Deep Learning-Based Rigorous Electromagnetic Framework for Direction of Arrival Estimation in Millimeter-Wave Communication Systems Based on Embedded Radiation Patterns

Direction of arrival (DoA) estimation is a fundamental problem in modern communication systems, such as 5G/6G cellular systems, V2X, and radar. Modern DoA estimation techniques enhance signal reception, mitigate interference, enhance communication efficiency, improve capacity, and improve spatial selectivity. In this paper, a two-channel residual neural network (ResNet) CNN is designed and trained based on the covariance matrix for a realistic electromagnetic antenna array model by expanding the steering vector obtained from the embedded element radiations. The regression DoA estimation is parameterized for three scenarios: regression using a trigonometric angle process, regression directly in degrees, and regression in radians. Then, the proposed network is compared with the modified conventional multiple signal classification (MUSIC), minimum variance distortion-less response (MVDR), and a two-channel deep CNN. A microstrip antenna array is designed, operating at 28 GHz, using Ansys Electronic Desktop to obtain the 3D embedded element radiation, for both co-polarized and cross-polarized components, considering mutual coupling among the antenna array elements, finite-element spacing, and array geometry. The proposed degree-based ResNet CNN achieves sub-degree azimuth and elevation RMSE for angular separations greater than 10° at an SNR of 0 dB in our simulations, clearly outperforming modified MUSIC, MVDR, and deep CNN learning-based 2D DoA methods that require significantly higher SNR to reach comparable accuracy. Moreover, the network operating directly on the real and imaginary parts of the covariance matrix and predicting angles in degrees consistently yields lower RMSE than variants trained to predict radians or sine–cosine representations, while avoiding the steering vector knowledge and postprocessing steps, spatial spectra, peak search, or root-finding, used in existing approaches.