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localizationsignal-processingrssiradio-transmission

What Received Power Model To Use For Localization

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:

  1. enter image description here

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.

  1. enter image description here

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:

  1. Which model is more suitable for my case
  2. What is the difference between the two models if I want to use them to localize the transmitter
Solution

  • 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 :)