# Radio Channel Scattering in a 28 GHz Small Cell at a Bus Stop: Characterization and Modelling
## 3 Results  
### Delay Spread  
The most immediate result from the measurement processing, as explained in the previous section, was the time-varying complex impulse response of the radio channel. In Figure 8, we plot the normalized amplitude of this impulse response for the record, corresponding to the van passing by the bus stop (Figure 7). Contributions of up to 40 dB below the main one have been measured. In Figure 9, we present the corresponding PDP, resulting from averaging the squared amplitude of the impulse responses.  
Figure 8: Amplitude of a measured time-varying impulse response.  
Several contributions with different delays and time-varying amplitudes grouped in clusters were appreciated. The different clusters were generated by propagation paths with very different lengths, while the components within a cluster were due to scattering objects surrounding the receiver or the transmitter. The power of the clusters varied with time. This may be not so clear for the zero-delay contribution, as there was a strong, direct component that dominated the propagation, but it could be seen for contributions with higher delays. This may suggest the channel is not stationary, as will become more evident after analyzing the DS.  
According to the measurement geometry, the contributions from the direct path and the path with a single reflection on the vehicle are included in the first cluster. A cluster with larger delays should be due to contributions with multiple reflections on the vehicle and other fixed scatterers present in the environment.  
The power of the clusters was reduced as the delay increased. The main contribution of each cluster decayed with the delay at a rate that was equal to or larger than the corresponding free-space losses for the equivalent distance. This is shown in Figure 9, where we have also plotted, in a thick, dashed red line, the free-space power decay with distance and delay.  
Within each cluster, the power relative to the main contribution in the cluster also decreased with the excess delay, but at a larger rate than that corresponding to the free space. This behavior is widely described in the literature and has even been incorporated into different channel models, like the Saleh-Valenzuela model [25], the Winner+ model [23] and the ETSI-3 GPP model [24].  
However, we have found that a linear fit better approximates the power decay (in dB) of the main contribution in each cluster with distance, as seen in the upper graph of Figure 10. The regression line has a negative slope of \(-0.0379\). Other captured records yield similar PDPs. For instance, the bottom graph in Figure 10 represents the PDP corresponding to the case of a car passing by the bus stop, as seen in Figure 11. Here, we can also identify the five clusters with decreasing power. The slope of the fitted line is \(-0.0343\).  
Figure 9: Power delay profile (solid blue line) and free-space (red dashed line) power decay.  
This agrees with the results presented in [37], where the empirical PDP obtained in urban environments at 1.8 GHz is modelled by a one-sided exponential decaying function:  
\[PDP(\tau)\propto\left\{\begin{array}{cc}\exp\!\left(-\frac{\tau}{\sigma_{D}} \right),&\quad\quad\text{for $\tau>0$}\\ 0,&\quad\quad\text{otherwise}\end{array}\right., \tag{1}\]  
This corresponds to a linear decay in logarithmic units.  
Figure 11: Car passing by the bus stop.  
Figure 10: Power delay profile (solid blue line) and fitted (red dashed) line for the records of a van (upper graph) and a car (bottom graph).