# MQC-MB: Multiphoton Quantum Communication Using Multiple-Beam Concept in Free Space Optical Channel
## 6 Numerical Results and Performance Analysis  
This section evaluates the performance of the proposed multiple-beam design against the standard beam, which is a single beam. The performance is evaluated under two scenarios: The first scenario with a static channel where the turbulence effects are ignored. In the second scenario, with fluctuating channel loss, turbulence effects are included. The important part of the problem is the value of \(\mu\) has to be adjusted to achieve a maximum secure rate. To find the optimum mean photon number \(\mu_{opt}\) related to the optimum secret key rate (\(K\)) and achievable maximum distance, the maximum number of photons that [PERSON] can use to encode her bits per pulse is \(N_{max}=12\), which is represented as multiphoton emission. The free space channel is assumed to be lossless by setting the channel length to \(L=0\) using the single beam. Figure 4 shows the increasing relationship between \(N_{max}\) and \(\mu_{opt}\), from \(N_{max}=1\) to \(N_{max}=12\). Therefore, from now onwards, the same value of \(\mu_{opt}\) will be used to evaluate the performance of the multiple beam for a fair comparison. The first part demonstrates the comparison between the single beam, two beams, three beams, and four beams by considering channel loss that consists of atmospheric and geometrical loss over the static channel, i.e., without turbulence effects. To ensure a fair comparison between single-beam and multiple-beam performance, it is assumed that the value of the parameters follow the settings as in Table 1. As depicted in Figure 5, it is clear that the total loss increased with the increment of the link range for all beams. As stated before, the total loss that comes from atmospheric and geometrical attenuation can be generated using Equation (6) for the single beam while Equation (7) for the multiple beams. It can be seen from the graph that multiple beams are able to reduce total loss compared to the single beam. It can be noted that the total loss by the proposed multiple beam at the link range of 5 km is 27 dB and it is lower than the result from the standard single beam, which achieved 34 dB. From single to multiple beams, the total loss keeps decreasing with the increasing link range. Theoretically, the geometrical loss depends on the number of the sender and receiver used when the values of the divergence angle and link range are set up at a fixed value. On the other hand, the received power level is one of the important parameters used to determine the link performance of FSO. Received power can be defined as the amount of  
Figure 5: Comparison of total loss (dB). power received at the antenna after being scattered by the sender. In other words, received power can be obtained after the geometric and atmospheric losses have been deducted. The simplified version of the received power equation is [5]:  
\[P_{RX}=\ P_{total}-L_{O}-L_{GEO} \tag{20}\]  
where \(L_{O}\) is the losses of optic while \(P_{total}\) is the total transmitted power in dBm:  
\[P_{total}=P_{TX}+\ 10\log_{10}N_{TX} \tag{21}\]  
where \(P_{TX}\) is the transmitter power in dBm and \(N_{TX}\) is the number of transmitters. The fundamental guideline to evaluate the received power can be expressed by \(P_{RX}\leq\ P_{TX}\)[15; 41]. Based on the analysis conducted by [5; 41], the received power increases as the number of beams increase. To make a fair comparison between a single and multiple-antenna system, the same transmitter power as stated in Table 1 is used in this work. Figure 6 plots the power received and the number of beams. It is analyzed through a graph that as the number of beams increases, the received power increases. The results show that the efficiency of the power received is increased by using up to four beams at the same initial transmit power value. Thus, the power consumption to transmit the data will be significantly lower compared to other combinations of beams. The graph also shows that the received power decreases as the distance between the transmitter and receiver increases.