## 1 Introduction
[24] explored the use of multiple satellites for bistatic and multi-static SAR acquisitions, focusing on data fusion techniques to enhance image resolution and information space. There are also studies on the impact and compensation of ionospheric effects in low-frequency spaceborne SAR imaging. [PERSON] et al. [25] introduced an application of the phase gradient autofocus to compensate for spatially varying and anisotropic scintillation phase errors. [PERSON] et al. [26] proposed a method integrated into the focusing process to estimate and mitigate ionospheric effects in bistatic SAR System, including imaging performance deterioration and geometric distortion. There are few studies in the existing literature that specifically analyze the impact of atmospheric effects in GNSS-BSAR long-time imaging. Considering aforementioned problems, this paper studies the GNSS-BSAR imaging processing under long synthetic aperture time. An ionospheric scintillation compensation-based modified Back Projection (BP) imaging method is proposed for dual-channel receiving GNSS-BSAR system. This method first extracts the Doppler phase errors of the reference channel, which includes the impact of local oscillator time-frequency error of the receiver and atmospheric effects. The ionospheric scintillation phase error is isolated individually using polynomial fitting. Subsequently, the modified BP algorithm is operated, which partitions the azimuth phase of the imaging channel into difference phase and reference phase. Through two-step azimuth phase compensation, the Doppler phase errors of the imaging channel can be accurately eliminated, effectively improving the focusing accuracy of SAR images. The main contributions of this study can be summarized below:  
1. Two-Step Azimuth Phase Compensation Method: To address the issue of atmospheric disturbances in GNSS-BSAR systems during long-time observations, this paper proposes a two-step azimuth phase compensation method. This strategy decomposes the azimuth phase of the imaging channel into difference and reference phases. Through phase compensation, Doppler phase errors are eliminated, and the processing resultsof actual data demonstrate that the proposed method achieves precise focusing in GNSS-BSAR imaging. 2. Novel Processing Mode: Unlike traditional autofocus-based error compensation algorithms, which have limitations requiring strong prominent points in the observation scene, multiple iterations for convergence, and limited capability for high-order phase error compensation, the proposed method utilizes the dual-channel receiving characteristic. It introduces a novel processing mode that directly uses the phase information extracted from the reference channel for error analysis and phase compensation, avoiding the practical challenges encountered by autofocus algorithms. 3. Potential for Ionospheric-Related Studies: By extracting ionospheric phase scintillation at different times of the day, this work preliminarily illustrates the potential of this technology for ionospheric-related studies. Moreover, the proposed method can also be adapted to other passive SAR imaging systems based on dual-channel receiving modes, demonstrating a certain level of versatility. The rest of the paper is organized as follows. Section 2 introduces the system configuration and signal model, analyzing the impact of atmospheric effects, particularly ionospheric scintillation, on GNSS-BSAR imaging. Section 3 describes the ionospheric scintillation compensation-based modified BP imaging method, including reference channel ionospheric scintillation phase error extraction technology and precise azimuth focus through two-step azimuth phase compensation. Section 4 presents the actual data processing results using GPS LS signal as the illuminator of opportunity to illustrate the validity of the proposed method. Section 5 analyzes the algorithm performance, evaluates the imaging results and outlines potential future research directions. Finally, Section 6 concludes the work.