## 3 Proposed Wi-Fi Backscatter System Using Multiple Antennas  
In this paper, we propose a method to obtain channel diversity by applying multiple antennas to a Wi-Fi backscatter tag sensor. In the Wi-Fi backscatter system, the tag sensor is a transmitter because it determines the amount of reflection of the Wi-Fi packet by adjusting the antenna's impedance. Since the number of antennas of the helper (Wi-Fi AP) does not affect the channel diversity, therefore, this paper assumes that the helper works with only one antenna. In the case of a tag sensor, the number of antennas is limited to two because of the size issue caused by the separation distance between the antennas. In this paper, two methods are proposed for increasing the data rate and improving the reliability of the Wi-Fi backscatter system. The method for increasing data rate uses two antennas of tag sensor (AntI/Ant2) to send the symbol 0 to the symbol 3 according to the four cases (off/off, on/off, off/on, on/on). In the case of a method for improving the reliability, a symbol of 0 or 1 is transmitted by turning on or off all antennas of tag sensor. Figure 1: Configuration of the existing Wi-Fi backscatter communication system. In Figure 2, we modify the frame structure of the Wi-Fi backscatter system, which uses power level modulation method [12] to suit the proposed system. As shown in Figure 2, the Wi-Fi tag sensor sends \(L\) preamble symbols (training sequence) first before data symbol transmission [12] (the tag sensor can tell its data by changing the Wi-Fi channel between a helper and a reader, and the symbol means the tag's backscatter pattern). Therefore, there is the symbol \(x_{k}\supset\{\text{preamble }p_{l},\text{ data }d_{m}\}\) in a frame, and \(k\) can be summarized as \(L+M\), where \(L\) and \(M\) are the numbers of preamble and data backscatter symbols, respectively. The number of preamble backscatter symbols, \(L\), is equal to the number of backscatter symbol types that can be sent. For example, when a tag sensor can send four types of symbols (can backscatter a Wi-Fi packet with four types of gains or patterns from pattern 0 to pattern 3), the number of preamble backscatter symbols is four in the frame. It is assumed that the path gain \(H_{ji}\) between the \(i\)-th transmit antenna and the \(j\)-th receive antenna is a complex independent identically distributed (iid) Gaussian random variable. It is also assumed that this fading coefficient (path gain) is a quasi-static channel without changing in the symbol interval. The complex baseband representation of the received signal \(y_{jk}\) received at the \(j\)-th receiver antenna in the \(k\)-th symbol interval is given by  
\[y_{jk}=\sum\
olimits_{i=1}^{2}H_{ji}x_{k}+z_{jk} \tag{1}\]  
where \(x_{k}\) is a normalized complex baseband signal transmitted in the \(k\)-th symbol interval and \(z_{jk}\) is a Gaussian random noise. The variables in Equation (1) can be expressed as a matrix where \(y_{jk}\), \(H_{ji}\), \(x_{k}\), and \(n_{jk}\) are expressed as \(N\times T\) matrix \(\Psi\), \(N\times 1\) matrix \(\mathbb{H}\), \(1\times T\) matrix \(\mathbb{x}\), and \(N\times T\) matrix \(\mathbb{Z}\), respectively. \[\Psi=\mathbb{H}\mathbb{x}+\mathbb{Z} \tag{2}\]  
\(N\) is the number of antennas, and \(T\) is symbol interval. For channel \(\mathbb{H}\), there are three channel environments, as shown in Figure 1. One is for the path from the helper to the tag sensor, \(\widetilde{h}_{\text{RXTX}}\), another is for the path backscattered by the tag sensor, \(\widehat{h}_{\text{RXTX}}\), and the other is for the path from the helper to the reader, \(h_{\text{RXTX}HR}\). The channel environments in the proposed system are shown in Figure 3. There is the helper with one antenna, the tag sensor with two antennas, and the reader with N antennas in the proposed MIMO Wi-Fi backscatter system. Figure 3 shows the channel environment of the path from the helper to the reader with the tag sensor backscattering Wi-Fi RF radio waves.