# Received Signal Strength Calculation for Probabilistic Line of Sight Channel

Scenario: Given a UAV which emits a beacon and the beacon is received by a node on the ground. The node calculates the received signal strength. Considering the channel is Probabilistic LoS, the average path loss is given as:

$$L_{a, k}^{av}(t) = \left[P^{LoS}\eta^{LoS} + P^{NLoS}\eta^{NLoS}\right]\left(\lambda_o d_{a, k}\right)^\alpha$$

Where

• $$\lambda_o = \frac{4\pi f_r}{c}$$
• the probability of line of sight is given as: $$P^{LoS}(t) = \frac{1}{1 + A\exp\left(-B\left[\left(\frac{h_a}{d_{a, k}(t)}\right) - A\right]\right)}$$
• $$h_a$$ is the platform height
• $$A$$ and $$B$$ are environment dependent parameters
• $$d_{a, k}$$is the distance between the UAV and node
• $$c$$ is the speed of light
• and $$f_r$$ is carrier frequency.
• $$P^{LoS}, \eta^{LoS}, P^{NLoS}, \eta^{NLoS}, \alpha, f_r$$ are the probability of line of sight, mean additional loss for line of sight, probability of non-line of sight, mean additional loss for probability of line of sight, path loss exponent and carrier frequency, respectively. Assume the transmit power is $$P_t$$ and received power is $$P_r$$. And the antenna gains at transmit and receive side are, $$G_t$$ and $$G_r$$ respectively.

Goal: My final aim is to get the distance from platform to node, the node receives the beacon from platform and based on the received power has to ascertain its approximate distance to platform.

Question: What would be relation for received power at the node, considering the given average path loss above from the platform.

• "RSSI" is not uniformly defined. Every standard, or sometimes every device, just invents a formula for that, which incorporates received signal power, noise floor, interference power, clock errors etc. You're missing a transmit power specification, so you can't even make any statement on the received signal strength, so what you've got is insufficient for that. Dec 16, 2020 at 9:38
• @MarcusMüller by the sounds of it, I think you might have answered the question or at least cleared up confusion that there is no absolute equation and it depends on the platform Dec 16, 2020 at 11:56
• Why do you want to use RSSI? Is it required to be used for some reason? I may be wrong, but I can't figure out what you'd be able to do with RSSI as opposed to say received SNR? Dec 16, 2020 at 11:57
• In my project I intend to use RSSI to calculate the distance of the node from the platform. The envisaged protocol I intend to develop deems it necessary. RSSI depends on the distance, hence the node must be cognizant of its distance from the platform. I was just not sure how to put it all together. Assuming we have a transmit power as Pt of the beacon. Dec 16, 2020 at 12:19
• Further I have edited my question for clarity. Dec 16, 2020 at 12:40