## 5 Results and Discussion  
In this section, the results of the proposed MDM-WDM FSO link have been investigated by employing DP-QPSK modulation under real weather conditions. The signal to noise ratio (SNR) of the received signal has been analyzed and compared as a function of transmission range considering diverse geographical regions for different channels. Next, the received power has been obtained as a function of the propagation range for the four regions, and ML techniques have been employed for SNR estimation of the received signal. Figure 8 depicts the comparative analysis of attenuation due to different weather conditions in the four regions. It can be observed that clouds and haze cause a maximum attenuation of 10.06 and 4.84 dB/km in the case of New Delhi and London regions, respectively. Fog is the main contributing factor affecting visibility in Washington and Cape Town regions. Maximum attenuation has been reported in the New Delhi region due to cloud and haze weather conditions in December, February, and January months, respectively. Next, a unified empirical model has been developed for the prediction of overall attenuation of a region due to different weather conditions at 1550 nm. To describe the relationship between a set of visibility values and average attenuation, a least squares method has been utilized. The performance of the model has been measured using R squared and mean square error (MSE) as performance metrics. R squared measures the percentage of variance of the dependent variable that can be predicted based on the independent variable. It indicates the goodness of fit of the regression model and is defined as [18]:  
\[\mathbb{R}^{2}=1-\frac{\sum{(y\text{actual}-\text{y predicted})2}}{\sum{(y \text{actual}-\text{y mean})2}} \tag{10}\]  
Mean square error is the ratio of the square of difference between the predicted and mean values compared to the number of observations. MSE measures the variance of the fitted curve and is given as [18]:  
\[\text{MSE}=\frac{\sum{(y\text{actual}-\text{y predicted})2}}{No.\,of\, observations} \tag{11}\]  
Table 5 depicts the regression models for predicting attenuation (dB/km) as a function of visibility for different regions along with corresponding R squared and MSE values as performance metrics. Values of R squared fall between 0 and 1. The higher the value better fit the model. MSE is best suited for regression problems, as with large deviations, they are penalized severely by squaring errors, which raises the penalty for large errors. The maximum and minimum attenuation have been predicted for Delhi and Washington regions, respectively. In the case of the Delhi region, there is a better correlation between visibility values for the data set with different weather conditions. A moderate value of R squared prevents over-fitting of the model so that it performs better on unseen values of visibility. MSE is a measure of the quality of the estimation. Performance metrics and generalization of empirical models may be further improved by increasing the values in the data set and by incorporating more regions. The minimum mean square error and  
Figure 8: Comparative analysis of attenuation of four regions in different months. Figure 10 displays the SNR range for the Washington region with the constellation diagram obtained at a transmission range of 2 km considering channel 9 and channel 10. It can be observed from the graphs that SNR varies from 52.84 dBm to 42.26 dBm and 54.86 dBm to 42.94 dBm for Ch 9 and Ch 10, respectively. Figure 10 displays the SNR values for the London region depicting channel 1 and channel 2 along with the constellation diagrams observed at a transmission range of 2 km. A 3 dB higher value for SNR has been achieved in the case of the LG 01 mode at a wavelength of 1550 nm. As the range increases, the signal to noise ratio decreases due to geometric absorption and scattering losses. Figure 9: SNR as a function of transmission range: (**a**) New Delhi region; (**b**) Cape Town region.