# Wake-Up Receiver with Equal-Gain Antenna Diversity +
## 3 Hardware  
The diversity node presented here uses the low-frequency wake-up receiver AS3932. This device supports the build up of a selection diversity system as introduced in Section 2.1, as it features three input channels. If several antennas are connected to the receiver, the AS3932 always selects the channel that has the highest RSSI value [22]. The node introduced in this section uses the AS3932 low-frequency wake-up receiver to implement an equal gain diversity system to further improve the wake-up reliability as discussed in Section 2.2. Figure 3 illustrates the block diagram of the proposed diversity system. As can be seen, the two antenna paths both include a matching network and a rectifier to demodulate the incoming wake-up messages. The two branches are combined after the demodulation stage and then fed into the wake-up receiver. Figure 2: Schematic of a selection diversity system where the receiver is always connected to the antenna with the highest RSSI value. Figure 4 depicts the schematic of the diversity system in further detail including the antenna switches (ADG918), the matching networks and the rectification stage of each antenna path. The two identical rectifiers are voltage doublers consisting of HSMS-285C zero bias Schottky diodes that are designed for input powers below \(-20\,\mathrm{dBm}\) and have a typical sensitivity of \(-57\,\mathrm{dBm}\) at \(915\,\mathrm{MHz}\)[23]. Both branches are then combined to achieve constructive interference. Figure 5 illustrates simplified two wake-up signals received at the two antennas. It is assumed that both antennas receive a signal of the same amplitude for reasons of simplicity. The high-frequency carrier signals \(v_{c1}(t)\) and \(v_{c2}(t)\) as illustrated in blue in Figure 5 are on-off-keying modulated to carry the low-frequency wake-up message. The demodulation stage filters the high-frequency carrier signal to achieve the low-frequency wake-up signals \(v_{w1}(t)\) and \(v_{w2}(t)\). Finally, the two low-frequency signals are added to form the combined wake-up signal \(y(t)\) according to Equation (2):  
\[y(t)=v_{w1}(t)+v_{w2}(t)=a_{1}\cos(\omega_{0}t+\phi_{1})+a_{2}\cos(\omega_{0}t +\phi_{2}), \tag{2}\]  
with \(\omega_{0}\) being the wake-up frequency, for example \(125\,\mathrm{kHz}\), and \(\phi_{i}\) being a possible phase shift of the two wake-up signals. Obviously, Equation (2) resembles Equation (1) with \(y(t)\) being the combination of the two antenna branches. Figure 4: Schematic of the receiver front-end with two antennas including matching networks rectifiers AS3932 wake-up receiver and antenna switches. Figure 3: Block diagram of a low-power wake-up receiver with antenna diversity. Each diversity branch consists of antenna, matching network and rectifier. It is obvious that destructive interference of two sinusoidal signals of the form \(y_{i}(t)=A_{i}e^{i(\omega+\phi_{i})t}\) with \(i=1,2\) happens when the phase shift \((\phi_{2}-\phi_{1})\) is in the range \(2/3\pi<\phi_{2}-\phi_{1}<4/3\pi\). The down converted signal at the wake-up receiver input is at \(125\,\mathrm{kHz}\). In case of destructive interference and by using the relation \(\Delta t=\Delta\varphi/\omega\), a time offset \(\Delta t\) in the range of \(2.66\times 10^{-6}\,\mathrm{s}<\Delta t<5.33\times 10^{-6}\,\mathrm{s}\) can be calculated. As the signals are transmitted at speed of light \(c=300\times 10^{6}\,\mathrm{m}\,\mathrm{s}^{-1}\), this translates to an antenna separation between \(800\,\mathrm{m}\) and \(1600\,\mathrm{m}\), which is impossible with the hardware used in this work. As can be seen, the block diagram in Figure 3 resembles an equal gain system as introduced in Section 2.2. Furthermore, the utilized diversity scheme is polarization diversity, as it requires less space than, for example, a space diversity system. Figure 6 shows a photo of the wireless sensor node with antenna diversity. To feature multiple antennas, the board is equipped with two antenna ports, which are connected to an ADG918 antenna switch from Analog Devices.