# Through-Floor Vital Sign Searching for Trapped Person Using Wireless-Netted UWB Radars
## 3 Through-Floor Vital Sign Search  
### Searching Path Design  
The wireless-netted UWB life-detection radars are deployed on the 2D floor to search for the trapped person, and the searching path should be designed accordingly. The searching path is composed of some specific deploying observation points where the radars are placed. Inspired by the design principle of 2D multiple-input multiple-output (MIMO) array topology, these deploying observation points can be designed and optimized. In our previous work [12], the 2D MIMO array topology is designed and presented, including \(N_{T}\times N_{R}\) virtual elements in total. \(N_{T}\) denotes the number of transmitters, and \(N_{R}\) denotes the number of receivers. Here, the desired topology of the UWB life-detection radar deployment is constructed based on the optimizing way of the 2D MIMO array topology, and the observation points where the mono-static UWB life-detection radars are placed are equivalent to virtual elements. We employ \(N_{T}=4\) transmitters, achieving a uniform-distribution characteristic in the 2D effective aperture, \(N_{R}=N^{2}\) receivers are arranged inside the square formed by the transmitters. The \(N_{T}=4\) transmitters are placed symmetrically at the four vertices of a square with a width of \(\Delta_{A}\). The Cartesian coordinate is established and the location of four transmitters are as follows:  
\[\mathbf{r}_{\text{T}}=\left\{ \begin{array}{cc}(\Delta_{A}/2,\Delta_{A}/2)&( \Delta_{A}/2,-\Delta_{A}/2)\\ (-\Delta_{A}/2,-\Delta_{A}/2)&(-\Delta_{A}/2,\Delta_{A}/2)\end{array} \right\} \tag{1}\]  
Therefore, the selection range of all \(N_{R}\) receivers are expressed as  
\[\mathbf{r}_{\text{R}}=\left\{(x_{R_{a}},y_{R_{a}})|x_{R_{a}}\in\mathbf{s},y_{R _{a}}\in\mathbf{s},n=1,\ldots,N_{R}\right\} \tag{2}\]  
where \(\mathbf{s}=\left[-\frac{N_{R}-1}{2}\cdot\frac{\Delta_{A}}{N_{R}}\cdot\frac{ \Delta_{A}}{N_{R}}\cdot\frac{N_{R}-1}{2}\cdot\frac{\Delta_{A}}{N_{R}}\right]\), and when \(i\
eq j\), there will be \(x_{R_{i}}\
eq x_{R_{j}}\) and \(y_{R_{i}}\
eq y_{R_{j}}\). Based on the configuration, observation points where the UWB life-detection radars are set equivalent to the virtual elements, and the desired topology of the UWB life-detection radar is achieved, optimizing the topology of the 2D MIMO array. The optimization method is summarized as follows. * Step 1: Two basic principles: (1) \"Uniform distribution\": All elements should uniformly cover over the 2D observation aperture with little redundancy, ensuring the equivalent line aperture of each angle cut can be as nearly uniform and periodic as possible. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Center frequency of UWB radar system & 500 MHz \\ Bandwidth of UWB radar system & 500 MHz \\ Equivalent sampling frequency (FS) & 20 GSPS * \\ Real-time sampling frequency & 125 MSPS * \\ Pulse Repeat Period (PRP) & 15.625 us \\ Number of averaged values (NA) & 16 \\ Resolution of the ADC * & 16 bits \\ Radar system scan rate & 25 scans/s (Hz) \\ Sampling length (N) & 16,384 \\ Average power of radar signal & \textless{}10 mW \\ Antenna type & Bow-tie Antenna \\ Beamwidth of the antenna & 60\({}^{\circ}\) (E-plane) \(\times\) 100\({}^{\circ}\) (H- plane) \\ Polarization of the antenna & Linear polarization \\ Gain of the antenna & 3 dbi \\ \hline \hline \end{tabular}  
* GSPS: gigabit samples per second, MSPS: million samples per second, ADC: analog to digital converter.  
\end{table} 
Table 1: Key parameters of the adopted wireless-netted UWB radar. (2) \"Little shadowing\": In the equivalent line aperture of each angle, element shadowing, which is the elements overlap during the projection, should be as little as possible to obtain a unit weighted aperture. * Step 2: Convert to MIMO topology design: (1) According to the size of the area to be detected, set the size of the 2D observation aperture as \(2\Delta_{A}\times 2\Delta_{A}\).