## 1 Introduction  
In recent years, radar and communication equipment has grown increasingly complex due to rapid technological advancements. Radar systems are essential in tracking and detecting targets [1; 2; 3], while communication devices serve to transmit information [4]. In certain applications, there is a need to not only detect targets but also provide communication capabilities. For instance, in smart transportation systems, base stations detect vehicle conditions and relay this information to other devices or base stations [5; 6; 7; 8; 9]. Similarly, unmanned aerial vehicles (UAVs) require the communication of air transportation information. To integrate radar and communication functionalities into a single device, digital signal processing techniques are indispensable. Integrated radar and communication systems (IRCSs) have garnered significant attention from researchers [10; 11; 12; 13; 14]. IRCSs involve hardware and software integration to merge radar and communication capabilities [15; 16; 17]. Central to IRCSs is the design of integrated radar and communication waveforms (IRCW), which unify radar and communication operations using the same waveform. Researchers have developed various IRCWs, categorized primarily into common waveforms and multiplexing waveforms [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. Multiplexing waveforms encompass techniques such as space division multiplexing, time division multiplexing, frequency division multiplexing, and code division multiplexing. Among these, the orthogonal frequency division multiplexing (OFDM) waveform stands out, widely recognized for its application in digital television broadcasting [23], digital video [24; 25; 26; 27], and wireless local area networks (WLANs) [28; 29; 30]. OFDM has also gained prominence in radar applications, includingsynthetic aperture radar (SAR) imaging [31], space-time adaptive processing (STAP) [32], radar target detection, and parameter estimation [33; 34; 35]. Consequently, extensive research focuses on OFDM IRCW, covering waveform design, ambiguity analysis, and receiving signal parameter estimation [36]. Due to differences between the DFRC OFDM waveform and traditional OFDM radar waveforms, the direct application of conventional radar parameter estimation methods for target detection is not feasible. OFDM radar typically employs pulse waveforms [32; 33; 34], whereas DFRC OFDM integrates communication signals, resulting in unique variations across each OFDM symbol. This variation complicates the application of standard radar target detection algorithms in DFRC systems. [PERSON] addresses this challenge by proposing an integrated OFDM radar and communication waveform approach, allowing the separate determination of the range and velocity. However, the algorithm described in [8] is effective primarily under the conditions of a high signal-to-noise ratio (SNR) and when the target echo energy is concentrated within the same range cell. The performance of detection is increasingly affected by advancements in stealth techniques and the presence of numerous moving targets, such as birds and UAVs. It is well known that the long-term integration of multiple sampling pulses significantly enhances the radar detection performance, addressing these challenges [37; 38; 39; 40]. Building upon the long-time coherent integration algorithm, several scholars have proposed intra-frame integration techniques. [PERSON] et al. proposed the Hough transform (HT) for the accumulation of energy from moving targets with a range walk (RW) [36; 41; 42]. [PERSON] et al. proposed the Keystone transform (KT), which utilizes range-frequency scaling to correct range ambiguities (RA) [43; 44]. [PERSON] et al. proposed the Radon Fourier transform (RFT) to achieve intra-frame coherent integration by leveraging the coupling between target motion and RW [45; 46; 47; 48; 49; 50]. In addition to intra-frame methods, researchers have also proposed inter-frame integration approaches [51; 52].