# A Novel Complex-Valued Blind Source Separation and Its Applications in Integrated Reception
## 7 Conclusions  
In this paper, a new method for CVBSS is proposed to address the problems of low separation accuracy, slow convergence, and poor robustness in the case of a low SNR and  
Figure 11: Pulsed Doppler processing of the echo signal. (**a**) Three dimensions, (**b**) two dimensions.  
Figure 10: Pulse compression of the observed signal (proposed). (**a**) Single pulse, (**b**) multiple pulses.  
Figure 9: Pulse compression of the observed signal (JADE). (**a**) Single pulse, (**b**) multiple pulses.  
high JSR. Firstly, a time delay mixing model based on a uniform line array is established, and an amplitude phase correction and DOA estimation method is given on the basis of this model. Then, the whitening matrix is calculated by the linear combination of multiple time delay correlation matrices based on the feature that the time delay correlation matrix is insensitive to noise. Secondly, the whitening matrix is calculated by the linear combination of multiple time delay correlation matrices based on the feature that the time delay correlation matrix is insensitive to noise. Thirdly, to further improve the optimization accuracy and convergence speed, a nonlinear convergence factor and chaotic perturbation operator are added to the GWO. Finally, NCGWO is used to optimize the joint diagonalization objective function. The solution of the separation matrix is transformed into the solution of the rotation angle in a complex-valued Givens matrix. Simulation results show that the proposed algorithm has higher separation accuracy and fewer iteration times compared with the traditional algorithm. At the same time, it can improve the DOA estimation accuracy, reduce the communication bit error rate, and achieve the joint estimation of the target distance and velocity.  
Due to equipment limitations and objective conditions, it is sometimes impossible to deploy an extensive number of sensors, resulting in a situation where the number of sensors is smaller than the source signal. BSS with fewer sensors than the source signal is called underdetermined blind source separation. Consequently, the problem of BSS with integrated reception under an underdetermined case emerges as a significant research area for the future.  
Conceptualization, W.L. and R.Y.; methodology, X.L.; software, W.L. and K.L.; validation, W.L., H.J. and X.L.; formal analysis, H.L.; investigation, W.L.; resources, H.J. and X.L.; data curation, K.L.; writing--original draft preparation, W.L.; writing--review and editing, W.L. and R.Y.; visualization, K.L.; supervision, H.J.; project administration, R.Y.; funding acquisition, X.L. and H.L. All authors have read and agreed to the published version of the manuscript.  
This paper is supported under the National Defense Science and Technology Innovation Zone Fund of China (Grant No. 17H86304 ZT00302) and the National Natural Science Foundation of China (Grant No. 61502522).  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors would like to acknowledge the National Defense Science and Technology Innovation Zone Fund of China (Grant No. 17H86304 ZT00302) and National Natural Science Foundation of China (Grant No. 61502522).  
The authors declare no conflict of interest.