# Device-Free Indoor Location Estimation System Using Commodity Wireless LANs
## 2 Channel Sounding Using IEEE 802.11n Wireless LANs
### MIMO Channel Sounding  
Figure 2 shows the MIMO transceiver configuration of the IEEE 802.11n wireless LAN. The stream parser creates \(N_{st}\) spatial streams from the encoded bit stream, and the quadrature is modulated to the symbol stream by constellation mapping. The transmitter can send \(N_{st}\) (\(\leq\mathrm{rank}(H)\leq\mathrm{min}(N_{T},N_{R})\)) parallel streams, where \(N_{T}\) and \(N_{R}\) denote the number of antennas in the transmitter and receiver, respectively. Then, the spatial streams are shifted cyclically by cyclic delay diversity (CDD), extending the communication area by transmitting the same signal at different carrier frequencies. This prevents beamforming that might be made in a specific direction when all the antennas send the signal with common header information. Spatial mapping (SM) is performed when the number of antennas is larger than the number of spatial streams (\(N_{T}>N_{st}\)). The frequency samples of each transmission branch are transformed into time-domain signals by the inverse Fourier transform and are transmitted simultaneously by all antennas. Figure 1: Frame format of IEEE 802.11n hybrid mode. The MIMO propagation channel matrix \(\mathbf{H}\) is estimated using the training signal (HT-LTF), which is contained in the frame format as shown in Figure 1. Figure 3 shows the block diagram of the three \(\times\) three MIMO channel-sounding system. Assuming that the number of spatial streams and the number of transmit antennas are the same (\(N_{\rm T}=N_{\rm st}=3\)), the received signal vector at the \(k\)th (\(k=1,\ldots,N_{\rm c}=56\)) sub-carrier is expressed as:  
\[\mathbf{y}^{(k)}=\mathbf{G}_{\rm agc}\mathbf{H}^{(k)}\mathbf{\Phi}^{(k)}\mathbf{dx}^{(k)}+\mathbf{n}^{( k)}\in\mathbb{C}^{3\times 1} \tag{1}\]  
where \(\mathbf{G}_{\rm agc}\), \(\mathbf{H}^{(k)}\), and \(\mathbf{\Phi}^{(k)}\) denote the gains of the automatic gain control (AGC), MIMO channel matrix, and CDD matrix, respectively. They are expressed as:  
\[\mathbf{G}_{\rm agc} = \text{diag}\Big{(}\left[ \begin{array}{cc}\sqrt{G_{\rm agc,1}} &\sqrt{G_{\rm agc,2}}&\sqrt{G_{\rm agc,3}}\end{array} \right]^{T}\Big{)}, \tag{2}\] \[\mathbf{H}^{(k)} = \left[ \begin{array}{ccc}H_{11}^{(k)}&H_{12}^{(k)}&H_{13}^{(k)} \\ H_{12}^{(k)}&H_{22}^{(k)}&H_{23}^{(k)}\\ H_{31}^{(k)}&H_{32}^{(k)}&H_{33}^{(k)}\end{array} \right],\] (3) \[\mathbf{\Phi}^{(k)} = \text{diag}\Big{(}\Big{[} \begin{array}{cc}1&e^{-\frac{1}{36} \pi}\delta_{2k}&e^{-\frac{1}{36}\pi}\delta_{3k}\end{array} \Big{]}^{T}\Big{)}, \tag{4}\]  
where \(x^{(k)}\) is the transmitted signal and \(\mathbf{n}^{(k)}=\left[ \begin{array}{cc}n_{1}^{(k)}&n_{2}^{(k)}&n_{3}^{(k)} \end{array} \right]^{T}\) is the noise vector. Here, \(\delta_{2}\) and \(\delta_{3}\) are specified as \(\delta_{2}=8\) (400 ns) and \(\delta_{3}=4\) (200 ns), and \(N_{\rm f}\) is the number of FFT points and is set to 64. Figure 3: Three times three MIMO channel sounding. Figure 2: IEEE 802.11n transceiver configuration. To separate the transmitted signals from multiple transmitting antennas, the signal \(x^{(k)}\) is transmitted four times with each transmitting antenna by setting \(\mathbf{d}\) as \(\mathbf{d}[\mathbf{1}]=\left[ \begin{array}{cccc}1&1&1&1\end{array} \right]^{T}\), \(\mathbf{d}[2]=\left[ \begin{array}{cccc}-1&1&1\end{array} \right]^{T}\), \(\mathbf{d}[3]=\left[ \begin{array}{cccc}1&-1&1\end{array} \right]^{T}\), \(\mathbf{d}[4]=\left[ \begin{array}{cccc}1&1&-1\end{array} \right]^{T}\) in Equation (1), then the matrix of the received signal can be obtained as:  
\[\mathbf{Y}^{(k)}=\mathbf{G}_{\text{age}}\mathbf{H}^{(k)}\mathbf{\Phi}^{(k)}\mathbf{D}x^{(k)}+\mathbf{N} ^{(k)}\in\mathbb{C}^{3\times 4}, \tag{5}\]  
where:  
\[\mathbf{Y}^{(k)} = \left[ \begin{array}{cccc}\mathbf{y}^{(k)}[1]&\mathbf{y}^{(k)}[2]&\mathbf{y} ^{(k)}[3]&\mathbf{y}^{(k)}[4]\end{array} \right], \tag{6}\] \[\mathbf{N}^{(k)} = \left[ \begin{array}{cccc}\mathbf{n}^{(k)}[1]&\mathbf{n}^{(k)}[2]&\mathbf{n} ^{(k)}[3]&\mathbf{n}^{(k)}[4]\end{array} \right], \tag{7}\]  
and:  
\[\mathbf{D} = \left[