How to represent time versus Pathloss ? V2V data at 5.9 GHZ

I would like to represent a figure of the path loss as a funcion of time. I know that

The PL0* term can be approximated to free space attenuation L=20*log10(4*π*d0*λ).

But I don't know how to get the value of the path loss exponent and the variable X. Can anyone help me to resolve this in order to do the representation I mentioned before??

[Renato SL]

I don't think time is a relevant variable in this equation. Distance could be the variable, as it is in the equation.

Regarding the path loss exponent and X, I believe you should find it in your textbook since it is based on empirical measurements. The values are mentioned here, but please refer to the mentioned textbook for more details.

One more thing, I think you should recheck the formula for L that you mentioned. As it is, the log will calculate something with a unit of meter squared (d0 multiplied by λ). Maybe it should be L = 20*log10(4*π*d0/λ) to make it dimensionless, but I'm not sure.

[youcha]

Thank you so much for your help, I really appriciate your comments. This is an example of what I have found : https://core.ac.uk/download/pdf/33495831.pdf

[youcha]

the measurments data I have has been gathered in a vehicular environment (Vehicle-to-Vehicle). According to the link you mentioned, the table mention the values of the path exponent in case of "Vacuum, infinite space". Is it correct to consider a V2V environement as a an infinite space?

[Renato SL]

Regarding your question about the use of exponent for vacuum, you should be aware that just before the table, it said "Empirical measurements of coefficients γ and σ in dB have shown the following values for a number of indoor wave propagation cases". Those values are for indoor use. They may not be appropriate to use for your case, which is a vehicular environment (related to roads, traffic with different intensity, maybe some influence of street lights, reflections from other vehicle, etc).

Plese refer to a proper textbook for your needs. I linked the Wikipedia page just as a start, not a definitive reference.

In the end, you might find that the values in the Wikipedia page are the same with the ones in a textbook but I would say that as it is, it is not appropriate to be used.

[Renato SL]

I have just read your reference. After a quick read, it looks like it can be a solid reference. It cited some other papers and textbook(s), so those would be interesting to read, too.

I cannot remember the exact title of the books that I used to use (it has been 3 years since then), but I remember several authors: JD Parsons, Roger L Freeman, John G Proakis. They have written textbooks related to planning of mobile, wireless networks so I believe their books should also have the details you need.

[youcha]

Thank you so much Renato

[youcha]

I have computed the Pathloss as PL(dB)=Ptx(dBm)-Prx(dBm). The emitted power has a fixed value equal to 76 dBm while the recieved power is a matrix of 180 line and 5000 column. Each line corresponds to a measured trace of 5000 values of measured recieved power and it's equivalent to a 5 seconds. I have computed the value of the Pathloss for each trace.

I have represented the emperical pahloss and the free space pathloss. Each time value in the axis x corresponds to a measured trace. I want to interpret the decrease in the pathloss at the values of time=39. In other words, What is the relationship between this decrease and the length of the observation window?

[Renato SL]

I think you should know the cause of the evolution of the pathloss through time. You did the simulation.

Since you said the emitted power is constant, then something must have happened during the transmission. I don't know what you did, but it has to be in the simulation.

[youcha]

The data comes from a Narowband V2V measurment campaign at 5.9GHz. The emitted power is fixed to 76dB. The pathloss variation is affected by the distance between the Tx and Rx. For example, at time=39 the distance between Tx and Rx decrease from 25m to 8m. I was thinking that probably I can use this iformation to estimate the "optimum" length of the observation window

[Renato SL]

If the distance between the Tx and Rx change through time, I would say that maybe you can also show the plot of change of distance through time. It would support the other plot.

Question: Why do you need to define a limited observation window? I can't imagine the benefit of doing it.

[youcha]

I have attached the representation you asked for.

In my case, the observation time window (Sample size) is used for the caracterization of the small scale fading statistics of the channel. the length of the window should be chosen such that the stationarity length of the process is not exceed. On the other hand, a large number of samples is needed in order to obtain meaningful statistical results.

[Renato SL]

I searched about stationarity just now, so now I see what you mean.

Based on the time plot, from a quick observation, I would think about (26s to 39s), (72s to 87s), (110s to 150s), or (150s to 162s). Those periods looks interesting for me, but again, just from a glance of the time plot.

You can try to plot the ideal pathloss value alongside the measurement data, I guess. Maybe it could also help you decide which is the best window.