# Performance Analysis of Interferometer Algorithm under Phase Measurement Error
## 6 Numerical Results
From Figures 2 and 5, the elevation MSE is greater than the azimuth MSE for small \(\psi^{(0)}=15^{\circ}\). Note that \(\frac{1}{(\sin(\psi^{(0)}))^{2}}\) is greater than \(\frac{1}{(\cos(\psi^{(0)}))^{2}}\) for \(\psi^{(0)}<45^{\circ}\). Figure 6: Performance for uniformly–distributed phase measurement error with \(\theta^{(0)}=120^{\circ}\) and \(\psi^{(0)}=45^{\circ}\). This figure shows the MSEs of azimuth and elevation with respect to phase error at a signal with medium incident elevation. It can be confirmed that the MSE of elevation is similar to that of the azimuth at medium elevation(uniform circular array). Figure 7: Performance for uniformly–distributed phase measurement error with \(\theta^{(0)}=120^{\circ}\) and \(\psi^{(0)}=75^{\circ}\). This figure shows the MSEs of azimuth and elevation with respect to phase error at a signal with high incident elevation. It can be confirmed that the MSE of elevation is smaller than that of the azimuth at high elevation(uniform circular array). On the other hand, from Figures 4 and 7, the elevation MSE is smaller than the azimuth MSE for large \(\psi^{(0)}=75^{\circ}\), which is consistent with (19) and (20) since \(\frac{1}{(\sin(\psi^{(0)}))^{2}}\) is smaller than \(\frac{1}{(\cos(\psi^{(0)}))^{2}}\) for \(\psi^{(0)}>45^{\circ}\). The observations summarized at the end of Section \"Performance analysis of phase comparison interferometer\" are validated from Figures 2-7. To see how the azimuth and elevation MSEs are dependent on true azimuth and true elevation of the incident signal for array geometry which is not uniform circular array, rectangular planar array is considered. The array geometry and simulation parameters for rectangular planar array are presented in Table 2. The results for the Gaussian-distributed measurement error are shown in Figures 8-10, and those for the uniform-distributed are illustrated in Figures 11-13. Figure 10: Performance for Gaussian\(-\)distributed phase measurement error with \(\theta^{(0)}=120^{\circ}\) and \(\psi^{(0)}=75^{\circ}\). This figure shows the MSEs of azimuth and elevation with respect to phase error at a signal with low incident elevation by monte-carlo simulation(rectangular planar array). Figure 9: Performance for Gaussian\(-\)distributed phase measurement error with \(\theta^{(0)}=120^{\circ}\) and \(\psi^{(0)}=45^{\circ}\). This figure shows the MSEs of azimuth and elevation with respect to phase error at a signal with low incident elevation by monte-carlo simulation(rectangular planar array). Figure 3:0 Performance for uniformly –distributed phase measurement error with \(\theta^{(0)}=120^{\circ}\) and \(\psi^{(0)}=15^{\circ}\). This figure shows the MSEs of azimuth and elevation with respect to phase error at a signal with low incident elevation by monte-carlo simulation(rectangular planar array). Figure 3:1 Performance for uniformly –distributed phase measurement error with \(\theta^{(0)}=120^{\circ}\) and \(\psi^{(0)}=45^{\circ}\). This figure shows the MSEs of azimuth and elevation with respect to phase error at a signal with low incident elevation by monte-carlo simulation(rectangular planar array). and (16), and the MSEs are obtained from (18) and (19), two demerits of the Monte-Carlo simulation-based performance analysis can be removed. We assume that an additive noise on the antenna elements is Gaussian distributed or uniformly distributed. Noise at each antenna is spatially white. In the case of azimuth/elevation estimation of an incident signal using the UCA, it has been shown that the azimuth estimate and the elevation estimate associated with the interferometer algorithm can be expressed in the closed-form as (15) and (16), respectively. The closed-form expressions of the MSEs of the azimuth estimate and the elevation estimate can be obtained from (18) and (19), respectively, without computationally intensive Monte-Carlo simulation. The dependence of the azimuth MSE and the elevation MSE on the true elevation has been derived.