In the area of near-field millimeter-wave imaging, the generalized sparse array synthesis (SAS) method is in great demand. The traditional methods usually employ the greedy algorithms, which may have the convergence problem. This paper proposes a convex optimization model for the multiple-input multiple-output (MIMO) array design based on the compressive sensing (CS) approach. We generate a block shaped reference pattern, to be used as an optimizing target. The pattern occupies the entire imaging area of interest in order to involve the effect of each pixel into the optimization model. In MIMO scenarios, we can fix the transmit subarray and synthesize the receive subarray, and vice versa, or doing the synthesis sequentially. The problems associated with focusing, sidelobes suppression, and grating lobes suppression of the synthesized array are examined in detail. The simulation results reveal that the proposed method can efficiently synthesize a sparse array within a significantly shorter time in comparison to state-of-the-art techniques. As a result, it can be applied to generate arrays with large apertures. Additionally, both numerical and experimental results demonstrate that the synthesized sparse array offers superior image quality when compared to both state-of-the-art and commonly used sparse arrays with an equivalent number of antenna elements.

To solve the problems of high computational complexity and unstable image quality inherent in the compressive sensing (CS) method, we propose a complex-valued fully convolutional neural network (CVFCNN)-based method for near-field enhanced millimeter-wave (MMW) three-dimensional (3-D) imaging. A generalized form of the complex parametric rectified linear unit (CPReLU) activation function with independent and learnable parameters is presented to improve the performance of CVFCNN. The CVFCNN structure is designed, and the formulas of the complex-valued back-propagation algorithm are derived in detail, in response to the lack of a machine learning library for a complex-valued neural network (CVNN). Compared with a real-valued fully convolutional neural network (RVFCNN), the proposed CVFCNN offers better performance while needing fewer parameters. In addition, it outperforms the CVFCNN that was used in radar imaging with different activation functions. Numerical simulations and experiments are provided to verify the efficacy of the proposed network, in comparison with state-of-the-art networks and the CS method for enhanced MMW imaging.

Subarray is widely used in array antennas to decrease the system complexity, which would also increase the sidelobes during scanning. To solve this problem, subarray partition solutions with larger coverage and lower sidelobes are selected from a series of results generated by search algorithms. However, searching for an appropriate result of a large array is time-consuming. In this study, to search subarray solutions of full coverage with less time, we introduce two pruning processes in Algorithm X. Additionally, a pair of coefficients associated with the sidelobes is adopted for further pruning and reducing the sidelobes. Numerical experiments have been carried out and verified the effectiveness and the performance of the proposed method.

A convex optimization-based method of sparse array synthesis (SAS) for wideband near-field millimeter-wave imaging is proposed by extending our previous work. We construct a monostatic sparse array synthesis optimization model from the electromagnetic propagation formula. The reweighted l ₁ norm decoding algorithm is utilized to enhance the sparsity. A modified iterative element weighting merging method is also proposed to put constraints on the minimum element spacing to synthesize a practicable sparse layout. Through the proposed SAS method, the customized sparse monostatic array for near-field imaging can be generated with different schemes, such as 1-D linear arrays, 2-D planar arrays, etc. The imaging performance of the synthesized planar sparse array, is studied by examining the properties of focusing, sidelobe-suppression, and grating lobe suppression both theoretically and by simulation. It is shown that the optimized array is superior to the arrays with equally spaced antennas or randomly spaced antennas, using approximately the same number of antenna elements. Experimental results further indicate the advantages of the optimized wideband sparse array through the three-dimensional imaging reconstruction.

Sparse arrays have gained increasing research attention due to their potential to reduce system cost and weight. However, current studies on sparse array synthesis often overlook the physical dimensions of the antennas and only consider the distance constraints of antenna centers. In this communication, we propose a novel matrix constraints method for the sparse planar array synthesis, taking into account the actual area occupied by each antenna unit. The proposed method introduces a matrix that relates the aperture lattices to each candidate antenna; this matrix is then used as a spatial constraint for the antennas. The synthesis problem, aimed at achieving a low sidelobe level, is formulated as a mixed-integer optimization problem under this matrix constraint. To obtain the array layouts efficiently, the synthesis problem is relaxed to a compressed sensing problem and subsequently solved using a combination of re-weighted l ₁ minimization convex optimization and the integer genetic algorithm. Numerical experiments and full-wave simulations were conducted, verifying the effectiveness of the proposed method.

Sidelobe calculation is a common procedure in phased array synthesis. However, the traditional sidelobe calculation method through pattern simulation and peak searching costs a large amount of time. In this letter, we derive a formula for fast sidelobe level calculation in arbitrary 2-D phased arrays. The formula describes the relationship between sidelobe (change throughout the article) level and the element feeding excitations. The result of numerical experiments shows that the proposed method is as accurate as the search method. When applying our formula in a genetic algorithm for sidelobe suppression, the proposed method consumes 0.1% of the computing time compared with the search method in a nonuniformly distributed array of 50 elements.