A Novel DOA Estimation Algorithm for Directional Borehole Radar Based on the Subspace Method and Full-Wave Simulation

Directional Borehole Radar (D-BHR) can acquire the 3D information of subsurface targets from a single borehole. However, there are several challenges in D-BHR when applying Direction of Arrival (DOA) estimation to obtain the directional information of the subsurface targets. This paper addresses the challenges in DOA estimation for Uniform Circular antenna array (UCAA)-based D-BHR, including wideband signals, electromagnetic coupling interference, and inhomogeneous borehole interference. We propose a modified DOA estimation algorithm integrating the subspace method with full-wave simulation. The proposed method begins by constructing a simulation model based on prior information. Next, the angular responses of the antenna array are acquired through full-wave simulation. Subsequently, the steering vector is derived by applying subspace decomposition to the array responses to extract the signal subspace. The steering vector obtained by combining full-wave simulation and subspace methods is referred to as the Subspace-based Universal Steering Vector (S-USV). Finally, DOA estimation is performed based on the orthogonality between the steering vector and the noise subspace of the signal. To address the high computational cost of the full-wave simulations part, we propose a highly efficient algorithm based on the Lorentz reciprocity theorem, which is applicable to various full-wave simulation methods. We simulated a fracture model and generated 3D imaging results using the proposed method. Compared with conventional methods, the proposed approach demonstrates several advantages, including stronger robustness against interference, higher computational efficiency, and lower memory requirements.