According to the characteristics of spinning targets, the narrow-band radar echoes can be directly used for imaging spinning targets. However, spurious peaks appear due to azimuth down sampling with a low pulse repetition frequency (PRF). By exploiting the sparsity of the targets, the compressed sensing (CS) theory can be adopted to obtain super resolution image under sub-sampling condition. This paper mainly focuses on analyzing the physical mechanism of the CS-based narrow-band imaging method. Firstly, the narrow-band radar's under-sampling echoes' model from rapidly spinning targets is established. The relationship between CS and the model is analyzed. Then the reasons why the CS-based narrow-band imaging method can guarantee the exact recovery of the spinning target are given from physical view. The theoretical lower limit of sub-sampling pulse numbers is provided. Finally, the simulation results verify the effectiveness of the theoretical analysis. The main results obtained in the paper are listed as follows. One is that the mechanism of the CS-based narrow-band imaging method differs from those of the conventional range Doppler imaging methods. The spurious peaks appear due to calculating the Doppler frequency directly under a low PRF. To avoid this phenomenon, the CS-based method searches the positions of the scatterers instead. The variation from calculating the Doppler frequency directly to searching the positions of the scatterers is the physical mechanism of the CS-based super resolution imaging method. The other is that the resolution and the allowable grid mismatch of the CS-based imaging method are related to the wavelength, which is 0.4 lambda and unrelated to the bandwidth. So the performance of the CS-based imaging method is related to the sub-sampling rate, the number of the scatters and the wavelength, and unrelated to the bandwidth of the wave. However, this paper only considers the ideal point scattering model and the grid is perfectly matched with the model. In the following, three aspects can be further studied. First, due to the spinning target distribution on a continuous scene, the off-grid problem would severely affect the performance of the CS-based imaging method. The continuous compressive sensing theory can be used for solving the off-grid problem and explaining the related physical mechanism. Second, the illumination of the radar cannot reach some scatterers on the target in some observation intervals, which results in the occlusion effect and the time-varying scattering amplitude. The dynamic CS theory can be used for reference in solving this problem. Finally, if the estimated spinning frequency has error, how to correct and compensate for the error adaptively needs to be further studied.
