Abstract
Estimating directions of arrival (DOA) without knowledge of the source number is regarded as a challenging task, particularly when coherence among sources exists. Researchers have trained deep learning (DL)-based models to attack the problem of DOA estimation. However, existing DL-based methods for coherent sources do not adapt to variable source numbers or require signal independence. Herein, we put forward a new framework combining parallel DOA estimators with Toeplitz matrix reconstruction to address the problem. Each estimator is constructed by connecting a multi-label classifier to a spatial filter, which is based on convolutional-recurrent neural networks. Spatial filters divide the angle domain into several sectors, so that the following classifiers can extract the arrival directions. Assisted with Toeplitz-based method for source-number determination, pseudo or missed angles classified by the estimators will be reduced. Then, the spatial spectrum can be more accurately recovered. In addition, the proposed method is data-driven, so it is naturally immune to signal coherence. Simulation results demonstrate the predominance of the proposed method and show that the trained model is robust to imperfect circumstances such as limited snapshots, colored Gaussian noise, and array imperfections.
Highlights
Direction-of-arrival (DOA) or spatial spectrum estimation is one of the most important content in array signal processing, which has been widely applied in navigation, acoustics, electronic reconnaissance [1,2], etc
Taking one of the most representative subspace-based techniques, for instance, multiple signals classification (MUSIC) [4], it conducts signal subspace decomposition to search for steering vectors approximately orthogonal to noise subspace, and the corresponding angles are considered as arrival directions
We describe the multi-label classification (MLC) [23] strategy employed in the proposed deep learning (DL), which fully meets the requirement of multiple directions finding
Summary
Direction-of-arrival (DOA) or spatial spectrum estimation is one of the most important content in array signal processing, which has been widely applied in navigation, acoustics, electronic reconnaissance [1,2], etc. Taking one of the most representative subspace-based techniques, for instance, multiple signals classification (MUSIC) [4], it conducts signal subspace decomposition to search for steering vectors approximately orthogonal to noise subspace, and the corresponding angles are considered as arrival directions These MUSIC-based algorithms [5,6,7,8]. During the past two decades, direction finding by sparse reconstruction aims at minimizing the difference between data covariance matrix and the sparsely reconstructed one, which can be formulated into a convex optimization problem [11,12,13] In this methodology, DOAs can be estimated on-grid or off-grid, and the source number is not compulsorily required. Present DNN-based DOA estimation models mostly ask for signal independence or a prior knowledge of source number. E{ a} represents the expectation of a and k · k denotes the Euclidean norm
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