# Smart Gateway for Healthcare Networks Based on Beam Steering Technology
## 2 Smart Gateway Antenna
### Interferometric AOA Estimation Method
Hence, we determined the array radius to be 3.9 cm because the accuracy of the estimation angle of the incoming wave may decrease with increasing array radius, as shown in Figure 4. Consequently, the distance between the elements, which are arranged at equal angular intervals on a circle, is approximately 5.5 cm, that is, at 0.37 \(\lambda\). Figure 5b shows the radiation gain in \(E_{\Delta}\) and \(E_{\Omega}\) at \(\phi=0^{\circ}\) as a function of the element length. The radiation gain takes into account the mismatch loss in order to consider the effects of electromagnetic mutual coupling. The black and red curves indicate the radiation gain in \(E_{\Delta}\) and \(E_{\Omega}\), respectively. The array radius is set to 3.9 cm. As shown in Figure 5b, the radiation gain in \(E_{\Omega}\) decreases with increasing element length. Similar to Figure 5a, that of \(E_{\Delta}\) is almost constant but is largest at \(l=6.8\) cm, that is, at 0.45 \(\lambda\). Hence, we determined the element length to be 6.8 cm because a shorter element length deviates from the operating principle of a half-wavelength dipole antenna. Figure 6 shows the calculated amplitude radiation pattern of \(E_{\Delta}\) and \(E_{\Omega}\) defined in the \(xy\)-plane. Figure 6a is the case of \(a=4.9\) cm and \(l=7.5\) cm as the configuration before the redesign, in which the number of elements has been reduced from the conventional AOA antenna [24; 25]. Figure 6b shows the case of \(a=3.9\) cm and \(l=6.8\) cm as the configuration after the redesign. The black curve indicates the radiation pattern of \(E_{\Delta}\), whereas the red curve is the radiation pattern of \(E_{\Omega}\). Figure 5: Radiation gain of the AOA estimation function in the proposed antenna: (**a**) array radius and (**b**) element length. It can be seen from Figure 6 that the difference between the maximum and minimum gains of the directivity after the redesign is smaller than that before the redesign for both \(E_{\Delta}\) and \(E_{\Omega}\), but especially for \(E_{\Delta}\), thereby enabling a more omnidirectional radiation pattern. Moreover, the radiation gain in \(E_{\Omega}\) after the redesign is greater than that before the redesign. Hence, the received level of \(E_{\Omega}\) is expected to improve by about 4 dB. To verify the accuracy of the estimation angle of the incoming wave, the radio-frequency (RF)-based interferometric monopulse technique was performed using the calculated complex radiation pattern. Figure 7a shows the phase characteristics of \(E_{\Delta}\) and \(E_{\Omega}\) as a function of the azimuth angle. The black and red lines indicate the configuration after and before the redesign, respectively. From the analytical results presented in Figure 7a, the severe fluctuations that existed before the redesign have disappeared in the phase characteristics of \(E_{\Delta}\), indicating that this is suitable as a reference angle. However, the phase characteristics of \(E_{\Delta}\) after the redesign also have oscillations, but they are smaller than those before the redesign. The  
Figure 6: Amplitude radiation pattern of the AOA estimation function: (a) \(a=4.9\) cm and \(l=7.5\) cm; (b) \(a=3.9\) cm and \(l=6.8\) cm. Figure 7: Analytical results of the angle estimated by the proposed antenna: (a) phase characteristics and (b) estimation error. reason is that the amplitude radiation pattern of \(E_{\Delta}\) approaches an omnidirectional form, as shown in Figure 6. The phase characteristics of \(E_{\Delta}\) seem to be at the limit because the radiation gain does not change much regardless of the array radius and element length, as shown in Figure 5. The improvement in the phase characteristics of \(E_{\Delta}\) will be a subject for future study. Figure 7b shows the error of the estimated angle of the incoming wave as a function of the actual angle. The black and red lines indicate the configuration after and before the redesign, respectively.