How to calculate the total signal strength and phase shift of multiple signals in a reciever

Question

I have a simulation to make where I have an array of transmitters that transmit the same signal. At a random point, which I have to consider as a receiver I have to measure the phase shift of the signals and also measure the total signal strength. The requirement is that the transmitter emit the same signal but with different phase offsets.

• As far I understood because the transmitters are separated apart, the received signal is already is offset by some phase because they travel distances. Is my assumption right?
• I know the formula to find the phase offset given the distance travelled of two signals - how do I calculate it for multiple signals? Or am I understanding the question wrong?
• How do I calculate the total signal strength for all signals combined? I know for one signal, assuming a free space, line of sight connection I can use friis equation. But how do I use it for multiple signals?

Any help is very much appreciated. I am Software Engineer who have recently taken up Wireless communications course, and I'm not sure if I understand the motivation and meaning behind the simulation right. Thanks!

Answer 1

Generally with this type of problem (1 receiver & multiple transmitter antenna elements, or 1 transmitter and multiple receive antenna elements), you take one of the paths and call that your reference. The total phase shift through that path is many multiples of 360 deg, because the path is longer than one wavelength. But by making that path your reference you're saying "I don't care what the total phase shift is, I'm going to assume it's zero". We'll call that path Path 0.

Now you only have to be concerned with the relative phase differences between Path 0 and the other paths, Path 1, Path 2, ... Path n. All you have to do is do is compute the complex sum of the signals through all the paths. Need to keep in mind the effects of modulo 360 phase differences because, for example, a phase shift of 360 deg looks exactly the same as a phase shift of 0 deg.

To get the total signal strength, you need to know the radiated power level from each transmitter (antenna element), the shape of the radiated beam and/or is directivity, the distance (since the power, measured in dBm, falls off with the square of the distance), any path attenuation, and the effective area of the receiving antenna element. Using the Friis equation you mentioned for each path, you can calculate the power at each element, which is summed in a complex fashion as discussed above.