###### Abstract  
Passive bistatic radar (PBR)-based moving target detection (MTD) has benefited greatly from multi-frequency (MF) integration, which can effectively improve the detection capability of weak targets. However, with the increase in the coherent processing interval (CPI) and carrier-frequency separation, Doppler spread will appear in the range-Doppler maps (RDMs) over different frequency bands, which severely limits the processing gain of MF integration. In this paper, a novel MTD algorithm is proposed to achieve both long-time integration and quasi-coherent MF integration. More specifically, the proposed method consists of two main steps, where a modified Radon-Fourier transform (RFT), termed as MF-based RFT (MF-RFT), is, firstly, used to eliminate the Doppler spread via designing a sequential of MF-based Doppler filter banks. Following the MF-RFT, a phase-compensation-based method is also developed to further remove the residual phase errors. This method involves formulating an optimization problem based on the minimum-entropy criterion and employing a particle swarm optimization (PSO) algorithm to solve it, after which quasi-coherent MF integration can be achieved with robustness. Both numerical results and field test results based on digital video broadcasting-satellite (DVB-S) signals demonstrate that the proposed algorithm outperforms the existing methods in the scenario of weak MTD. p 2023 15 4309 1233 1 [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30  
unmanned aerial vehicles (UAVs) [14], offshore vessels [15], and ground vehicles [16; 17]. Hence, this article selects the DVB-S signal as the IO for investigation. The main challenge of the DVB-S-based PBR is its extremely low power density on the Earth's surface [18]. To cope with this limitation and achieve a robust detection of moving targets, long time integration and increasing the number of fusion channels are required to enhance the SNR of the weak echo. However, both of these will result in the energy misalignment [19], which can be divided into two parts: range cell migration (RCM) and Doppler frequency migration (DFM) [20]. Specifically, the target's energy will disperse in multiple range cells due to the effect of RCM. Abundant solutions have been proposed to address the RCM, such as keystone transform (KT) [21], Hough transform (HT) [22], and their variants [23]. However, in the case of MFI, RCM occurs mainly due to the time-varying bandwidth, and RCM is particularly evident in FM-based PBR [9]. To circumvent this effect, a number of channels with consistent bandwidth are selected so that the target will locate in the same range bin at different frequency bands, due to the same physical path and range resolution. On the other hand, the conventional DFM is generated by the maneuverability (i.e., acceleration or jerk) of a moving target [20]. Typical methods for solving the DFM effect could be the phase matching (PM) approach [24], de-chirp method [25], chirp-Fourier transform [26], and fractional Fourier transform (FRFT) [27], etc. However, different from the conventional DFM, the DFM in MFI, called MF-DFM, imposes great challenges to MTD which need to be accounted for. According to [28], MF-DFM is caused by the frequency-hopping characteristic of the transmitted signal. If the same coherent processing interval (CPI) is employed in each frequency channel, the MF-DFM effect will result in the target appearing in different Doppler frequency bins, although the target moves with a constant velocity during the observations. Furthermore, when the radial velocity of the target is too high, or the CPI is too long, MF-DFM will become more evident, resulting in significant Doppler migration, which is also known as Doppler spread. This kind of migration cannot be eliminated by the conventional time-frequency method [28]. To address the MF-DFM, ref.