High-Resolution Multimode Electromagnetic Vortex Imaging Driven by the RELAX Algorithm

Vortex electromagnetic waves carrying orbital angular momentum (OAM) enable differentiated scaling of multiple targets within the beam coverage, granting them superior theoretical performance in multi-dimensional multi-target staring imaging. Owing to the approximate dual relationship between OAM modes and target azimuth angles, multi-mode vortex scanning can rapidly and accurately determine spatial azimuth information of targets, significantly enhancing radar imaging resolution and speed in the azimuthal dimension. Recently, multiple factors, including insufficient OAM mode diversity, complex noise environments and low mode purity, collectively hinder the practical implementation of existing vortex imaging algorithms for high-resolution OAM based radar systems. To address these challenges, this article proposes a high-resolution RELAX algorithm for vortex imaging technology based on precise analysis of echo signal components. The method treats echo signals as superpositions of multiple complex sinusoidal signals and achieves accurate extraction of target positional information through iterative refinement. A comparative analysis of spectral estimation methods, sparse recovery methods and the RELAX method is presented. Experimental results demonstrate that compared to conventional imaging algorithms, the RELAX algorithm exhibits superior target recovery capability, effectively suppresses spurious targets, mitigates noise interference, and significantly improves image resolution, which is particularly pronounced under limited OAM mode diversity. The experimental findings reveal that under with the OAM modes of [-7,7], the RELAX algorithm achieves a limiting resolution of 6.7cm×19°, with the normalized mean-square error of 0.4557 and the image correlation value of 0.6917. This approach substantially alleviates the inherent dependence on OAM mode quantity in vortex radar systems, providing a robust resolution for practical scenarios with constrained electromagnetic (EM) resources. The proposed method notably expands the application scope of vortex EM waves in radar imaging architectures, establishes a solid new technical pathway for vortex radar signal processing, and facilitates the practical deployment of vortex radar.