I need a model to calculate the received power in a short distance (within 3 meters) at a low-power receiver that could be within 3 meters away from the receiver in outdoor environment. I assume that there is no obstruction between the receiver and the transmitter. I want then to add some noise to the transmitted power and do some measurements.
I have seen two models to calculate the received power:
where Pr is the received power by receiver x, Pt is the transmitted power, and lambda is the wavelength which we calculate as lambda = v/f where v is the speed of light, f is the frequency. The gains of the receiver and transmitter antennas are assumed to be 1.
where Pr(d) is the received power from distance d in dBm, d0 is the distance between the receiver and the reference node and X is a Guassian random variable represent the noise
My questions are:
- Which model is more suitable for my case
- What is the difference between the two models if I want to use them to localize the transmitter
The second model is more general, assuming dx is distance in the first model, the second model will match the first with np = 2.
Depending on the wave length and the shape of the antena it could be a planar wave, a cylindrical wave, or a spherical wave. In reality it will be none of those and there may be some reflection from the ground as well.
Having no experience with this what I would collect some points (Pr, d), do a linear regression on the second equation to determine P(d0) and np. If np is 2 than you will conclude that the first equation was suitable for your application, but then you already have the second :)