# Performance Evaluation of Directional Antennas in ZigBee Networks under NLOS Propagation Conditions
## 3 Results
### Location 1--Terrace
Table 1 shows the results for the six receiver positions. Figure 5: Measurements results of XBee for location 1: (**a**) average RSSI; (**b**) PDR. Figure 6: Measurements results with a signal generator: (**a**) received power; (**b**) received signal after deconvolution. Figure 7: Calculated received power for the directional antenna—orientation 2. The RSSI values are those represented in Figure 5a, and \(P_{s}\) is the received power from the generator. As we can observe, \(P_{s}\) was always below the RSSI because it corresponded to a received power of a narrowband signal. On the other hand, RSSI corresponded to the received signal plus noise and interference measured in the ZigBee bandwidth of about 2 MHz. Figure 8a shows the difference between the average power received by the directional antenna and the omnidirectional antenna. As can be seen, the results obtained by the generator followed those obtained by the XBee. Despite the higher gain of the directional antenna, the received power difference decreased with increasing distance to the transmitter. The power received by the directional antenna--orientation 1--was always below the power of the omnidirectional antenna. The estimated power was, on average, 3.6 dB below the measured power, with a standard deviation of 1.5 dB. Figure 8b shows the estimated Signal-to-Interference-plus-Noise Ratio (SINR). The received power is defined by  
\[P_{r}=P_{s}+P_{ni} \tag{5}\]  
where \(P_{s}\) is the received signal power and \(P_{ni}\) is the interference and noise power. With \(P_{r}\) determined from the RSSI and \(P_{s}\) approximated by the values presented in Table 1, the \(SINR\) was given by  
\[SINR\ (\mathrm{dB})=10\log_{10}\left(\frac{P_{s}}{P_{ni}}\right)=10\log_{10}(P_{ s})\ -\ 10\log_{10}\left(10^{\frac{RSSI}{10}}\ -\ P_{s}\right) \tag{6}\]  
From Figure 8b, the \(SINR\) was always negative due to Wi-Fi interference. The directional antenna--orientation 1--had the lowest \(SINR\) for almost all receiver positions. The \(SINR\) confirmed the high loss of packets for longer distances for the three antenna situations. These results also confirmed why the directional antenna could not increase the range compared to the omnidirectional one. Although the directional antenna had \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Omnidirectional**} & \multicolumn{2}{c}{**Directional—Orient. 1**} & \multicolumn{2}{c}{**Directional—Orient. 2**} \\ \hline
**Position** & **RSSI (dBm)** & \(P_{s}\) (dBm)** & **RSSI (dBm)** & \(P_{s}\) (dBm)** & **RSSI (dBm)** & \(P_{s}\) (dBm) \\ \hline
1 & \(-\)77.6 & \(-\)80.9 & \(-\)81.5 & \(-\)85.0 & \(-\)69.7 & \(-\)74.1 \\
2 & \(-\)79.4 & \(-\)82.8 & \(-\)81.0 & \(-\)84.6 & \(-\)72.9 & \(-\)76.2 \\
3 & \(-\)78.0 & \(-\)81.2 & \(-\)80.6 & \(-\)85.1 & \(-\)73.0 & \(-\)76.8 \\
4 & \(-\)82.2 & \(-\)85.8 & \(-\)80.8 & \(-\)85.5 & \(-\)76.8 & \(-\)79.9 \\
5 & \(-\)85.8 & \(-\)89.9 & \(-\)85.1 & \(-\)91.0 & \(-\)82.2 & \(-\)86.5 \\
6 & \(-\)88.0 & \(-\)93.4 & \(-\)88.9 & \(-\)95.6 & \(-\)86.7 & \(-\)92.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measurement results. Figure 8: (**a**) Power difference between omnidirectional and directional antennas; (**b**) estimated SNIR. an additional 7.5 dBi gain, the received power was only about 1 dB above that of the omnidirectional antenna.