For the multi-target DOA estimation problem of uniform linear arrays, this paper proposes a DOA estimation method based on the deep convolution neural network. The algorithm adopts the deep convolutional neural network, and the DOA estimation problem of the array signal is transformed into the inverse mapping problem of the array output covariance matrix to a binary sequence in which “1” indicates that there is a target incident in the corresponding angular direction at that position. The upper triangular array of the discrete covariance matrix is used as the data input to realize the DOA estimation of multiple sources. The simulation results show that the DOA estimation accuracy of the proposed algorithm is significantly better than that of the typical super-resolution estimation algorithm under the conditions of low SNR and small snapshot. Under the conditions of high SNR and large snapshot, the estimation accuracy of the proposed algorithm is basically the same as those of the MUSIC algorithm, ESPRIT algorithm, and ML algorithm, which are better than that of the deep fully connected neural network. The analysis of the simulation results shows that the algorithm is effective, and the time and space complexity can be further reduced by replacing the square array with the upper triangular array as the input.

Sparse arrays are of deep concern due to their ability to identify more sources than the number of sensors, among which the hole-free difference co-array (DCA) with large degrees of freedom (DOFs) is a topic worth discussing. In this paper, we propose a novel hole-free nested array with three sub-uniform line arrays (NA-TS). The one-dimensional (1D) and two-dimensional (2D) representations demonstrate the detailed configuration of NA-TS, which indicates that both nested array (NA) and improved nested array (INA) are special cases of NA-TS. We subsequently derive the closed-form expressions for the optimal configuration and the available number of DOFs, concluding that the DOFs of NA-TS is a function of the number of sensors and the number of the third sub-ULA. The NA-TS possesses more DOFs than several previously proposed hole-free nested arrays. Finally, the superior direction of arrival (DOA) estimation performance based on the NA-TS is supported by numerical examples.

For the DOA (direction of arrival) estimation of a low-elevation-angle target under the influence of a multipath effect, this paper proposes a DOA estimation method based on CAE (convolutional autoencoder) and CNN (convolutional neural network). The algorithm firstly inputs the signal covariance matrix of the array of the low-elevation target containing direct and reflected waves into the convolutional autoencoder to realize the de-multipath, and uses the spatial features extracted by the convolutional autoencoder as the input of the extreme learning machine to realize the DOA preclassification of direct waves; based on the preclassification results, one branch of the three parallel convolutional neural nets is selected, and the output of the convolutional autoencoder is used as the input of this branch to realize DOA estimation. The simulation results show that the algorithm has better estimation accuracy and efficiency than the conventional algorithms, especially when the DOA of the target is in the lower range. The analysis of the simulation results shows that the algorithm is effective, in which the convolutional autoencoder can effectively realize the de-multipath, and the use of parallel convolutional neural networks can avoid overfitting and underfitting and realize DOA estimation more accurately.

To address the weakness that the difference co-array (DCA) only enhances the degrees of freedom (DOFs) to a limited extent, a new configuration called the generalized nested array via difference–sum co-array (GNA-DSCA) is proposed for direction of arrival (DOA) estimation. We consider both the temporal and spatial information of the array output to construct the DSCA model, based on which the DCA and sum co-array (SCA) of the GNA are systematically analyzed. The closed-form expression of the DOFs for the GNA-DSCA is derived under the determined dilation factors. The optimal results show that the GNA-DSCA has a more flexible configuration and more DOFs than the GNA-DCA. Moreover, the larger dilation factors yield significantly wider virtual aperture, which indicates that it is more attractive than the reported DSCA-based sparse arrays. Finally, a hole-filling strategy based on atomic norm minimization (ANM) is utilized to overcome the degradation of the estimation performance due to the non-uniform virtual array, thus achieving accurate DOA estimation. The simulation results verify the superiority of the proposed configuration in terms of virtual array properties and estimation performance.