In this section, results obtained in the auditorium and the corridor, are presented. Every measurement results in three different S-parameters, measured at the same time, which allows observing the difference between multipath components arriving at the three antennas. All wideband results are shown, relative to the delay of the main LOS component.
3.1. Auditorium
Figure 8a–c show the PDP for the three S-parameters at 41.5 GHz. Taking a closer look at the area of the component arriving first, it is easy to see that antenna “2” (closest to the transmitter) gets the most energy of the three. This can be explained by the fact that also reflections from the floor, tables and chairs are taken together, where those are at the same time partially blocked to the other antennas. Another explanation can be the coupling of the different receiving antennas, resulting in (smaller) modifications of the radiation pattern and hence reducing efficiency and performance.
The direct component can be easily identified as the one with the smallest delay. As the receivers move away from the transmitter, that relative delay increases. The same trend can be seen in other contributions produced by scatterers placed between the transmitter and the receivers.
However, at the central part of the graphs, there is a contribution that can be seen in
Figure 8a (and less clearly in
Figure 8c) starting at 20 ns delay and lowering its delay as the receivers move away from the transmitter. This indicates that the contribution is arriving from a direction opposite to that of the direct component. It was probably produced by the laptop, which was the closest to antenna “2”.
As our simple ray-tracing tool does not take into account the amplitude of the components, it could predict some components that do not appear in the actual measured results due to their large attenuation and low power in the real world. This is the case for the sidewall reflection in
Figure 8.
Finally, the contributions coming from the chairs at the back area of the auditorium can also be identified by their initially longer delays, getting shorter when the receiver moves closer to these scatterers.
Figure 9 shows the measured PDP at the 60 GHz band together with the ray-tracing predictions. Aside from the difference between the three receivers, it is also interesting to recall the differences on the PDP between 40 GHz and 60 GHz. While for 40 GHz there are several multipath components, in 60 GHz only the line of sight and the reflection on the floor are present. The other contributions from the side and back wall suffer stronger attenuations and fall below the receiver’s sensitivity (
Figure 9a–c). In fact, the ray-tracing simulations predict the time delays that would correspond to those contributions, as can be seen in
Figure 10, but no signal over the noise threshold was detected in the measurements.
As stated before, time dispersion affects the maximum symbol rate that can be used without suffering ISI. In
Figure 11, the RMS delay spread for all three S-parameters at both frequencies is plotted as a function of the receiver’s position. The results are consistent with what was shown before (
Figure 8 and
Figure 9). At 40 GHz the amount of multipath is more significant than at 60 GHz; therefore, the RMS delay spread is also larger.
Another interesting way to analyze the RMS delay spread values is by means of their cumulative distribution functions (CDFs). Computing the CDFs of the RMS delay spread can help to establish a reference value for the delay spread in that environment, by setting a level below which it stays for 99 percent of the time.
Taking a closer look at
Table 1, it shows that the most restrictive antenna (the one with the larger value of RMS delay) is antenna “3”, which is the one at the front. Hence the system must be designed to take that value into account. Again, the lower delay spread at 60 GHz, when compared to 40 GHz, is obvious in
Table 1.
The second computed parameter is the coherence bandwidth. At 40 GHz, the results are very similar for all three antennas, as can be seen in
Figure 12. For the signal received by antenna “2” and “4” similar behavior is observed: A level of about 800 MHz for
α = 0.5 until the antennas are moved 100 cm on the rail. The reason for this large coherence bandwidth is that at short distances the main contribution is the direct one, while the ground reflection is attenuated by the antenna pattern (as seen in
Figure 9). As the distance increases, the ground reflected component is received through the center of the main lobe of the antenna pattern, and the coherence bandwidth decreases drastically. Comparing those results with the ones obtained by antenna “3”, the level of the coherence bandwidth in the latter is smaller and the decay is produced at a closer distance to the transmitter.
When looking at the results for 60 GHz in
Figure 13, one can observe the increase in the mean level of the coherence bandwidth for all correlation levels. This can be explained by the reduced number of echoes, compared to the 40 GHz frequency campaign.
As with the RMS delay, the percentage of the time the coherence bandwidth is above a desired threshold and is a useful metric for the design of communication systems. Here, the results for the 99th percentile can be seen in
Table 2.
We can observe that for a coherence level of 0.9, 60 GHz clearly outperforms 40 GHz. For lower correlation levels, that behavior is not that clear. In addition, for both frequency bands, the worst scenarios are given when receiving through antenna “3”.
Comparing the coherence bandwidth and the RMS delay spread values, it is clear that there is an inverse relation. The more replicas of the signal received, the larger the RMS delay spread and the lower the coherence bandwidth become. The mathematical relation is given by Fleury’s limit [
14,
15] in Equation (5).
where
Bc is the coherence bandwidth for a correlation level
and
τrms is the RMS delay spread.
Figure 14 illustrates both theoretical lower limits for the coherence bandwidth with different correlations and the results obtained by analyzing the available data and plotting them as a function of RMS delay at 60 GHz.
3.2. Corridor
Wideband results obtained in the corridor, in both LOS and OLOS, were processed in a similar way.
Table 3 and
Table 4 provide RMS delay spread values and
Table 5 and
Table 6 coherence bandwidth values, for LOS and OLOS conditions.
Observing
Table 3 and
Table 4, one can notice a clear difference between 40 GHz and 60 GHz. Both in LOS and OLOS, the 60 GHz signals demonstrate a lower delay spread. Indeed, the lower the frequency the more multipath is observed in the measurement campaign. Obviously, the multipath scheme is the same in both environments. However, the attenuation at 60 GHz is stronger than at 40 GHz as many multipath components at 60 GHz arrive at the receiver with a level below its sensitivity, and hence do not contribute to the received signal. Less multipath components result in a lower RMS delay spread.
The difference in RMS delay spread between LOS and OLOS is clear at 60 GHz, with lower values in LOS and with a stronger dominant direct path than in OLOS. The difference is not so clear at 40 GHz.
In general, the coherence bandwidth in these corridor scenarios is higher in the first part of the rail. After a certain distance, it drops to nearly half its value. The drop appears around 130 cm for 60 GHz and 150 cm for 40 GHz. There are two explanations for this behavior. The first one is that the antenna quits the main lobe, resulting in a weaker value in the PDP. The second one is that the multipath components are reduced, due to the environment geometry.
In the LOS scenario, the coherence bandwidth is higher at 40 GHz than at 60 GHz, as can be seen in
Table 5. As previously stated, this is expected due to the higher amount of multipath. In OLOS (
Table 6) the 60 GHz seems to be higher, but this is due to the absence of received signal at some places along the path.
Regarding the theoretical limits for the coherence bandwidth,
Figure 15 shows the Fleury’s limit for the case of the measurements in the 40 GHz band at the corridor.