## 5 Detection of Received Signal Data Processing and ISI/BER Analysis
The ISI waveforms of the received pulse signal and the simulation results of the eye diagram and BER performance for the airborne channel after transmission with a visibility of \(V=20\) km and a standard deviation of the atmospheric refractive index fluctuation of \(\sigma_{n}=1\times 10^{-8}\) are shown in Figure 11.  
The simulation results show that the received pulse signal pulse spreading statistics after transmission over the airborne channel with a visibility of \(V=20\) km and standard deviation of atmospheric refractive index fluctuation averages \(\Delta\tau=86\) ps. In addition, the total pulse width statistics after transmitting 10,101 fixed code elements averages about 3000 ps, with some evidence of ISI influence on the system; the receiving eye diagram shows a microlosed state and the bit error rate is BER = \(2.9\times 10^{-3}\). Combined with the simulation results in Figure 10a,b, it can be seen that the laser pulse broadening after transmission via the air-to-air channel shows an inverse relationship with the channel's visibility parameter: the higher the visibility, the smaller the pulse broadening. The comparison of the phase and amplitude distortion corresponding to the time-domain pulse broadening extremes (maximum and minimum values) and the output waveforms under ideal conditions (without considering the effects of turbulence and absorption) under the typical operating conditions of airborne air-to-air channels is shown in Figure 12.  
Figure 11: ISI waveforms, eye diagram, and BER simulation results at visibility V = 20 km and \(\sigma_{n}=1\times 10^{-8}\) (threshold \(VT=0.46\)). (**a**) ISI waveform and (**b**) eye diagram and BER; SNR = 0.008 dB. An analysis of these results is presented below. 1. Under the simulation conditions of the thesis, the received time-domain pulse waveforms are all subject to different degrees of phase distortion after transmission over the airborne air-to-air channel. Among them, the received time-domain pulse signal with the most serious waveform distortion has a peak time shift of 1502.6 ns, which corresponds to a pulse spread of 98 ps, while the received time-domain pulse signal with a smaller waveform distortion has a peak time shift of 1502.0 ns, which corresponds to a pulse spread of 56 ps;
2. Under the simulation conditions of the thesis, the received time-domain pulse waveforms after transmission through the airborne air-to-air channel are subject to different degrees of amplitude distortion (manifested as a decrease in the peak amplitude). Compared with the peak value of the ideal received waveform, the maximum decrease in amplitude is \((4.22-2.05)/4.22=51.42\%\) and the minimum decrease in amplitude is \((4.22-3.28)/4.22=22.27\%\). The time-domain pulse waveform signal obtained after laser transmission through the airborne air-to-air channel reflects the channel's characteristics. After the time-varying airborne air-to-air channel transmission with waveform distortion characteristics of the impulse response signal at the receiving end of the sampling process after the formation of the received signal sequence, the paper that analyzed airborne channel conditions combined with this paper on the airborne air-to-air channel laser transmission of the analysis of the time-domain pulse spreading results of the dual-mode (variable-step CMA + DDLMS) blind equalization scheme can be selected as one of the more reasonable equalization schemes. As shown in Figure 13, the blind equalization scheme is one of the more reasonable equalization schemes. The received sequence is processed by the transversal filter to form an output signal estimate \(\hat{d}(n)\), based on which the receiver decides that the output is the symbol of the transmitted message closest to \(\hat{d}(n)\) as \(d(n)\) (defined as the desired response signal). The error function is defined as \(e(n)=d(n)-\hat{d}(n)\) and the size of the error function value can be used to guide the different equalization schemes actually adopted for subsequent data processing.