###### Abstract
[11] has proposed a practical solution, where different CPI in each frequency channel is allowed, thus enabling fusion with the same velocity resolution. Rather than fusion in range-Doppler mapping (RDM), ref. [11] performs fusion in the range-velocity mapping (RVM). However, there are two main limitations of using the approach in [11]. First, the CPI of each channel is specially selected, so it is non-trivial to generate multiple uniform RVMs for MF-based centralized detection. Interpolation or zero-padding is required at the cost of computational load. Second, ref. [11] combines multiple RVMs via non-coherent integration (NCI), which inevitably achieves less processing gain than the coherent ones. Based on the principle of whether the phase information of the radar returns is used or not, the long-time integration methods can be divided into non-coherent integration and coherent integration. By exploiting the phase information, coherent integration can outperform non-coherent integration [29]. As an approach of coherent integration, Radon-Fourier transform (RFT) achieves moving target detection (MTD) with a long CPI [30; 31]. Unlike the existing methods, RFT can be viewed as a generalized Doppler filter bank and processes signals jointly in the space-time-frequency domain [30]. Due to its outstanding performance, RFT and its variants have been extensively studied in various radar systems, such as offshore-based linear frequency-modulated (LFM) radar [32], and GNSS-based PBR [33; 34]. However, thus far, there are limited studies that propose an RFT-based solution for migrating MF-DFM in MF-PBR. Moreover, RFT-based processing requires the nearly consistent phase of the target unit within the integration domain; otherwise, it will suffer from coherent integration loss if the standard deviation of the phase estimate exceeds a certain degree [35]. Consequently, it is imperative that the phase of the target in MF-RDMs should be estimated and compensated for prior to the coherent integration. Motivated by the previous works, in this paper, we consider the quasi-coherent integration problem for MTD in MF-based PBR with an equal and long CPI in each frequency channel. According to our analysis, MF-DFM is likely to occur prior to the RCM, as the CPI increases. To focus on the issues in MF integration, including MF-DFM and residual phase errors, we primarily consider the detection scenario of a single point-like target with a constant velocity. The main contributions of this work are summarized as follows:  
1. To eliminate the MF-DFM, a novel approach based on MF-based RFT (MF-RFT) is proposed. Specifically, a set of MF-Doppler filter banks (MF-DFBs) is dedicatedly designed, which is realized via conducting a thorough velocity search in the range/slow-time domain. By implementing this technique, the reflections of the moving target in the MF-RDMs can be focused on the Doppler centroid (DC) of the target, ultimately achieving the correction of the MF-DFM. 2. To remove the residual phase errors following the MF-RFT, a phase-compensation-based method is also developed by formulating an optimization problem based on the minimum-entropy criterion. The particle swarm optimization (PSO) algorithm is then employed to solve the optimization problem for estimating the residual phase errors. Combining with MF-RFT, the proposed method could allow effective phase compensation, and quasi-coherent MF integration is then robustly achieved, improving the SNR of the weak target significantly. Both simulated and field test results based on DVB-S signals show that the proposed algorithm could greatly improve the detection performance in the presence of MF-DFM and substantial residual phase errors, achieving better detection performance at low-SNR conditions, as compared with the existing algorithms. The remainder of this article is organized as follows: Section 2 describes the signal model and the challenge in MFI, i.e., MF-DFM. The proposed method is then illustrated in Section 3.