# Smart Gateway for Healthcare Networks Based on Beam Steering Technology
## 2 Smart Gateway Antenna
### Mean IQ-Value Method in Rice Propagation Environment
Then, the channel response of a direct wave \(h_{d}\) (illustrated as the red arrow in Figure 9b) can be expressed as follows:  
\[h_{d}=\sqrt{2 KP_{r}}\frac{E(\phi_{d})}{|E(\phi_{d})|} \tag{9}\]  
where \(K\) is defined as the ratio of \(P_{d}\) to \(P_{r}\), which is usually known as the Rice factor or K-factor. \(E(\phi_{d})\) denotes the complex electric field directivity of the AOA estimation  
Figure 9: Channel model dependent multipath characterization: (**a**) Rice channel model and (**b**) vector diagram. function in the proposed antenna (\(E_{\Delta}\) or \(E_{\Omega}\)). As shown in Figure 9b, the signal response \(h_{s,c}\) (illustrated as the black arrow in Figure 9b) is expressed as follows:  
\[ \begin{split} h_{s,c}&=h_{d}+h_{s,r}\\ &=\sqrt{2 KP_{r}}\frac{E(\phi_{d})}{|E(\phi_{d})|}+\sum\limits_{n= 1}^{N}\left(h_{n}\exp\left\{j\frac{2\pi d_{d}}{\lambda}\cos(\phi_{n}-\phi_{v}) \right\}\right)\end{split}  \tag{10}\]  
Figure 10a shows the results of the estimation of the AOA based on the cooperative operation of the MIQ method with the K-factor as a parameter, whereas Figure 10b is the estimation error of that method. The solid lines, the broken lines, and the chain lines show the case of \(K=10\) dB, \(0\) dB, and \(-10\) dB, respectively. The black and red lines indicate the configuration after and before the redesign, respectively. In the Monte Carlo simulation, the cross-polarization power ratio (XPR) is set to \(50\) dB, which is equivalent to a vertically polarized propagation environment. The number of snapshots is \(5000\). The initial phase of the scatterers is generated by a random number. It can be seen from Figure 10a that the estimated angle of the proposed antenna after the redesign, as given by Equation (6), agrees well with the actual angle of the incoming wave, as denoted by the thin black line, regardless of the K-factor. In contrast, the estimation angle before the redesign observes a sinusoidal variation. Furthermore, Figure 10b shows that the estimation error of the proposed antenna before the redesign is from about \(-30^{\circ}\) to \(10^{\circ}\) regardless of the K-factor. However, after the redesign, this is less than \(\pm 10^{\circ}\) even in the severe case of \(K=-10\) dB, where there are large signal fluctuations due to highly scattered fields, as if it is a free-space environment. For the beamforming function of the proposed antenna described in the next section, since the beams for high-reliability communication are formed toward the estimated angle, the large estimated error causes a discrepancy between the beam direction and the actual incoming wave angle, resulting in a degradation of the received power. If the estimated error is within \(\pm 10^{\circ}\), the radiation gain in the direction of the actual incoming wave is expected to be within the half-width of the formed beam. We can, therefore, conclude that the ability of the AOA estimation method in the proposed antenna after the redesign, in cooperation with the MIQ method, gives a remarkably high accuracy even when the LOS component is extremely small. Figure 10: Estimation accuracy of the proposed antenna through Monte Carlo simulation: (**a**) estimated angle and (**b**) error of estimated angle.