# Dispersive FSO Performance Estimation with Gaussian Pulses and Laplace Modeled Time Jitter
## 4 Numerical Results  
In this section, the numerical outcomes from the model equations above are presented using indicative realistic parameter values. It should be mentioned here that using the above-derived mathematical expressions, the FSO link's performance can be accurately estimated for any parameter values set for each optical wireless communication system under consideration. Thus, we assumed a horizontal terrestrial FSO link operating at 0.85 \(\upmu\)m with a transmission rate of 7 Gbps at a height of 30 m above the earth surface. The length of the link was assumed to be either 5 or 10 km, whereas two pulsewidths are examined, i.e., \(T_{pw}=25\) ps or 15 ps. Additionally, the propagated pulses can be either up-chirped or down-chirped, i.e., \(C=\pm 15\), with power losses, i.e., \(l=0.1\) km\({}^{-1}\). Finally, the TJ influence was investigated for two strength parameter values, i.e., \(\sigma_{T}=30\) ps and 50 ps.  
The irradiance amplitude profiles are illustrated in Figure 1 for many pulses, corresponding to some interesting characteristic values of the studied model. At first, three pulse couples were distributed at three different TJ instants of 0 ps, 30 ps and 50 ps, representing cases without TJs and with TJs, which are equal to the two strength parameter values studied. To avoid misunderstandings, the time-jittered cases illustrated are neither fixed nor the most probable ones since the mean of the Laplace distribution has been set to zero. However, they are indicative cases of the respective TJ strength since the probability of a TJ to be between zero and either \(\sigma_{T}\) is exactly \(0.5[1-\exp(-1)]\approx 31.6\%\). Hence, the green curves correspond to the original pulses at \(z=0\) for two different original pulsewidths,while the black and the red curves represent the up-chirped and the down-chirped versions of the green pulses, respectively, received after 5 km (left panel) and 10 km (right panel) and affected by power losses action. Additionally, at the time instant of 71.4 ps, the time slot edge corresponding to the studied bit rate is illustrated. Remarkably, the height of each pulse case, as detected at the time slot center line, was crucial for both the availability and reliability of the respective case. Among the curves with the same original pulsewidth, the most time-jittered pulses had lower irradiance height at the time slot center, according to the distinguishing inset plots on the left of each panel. Additionally, among cases with the same TJ, the larger the original pulsewidth, the higher the irradiance at the time slot center. In all cases, the down-chirped pulses had a little less height than the corresponding up-chirped pulses at that point.  
Next, Figure 2 represents the OP as a function of the normalized average SNR, \(\overline{\gamma}/\gamma_{thr}\), with various original pulsewidths, TJ strength parameters, and opposite chirp values for an FSO link of either 5 km or 10 km. In all cases, the curves' slopes constantly declined, implying lower OP for larger normalized average SNR values. Additionally, larger pulsewidth cases had lower OP performance compared with the smaller ones. Additionally, weaker TJ cases were more available than stronger ones. Lastly, the average BER as a function of the average SNR is depicted in Figure 3 for the same parameter combinations as in Figure 2. The curves here followed the monotony and arrangement of the corresponding curves of Figure 2. Hence, similar comments for the system's reliability can be made in accordance with the notes of the Figure 1 discussion.  
Figure 1: Irradiance amplitude profiles of some characteristic pulses within a time slot range with power losses (\(l=0.1\) km\({}^{-1}\)) and various original pulsewidths, TJ strength parameters, and opposite chirp values for an FSO link of (**a**) \(z=5\) km and (**b**) \(z=10\) km. The time slot edge indicated at the time instant of 71.4 ps corresponds to 7 Gbps.