Cooperative Multi-constraint of a Sparse Array in Multiple-input Multiple-output Radar for Near-field Imaging

In near-field imaging with Multiple-Input Multiple-Output (MIMO) radar, spatial resolution is effectively enhanced by extending the aperture of a two-dimensional MIMO array. The proposed system is based on a time-division multiple-access waveform and performs near-field aperture synthesis imaging using the MIMO array. High-resolution three-dimensional coverage of the near-field region is achieved by coherently accumulating multichannel raw echo data in the wavenumber domain. Compared with traditional mechanical scanning, this system is considered more suitable for scenarios with extremely high real-time requirements, such as civil aviation security inspection. However, millimeter waves have a short wavelength, so numerous transmit/receive elements must be placed in MIMO arrays to satisfy the Nyquist sampling criterion. This necessity leads to a substantial resource overhead. Thus, the Cooperative Multi-Constraint of Sparse Array (CMC-SA) algorithm is proposed for MIMO radar near-field imaging. Under the constraints of maintaining constant main lobe gain and suppressing sidelobe levels in the array pattern, an optimization model for near-field MIMO radar array configurations is constructed, with the weight $ {\ell}_{\rm P} $ norm regularization of the weight vector serving as the objective function. By introducing auxiliary variables, a closed-form solution for the array weight vector is derived. The sparse processing of uniformly configured MIMO arrays is achieved, and the array configuration problem of minimizing the number of nonzero excitations is solved while meeting the high-resolution imaging requirements. To reduce the propagation error among multiple constraints and alleviate the difficulty of coupling the objective function with complex constraints, the coupled variables in the original optimization problem are decomposed into multiple independent variables, with their consistency enforced through equality constraints. The “decomposition-coordination” concept is employed to determine weight vectors under multi-constraint conditions. In near-field 2D MIMO radar, this collaborative sparse design method is implemented to effectively reduce system complexity while ensuring imaging performance. The simulation results demonstrate that, compared with sparse algorithms such as the single-constraint and Bayesian methods, the CMC-SA algorithm achieves lower sidelobe levels and superior focusing performance under near-field MIMO radar focusing conditions, with an element sparsity rate of 72.6%. Furthermore, high-resolution imaging of the sparse MIMO radar is realized using measured echo data acquired with the designed sparse array, processed via the Range Migration Algorithm (RMA) and a feature recovery algorithm. The results confirm that the proposed CMC-SA-MIMO near-field imaging algorithm considerably reduces system complexity while maintaining imaging quality.