# Cluster Analysis of Pedestrian Mobile Channels in Measurements and Simulations
## 3 Mobile Channel Simulations by IMT-2020 Channel Model
### Simulation Generation Procedures  
The generation of a channel model is divided in three main parts: general parameters, small-scale parameters, and coefficient generation (see Figure 6). Figure 6: Framework of primary module in IMT-2020 channel model. The first part, the generation of general parameters, includes the initial setup of the whole system, and how to generate the corresponding path loss model and its large-scale parameters. Users must choose one of four typical scenarios: InH, UMa, UMi, and RMa. Base station (BS) and user terminal (UT) antenna-array details need to be set, such as the number of antennas, 3D locations, antenna field patterns, and array geometries. The speed and direction of UT motion, center frequency, and bandwidth must be set, too. Then, the corresponding path loss model with the formulas is formed. Finally, large-scale parameters are calculated, including root mean square delay spread, root mean square angular spreads, Ricean K-factor, and shadow fading. In the second part, small-scale parameters are calculated. This is a group of parameters that represents the characteristics of dynamic clusters in the model, which include the delay, power, AoA, AoD, EoA, and EoD of each cluster. After this step, we can obtain the full information of the model clusters. In the third part, initial phases are generated randomly at first. Each ray \(m\) of cluster \(n\) has four initial phases: \(\left\{\Phi_{n,m}^{\theta\theta},\Phi_{n,m}^{\theta\phi},\Phi_{n,m}^{\phi \theta},\Phi_{n,m}^{\phi\phi}\right\}\) for four different polarization combinations (\(\theta\theta,\theta\phi\), \(\phi\theta\), \(\phi\phi\)). Their distribution is uniform within \((-\pi,\pi)\). Then, CIRs, also known as channel coefficients, are calculated. Finally, we apply path loss and shadowing to the CIR generation formula. For a channel simulation with \(S\) antenna elements at the Tx side and \(U\) antenna elements at the Rx side, the equation of generating a channel CIR is expressed as  
\[H_{u,\phi,n}(t) = \sqrt{\frac{P_{\mathrm{tr}}}{M}}\sum_{m=1}^{M}\left[ \begin{matrix} F_{rx,u,\phi}(\theta_{n,m,EoA},\phi_{n,m,AoA})\\ F_{rx,u,\phi}(\theta_{n,m,EoA},\phi_{n,m,AoA})\end{matrix} \right]^{T} \tag{16}\] \[\left[ \begin{matrix}exp(j\Phi_{n,m}^{\theta\theta,n})&\sqrt{\kappa ^{-1}}exp(j\Phi_{n,m}^{\phi\phi})\\ \sqrt{\kappa^{-1}}exp(j\Phi_{n,m}^{\phi\theta})&exp(j\Phi_{n,m}^{\phi\phi}) \end{matrix} \right]\] \[\left[ \begin{matrix}F_{rx,s,\theta}(\theta_{n,m,EoD},\Phi_{n,m,AoD })\\ F_{rx,s,\phi}(\theta_{n,m,EoD},\phi_{n,m,AoD})\end{matrix} \right]\] \[exp(j2\pi\frac{\hat{r}_{rx,u,m}^{T}\cdot\tilde{d}_{rx,u}}{\lambda_ {0}})exp(j2\pi\frac{\hat{r}_{rx,u,m}^{T}\cdot\tilde{d}_{rx,s}}{\lambda_{0}})\] \[exp(j2\pi\frac{\hat{r}_{rx,u,m}^{T}\cdot\tilde{v}}{\lambda_{0}})\]  
where \(F_{rx,u,\phi}\) and \(F_{rx,u,\phi}\) are the field patterns of receiver antenna element \(u\) in the direction of spherical basis vectors \(\hat{\theta}\) and \(\hat{\phi}\), respectively, while \(F_{rx,s,\phi}\) and \(F_{tx,s,\phi}\) are the field patterns of transmitter antenna element \(s\) in the direction of spherical basis vectors \(\hat{\theta}\) and \(\hat{\phi}\) respectively. \(\hat{r}_{tx,n,m}\) and \(\hat{r}_{rx,u,m}\) are the spherical unit vector with azimuth departure angle \(\phi_{n,m,AoD}\) and elevation departure angle \(\theta_{n,m,EoD}\) at the Tx side, and with azimuth arrival angle \(\phi_{n,m,AoA}\) and elevation arrival angle \(\theta_{n,m,EoA}\) at Rx side, respectively. The Doppler frequency component depends on arrival angles AoA and EoA, and UT velocity vector \(\tilde{v}\) with speed \(v\), travel azimuth angle \(\phi_{v}\), elevation angle \(\theta_{v}\), and other details can be found in Reference [3]. To bring the channel model closer to a realistic mobile scenario, a feature called spatial consistency is added. Without this feature, small-scale parameters generate randomly in each drop. Although they follow certain distributions defined in the model, this makes no sense in dynamic scenarios.