# A Dual-Channel End-to-End Speech Enhancement Method Using Complex Operations in the Time Domain
## 5 Conclusions  
In this study, we propose a novel complex time-domain process and design a complex neural network structure called CNABCFCN for dual-channel end-to-end speech enhancement. We leveraged the Hilbert transform to generate complex time-domain waveforms and incorporated complex operation rules to develop a network consisting of a CNAB and a CFCN. The CNAB takes dual-channel complex inputs to produce a complex single-channel output, while the CFCN is cascaded to obtain the final enhancement. Furthermore, we used a new loss function called SI-SDR, which considers both the real and imaginary parts of the speech waveform to balance speech quality. We evaluated the proposed network under different scenarios and demonstrated its versatility and effectiveness. Our results show that adding imaginary information improves denoising performance, and the proposed network outperformed existing methods in all scenarios based on both objective and subjective evaluations. Future research should explore extensions to more than two channels. Conceptualization, J.P. and H.L. ([PERSON]); Methodology, J.P.; Software, H.L. ([PERSON]) and T.J.; Validation, H.L. ([PERSON]) and H.W. ; Formal analysis, J.P.; Investigation, H.W. ; Resources, X.L. ; Data curation, T.J. and X.L. ; Writing--review & editing, H.L. ([PERSON]); Supervision, L.L. ; Project administration, L.L. ; Funding acquisition, H.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript. This study was supported by State Key Laboratory of Intelligent Vehicle Technology (NVHSKL-202205) and Natural Science Foundation of Chongqing, China (No. cstc2021 jcyj-bshX0206). This study did not require ethical approval. * [PERSON] and [PERSON] (2019) [PERSON]; [PERSON] A new framework for CNN-based speech enhancement in the time domain. _IEEE/ACM Trans. Audio Speech Lang. Process._**2019**, _27_, 1179-1188. [CrossRef] [PubMed]
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