## 2 Related Work  
The concept of FTN was first introduced by [PERSON] of Bell Labs in his 1975 research results [6], where he found that for a PAM(Pulse Amplitude Modulation) transmission system that uses SINC Pulses as a shaping filter, when the symbol interval isower than the Nyquist criterion and is transmitted in the AWGN channel, the minimum Euclidean distance between signals will not decrease in the symbol interval \(\tau\)T within the range of \(0.802\leq\tau\leq 1\). This means that the system can increase the spectrum efficiency by 25% while ensuring that the bit error rate performance is not affected. FTN re-examined the relationship between signal bandwidth, symbol rate, and spectrum efficiency, but it was not taken seriously at that time due to theimitations of hardware conditions. After a period of silence,iterature [7] observed that the FTN system formed by root raised cosine (RRC) also has Mazo-limited properties. Subsequently, the team from Sweden completed a series of groundbreaking studies on the development of FTN. They have successively confirmed that the Mazoimit is universal in the frequency domain [8], high-order modulation [9], multiple-antenna Multiple-Input and Multiple-Output (MIMO) [10], carrier [11], and other systems. In addition, it was proven that when the time domain compression factor \(\tau\) is set appropriately, the FTN system can achieve a higher channel capacity than the general orthogonal modulation system [12]. The research on FTN has gradually heated up in recent years, and the design of the FTN detection algorithm is the top priority of FTN research. Existing common model-driven FTN signal detection technologies mainly include methods based on maximumikelihood sequence estimation (MLSE) or maximum a posteriori (MAP). As part of the ISI information is known, and FTN signaling can be equivalently regarded as trellis coding, most of them are realized by the Viterbi algorithm (VA) [13] or BCJR [14] algorithm. The complexity of these optimal methods increases exponentially with the number of ISI taps and modulation order considered. Therefore, there are many efforts to find sub-optimal implementations. For example, the work in [15] introduces the successful symbol-by-symbol with go-back-K sequence estimation (SSSgbKSE) detection technology into the polar codes of FTN signaling, which is closer to the BCJR algorithm while reducing the complexity. The authors of [16] proposed an FPGA-based sliding-window max-log MAP algorithm that can be directly applied to FTN transmission systems to mitigate ISI. Theiterature [17] proposed a convex quadratic relax-and-quantize sequence estimation (CQRAQSE) algorithm suitable forow-rate FTN transmission based on convex relaxation. Although suboptimal implementation algorithms based on MLSE or MAP can achieve good detection accuracy, the implementation complexity is always exponential. Compared with the exponential complexity algorithm with higher complexity, the frequency domain equalization based oninear complexity hasover complexity, but the performance is relatively poor. Compared with the exponential complexity algorithm with higher complexity, the frequency domain equalization based oninear complexity hasover complexity, but the performance is relatively poor. The article [18] proposed a cyclic block transmission scheme, namely CB-FTN, which uses cyclic convolution instead ofinear convolution for pulse shaping, andow-complexity frequency domain equalization can be used at the receiver to compensate for channel damage and Inherent ISI. In reference to the CB-FTN scheme, the authors of [19] proposed a transceiver equivalent implementation scheme based on DFT (DBT-FTN), which can effectively reduce the complexity of base-band signal processing at both ends of the transceiver. The works in [20; 21] extended the DBT-FTN transmission scheme from single-carrier to multicarrier, forming a multicarrier DBT-FTN (DBT-MC-FTN) scheme.