Gridless Underdetermined DOA Estimation for Mobile Agents with Limited Snapshots Based on Deep Convolutional Generative Adversarial Network

Deep learning techniques have made certain breakthroughs in direction-of-arrival (DOA) estimation in recent years. However, most of the current deep-learning-based DOA estimation methods view the direction finding problem as a grid-based multi-label classification task and require multiple samplings with a uniform linear array (ULA), which leads to grid mismatch issues and difficulty in ensuring accurate DOA estimation with insufficient sampling and in underdetermined scenarios. In order to solve these challenges, we propose a new DOA estimation method based on a deep convolutional generative adversarial network (DCGAN) with a coprime array. By employing virtual interpolation, the difference co-array derived from the coprime array is extended to a virtual ULA with more degrees of freedom (DOFs). Then, combining with the Hermitian and Toeplitz prior knowledge, the covariance matrix is retrieved by the DCGAN. A backtracking method is employed to ensure that the reconstructed covariance matrix has a low-rank characteristic. We performed DOA estimation using the MUSIC algorithm. Simulation results demonstrate that the proposed method can not only distinguish more sources than the number of physical sensors but can also quickly and accurately solve DOA, especially with limited snapshots, which is suitable for fast estimation in mobile agent localization.