# Performance Analysis of Amplitude Comparison Monopulse Direction-of-Arrival Estimation
## 5 Performance Analysis of Amplitude Comparison Monopulse  
This section shows the performance of monopulse radar in a noise environment. Table 1 tabulates various parameters of the simulation. The MSEs with respect to the standard derivation of an additive noise are illustrated in Figures 3 and 4 for amplitude comparison monopulse radar. The estimates used for getting 'Simulation \(E\left[\left(\bar{\theta}^{\prime}-\bar{\theta}_{\mathrm{T}}\right)^{2}\right]\)' in Figures 3 and 4 are obtained from (15), and those for getting 'Simulation \(E\left[\left(\bar{\theta}^{\prime}-\bar{\theta}_{\mathrm{T}}\right)^{2} \right]\)', in Figures 3 and 4 are obtained from (18), and those for getting 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=2})-\bar{\theta}_{ \mathrm{T}}\right)^{2}\right]\)', in Figures 3 and 4 are obtained from (19) and (20). Empirical MSEs of 'Simulation \(E\left[\left(\bar{\theta}^{\prime}-\bar{\theta}_{\mathrm{T}}\right)^{2} \right]\)', 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=1})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', and 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=2})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', in Figures 3 and 4 are calculated from (27). The results in Figures 3 and 4 with 'Analytic \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=1})-\bar{\theta}_{ \mathrm{T}}\right)^{2}\right]\)', are obtained from (28), and those in Figures 3 and 4 with 'Analytic \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=2})-\bar{\theta}_{ \mathrm{T}}\right)^{2}\right]\)', are obtained from (29) and (30). There is a little difference between 'Simulation \(E\left[\left(\bar{\theta}^{\prime}-\bar{\theta}_{\mathrm{T}}\right)^{2}\right]\)', and 'Simulation \(E\left[\left(\bar{\theta}^{\prime}-\bar{\theta}_{\mathrm{T}}\right)^{2} \right]\)', because \(\theta^{\prime}\) and \(\phi^{\prime}\) are approximated estimates defined from the approximate antenna pattern. Note that \(\theta^{\prime o}\) and \(\phi^{\prime o}\) are true estimates defined from (3). Also, 'Simulation \(E\left[\left(\bar{\theta}^{\prime}-\bar{\theta}_{\mathrm{T}}\right)^{2}\right]\)' is not equal to 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=1})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', as the first-order approximation is used to get 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=1})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', from 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=1})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)'. Similarly, 'Simulation \(E\left[\left(\bar{\theta}^{\prime}-\bar{\theta}_{\mathrm{T}}\right)^{2}\right]\)' is not equal to 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=2})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', as the second-order approximation is used to get 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=2})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', from 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=1})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', and 'Analytic \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=1})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', show excellent agreements, which validates (5.8) with 'approxi = 1'. Also, 'Simulation \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=2})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', and 'Analytic \(E\left[\left(\bar{\theta}^{\prime}(\mathrm{approxi=2})-\bar{\theta}_{\mathrm{ T}}\right)^{2}\right]\)', show excellent agreements, which validates (19) and (20) with 'approxi = 1'.