced covariance matrix is subsequently decomposed using Eigenvalue Decomposition (EVD), and the MUSIC algorithm is employed to accurately estimate the directions of arrival. To facilitate real-time implementation, the proposed algorithm is mapped onto an FPGA using a hardware-efficient pipelined architecture, providing reduced computational latency and optimized resource utilization. Simulation and hardware evaluation demonstrate that the proposed framework achieves superior angular resolution, lower root mean square error (RMSE), and improved robustness under low-SNR and single-snapshot scenarios compared with existing covariance reconstruction methods, making it well suited for real-time embedded radar, wireless communication, and smart antenna applications.