# On the Communication Performance of Airborne Distributed Coherent Radar
## 3 Results and Discussion  
In this section, the correctness of (50) will be verified by numerical simulation. We will change different system parameters (such as the distance of communication link, propagation loss coefficient, parameters of multi-path fading, etc.) to verify the correctness and robustness of (50) under different conditions. The method consists in, applying the Monte Carlo method under different parameters to generate a large number of samples of \(\gamma_{c}\) and \(\gamma_{b}\), and the kdensity function of MATLAB R2020a is also applied to fit the PDF of the samples. Then the OP can be calculated. This Monte-Carlo-based result will be denoted by \"simulation\" in the figures, while the corresponding theoretical value of (50) is represented by \"analysis\" in the figures. Before presenting the results, we first give the default parameters in Table 1. The meaning of default parameters is that unless otherwise specified in the results shown in this section, all parameters are taken based on the default parameters. It should be noted that we set \(\overline{\theta_{t}^{i}}=\overline{\theta_{r}}=0^{\circ}\). This is because we assume that each radar UAV is associated with a dedicated independent receiving antenna on communication UAV. In order to visually demonstrate the correctness of our theoretical derivation, we give the analysis and simulation curves of PDF of \(\sqrt{P_{r}^{i}{{{\left({F_{1}^{i}}\right)}^{2}}}}\sqrt{P_{r}^{i}G_{i}^{i}G_ {r}{{{\left({F_{1}^{i}}\right)}^{2}}}}\) by (27),\(\sqrt{P_{r}^{i}G_{i}^{i}G_{r}{{{\left({F_{1}^{i}}\right)}^{2}}}}\) by (30),\(\sqrt{P_{c}{{{\left({F_{2}^{i}}\right)}^{2}}}}\) by (37),\(\sqrt{P_{c}{{{\left({F_{2}^{i}}\right)}^{2}}}}\) by (40), and \(\sqrt{\gamma_{b}}\) Figure 3 under the default parameter conditions in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbols** & **Meaning** & **Value** \\ \hline \(N_{c}\) & Noise variance of communication UAV receiver & 1 \\ \(N_{b}\) & Noise variance of base station receiver & 1 \\ \(L_{1}\) & Distance of communication link 1 & 100 m \\ \(L_{2}\) & Distance of communication link 2 & 100 m \\ \(\alpha\) & Propagation loss coefficient & 2 \\ \(\mu_{r}^{i}\) & Mean of amplitude of radar UAV transmitter & 10 \\ \(\mu_{c}\) & Mean of amplitude of communication UAV transmitter & 10 \\ \(\sigma_{r}^{i}\) & Standard deviation of amplitude of radar UAV transmitter & 0.1 \\ \(\sigma_{c}\) & Standard deviation of amplitude of communication & 0.1 \\  & UAV transmitter & 0.1 \\ \(N_{radar}\) & Number of radar UAVs & 3 \\ \(N_{MC}\) & Number of SNR samples generated by Monte & \(10^{6}\) \\ \(k,l\) & Approximation order of noncentral chi-squared distribution & 80.80 \\ \(N_{t}\) & Number of radar UAV transmitting antenna array elements & 10 \\ \(N_{r}\) & Number of receiving antenna elements of & 10 \\  & communication UAV & 10 \\ \(\overline{\theta_{t}^{i}}\) & Radar UAV transmitting antenna pointing average & 0 \\ \(\overline{\theta_{r}}\) & Average direction of communication UAV receiving antenna & 0 \\ \(\sigma_{mt}^{i}\) & Standard deviation of radar UAV transmitting antenna & 0.06 \\  & misalignment & \\  & Standard deviation of communication UAV receiving & 0.06 \\ \(\sigma_{mr}\) & antenna misalignment & 0.06 \\ \(N_{s}\) & Number of antenna pattern samples & 100 \\ \(m\) & Nakagami fading parameters & 1 \\ \(\Omega\) & Nakagami fading parameters & 1 \\ \(K\) & Rice fading parameters & 1.5 \\ \(G\) & Approximate order of rice distribution & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Default parameters for numerical simulation. Figure 3: Numerical simulation of PDF. (**a**) \(\sqrt{p_{t}^{i}\left(F_{1}^{i}\right)^{2}}\), (**b**) \(\sqrt{p_{t}^{i}G_{t}^{i}G_{r}\left(F_{1}^{i}\right)^{2}}\) by (27), (**c**) \(\sqrt{p_{t}^{i}G_{t}^{i}G_{r}\left(F_{1}^{i}\right)^{2}}\) by (30), (**d**) \(\sqrt{\gamma_{c}}\), (**e**) \(\sqrt{p_{c}\left(F_{2}\right)^{2}}\) by (37), (**f**) \(\sqrt{p_{c}\left(F_{2}\right)^{2}}\) by (40), (**g**) \(\sqrt{\gamma_{b}}\), respectively.