# Pattern-Based Decoding for Wi-Fi Backscatter Communication of Passive Sensors
## 3 System Model  
The communication system under consideration is depicted in Figure 1. A background signal, i.e., Wi-Fi frame, is transmitted from a Wi-Fi transmitter (e.g., AP) to a Wi-Fi receiver (e.g., smartphone). A backscatter tag modulates its bits on received Wi-Fi signals; the bits to transmit are either coded or uncoded, and each bit value (one or zero) is mapped to an RF switch's state (reflection or absorption).  
The backscattered signal is then received by the Wi-Fi receiver as the sum of the signals along both paths. The received signal is expressed as  
\[y[k]=h_{1}\rho r[k]x[k]+h_{2}x[k]+\sigma[k] \tag{1}\]  
where \(x\) and \(y\) are the amplitudes of the transmitted and received Wi-Fi signal samples, respectively, \(h_{1}\) and \(h_{2}\) are the channel gains of backscattered and other signal components, respectively (for simplicity, they are assumed static during a single frame period), \(\rho\) is the reflection loss of the tag, \(r\in\{1,0\}\) is the switching state of the tag (1 is reflection and 0 is absorption), and \(\sigma\) is the noise floor including thermal noise; \(k\) is the sample index.  
We assume that the backscatter tag reflects signal (\(r=1\)) for data one, and this results in an increased (high) amplitude level of the backscattered signal; it absorbs the signal (\(r=0\)) for data zero, and the backscattered signal has no increased (low) amplitude level. The tag maintains its switching state for period \(T\) (given as the number of signal samples), which we call a slot (one bit is transmitted during a slot) and can switch the state at the end of each slot depending on the value of the next bit to transmit. Slot \(n\) is represented as \([\tau_{n},\tau_{n}+T]\) (samples), where \(\tau_{n}\) is the first sample of slot \(n\).  
We assume that the bits to transmit are coded by, but not limited to, FM0 coding [8], i.e., the code rate is \(1/2\) (one information bit needs the transmission of two coded bits). In FM0 coding, if the information bit to transmit is data one, the signal level is maintained (represented by bit pair (1, 1) or (0, 0)); if it is data zero, the level is inverted in the middle (represented by bit pair (0, 1) or (1, 0)). The signal level is inverted at the end of every slot. Unless otherwise specified, the transmission bit rate is represented as the transmitted number of coded bits per unit time.  
We limited the focus of the paper to the communication scenario where a backscatter tag transmits its data to more powerful receiver nodes, such as smartphones and IoT gateways, which is common in IoT environments, in that things are equipped with sensors and report sensing results to the outer world (e.g., the Cloud).  
In addition, we make the following assumptions.  
**Assumption 1**.: _Digital-domain processing of received signal samples: Receiver nodes are assumed to have sufficient computing power and thus run a decoding process in the digital domain for better performance._  
**Assumption 2**.: _In-frame switching: To achieve a higher transmission bit rate with occasional Wi-Fi signals, a backscatter device changes its switching state within a Wi-Fi frame reception so that it modulates multiple data bits on the frame._