A Validated 5.9 GHz Non-Line-Of-Sight Path-Loss and Fading Model for Inter-Vehicle Communication
Due to the ITST 6-page limit, and to keep the paper focussed, we did not discuss three things in full detail:
The plot on the left is the not corrected version of the plot in the paper (for comparison in the right). The gap becomes obvious. There are almost no values reported by the radio with power values of -69,-68,-67dBm (this is not due to dropped packets!). The right shows the plot after correcting the issue by subtracting 3 from all values reported greater -59dBm.
On the left, the same fading plot as in the paper, but for LOS conditions. On the right, the NLOS paper plot for comparison. The LOS plot shows a very good fit to the Nakagami-m power probability distribution. The resulting m value is 1.05, corresponding almost to Rayleigh fading (Nakagami-m=1), as it is mostly assumed in urban/suburban conditions.
Fitted data:
- We selected to fit the intersection wide average reception power per tx-distance curve. Each of this curves abstracts (averages) 8 measurements; 2 measurement runs per side-street. This decision was made to provide stable input to the fit and keep the complexity on a moderate level. The previous paper showed that this averaging is viable, as the performance is very similar despite the transmitter being in the different side streets. This is a result of the inter-building distance in the two streets selected similar in most intersections. 5 meter bins were selected to provide fine grained distance resolution, especially at the LOS to NLOS change region.
- We fitted the median reception power curve, as it is more stable at lower reception rates. The average reception power curve suffers (bin values are too high) from incomplete data as soon as the reception rate sinks below 100%. The median is technically accurate as long as reception rate is greater 0.5. However, due to small-scale fading leading to variations and eventual measurement inaccuracies around the reception threshold of the radio, also median values are slightly too high at reception rates close to 0.5. This is visible in plots. To prevent a negative influence on the fit, an exclusion criterion of reception-rate > 0.65 was selected.
Selected intersections for the fitting:
Due to different non-trivial reasons, we had to exclude 3 out of the 8 tested intersections from the fit. However, this does not influence the fit quality, as we did not artificially removed “bad” intersections:
-> Intersection 1 was the very first tested intersection. Here, we measured with alternating transmission power (20+10dB) and rate (3+6 Mbps). In each second, one of the 4 configurations was measured. In consequence, there are gaps within the later on selected main configuration of 20dB and 3Mbit. For 5 meter bins as used in the fit, there are empty bins. Due to this, intersection 1 was excluded. Anyhow, the performance is very close to intersection 2 and 3, as the previous paper showed.
-> Intersection 9 has missing reflection facades. This dimension was not incorporated in the fit, as it would have complicated the fit again by another dimension. Furthermore, we only tested one of such intersection type (as it is rare), leading to insufficient data to provide a reliable fit in such another dimension.
-> Intersection 21 was excluded due to two reasons: First, one of the street legs has a non 90 degree angle. Second, the inter-building distance in the 2 streets differs a lot (55 against 30 meter). As we fit against intersection wide averages, and both distances are part of the formula, it is questionable if the averaging over the 4 side street simplification is applicable for this intersection.
Despite the exclusion of these 3 intersection, the fit covers 11 data rows from 5 intersection; where each data row is averaged from 8 measurment runs.
This research was executed by Thomas Mangel at BMW Group Research and Technology, in 2010/2011. Thanks for hosting goes to the Decentralized Systems and Network Services Research Group at the Karlsruhe Institute of Technology.