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Introduction for Simulation Parameter Setup of $\operatorname{Im}\{H_{\text{sum}}(f)\}$, $\left|H_{\text{sum}}(f)\right|$ and Power Delay Profile (PDP)

In the following three demos, instead of the calculation of stop frequency by using $f_{\text{stop}} = B_{\text{Rot}} \cdot N_{\text{Rot}}$, we introduce coherence bandwidth $B_{\text{coh}} = \frac{1}{c \cdot \tau_{\text{rms}}}$ (c is determined by certain threshold). Here, the received signal power after the time delay $\tau_k$ ($1 \leq k \leq N_{\text{iter}}$) can be expressed as $P(\tau_k) = \left|H_k(f)\right|^2$ for each iteration. For normalization, the total power of the channel Power Delay Profile (PDP) is introduced as $ P_{\text{Total}} = \sum_{k=1}^{N_{\text{iter}}} P(\tau_k)$. Therefore, $\tau_{\text{rms}}$ is root mean squared Delay Spread [2] which can be calculated as: $$ \tau_{\text{rms}} = \sqrt{\frac{\sum_{k=1}^{N_{\text{iter}}} \tau_k^2 \cdot P(\tau_k)}{P_{\text{Total}}} - \tau_{\text{d}} ^2} = \sqrt{\frac{\sum_{k=1}^{N_{\text{iter}}} \tau_k^2 \cdot P(\tau_k)}{\sum_{k=1}^{N_{\text{iter}}} P(\tau_k)} - \tau_{\text{d}} ^2} = \sqrt{\frac{\sum_{k=1}^{N_{\text{iter}}} \tau_k^2 \cdot \left|H_k(f)\right|^2}{\sum_{k=1}^{N_{\text{iter}}} \left|H_k(f)\right|^2} - \tau_{\text{d}} ^2} $$ where $$\tau_{\text{d}} = \frac{\sum_{k=1}^{N_{\text{iter}}} \tau_k \cdot P(\tau_k)}{P_{\text{Total}}} = \frac{\sum_{k=1}^{N_{\text{iter}}} \tau_k \cdot P(\tau_k)}{\sum_{k=1}^{N_{\text{iter}}} P(\tau_k)} = \frac{\sum_{k=1}^{N_{\text{iter}}} \tau_k \cdot \left|H_k(f)\right|^2}{\sum_{k=1}^{N_{\text{iter}}} \left|H_k(f)\right|^2}$$ is the average time delay of all time delay components.

Also, $\tau_1 = \frac{\ell_1 + \ell_3}{v_{\text{ph}}}$, $\tau_2 = \tau_1 + \tau_{\text{period}}$, therefore, $\tau_k = \tau_1 + (k-1) \cdot \tau_{\text{period}} = \frac{\ell_1 + \ell_3}{v_{\text{ph}}} + (k-1) \frac{2\ell_2}{v_{\text{ph}}}$.

The Power Delay Profile (PDP) which gives the intensity of a signal received at all time instants as a function of time delay is demostated in the last demo.