# Enhancing Communication Security in Drones Using QRNG in Frequency Hopping Spread Spectrum
## 4 Methodology and System Architecture
### Enhanced Security Analysis
#### 4.5.3 Latency and Throughput Models  
In communication systems, latency \(L\) refers to the time delay experienced by data as it travels through the system. It can be expressed as:  
\[L=L_{\text{prop}}+L_{\text{proc}}+L_{\text{sync}}+L_{\text{queue}} \tag{13}\]  
where:  
* \(L_{\text{prop}}\) is the propagation delay,
* \(L_{\text{proc}}\) is the processing delay,
* \(L_{\text{sync}}\) is the synchronization delay,
* \(L_{\text{queue}}\) is the queuing delay. While latency is an important parameter affecting the system's responsiveness, throughput \(T\) is a measure of how much data can be successfully transmitted over the communication channel per unit time. It is influenced by factors such as bandwidth, modulation schemes, coding rates, and error rates. The throughput can be modeled as:  
\[T=R\times(1-P_{e}) \tag{14}\]  
where:  
* \(R\) is the raw data rate (bits per second),
* \(P_{e}\) is the bit error rate (BER). The raw data rate \(R\) depends on the bandwidth \(B\) and the spectral efficiency \(\eta\) (measured in bits per second per Hertz):\[R=B\times\eta \tag{15}\]  
In the context of our FHSS system with true random frequency hopping, the hopping rate \(R_{h}\) can impact the effective data rate due to factors such as the time required for frequency switching and synchronization overhead. The effective data rate \(R_{\text{eff}}\) can be adjusted to account for these factors:  
\[R_{\text{eff}}=R\times\left(1-\frac{t_{\text{switch}}+t_{\text{sync}}}{T_{ \text{hop}}}\right) \tag{16}\]  
where:  
* \(t_{\text{switch}}\) is the time taken to switch frequencies,
* \(t_{\text{sync}}\) is the time spent on synchronization during each hop,
* \(T_{\text{hop}}\) is the duration of each hop (i.e., \(T_{\text{hop}}=\frac{1}{R_{h}}\)). The throughput then becomes:  
\[T=R_{\text{eff}}\times(1-P_{e}) \tag{17}\]  
This formulation acknowledges that while latency affects the timing of data delivery, throughput is primarily determined by the data rate and the error performance of the system. High latency does not necessarily reduce the throughput but can impact the overall system performance in terms of delay-sensitive applications. It is important to understand that in practical FHSS systems, certain physical and protocol-level factors can introduce delays during frequency hopping. Firstly, although the transmitter and receiver are synchronized in terms of timing and frequency hopping sequence, the actual process of switching frequencies involves hardware components that require a finite amount of time to change from one frequency to another. This time is known as the frequency switching time \(t_{\text{switch}}\), and it can vary depending on the specific hardware used in the system. During this switching period, the transmitter and receiver may not be able to send or receive data, resulting in a brief interruption in communication. Secondly, maintaining synchronization often involves the exchange of synchronization signals or the execution of synchronization algorithms, which consume processing time \(t_{\text{sync}}\). Even with precise synchronization, periodic adjustments and computations are necessary to compensate for clock drift and other factors, introducing processing delays. Therefore, the total effective time available for data transmission during each hop is reduced by the sum of \(t_{\text{switch}}\) and \(t_{\text{sync}}\). This reduction in available transmission time per hop effectively decreases the data rate, which is why we adjust the effective data rate \(R_{\text{eff}}\) to account for these factors in the throughput model. Including \(t_{\text{switch}}\) and \(t_{\text{sync}}\) in the calculations allows for a more accurate representation of the system's performance, especially when considering high hopping rates \(R_{h}\). As \(R_{h}\) increases (i.e., the duration of each hop \(T_{\text{hop}}\) decreases), the proportion of time spent on frequency switching and synchronization relative to the total hop duration becomes more significant, potentially impacting the overall throughput.