# Optimization of Effective Throughput in NOMA-Based Cognitive UAV Short-Packet Communication
## 4 Numerical and Simulation Results  
In this section, we provide the simulation results to show the performance of the proposed algorithm. The simulation parameters are set as follows: \(B=2\) MHz, \(N=200\), and \(H=120\) m. The horizontal distance from the UAV to \(u_{1}\) and \(u_{2}\) are \(r_{1}=10\) m and \(r_{2}=200\) m, respectively. The maximum transmission power of the UAV is \(P=10\) W. The sensing SNR is \(\gamma_{p}=-10\) dB. The noise power at the two secondary users is set to be \(\delta_{1}^{2}=\delta_{2}^{2}=-70\) dBmW. The probability of the idle state of the GBS is \(P(H_{0})=0.8\) and the detection probability is \(P_{d}=0.9\). The channel power gain at a distance of one meter is \(\beta_{0}=-50\) dB. The maximum decoding error probability is \(\epsilon_{\max}=10^{-6}\) and the maximum number of iterations of Algorithm 1 is \(t_{\max}=100\). In the OMA scheme, the resource allocation factor for \(u_{2}\) is 50%. Figure 2 shows \(\Phi_{2}\) versus the number of iterations for different values of \(P\). As shown in Figure 2, Algorithm 1 converges rapidly. It usually reaches convergence in ten iterations for the considered UAV transmission power, which indicates that the proposed algorithm has low complexity. Figure 3 shows the impact of the sensing time on \(\Phi_{2}\) when \(I=270\) bits, 300 bits, 330 bits. When the transmitted information bits are given, \(\Phi_{2}\) firstly increases and then decreases with the sensing time, and there is a unique optimal value such that \(\Phi_{2}\) achieves the maximum value. This coincides with the analysis in Theorem 1. When the value of \(N_{s}\) is small, the increase in the sensing time mainly leads to a decrease in the false alarm probability, thus \(\Phi_{2}\) is increased. However, when \(N_{s}\) is increased further, the increase in the sensing time mainly leads to an increase in \(\tilde{\epsilon}_{2}\) and \(\Phi_{2}\) is decreased. In addition, the optimal value of \(\Phi_{2}\) in the NOMA scheme is higher than that in the OMA scheme. Figure 4 illustrates the impact of information bits on \(\Phi_{2}\) for different values of the sensing time. When the sensing time is given, \(\Phi_{2}\) firstly increases and then decreases with the increase in the information bits and there exists a unique value that maximizes \(\Phi_{2}\). Therefore, Theorem 5 is verified. The increase in the information bits can enhance the value of \(\Phi_{2}\), but when the information bits reach a certain value, \(\tilde{\epsilon}_{2}\) will decrease sharply, causing \(\Phi_{2}\) to decrease to zero. It can be observed in Figure 4 that the NOMA scheme can achieve higher optimal values compared to the OMA scheme with the same sensing time. In Figure 5, the decoding error probability \(\varepsilon\) versus the SNR \(\gamma\) is shown. In Figure 5, it can be seen that the decoding error probability decreases as the SNR increases, which verifies Theorem 2. It can be seen in the figure that the information bits, sensing time, and SNR have a significant impact on the decoding error probability of the short-packet communication. Therefore, these three parameters need to be optimized in short-packet communication to reduce the impact of the decoding error probability on system communication performance. Figure 3: \(\Phi_{2}\) versus the sensing time for different schemes and \(I\). Figure 2: Convergence behavior of Algorithm 1 for various values of \(P\). Figure 6 describes the false-alarm probability versus the sensing time. In Figure 6, it can be seen that the false alarm probability decreases with the increase in the sensing time. It can also be seen in the figure that when \(\gamma_{p}\) is smaller and \(P_{d}\) is larger, the sensing time that the UAV uses to reduce the false-alarm probability will be larger. In order to ensure that the communication of the GBS is not interfered with by the UAV, the sensing SNR is usually required to be as low as possible, whereas the detection probability is less than but close to 1.