# Impact of Weather Factors on Unmanned Aerial Vehicles' Wireless Communications
## 2 Methodology
### Mathematical Models
#### 2.1.5 BER Evaluation  
In this section, we evaluate the impact of weather-induced attenuation in terms of BER performance for different weather conditions and different modulation schemes (binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), 16-quadrature amplitude modulation (QAM), 64-QAM, and 256-QAM). The BER of a communication system represents the probability that a transmitted bit is received erroneously. It is influenced by various parameters, including the modulation order \(M\), which denotes the number of distinct symbols utilized to encode the data. Figure 4: Attenuations along the path of propagation due to atmospheric weather variations. We included higher order modulation schemes as the next generation command and control systems are poised to use 5G and 6G technologies. These new generations of wireless technologies are specified to use higher order modulation for more efficient use of the limited wireless spectrum, while supporting lower order modulation schemes for backward compatibility reasons. Higher modulation orders enable the transmission of more bits per symbol, thereby increasing data rates over a given bandwidth. For instance, given a specific symbol rate over a corresponding bandwidth, 1-bit per symbol is transmitted utilizing the BPSK modulation scheme, whereas the implementation of QPSK, 16, 64, and 256-QAM facilitates the transmission of 2, 4, 6, and 8-bits per symbol, respectively. Due to the limited availability of wireless bandwidth, maximizing the number of bits per symbol is a fundamental requirement in all wireless communications. Consequently, although the utilization of lower modulation orders may satisfy the command and control data transmission requirements between the UAV and the GCS, considering the constraints of narrow bandwidth availability, we have incorporated higher modulation schemes in our simulations. The utilization of higher modulation schemes renders the system more susceptible to noise and interference. This is due to tighter packing of the symbols within the in-phase and quadrature plane (IQ-plane), making the symbols more susceptible to noise, as small positional variation of the symbol within the IQ-plane increases the probability of symbol boundary crossing and hence a higher probability of symbol misinterpretation. For BPSK and QPSK modulations, the probability of bit error (\(P_{b}\)) is approximated by [21] as follows:  
\[P_{b}=Q\Big{(}\sqrt{2\gamma_{b}}\Big{)} \tag{7}\]  
where \(Q(. )\) indicates the error function and \(\gamma_{b}\) is the SNR per bit. For M-QAM, \(P_{b}\) is approximated by [21] as follows:  
\[P_{b}=\frac{4}{\log_{2}M}Q\Bigg{(}\sqrt{\frac{3\overline{\gamma_{b}}\log_{2}M} {M-1}}\Bigg{)} \tag{8}\]  
where \(M\) indicates the number of constellation points in the QAM array and \(\overline{\gamma}_{b}\) represents the average SNR per bit. SNR is a critical factor in BER computation. For a given set of operating parameters, such as power transmission, propagation distance, operating frequency, and GCS and UAV heights, experimental measurements show that propagation environments have a detrimental effect on its value at the receiver. Path loss is an important factor that governs the SNR at the receiver. Several models exist in the literature that aim to model the path loss associated with GCS-to-UAV and UAV-to-UAV communications [22; 23; 24; 25]. Inclusion of wide variations of weather conditions are not included in these models. Therefore, to include the effect of weather conditions on the received power at the receiver, we added the attenuation caused by weather conditions to the path loss predicted by the selected path loss model. The received power \(P_{\kappa}\) in dB is then computed as follows:  
\[P_{rx}=P_{tx}-(PL+A_{total}) \tag{9}\]  
where \(P_{tx}\), \(PL\), and \(A_{total}\) are the power transmission, path loss, and weather-based total attenuation along the path of propagation; all in dB.