# Smart Gateway for Healthcare Networks Based on Beam Steering Technology
## 2 Smart Gateway Antenna
### Interferometric AOA Estimation Method  
The proposed antenna estimates the angle of the incoming wave using a radio-frequency (RF)-based interferometric monopulse technique. The Butler matrix, which is used to give an appropriate phase delay to the received signals [27], has the drawback of being a bulky microwave component, which leads to hardware complexity. The AOA method proposed in this paper employs an RF-based interferometric monopulse technique without a Butler matrix, which reduces hardware complexity. Here, we explain the AOA estimation method. When a radio wave originates from the \(\phi\) direction, as measured from the \(x\)-axis, the voltage induced on the \(i\)-th element located on the circle with radius \(a\) can be calculated using the following equation:  
\[V_{i}=e^{j\frac{2\pi}{\lambda}a\cos{(\frac{2i-1}{4}\pi-\phi)}} \tag{1}\]  
where all the elements are assumed to be isotropic antennas, and \(\lambda\) denotes  
of the incoming wave. The effect of mutual couplings is not adequately considered in the theoretical formula. In fact, the electromagnetic mutual coupling between the elements occurs, so the amplitude and phase of the directivity will be fluctuating, resulting in an estimation angle error of the incoming wave. Figure 3 shows the summation of the whole voltage denoted by Equation (3) as a function of the array radius \(a\), together with the Bessel function drawn as the red broken curve. The magnitude of \(E_{\Delta}\) reaches a maximum value when the radius is 5.3 cm. This configuration of a narrow element spacing may lead to a significant gain reduction in the antenna due to the strong electromagnetic mutual coupling. Figure 4 shows the estimated angle \(\phi_{m}\) defined by Equation (5) as a function of the actual azimuth angle \(\phi\) with the array radius as a parameter. It can be seen from Figure 4 that the estimated angle is approximately proportional to the actual azimuth angle. However, the error of the estimation angle of the incoming wave increases with increasing array radius, indicating a tradeoff relationship between the radiation gain and the accuracy of the estimation angle. Figure 4: Estimation angle vs. angle of incoming wave. Figure 3: Summation of the whole voltage induced on the four elements. In general, a narrow element spacing may lead to a significant directivity fluctuation due to strong electromagnetic mutual coupling. To fulfill high performance in a small gateway antenna system, the proposed antenna needs to be redesigned to increase the radiation gain and to improve the estimation accuracy of the angle of the incoming wave. The directivity of the AOA estimation function with regard to the proposed antenna is calculated using the method of moments, and the effect of electromagnetic mutual coupling on the characteristics of the proposed antenna has been investigated. The dipole antenna with length \(l\) is used for the five array elements shown in Figure 2. All the dipoles are terminated at 50 \(\Omega\). It should be noted that, although the proposed smart gateway antenna is a receiving antenna, the analysis is conducted with a transmitting antenna on the basis of the reciprocal theorem throughout this paper. Figure 5a shows the radiation gain in \(E_{\Delta}\) and \(E_{\Omega}\) at \(\phi=0^{\circ}\) as a function of the array radius. The radiation gain takes into account the mismatch loss in order to consider the effects of the electromagnetic mutual coupling. For information, the array radius of a previous AOA antenna with eight elements on the circle is 4.9 cm [24; 25]. The black and red curves indicate the radiation gain in \(E_{\Delta}\) and \(E_{\Omega}\), respectively. The element length is set to 7.5 cm, i.e., half-wavelength. As shown in Figure 5a, the radiation gain in \(E_{\Omega}\) increases with increasing array radius. On the other hand, that of \(E_{\Delta}\) is almost constant but is largest at \(a=3.9\) cm, that is, at 0.26 \(\lambda\), it is roughly equivalent in size to the conventional ESPER antenna.