# Wake-Up Receiver with Equal-Gain Antenna Diversity +
## 4 Experimental Results
### Static Measurements  
At first, a signal generator was connected to the antenna ports of the board, feeding them consecutively with a \(868\,\mathrm{MHz}\) signal at different input levels. Since both measurements achieved almost equal results, Figure 9 shows the output voltage over the input level for the straight antenna, only. The measurements with the angular antenna revealed similar results and can be found in the third column of Table 1.  
An exponential function was used to fit the measurement data, superimposed on a constant noise level, that is \(y_{1}=a+b\exp(cx)\) with \(a=0.043\), \(b=26,734\) and \(c=0.23\). The theoretical sensitivity of the AS3932 intersects the fitted curve at \(-50.6\,\mathrm{dBm}\). The circle in Figure 9 shows the sensitivity measured by using the AS3932 receiver: when the receiver did not further react to the input signals, its sensitivity limit was reached. Using one antenna input feed, it was found at \(-51.3\,\mathrm{dBm}\), which fits very well to the results reported by [6] and as discussed above.  
In a second step, a second signal generator was connected to the other antenna input port, also feeding it with a \(868\,\mathrm{MHz}\) signal. Figure 10 shows the data curve fitted with an exponential function of the form \(y_{2}=a+b\exp(cx)\) with \(a=0.031\), \(b=45,410\) and \(c=0.226\). The intersection of the fitted curve and the theoretical sensitivity line is at \(-53.7\,\mathrm{dBm}\).  
Figure 8: Reflections measured at the straight (yellow) and angular (green) antenna input ports over frequency.  
The voltage where the AS3932 did no longer sense the input signal was found to be at \(-53.8\) dBm, depicted as a circle in Figure 10. This is a gain of around 3 dB compared to the system with one antenna. Table 1 lists the experimentally received data that is also plotted in Figures 9 and 10 plus the measured voltage for the case of only the angular antenna input powered.  
Figure 10: Measured voltage at the rectifier output with two active antennas. Typical sensitivity of the AS3932 is depicted as the blue dotted line. The red circle marks the measured sensitivity.  
Figure 9: Measured voltage at the rectifier output with one active antenna. The typical sensitivity of the AS3932 is depicted as the dotted line and the red circle shows the measured sensitivity.  
Table 2 summarizes the experimentally identified wake-up sensitivities for the four possible combinations of the experiments above. Figure 11 compares the input signal strength with one receiving antenna to the input signal strength with two receiving antennas in dB. The red crosses illustrate the measurement data the solid curve depicts the fitted curve achieved by dividing \(y_{1}\) by \(y_{2}\). It can be observed that the signal gain reaches approximately \(3\,\mathrm{dB}\) in the area where the input signal strength varies from \(-50\,\mathrm{dBm}\) to \(-30\,\mathrm{dBm}\), which correlates well to Equation (2) with \(a_{1}=1\) and \(a_{2}=1\). Below an input signal strength of \(-50\,\mathrm{dBm}\) and above \(-30\,\mathrm{dBm}\), the gain decreases, probably because of decreased efficiency of the rectifier diodes that are specified for the region from \(-20\,\mathrm{dBm}\) to \(-57\,\mathrm{dBm}\)[23].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Level** & \multicolumn{3}{c}{**Measurement (mV)**} \\ \cline{2-4}
**(dBm)** & **Straight Antenna** & **Angular Antenna** & **Both Antennas** \\ \hline \(-10\) & \(1050\) & \(1036\) & \(1190\) \\ \(-20\) & \(234\) & \(228\) & \(316\) \\ \(-30\) & \(26.9\) & \(26.1\) & \(52.1\) \\ \(-40\) & \