# Cluster Analysis of Pedestrian Mobile Channels in Measurements and Simulations
## 2 Cluster Tracking in Mobile Measurements
### Measurement Setup and Data Processing  
Channel measurement took place in a square at the Beijing University of Posts and Telecommunications (see Figure 1), which can be seen as a typical UMa scenario. The used channel sounder had a carrier frequency of 3.5 GHz and 200 MHz bandwidth and collected the raw data of channel impulse responses (CIRs). A 32-element uniform planar array (UPA) was used at the Tx side, shown in Figure 2a. At the Rx side, the dual-polarized omnidirectional array (ODA) was equipped with a 56-element antenna. In this case, Antennas 1-16 were chosen for the measurement campaign (see Figure 2b). Measurement details are listed in Table 1.  
During measurement, the Rx moved along with the 8 m rail at a constant speed of 1.4 m/s (pedestrian speed). The Tx side was set on the roof of a teaching building. Two measurement routes were in line-of-sight (LoS) and non-line-of-sight (NLoS) conditions, respectively. Route R1, moving from east to west, had LoS conditions. R2, moving from north to south, had NLoS conditions, and was mainly blocked by the building and shrubs. To form the massive MIMO array with 256 antennas, a virtual-measurement method was adopted. Figure 3 shows the scheme of 256-element combining antenna array, giving 8 continuous positions. After collecting the raw data, we combined the 8 CIRs into one group. \[h_{i}(t,\tau)=\sum_{n=1}^{N}\alpha_{n}^{(i)}e^{-j\phi_{n}^{(i)}}(t)\delta(\tau- \tau_{n}^{(i)}), \tag{1}\]  
where \(i=1,2,\cdots,8\). \(\alpha_{n}^{(i)}\), \(\phi_{n}^{(i)}(t)\) and \(\tau_{n}^{(i)}\) represent the amplitude, phase, and delay of the \(n\)th sample in the time domain at the \(i\)th angle bin, respectively. \(N\) is the number of collected CIRs. Then, CIRs are combined into one group as  
\[h_{virtual}(t,\tau)=[h_{1}(t,\tau),h_{2}(t,\tau),\cdots,h_{8}(t,\tau)], \tag{2}\]  
where \(h_{virtual}(t,\tau)\) can be considered as the equivalent CIR collected from a 256 antenna UPA. The rationality of this method was proven in Reference [15]. It shows that there is a good match between the power delay profile (PDP) calculated from CIRs collected from the measurement campaigns and the combined CIRs. Furthermore, spatial angular characteristics, including elevation angle of departure (EoD), azimuth angle of departure (AoD), elevation angle of arrival (EoA), and azimuth angle of arrival (AoA), which were estimated from the combination, fit well with those from the measurement campaigns. Figure 1: Measurement map (Red triangle is the Tx location. R1 and R2 are the measurement routes in LoS and NLoS conditions, respectively). After combining the 8 groups of CIRs sequences into one group of sequences, the space-alternating generalized expectation maximization (SAGE) algorithm was used to estimate the channel parameters from the raw data [16], which provides a joint estimation of parameter set \(\theta_{l}=\{\tau_{l},f_{d,l},\Phi_{l},\Omega_{l},\alpha_{l}\}\), \(l=\{1,\ldots,L\}\). \(\tau_{l}\), \(f_{d,l}\), \(\Phi_{l}\), \(\Omega_{l}\), and \(\alpha_{l}\) denote propagation delay, the Doppler shift, the AoD, the AoA, and polarization of the \(l\)th propagation subpath, respectively. Specifically, \(\Phi_{l}=[\theta_{T,l},\phi_{T,l}]\), \(\Omega_{l}=[\theta_{R,l},\phi_{R,l}]\), where \(\theta_{T,l}\), \(\phi_{T,l}\), \(\theta_{R,l}\) and \(\phi_{R,l}\) denote the EoD, AoD, EoA, and AoA, respectively. The number of estimated multipath components (MPCs) was set to 100 in each snapshot.