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Reconfigurable intelligent surface (RIS) or intelligent reflecting surface (IRS) has been an attractive technology for future wireless communication and sensing systems. However, in the practical RIS, the mutual coupling effect among RIS elements, the reflection phase shift, and amplitude errors will degrade the RIS performance significantly. This article investigates the two-dimensional direction-of-arrival (DOA) estimation problem in the scenario using a practical RIS. After formulating the system model with the mutual coupling effect and the reflection phase/amplitude errors of the RIS, a novel DNN-DANM method is proposed for the DOA estimation by combining the deep neural network (DNN) and the decoupling atomic norm minimization (DANM). The DNN step reconstructs the received signal from the one with RIS impairments, and the DANM step exploits the signal sparsity in the two-dimensional spatial domain. Additionally, a semi-definite programming (SDP) method with low computational complexity is proposed to solve the atomic minimization problem. Finally, both simulation and prototype are carried out to show estimation performance, and the proposed method outperforms the existing methods in the two-dimensional DOA estimation with low complexity in the scenario with practical RIS.

DNN-DANM: A High-Accuracy Two-Dimensional DOA Estimation Method Using Practical RIS