3-D Millimeter-Wave Imaging for Sparse MIMO Array With Range Migration and <i>l</i>₂-Norm-Reinforced Sparse Bayesian Learning

Sparse multiple-input-multiple-output (MIMO) millimeter-wave (MMW) near-field imaging systems, based on the principle of phase coherence, can reduce the hardware cost and system complexity and improve the speed of perception while ensuring high resolution. Conventional frequency-domain imaging algorithms such as range migration cannot be directly applied to such systems due to the spatial downsampling of the antenna array, while conventional time-domain imaging methods such as back projection are highly computationally ineffective. To address this issue, we propose a two-stage imaging algorithm. The first stage deals with the sparse array as a virtual full array for fast frequency-domain imaging using phase center approximation (PCA). However, the PCA process cannot accurately compensate for the phase errors, especially in near-field imaging scenarios with large field-of-view and undersampling. Thus, in the second step, we introduce a compressive sensing (CS) algorithm based on sparse Bayesian learning (SBL) to correct the phase errors, where an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> norm term is introduced to balance the sparsity and fidelity of the reconstructed image. The optimization problem is iteratively solved to refocus the imaging results obtained in the first step, leading to 3-D images with high quality. Simulations and experiments confirm that our proposed algorithm achieves high imaging performance with good computational efficiency for a large undersampling ratio (USR).