In most scenarios in wireless communications we don't know the TX power because we don't have access to the transmitter, but we can measure the RX power from the RX signal. Is there a way to estimate the power of the transmitted signal?
Radio Transmit Power (dBm) – Loss from Cables & Connectors (dB) + Antenna Gain (dBi) = Output Power (dBm/W/mW)
When measuring a transmitter output, the measurements must be made in the "far field". In the far field, the power received per unit area from an isotropic antenna is calculated from the following equation:
Pr =Pt/(4 π d^2)
where Pr = received power, Pt = transmitted power and d is distance from transmitter in meters.
This equation is also referred to as the inverse square law, since doubling the distance gives a four-fold reduction in signal power. Many radio receivers have a manual which includes a specification sheet. One of the properties quoted is sensitivity, this indicates the "weakest" signal that can be received. Sensitivity is usually quoted in units of V/m or volts per meter. The equation below is used to calculate field strength in V/m :
E =√ (30 Pt) /d
where E is field strength in V/m, Pt = transmitted power and d is distance from transmitter in meters.
The following page contains some typical numbers of transmit powers for different technologies:
https://en.wikipedia.org/wiki/DBm
you can estimate the transmitted power and also the location of unknown transmitter
Take simple wire antenna, at distance d from Tx, move 90^० and measure again the Pr, repeat the same all 4 directions from Tx. Then average it. Then Pt= Pr/ d^2
Like U. Dreher has write, only with the RX power no, you need some other information, like distance, antenna type, obstacles, type of material of obstacles, ….
Depending of the technology, like Emil has write, it is possible to determine (more or less ) the transmission power, in this case, if you assume typical transmission power and omni antennas, you can, (in absence obstacles) compute the distance. Even in this case if the propagation model is not free space or two ray (for example, nakagami) it can be imposible to compute the distance.
Thank you all for your answers,
S.B. Chougule, could you please explain the intuition behind your formula Pt=Pr/d^2?
Also, Walid Ghanem, how can we estimate the TX power?Could you please suggest some algorithms?
It is the free space model, the attenuation is proportional to d^2
https://en.wikipedia.org/wiki/Free-space_path_loss
There are abundant bibliography about this, for example
http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470751843.html
I am sure that you will be able to find in any university library several books about the subject
This link provides basic information about propagation models
http://people.seas.harvard.edu/~jones/es151/prop_models/propagation.html
The tx power can be possibly estimated by a two-phase method. We assume that the channel is static block fading during the two-phase measurement, i.e., the channel keeps constant during the measurement. In the first phase, sending a pilot signal (with a predefined power) from the Tx to the Rx. At the Rx, the channnel state information (CSI) can be estimated since the Rx knows the pilot signal. In the second phase, the Tx can send a signal with an arbitrary transmit power to the Rx. At the Rx, using the estimated CSI, the transmit power can be estimated roughly. This is my thought. Can anyone provide a related reference for this possible way?
Tx power, antenna gain etc are set based on the path loss.
It is not some thing to be measured, it is something that we set. Still, if you need to measure tx power simply cancel the pathloss from the rx power.
In order to estimate the transmitted power you have to know the location of the transmitter that is its distance from the receiver. The nature of the wireless path that is line of sight or nonline of sight. The formula brought by Khalid is for line of sight propagation. You have to know also the antenna gain other wise you can estimate what is known as effective isotropic power which is the radiated power time the antenna gain.
With this known you may estimate a value which far from the real value but it may be a very crude of the transmitter power.
Best wishes
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