3-D Imaging With Vortex Electromagnetic Wave Radar Based on Nested Array Structure—Part I: Sparse Imaging Algorithm

The orthogonal orbital angular momentum (OAM) mode domain of vortex electromagnetic wave (VEMW) provides a new observation dimension for radar imaging. However, on the one hand, the beam pointing and radiation intensity of VEMWs carrying different OAM modes are inconsistent, which is reflected in the echo as amplitude modulated by Bessel function terms, resulting in azimuth defocusing. On the other hand, a large number of OAM modes are required in target imaging, consuming considerable resources in the radar system. To address the above problems, a VEMW radar 3-D imaging method with sparse observation based on a nested array structure is proposed in this article. First, a nested array structure based on a uniform circular array is proposed. On this basis, an imaging model with an adjustable carrier frequency and the number of emitting array elements is established with orthogonal frequency-division multiplexing (OFDM) technology, which increases the freedom of beam modulation and the opportunity to save radar resources. Second, according to the sparse signal reconstruction theory and the maximum beam radiation intensity criterion, a sparse observation matrix in the OAM mode domain is established. Then, with further consideration of mode purity and beam radiation intensity equalization, the carrier frequency and the number of emitting elements of each selected mode are jointly selected. According to these allocation results, range–azimuth imaging can be obtained with a small number of OAM modes in a short period of time based on the sparse recovery algorithm. Furthermore, an elevation reconstruction method with phase interferometry is proposed based on the characteristics of OFDM signals. As a result, 3-D imaging results can be achieved. The effectiveness of the proposed method is demonstrated by simulations.