# Bandwidth-Based Wake-Up Radio Solution through IEEE 802.11 Technology
## 4 Wake-Up Radio Receiver Design  
To carry out the design of the WuRx described in Section 3.2, we have used the Matlab software tool. Moreover, we have used functions from the WLAN System Toolbox for the generation of IEEE 802.11 frames and their transmission through a communication channel, taking into account the influence of multi-path and fading. Propagation models from TGn/ac [26] have been employed. For the WuRx design, it is necessary to decide on the thresholds of the different comparator blocks. For this issue, we consider propagation model B from [26], as it is the most restrictive (model B applies to indoor, residential, or small office environments). We begin with the WuRx design of Figure 5 (scenario with two symbols and one bit per symbol) and choose a fifth-order Chebyshev filter with a cut-off frequency of 12 MHz. This filter configuration has been chosen to filter a 20 MHz signal using the lowest filter order providing enough attenuation to differentiate between a 20 MHz IEEE 802.11 signal and a signal with a larger bandwidth. The signal level at filter output for a 20 MHz and a 40 MHz IEEE 802.11 signal is shown in Figure 8a as a function of the distance between transmitter and receiver. Note that if differentiation between a 20 MHz and a 40 MHz signal is successfully achieved, it is also feasible between a 20 MHz signal and a signal with bandwidth larger than 40 MHz (i.e., 80 MHz and 160 MHz). A transmission power of 1 W is considered at 5 GHz. From this figure, we observe around 30 dB of difference between output signals at 1 m of distance and, thus, we establish the 20 MHz signal level at 1 m (i.e., \(-\)73 dBm) as the threshold value at the comparator block. This means that a received IEEE 802.11 signal with a signal level at the filter output below this threshold will be decoded as a 20 MHz signal; otherwise, it will be decoded as a 40 MHz signal, thus leading to an effective operational range covering distances from 1 m to 12 m. If we consider a stream of 10,000 random bits, where IEEE 802.11 frames of 20 MHz of bandwidth encode WuC bits with a value of \"0\", and frames of 40 MHz of bandwidth encode bits with a value of \"1\", Figure 8b shows corresponding Bit Error Rate (BER) at the output of WuRx of Figure 5. As shown, BER = 0 is achieved in the range between 1 m and around 12 m. Choosing a lower threshold value would improve the performance in short distances (i.e., <1 m), however, it will also decrease the effective range below 12 m. In this way, we choose a lower bound of 1 m, which we found reasonable for the WuR use case, where the aim is the management of remote devices beyond 1 m.  
With regard to the WuRx of Figure 6 (scenario with four symbols and two bits per symbol), threshold values for the comparator blocks of second and third chains have to be defined (note that the aforementioned threshold for WuRx of Figure 5 is employed in the first chain of the WuRx of Figure 6). Following the same approach, we choose a fourth-order Chebyshev filter and cut-off frequency of 33 MHz in the second chain to filter a 40 MHz signal using the lowest filter order providing enough attenuation to differentiate between a 40 MHz IEEE 802.11 signal and a signal with a larger bandwidth. Finally, a third-order Chebyshev filter and cut-off frequency of 63 MHz is chosen in the third chain to filter an 80 MHz signal. The signal level at filter output of the second chain for a 40 MHz and an 80 MHz IEEE 802.11 signal, as a function of the distance between transmitter and receiver, is observed in Figure 9a. Note that if differentiation between a 40 MHz and an 80 MHz signal is successful, then it is also suitable with signals of bandwidth larger than 80 MHz (i.e., 160 MHz). A value of \(-\)77 dBm is chosen as the threshold at the comparator block (i.e., 40 MHz signal level at 1 m), leading to an operational range (BER = 0) from 1 m to 18 m. Corresponding BER at the output of the second chain of the WuRx of Figure 6 is shown in Figure 9b.