## 3 Results and Analysis
Meanwhile, for the uplink transmission with the same distance, the reflectance values increase to 19%, 18%, 17.5%, and 17% at the 1524, 1524.8, 1525.6, and 1526.4 nm wavelengths, respectively, as depicted in Figure 8b. It is realized that at 1524 nm, the system undergoes BER deviation compared to other wavelengths, owing to the impact of temperature-induced variations, material non-uniformity, interference effects, and Fresnel reflection alternations at a high lens reflectance. Table 3 depicts the summarized results for both the downlink and uplink transmission for varied lens reflectance values. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Downlink** & **Lens** & **Uplink** & **Lens** \\
**Wavelength** & **Reflectance (\%)** & **Wavelength** & **Reflectance** \\  & & **(nm)** & **(\%)** \\ \hline
1596 & 14.5 & 1524 & 19 \\
1596.8 & 13 & 1524.8 & 18 \\
1597.6 & 12 & 1525.6 & 17.5 \\
1598.4 & 13 & 1526.4 & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summarized results for varied lens reflectance values for different wavelengths. Figure 7: Eye patterns for different downlink and uplink wavelengths at a 0.085 m focal length. Figure 9a,b depict the system's performance in terms of the GIMMF mode versus the coupling coefficient for the downlink and uplink wavelengths at the LP[0,1] mode. The fiber range of 4.5-5.5 km with an aggregate symmetric data rate of 40 Gbps is presented. For all operating wavelengths, the lowest power fractions of \(\sim\)10\({}^{-11}\) in the downlink and 10\({}^{-10}\) in the uplink are observed for the higher-order modes, viz., LP[1,1] and LP[\(-\)1,1]. At the fundamental LP[0,1] mode, the maximum power is received, i.e., 0.52 in the downlink and 0.53 in the uplink. Meanwhile, after the LP[0,2] mode, the fraction of power decreases sharply for LP[4,2] until \(\sim\)1 \(\times\) 10\({}^{-7}\) in both the uplink and downlink transmission. Additionally, the corresponding phase value for each LP mode decreases from the LP[0,1] to the LP[\(-\)1,1] mode, as depicted in Figure 9a,b. Here, the LP mode phase changes from 0.23 to 4.79 rad in the downlink and 0.96 to 5.81 rad in the uplink. Higher-order LP modes lead to fluctuations in the power penalty among the diverse LP modes, owing to scattering losses and fiber nonlinearity [22]. Figure 10a-d depict the system's performance analysis for a varied fiber range from 4.6 to 5.5 km for both the downlink and uplink transmission. In an optical network, high gain is used to compensate for the fiber losses; a low noise figure and a high OSNR signify better signal quality at the receiver side. Mathematically, gain, noise figure, and OSNR are described as follows:  
\[Gain=10 log_{10}\bigg{(}\frac{Output\ Power}{Input\ Power}\bigg{)}\ \mathrm{dB} \tag{5}\]  
and  
\[Noise\ Figure=10 log_{10}\bigg{(}\frac{Input\ SNR}{Output\ SNR}\bigg{)}\ \mathrm{dB} \tag{6}\]  
and  
\[OSNR=10 log_{10}(SNR)\ \mathrm{dB} \tag{7}\]  
For the downlink transmission, the system gain varies from \(-\)30.42 to \(-\)29.47 dB, and the noise figure varies from 34.54 to 36.72 dB, as depicted in Figure 10a. For the uplink transmission, the gain and noise figure range from \(-\)25.58 to \(-\)47.33 dB and 28.84 to 42 dB, respectively, as shown in Figure 10b. Also, the \(-\)21.86 to \(-\)36.1 dBm and 30.51 to 28.28 dB values are obtained for the downlink output signal and the optical signal-to-noise ratio (OSNR), respectively, as shown in Figure 10c, while for the uplink transmission, the  
Figure 8: Lens reflectance vs. BER of (**a**) downlink and (**b**) uplink transmission. values of \(-18.46\) to \(-39.99\) dBm and \(18.05\) to \(-1.28\) dB for the output signal and OSNR are received, respectively, as depicted in Figure 10d. Figure 9: Observed fraction of power and phase performance for (a) downlink and (b) uplink transmission. Figure 10: _Cont._