# Parameter Estimation and Error Calibration for Multi-Channel Beam-Steering SAR Systems
## 5 Conclusions  
Multi-channel BS-SAR is a promising approach for high resolution and wide-swath observation, but is subject to errors that can lead to degradation of image quality. To overcome spectrum aliasing caused by beam steering and non-uniform sampling of the azimuth channels, pre-processing, combined with derotation and spectrum reconstruction, is used by most multi-channel BS-SAR imaging algorithms; this requires accurate system parameters and error calibration. However, the derotation rate error is not always accurately calculated, and the constant Doppler centroid and phase inconsistency errors cannot be calibrated by conventional methods. The interaction between different errors also makes the error estimation more difficult.  
The derotation rate error leads to a time shift in the pre-processed signal and signal scaling. The shift varies with the azimuth positions of targets, which breaks the overlap of the pre-processed signal, so azimuth antenna pattern correction and signal weighting cannot be performed correctly. Furthermore, the spectra of targets located at the edge of the illuminated scene may shift out of the processing bandwidth and cause resolution degradation and radiometric loss. The CDC error can also lead to a constant spectral shift, which allows the DRR and CDC errors to be determined by detecting the time shifts between two halves of the data after performing pre-processing. The method for estimating the derotation rate and CDC errors is validated by simulation, and the results show it to be robust against SNR and uniformity factor.  
Figure 15: Simulated results from distributed targets: (**a**) is the image without errors, (**b**) is the image with errors and (**c**) is after error correction.  
Phase inconsistency errors between azimuth channels are inherent in multi-channel SAR systems but most estimation methods for multi-channel strip-map SAR cannot be used in multi-channel BS-SAR because the spectra of different azimuth targets are separated in the Doppler domain, which prevents the use of traditional MUSIC methods. Methods based on the spectrum energy distribution are applicable to multi-channel BS-SAR but are sensitive to the CDC error because they depend on the spectrum only inside or outside the processing bandwidth. To overcome this, we use a minimum entropy estimation method based on the full spectrum which is robust against the CDC error. With the help of novel weighting strategy, the ME method can achieve excellent performance even in bad SNR and uniformity factor. Estimation and correction simulations demonstrate its excellent performance.  
[PERSON] and [PERSON] conceived and developed the methods and performed the experiments; [PERSON], [PERSON] and [PERSON] supervised the research; and [PERSON] wrote the paper.  
This research received no external funding.  
**Acknowledgments:** This work is supported by the National Natural Science Foundation of China (NSFC) under Grant No. 61861136008 and Grant No. 61701012, Fundamental Research Funds for the Central Universities under Grand No. YWF-19-BJ-J-304 and China Scholarship Council (CSC) under Grant No. 201806020013.  
**Conflicts of Interest:** The authors declare no conflict of interest.