Structured Sparsity Learning With Group <i>L</i> _1/2 Regularization for Efficient Synthesis of Near-Field Multifocus Sparse Planar Arrays

In this letter, an efficient synthesis method for near-field multifocus (NFMF) sparse planar arrays (SPAs) is proposed, utilizing a structured sparsity learning (SSL)-based deep neural network (DNN) model. The model is established by connecting physical equations in tandem with the DNN to map the relation between the desired near-field radiation characteristics and SPA geometry. To enhance the sparsity of the SPA, the SSL method, incorporating a group <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub> (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GL</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sub>) regularizer seamlessly embedded into the model, is employed to prune redundant nodes that represent unnecessary array elements. By incorporating both the physical equations and SSL method, prior knowledge is provided to improve the training efficiency of the model. Through appropriate training, the synthesis of the SPA is achieved, generating an optimal SPA layout along with element excitations. The proposed method allows for precise control of the focal position and sidelobe level (SLL) of the near-field pattern with a minimal number of array elements. The effectiveness of this method is demonstrated by two examples focusing on single- and eight-point near-field targets with low SLL. Results show that the proposed method achieves over 65% savings in the number of array elements and at least a 45% reduction in synthesis time compared with the existing synthesis methods.