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High-resolution Sparse Self-calibration Imaging for Vortex Radar with Phase Error
DOI: 10.12000/JR21094
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摘要:
基于轨道角动量(OAM)的涡旋雷达因其在高分辨率成像方面具有巨大潜力而受到广泛关注。有限OAM模式下的涡旋雷达高分辨率成像问题，通常采用稀疏恢复的方法来解决，这种方法需要精确地已知成像模型的先验知识。然而，系统中不可避免存在的相位误差，会导致成像模型失配，严重影响成像性能。为了解决这一问题，该文首次建立了存在相位误差时的涡旋雷达成像模型。同时，提出了一种涡旋雷达两步自校正成像方法，用于直接估计相位误差。首先在第1步中提出了一种稀疏驱动算法来促进目标稀疏性，同时提升成像重构性能。其次，在第2步中提出了一种直接补偿相位误差的自校正操作。该方法通过对目标重构和相位误差估计的交替迭代，能够很好地重建目标并有效地补偿相位误差。仿真结果表明，该方法在提高成像质量和改善相位误差估计性能方面具有潜在的优势。
Abstract:The Orbital Angular Momentum (OAM)-based vortex radar has drawn increasing attention because of its potential for high-resolution imaging. The vortex radar high resolution imaging with limited OAM modes is commonly solved by sparse recovery, in which the prior knowledge of the imaging model needs to be known precisely. However, the inevitable phase error in the system results in imaging model mismatch and deteriorates the imaging performance considerably. To address this problem, the vortex radar imaging model with phase error is established for the first time in this work. Meanwhile, a two-step self-calibration imaging method for vortex radar is proposed to directly estimate the phase error. In the first step, a sparsity-driven algorithm is developed to promote sparsity and improve imaging performance. In the second step, a self-calibration operation is performed to directly compensate for the phase error. By alternately reconstructing the targets and estimating the phase error, the proposed method can reconstruct the target with high imaging quality and effectively compensate for the phase error. Simulation results demonstrate the advantages of the proposed method in enhancing the imaging quality and improving the phase error estimation performance.
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Key words:
- Vortex radar imaging /
- Orbital Angular Momentum (OAM) /
- Phase error /
- Self-calibration /
- Sparse recovery
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Figure 3. In mode number [–10, 10], the obtained vortex EM images with phase error using different algorithms for SNR=20 dB
Figure 5.
${\rm{NMSE}}({\hat{\boldsymbol \beta }})$ of phase error under different SNRs and different phase error range
Figure 6. In mode number [–10, 10], the obtained vortex EM images of target 1 scene with phase error using different algorithms for SNR=5 dB
Figure 7. Under different SNRs, and obtained of original target 1 scene in mode number [–10, 10]
Figure 8. In mode number [–10, 10], the obtained vortex EM images of target 2 scene with phase error using different algorithms for SNR=20 dB
Figure 9. In mode number [–10, 10], the obtained vortex EM images of target 3 scene with phase error using different algorithms for SNR=20 dB
Figure 10. Under different SNRs,
${\rm{NMSE}}({{\boldsymbol{\hat{\sigma}} }})$ and${\rm{Corr}}({{\boldsymbol{\hat{\sigma }}}},\,{\boldsymbol{\sigma }})$ obtained of original target 2 scene in mode number [–10, 10]
Figure 11. Under different SNRs,
${\rm{NMSE}}({{\boldsymbol{\hat{\sigma }}}})$ and${\rm{Corr}}({\boldsymbol{{\hat{\sigma }}}},\,{\boldsymbol{\sigma }})$ obtained of original target 3 scene in mode number [–10, 10]Algorithm 1 Algorithm flow of VSCIP Input: $ {{\boldsymbol{y}},{\boldsymbol{S}}},\epsilon,{a}_{0},{b}_{0}$ Initialization: ${\boldsymbol{\zeta } } = {\boldsymbol{1} },{\boldsymbol{\mu } } = { {\boldsymbol{S} }^{\rm{H}}}{\boldsymbol{y} }$ While $j < {j_{\max }}$ do For $t = 1$ to ${t_{\max }}$ do Update ${{\boldsymbol{\mu }}^j}$ and ${{\boldsymbol{\varSigma }}^j}$ by Eqs. (30) and (29); Update ${{\boldsymbol{\lambda }}^j}$ by Eq. (39); Update $\left\langle {\ln {\pi _m} } \right\rangle$ and $\left\langle {\ln \left( {1 - {\pi _m} } \right)} \right\rangle$ by Eqs. (42) and (43); Update ${{\boldsymbol{\zeta }}^j}$ by Eq. (50); Update ${\eta ^j}$ by Eq. (46); If $\left\| { { {\hat {\boldsymbol{\mu } } }^j}(t + 1) - { {\hat {\boldsymbol{\mu } } }^j}(t)} \right\|_2^2/\left\| {\hat {\boldsymbol{\mu } }{ {(t)}^j} } \right\|_2^2 < \epsilon$, break; ${{\boldsymbol{x}}^j} = {{\boldsymbol{\mu }}^j}(t + 1),{{\boldsymbol{w}}^j} = {{\boldsymbol{w}}^j}(t + 1)$; ${{\boldsymbol{\sigma }}^j}={{\boldsymbol{x}}^j} \odot {{\boldsymbol{w}}^j}$; End For Update ${{\boldsymbol{\beta }}^j}$ by Eq. (53); Recompute ${\boldsymbol{S}}({{\boldsymbol{\beta }}^j})$; End While Output: ${{\boldsymbol{\sigma }}^j}$, ${{\boldsymbol{\beta }}^j}$ 
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Table 1. Key radar parameters for simulations
Parameters Value Frequency of the first subpulse $ f_0 $ 9.9 GHz Bandwith $B_r $ 200 MHz Number of subpulse $D $ 41 Topological charge $ \alpha $ [–10, 10] Array radius $a $ 0.25 m Array elements number N 22 Target range (985, 1015) m Target azimuth (0.2, 0.6)π rad
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