In this paper, the convolution neural networks (CNN) are developed for the classification and localization of mixed near-field and far-field sources by using the geometry of symmetric nested array. We first transform the received data into frequency domain. Then, we preprocess the phase difference matrix to decouple mixed sources. Considering that the counter-diagonal elements in the phase difference matrix only contain the direction of arrival (DOA) parameter of each mixed source, we utilize the upper right elements as the input of CNN to estimate the DOA of each mixed source. In order to avoid the influence of noise, we construct a particular range vector without the estimated DOA and employ the output of autoencoder to classify the mixed sources. Finally, we further exploit the output of autoencoder and apply the CNN without bias vectors to estimate the range of near-field sources. In contrast to the traditional learning-based approaches regarding the parameter estimation as a classification problem, the proposed approach considers the parameter estimation as a regression problem and can significantly reduce the complexity of networks. Simulation results demonstrate that the proposed learning-based method can improve the precision for the mixed source localization. Moreover, the proposed method is robust to the off-grid parameters and the different numbers of mixed sources.

Recently, deep unfolded networks have been widely utilized in direction of arrival (DOA) estimation due to the reduced computational complexity and improved estimation accuracy. However, few consider the nested array for off-grid DOA estimation, where the estimated DOAs are not on the prespecified grids. In this paper, we propose a deep unfolded FOCal Underdetermined System Solver (FOCUSS) network and a deep unfolded Alternating Direction Method of Multiplies (ADMM) to address the problem, which respectively aim to improve estimation accuracy and further reduce computational complexity. We first apply first-order Taylor expansion and vectorize the covariance matrix into a real-valued single snapshot for network input. We then train the proposed networks to obtain on-grid DOA spatial spectrum and off-grid values, where the off-grid DOA estimation is calculated by the peaks of on-grid DOA spatial spectrum and corresponding off-grid values. We demonstrate that the proposed networks with interpretable parameters can accelerate the convergence rate and achieve better generalization. Simulations verify the performance of proposed networks in comparison with the existing methods.

Recently, deep unfolding networks with interpretable parameters have been widely utilized in direction of arrival (DOA) estimation due to the faster convergence speed and better generalization ability. However, few consider the nested array for gridless DOA estimation. In this letter, we propose a deep alternating projection network to address the problem. We first convert the covariance matrix into a measurement vector in the form of atomic norm, which can reduce the matrix dimension during projection. We then train the proposed network to alternately obtain the positive semi-definite matrix and the corresponding irregular Hermitian Toeplitz matrix, where the loss function is derived by employing the trace of network output. Finally, we apply the irregular root Multiple Signal Classification (MUSIC) method to obtain gridless DOA via nested array. We demonstrate that the proposed networks can accelerate the convergence rate and reduce computational cost. Simulations verify the performance of proposed networks in comparison with the existing methods.

The radar jamming technology based on metasurfaces has attracted widespread attention in recent years due to its advantages of flexible modulation and low power consumption. However, the deception effect of the radar target characteristics imitation technique is greatly reduced by the limited modulation states of the digital coding metasurface. To address this issue, this article proposes a novel time-domain equivalent amplitude and phase (EAP) generation method that can significantly increase the number of time modulation states of the metasurface without increasing hardware complexity. The time-domain EAP generation model based on the spatial vector synthesis is established first, and theoretical analysis demonstrates that the number of modulation states of 1- and 2-bit phase-coding metasurfaces under vertical incidence can be expanded from 2 to (the number of units +1), and from 4 to the square of (the number of units +1), respectively. Based on the time-domain EAP, a more efficient and accurate metasurface-based target high-resolution range profile (HRRP) imitation scheme compared with the state of the art is proposed, and its superiority is verified through simulations. Experiment results based on a 1-bit phase-coding metasurface further validate the practicality of both the EAP generation method and the EAP-based target HRRP imitation scheme.

Recently, deep unfolding networks have been widely used in direction of arrival (DOA) estimation because of their improved estimation accuracy and reduced computational cost. However, few have considered the existence of a nested array (NA) with off-grid DOA estimation. In this study, we present a deep sparse Bayesian learning (DSBL) network to solve this problem. We first establish the signal model for off-grid DOA with NA. Then, we transform the array output into a real domain for neural networks. Finally, we construct and train the DSBL network to determine the on-grid spatial spectrum and off-grid value, where the loss function is calculated using reconstruction error and the sparsity of network output, and the layers correspond to the steps of the sparse Bayesian learning algorithm. We demonstrate that the DSBL network can achieve better generalization ability without training labels and large-scale training data. The simulation results validate the effectiveness of the DSBL network when compared with those of existing methods.

We present a second-order statistics (SOS)-based algorithm for three-dimensional (3-D) localization of multiple near-field sources using an uniform circular array (UCA). Based on the centro-symmetric property of UCA steering vectors, a particular diagonal matrix, which only includes two-dimensional (2-D) direction of arrival (DOA) is constructed by utilizing the rotational relationship of the different UCA outputs. By exploiting the subspace of an SOS for UCA output, an estimation of signal parameters via rotational invariance techniques (ESPRIT)-like and a one-dimensional MUSIC methods are performed to obtain the 2-D DOA and range spatial spectrum, respectively. The proposed SOS-based algorithm does not require high-order statistics computation and also does not require additional eigenvalue decomposition for range estimation. Simulation results demonstrate the superior performance of the proposed algorithm compared with a TSMUSIC method and a phase-based method.