## 4 Simulation Results and Discussion  
### Simulation Parameters  
The accuracy of methods for determining the distance and characteristics of a multilayered reflective environments using UWB pulses is strongly dependent on UWB signal processing techniques. UWB-PPM is one of the candidates for positioning technology in a nondestructive environment with multiple reflective layers; with the proposed UWB-PPM-ATS, our trials indicated that the UWB-PPM pulses shifted with a certain time constant can be used to improve the precision in estimating the distance. All the numerical results in this paper were computed using Matlab. First, we compare the exact estimation errors of the UWB-OOK, UWB-PPM and UWB-PPM-ATS systems with the results obtained from the simulations and the actual value of the parameters use (6), (8), (11), (13) and (30). Here OOK is one of the UWB pulse amplitude modulation techniques and has two level modulation with the bits are 0 and 1. When sending a bit 0, the transmitter will not send anything. When sending a bit 1, the transmitter will send a pulse [29], and the template waveform \(\omega(t)\) at the receiver of UWB-OOK system is \(g_{4}(t)\). In addition, the performance of UWB-OOK, UWB-PPM and UWB-PPM-ATS systems were evaluated for an environment with known characteristics (for example, here are three layers as indicated in Figure 1). Finally, the location determination technique in a unknown environment with multiple reflection layers using the LMFA based on the estimated parameters of those UWB systems is presented with the system model as shown in Figure 9. The comparisons between the above systems are evaluated in term of errors between the estimated values from the considered system and the true values. Based on the PSD plot of the Gaussian impulses shown in Figure 4, most of the numerical results presented in this section are based on analysis using the fourth-order Gaussian monocycle. The parameters of the example UWB systems are listed in Table 1 and follow [5]. To assess the performance of those UWB systems, the error of estimated distance is defined as follows:  
\[\delta_{d}=\left|\hat{d}_{i}-d_{tri}\right|, \tag{30}\]  
where \(\hat{d}_{i}\) denotes the estimated distance and \(d_{tri}\) is the true value. In Figure 1, without generality, we assume that the propagation environment is heterogeneous with three layers: sand (dry), sandy soil (dry) and granite (dry) and the relative permittivities \(\varepsilon_{1},\varepsilon_{2},\varepsilon_{3}\) are 4, 3, 5, respectively. Those layers are assumed to be dry to reduce the attenuation of environment, so propagation velocity in those layers are 15 cm/ns, 17.32 cm/ns, 13.42 cm/ns and the attenuation is 0.01 dB/m [30]. With a known transmission environment, those distance can be estimated using (6), where \(\tau_{i}\) is computed according to (8), (11) and (13). Then the errors of estimated distances are calculated according to (30) and illustrated in Figure 11 for OOK, PPM, ATS systems with \(\zeta=-0.08\) ns and \(\zeta=-0.16\) ns. In Figure 11, the black line denotes the average error of the OOK \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Notation** & **Value** \\ \hline Time normalization factor & \(\mu_{p}\) & 0.2877 ns \\ Transmitted power & \(P_{Tx}\) & \(-35.4\) dB \\ The amplitude factors & \(A_{1},A_{2},A_{3}\) & 0.33, 0.13, 0.14 \\ Number of pulses & \(N\) & 100 \\ Noise power & \(N_{0}/2\) & \(-102\) dB \\ Time shift of PPM & \(T_{PPM}\) & 0.2 ns \\ Additional time shift & \(\zeta\) & \(-0.08\) ns, \(-0.16\) ns \\ Relative permittivity & & \\ with heterogeneous medium & \(\varepsilon_{1},\varepsilon_{2},\varepsilon_{3}\) & \(4;3;5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. system, the blue line denote the error of the PPM system and the red lines denote the error of the ATS system, all with the same system parameters.