Deep unfolded networks have recently been regarded as an essential way to direction of arrival (DOA) estimation due to the fast convergence speed and high interpretability. However, few consider gridless DOA estimation. This paper proposes two deep unfolded gridless DOA estimation networks to resolve the above problem. We first consider the atomic norm-based 1D and decoupled atomic norm-based 2D gridless DOA models solved by the alternating iterative minimization of variables, respectively. Then, the corresponding deep networks are trained offline after constructing the corresponding complete training datasets. At last, the trained networks are applied to realize the 1D DOA and 2D estimation, respectively. Simulation results reveal that the proposed networks can secure higher 1D and 2D DOA estimation performances while maintaining a lower computational expenditure than typical methods.

With a small number of training range cells, sparse recovery (SR)-based space–time adaptive processing (STAP) methods can help to suppress clutter and detect targets effectively for airborne radar. However, SR algorithms usually have problems of high computational complexity and parameter-setting difficulties. More importantly, non-ideal factors in practice will lead to the degraded clutter suppression performance of SR-STAP methods. Based on the idea of deep unfolding (DU), a space–time two-dimensional (2D)-decoupled SR network, namely 2DMA-Net, is constructed in this paper to achieve a fast clutter spectrum estimation without complicated parameter tuning. For 2DMA-Net, without using labeled data, a self-supervised training method based on raw radar data is implemented. Then, to filter out the interferences caused by non-ideal factors, a cycle-consistent adversarial network (CycleGAN) is used as the image enhancement process for the clutter spectrum obtained using 2DMA-Net. For CycleGAN, an unsupervised training method based on unpaired data is implemented. Finally, 2DMA-Net and CycleGAN are cascaded to achieve a fast and accurate estimation of the clutter spectrum, resulting in the DU-CG-STAP method with unsupervised learning, as demonstrated in this paper. The simulation results show that, compared to existing typical SR-STAP methods, the proposed method can simultaneously improve clutter suppression performance and reduce computational complexity.

For airborne radar space-time adaptive processing (STAP), conventional statistic-based non-homogeneous detectors (NHDs) can help to eliminate the range cells contaminated by outliers, while their performance usually depends on the available training range cells. To solve this problem, the non-homogeneous detection problem is transformed to an out-of-distribution (OOD) data detection problem and a deep learning (DL) based NHD is then proposed in this study. According to the reconstruction errors of their corresponding radar signals in a trained complex-valued memory-augmented autoencoder, the DL-NHD can detect and eliminate the contaminated range cells and thus improve the performance of STAP effectively. Simulation results show that, compared with three existing NHDs, the proposed DL-NHD can detect outlier-contaminated range cells with 0 miss-detection and 0 false-detection. After using DL-NHD to eliminate the outlier-contaminated range cells, the STAP output signal-to-clutter-plus-noise-ratio (SCNR) loss can be improved by about 10~20 dB.

The lack of independent and identically distributed (IID) training range cells is one of the key factors that limit the performance of conventional space-time adaptive processing (STAP) methods for airborne radar. Sparse recovery (SR)-based and convolutional neural network (CNN)-based STAP methods can obtain high-resolution estimations of the clutter space-time spectrum by using few IID training range cells, so as to realize the clutter suppression effectively. However, the performance of SR-STAP methods usually depends on the SR algorithms, having the problems of parameter setting difficulty, high computational complexity and low accuracy, and the CNN-STAP methods have a high requirement for the nonlinear mapping capability of CNN. To solve these problems, CNNs can be used to reduce the requirements of SR algorithms for parameter setting and iterations, increasing its accuracy, and the clutter space-time spectrum obtained by SR can be used to reduce the network scale of the CNN, resulting in the method proposed in this paper. Based on the idea of deep unfolding (DU), the SR algorithm is unfolded into a deep neural network, whose optimal parameters are obtained by training to improve its convergence performance. On this basis, the SR network and CNN are trained end-to-end to estimate the clutter space-time spectrum efficiently and accurately. The simulation and experimental results show that, compared to the SR-STAP and CNN-STAP methods, the proposed method can improve the clutter suppression performance and have a lower computational complexity.