# Pattern-Based Decoding for Wi-Fi Backscatter Communication of Passive Sensors
## 4 Patterns in Smoothed Wi-Fi Signal  
Figure 1(a) shows the received signal samples of a backscattered Wi-Fi data frame for which a backscatter tag modulates coded bits at 100 kbps. The beginning non-OFDM part of the frame  
Figure 1: System model of Wi-Fi backscatter communication. (32 \(\upmu\)s for a preamble and part of the physical-layer header) has small fluctuation, but the following OFDM-modulated part shows considerable fluctuation. Due to such fluctuation of the Wi-Fi signal itself, no amplitude patterns of the tag's backscattering are noticeable in raw signal samples. In general, a backscatter tag's bit modulation on a Wi-Fi signal is at a much lower rate than for Wi-Fi. Therefore, we can smooth the fluctuation of the Wi-Fi signal out while letting backscattered amplitude patterns remain [8]. To this end, we applied moving average to signal samples, i.e., a window of signal samples were averaged to produce another signal value, which is a representative low-complexity method of low-pass filtering. The moving average process we considered is given as  
\[\hat{g}[i]=\frac{1}{N}\sum_{k=i-N/2+1}^{i+N/2}y[k] \tag{2}\]  
where \(y\) and \(\hat{y}\) are the amplitudes of received Wi-Fi signal samples before and after the moving average, respectively, and \(N\) is the window size (in the number of samples) of the moving average. The signal samples after smoothing are shown in Figure 2b with several values of window size \(N\). It was observed that a significant amount of fluctuation disappeared, and amplitude patterns were then noticeable. However, the following points show that conventional threshold-based decoding still suffers:  
* As the window size of the moving average increases, the fluctuation of the Wi-Fi signal is better reduced, but backscattered amplitude patterns are also smoothed out more, which becomes more severe for a higher backscatter bit rate. That is, the window size of the moving average is one of the factors determining decoding performance. * The entire samples of a slot period are not above or below a threshold. This results not only from residual fluctuation, but also from the nature of the moving average. Thus, a small variation of the signal may lead to the wrong decision of threshold-based decoding for an information bit. * The scale of amplitude changes is significantly reduced. Therefore, a small variation of a threshold from the optimal one may result in decoding failures. Figure 2: Samples of a received Wi-Fi frame with backscattering for variously sized average windows. * The scale of amplitude changes changes depending on the window size of smoothing and the switching rate of a backscatter tag. This means that an adequate threshold has to be adaptive to such parameters, which makes threshold configuration even more difficult. To tackle the above challenges, we paid attention not to amplitude levels, but to the pattern of its changes after signal smoothing was applied. Ideally, as illustrated in Figure 3, if a tag alternates reflection and absorption states, the signal is modulated as a square wave. When the signal goes through the smoothing (moving average) of Equation (2), the distortion patterns are twofold: (1) inclining slope around a rising edge; (2) declining slope around a falling edge. Suppose that the tag changes the switching state at \(1/7\)Hz, i.e., the reflection state remains unchanged during \(T\) (in the number of samples). In order not to filter out the reflection patterns of the tag, we must let \(N<T\). Then, these signal-distortion patterns after smoothing are formally proved in the following proposition. **Proposition 1**. : _If \(N\) is large enough to filter out the signal fluctuation resulting from OFDM, channel-gain variations, and thermal noise, while \(N\leq T\), \(\hat{y}\) of Equation (2) monotonically increases (decreases) when the window of signal samples for smoothing includes a rising (falling) edge._  
Proof.