## 2 Related Work
### CSI-Based Signal Attenuation Model for Indoor Ranging  
OFDM systems can modulate signals into multiple subcarriers and transmit them simultaneously in 802.11 a/g/n networks [25; 26; 27]. The CSI information obtained from the physical layer can reflect the channel quality between the transmitter and receiver. The CSI describes that signals are affected by multiple paths during propagation. Therefore, the channel can be estimated by CSI [28] analyzing the channel characteristics of the communication link. Table 2 shows the available information about CSI. In an OFDM system, the received signal in the indoor environment can be expressed by Equation (4):  
\[Y=HX+N \tag{4}\]  
where \(Y\) is the received signal vector. \(H\) is the channel matrix. \(X\) is the transmitted signal vector. \(H\) is the channel matrix, and \(N\) is the additive Gaussian white noise. The estimated CSI of all subcarriers is: \begin{table}
\begin{tabular}{c c} \hline \hline
**Data Information** & **Properties** \\ \hline Bfee-count & Number of Bfee count beamforming sent to user space by drive record \\ Nrx & Number of Nrx receiving antennas (Intel5300 network card is usually 3) \\ Ntx & Number of Ntx transmit antennas \\ rssi-a, rssi-b, rssi-c & Received signal strength of each receiving antenna \\ rate & Rate the transmission rate of each packet \\ noise & noise \\ CSI & CSI data itself is a three-dimensional arrays of Nrx * Ntx * 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Channel state information. \[\hat{H}=\frac{Y}{X} \tag{5}\]  
where \(\hat{H}\) represents the channel frequency response (CFR) in the frequency domain. A set of CSI values can be obtained from the received packets, which can be expressed by Equation (6):  
\[H=[H_{1},H_{2},H_{3},...,H_{k},...,H_{n}], \tag{6}\]  
where \(H_{k}\) is the k-th subcarrier of CSI. By modifying the wireless network card, CFR samples with 30 subcarriers \((n=30)\) can be obtained by the Wi-Fi devices. Each group of CSI includes the amplitude and phase of subcarriers, as shown in Equation (7):  
\[H_{k}=\|H_{k}\|\,e^{\hat{z}/H_{k}} \tag{7}\]  
where \(\|H_{k}\|\) represents the amplitude. \(\angle H_{k}\) represents the phase of \(k\)-th subcarriers. An Intel 5300 wireless network card operating in a 20 MHz high-throughput mode (HT mode) under a MIMO system has \(p\) transmitting antennas and \(q\) receiving antennas. CSI can be expressed as a matrix of \(pxq\) dimension, as follows:  
\[H(f_{x})= \begin{bmatrix}h_{11}&h_{22}&\cdots&h_{1q}\\ h_{21}&h_{22}&\cdots&h_{2q}\\ \vdots&\vdots&\ddots&\vdots\\ h_{p1}&h_{p2}&\cdots&h_{pq}\end{bmatrix}  \tag{8}\]  
where \(H_{pq}\) is a complex number, which contains the amplitude and phase of the subcarrier on each antenna. Figures 3 and 4 show the amplitude-frequency response and phase-frequency response of CFR under three receiving antennas. Analysis of Figure 4 shows that the phase information measured at the receiver is chaotic and we can not use it directly. Figure 3: The amplitude frequency response of channel frequency response (CFR) under three receiving antennas. Currently, WLAN protocols, especially 802.11n, use OFDM and MIMO as their standard technologies. The MIMO technology enables the diversity transmission and reception of signals. These two technologies play an important role in the formation of CSI data. FILA [8] utilizes effective CSI to propose an indoor ranging algorithm. The CSI-based ranging formula is as follows:  
\[CSI_{eff}=\frac{1}{K}\sum_{k}\frac{f_{k}}{f_{c}}\times||A||_{k} \tag{9}\]  
where \(CSI_{eff}\) represents the effective CSI. \(K\) is the number of subcarriers. \(f_{c}\) represents the calculated center frequency, and \(||A||_{k}\) represents the amplitude of the filtered CSI on the \(kth\) subcarrier.