# Smart Gateway for Healthcare Networks Based on Beam Steering Technology
## 3 Directivity Measurements
### Interferometric AOA Estimation  
To implement the weight functions defined by Equation (2), we introduce the use of a simple AOA network. Figure 12 shows the network that generates the received signal \(E_{\Delta}\) utilized for the AOA estimation. Figure 12a illustrates a schematic diagram of an AOA network, whereas Figure 12b depicts a fabricated microwave circuit using a double-sided printed circuit board (an FR4-based PCB) with a thickness of 1 mm and a relative permittivity of 4.2.  
Figure 12: Small-sized AOA network: (**a**) schematic diagram and (**b**) fabricated AOA network.  
The phase of the received signals for each element is delayed in accordance with Equation (2). A 180\({}^{\circ}\), a rat-race hybrid allows a 180\({}^{\circ}\) phase reversal to be involved in the two signals, and the 90\({}^{\circ}\) phase difference for the two signals synthesized in the two Wilkinson power combiners is introduced by using differing lengths of microstrip transmission lines, enabling a small-sized AOA network to be realized.  
Figure 13 shows the phase characteristics of the fabricated AOA network. The phase difference between Port #\(i\) (\(i=1,2,\ldots,4\)) and output port (\(E_{\Delta}\)) is measured at 2 GHz using a vector network analyzer. In Figure 13, the phase difference between Port #1 and the output port is used as the reference.  
As shown in Figure 13, the measured phase increases by 90\({}^{\circ}\) intervals with an increase in the element number. Furthermore, the difference between the measured and designed phases is 1.6\({}^{\circ}\) on average. These facts indicate that the fabricated AOA network works properly to achieve the operation of the weight function given by Equation (2).  
An experimental verification of the AOA estimation function in the proposed antenna was conducted in an anechoic chamber. The fabricated antenna is composed of four dipole antennas (#1-#4), which are mounted on a circle with a radius \(a=3.9\) cm, and another dipole antenna (#5) is located at the center of the circle. The length of all dipole antennas is 6.8 cm. A photograph of the fabricated antenna will be presented later.  
Figure 14 shows the complex radiation patterns of \(E_{\Delta}\) and \(E_{\Omega}\) defined in the \(xy\)-plane. Figure 14a,b show the amplitude and the phase characteristics, respectively. The black curves depict the vertical polarization component of \(E_{\Delta}\), whereas the red curves are that of \(E_{\Omega}\). The solid and broken curves indicate the measured and calculated results, respectively.  
Figure 14: Measured complex directivity for the AOA estimation function: (**a**) amplitude and (**b**) phase.  
Figure 13: Phase characteristics of the fabricated AOA network.  
As shown in Figure 14a, the measured radiation patterns of \(E_{\Delta}\) and \(E_{\Omega}\) agree well with the calculated patterns obtained through the method of moments and have an omnidirectional pattern overall. The maximum radiation gain is approximately 0 dBd, which is equivalent to that of a half-wavelength dipole antenna. Hence, the fabricated antenna can receive the signal radiated from the sensor device during the AOA estimation.  
In Figure 14b, the measured phase characteristic of \(E_{\Omega}\) coincides with the calculated value and remains constant regardless of the azimuth angle, indicating that this works as the reference angle for the AOA estimation. On the other hand, there is a little difference between the measured phase characteristic of \(E_{\Delta}\) and the calculated value at the azimuth angles from \(135^{\circ}\) to \(270^{\circ}\). The reason for this is the electromagnetic distortion arising from the coaxial cables connected between the dipole antennas and the AOA network circuit. However, the two phases' characteristics are generally consistent, indicating that the angle of the incoming wave can be estimated by the proposed antenna.