# Cluster Analysis of Pedestrian Mobile Channels in Measurements and Simulations
## 2 Cluster Tracking in Mobile Measurements
### Measurement Setup and Data Processing
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Antenna Type** & **ODA(Rx)** & **UPA(Tx)** \\ \hline
**Number of antenna ports** & 56 (16 ports were used) & 32 \\ \hline
**Radiation pattern** & Omnidirectional & Hemispherical \\ \hline
**Inter element spacing** & 41 mm & 41 mm \\ \hline
**Number of elements** & 28 & 16 \\ \hline
**Polarized** & \(\pm 45^{\circ}\) & \(\pm 45^{\circ}\) \\ \hline
**Angle range** & **Azimuth** & \(-180^{\circ}\)\(\sim\)\(180^{\circ}\) & \(-70^{\circ}\)\(\sim\)\(70^{\circ}\) \\ \hline
**Elevation** & \(-70^{\circ}\)\(\sim\)\(90^{\circ}\) & \(-70^{\circ}\)\(\sim\)\(70^{\circ}\) \\ \hline
**Center frequency** & \multicolumn{2}{c}{3.5 GHz} \\ \hline
**Bandwidth** & \multicolumn{2}{c}{200 MHz} \\ \hline
**PN sequence** & \multicolumn{2}{c}{255 chips} \\ \hline
**Speed of Rx** & \multicolumn{2}{c}{1.4 m/s (pedestrian)} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of measurement campaign. Figure 3: Scheme of antenna combining array in virtual measurements. Figure 2: Antenna used in the measurement. (**a**) Tx: 4 \(\times\) 4 patches, with each patch comprising a pair of cross-polarized antennas. (**b**) Rx: 8 adjacent sides with 3 patches each, a top surface with 4 patches; each patch contains a pair of cross-polarized antennas. With this information on the MPC level, we could cluster them with similar parameters, e.g., AoA, AoD, and delay. In References [9; 10], we only used KPM for clustering, and the process worked independently in each snapshot. Although the evolution of clusters could be observed along with the movement, the relationships among continuous snapshots and statistical analysis cannot be seen by KPM. For parameterizing clusters in mobile channels over time and showing their continuous evolution, KPM was used for clustering and KF was used for tracking [17; 18]. The flowchart of the KPMKF algorithm is shown in Figure 4, where \(\overrightarrow{X}^{(n)}\) is the data matrix of 100 MPCs in an _nth_ snapshot. \(\overrightarrow{X}^{(n)}=[x_{1}^{(n)},x_{2}^{(n)},\cdots,x_{i}^{(n)},\cdots,x_{ 100}^{(n)}]^{T}\), \(x_{i}^{(n)}=[\tau_{i}^{(n)}\ \theta_{Txj}^{(n)}\ \phi_{Txj}^{(n)}\ \theta_{ Rxj}^{(n)}]\), \(\overrightarrow{P}^{(n)}\) represents the matrix of MPC power. State model \(g_{c}^{(n)}=[\tau_{i}^{(n)}\ \theta_{Txj}^{(n)}\ \theta_{Txj}^{(n)}\ \theta_{ Rxj}^{(n)}\ \theta_{ Rxj}^{(n)}\ \Delta\tau_{i}^{(n)}\ \Delta\theta_{Txj}^{(n)}\ \Delta\theta_{ Rxj}^{(n)}\ \Delta\theta_{ Rxj}^{(n)}]^{T}\). The matrix of cluster centroids is \(\mu_{c}^{(n)}=[\tau_{c}^{(n)}\ \theta_{Txj}^{(n)}\ \ \phi_{Txj}^{(n)}\ \theta_{ Rxj}^{(n)}\ \theta_{ Rxj}^{(n)}]^{T}\). In this framework, \(\overrightarrow{X}^{(1)}\) and \(\overrightarrow{P}^{(1)}\) were used as initial input to the KPM part. After clustering in the first snapshot, we obtained \(\mu_{c}^{(1)}\) and initial state \(g_{c}^{(1|0)}\). Then, KF uses these two parameters to update the state as \(g_{c}^{(1|1)}\), and predict the state as \(g_{c}^{(2|1)}\) for the second snapshot. Then, we input the \(\overrightarrow{X}^{(2)}\) and \(\overrightarrow{P}^{(2)}\) to perform clustering in the second snapshot. Then, KF takes both the predicted and KPM-processed values into consideration to get \(g_{c}^{(3|2)}\). The process cycle keeps working until the last snapshot is considered. The details of KPM and KF are given as follows, respectively.