*4.2. Complexity Analysis*

We further analyze the complexity of the proposed J-DBN nonlinear equalizer and make a comparison with blind CMA and DD-LMS equalizers. We consider the complexity in two aspects, convergence steps and computation time, as is shown in Figure 8. Figure 8a shows that the convergence speeds of the DBN-1 and DBN-2 equalizers are faster than the conventional CMA and DD-LMS equalizers, which verifies the well-trained neural

networks. Moreover, the computation time of DBN-based equalizers can be approximately 36.3% and 46% lower than that of CMA and DD-LMS-based methods with similar BER performance, as is shown in Figure 8b. Therefore, the conclusion can be reached that the J-DBN equalizer has a significant advantage in dealing with nonlinear distortion, making it quite suitable in high-speed THz-band wireless communication systems.

**Figure 8.** Complexity analysis of the 36 Gbaud QPSK signals with different equalization options when the input power into AIPM is 12.8 dBm. (**a**) Loss function versus iteration numbers. (**b**) Comparison of the computation time.

#### **5. Conclusions**

In this paper, a novel J-DBN equalizer for the 144-Gbps QPSK signal transmission system over a 20-km SSMF and 3-m THz-band wireless link at 500-GHz is experimentally demonstrated, which consists of two steps including a DBN-1 adaptive equalizer based on the CMA algorithm and a DBN-2 blind equalizer based on the DD-LMS algorithm. We compare the J-DBN equalizer with the classical equalizer in terms of the BER performance. Meanwhile, our proposed J-DBN equalizer in the adaptive equalization step can reduce the computational complexity and obtain better training accuracy during the self-recovering blind equalization process. The experimental results show that the J-DBN method has good training accuracy, a smaller requirement for training sequences, and satisfactory computational complexity. Thanks to our proposed J-DBN scheme, an improvement of 0.2 dB and 0.8 dB over the J-DBN equalizer in receiver sensitivity and SNR gains at a BER of 3.8 × <sup>10</sup>−<sup>3</sup> is achieved compared with conventional equalizers. Moreover, the computational time is effectively improved, being up to 46% lower than the conventional equalizer. To our knowledge, this is the first time that joint DBN equalizers have been deployed in the THz-band wireless transmission link. Our proposed J-DBN equalization scheme is promising for future 6G fiber-optical and THz-wireless seamless integration communication systems.

**Author Contributions:** Conceptualization, X.L. and J.Z.; methodology, X.L. and J.Z.; software, W.T. and Y.W.; validation, B.H., M.L. and Y.C.; formal analysis, X.L., S.G. and J.Z.; investigation, X.L. and J.Z.; resources, X.L.; data curation, X.L.; writing—original draft preparation, X.L.; writing—review and editing, X.L., Y.Z. and J.Z.; supervision, M.Z.; project administration, M.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported in part by the National Natural Science Foundation of China (62101121 and 62101126), the project funded by the China Postdoctoral Science Foundation (2021M702501 and 2022T150486), the open project (2022GZKF003) of the State Key Laboratory of Advanced Optical Communication Systems and Networks of Shanghai Jiao Tong University,

the Transformation Program of Scientific and Technological Achievements of Jiangsu Province (BA2019026), the Key Research and Development Program of Jiangsu Province (BE2020012), and the Major Key Project of Peng Cheng Laboratory (PCL 2021A01-2).

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
