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I have a question regarding to detect the location of the antenna.

I read this link: https://en.wikipedia.org/wiki/Plane_wave

In the "Complex exponential form" part, the equation:

U(r,t) = U0 * exp(j*(k.r - w*t) as the function of location and time

U0 = A0 * exp(j*phi) : A0 and phi are amplitude and phase respectively.

From U0, I can write down a complex number x and y (still in time domain)

x and y should be vector on the complex coordinate.

Now, I need to define value of amplitude and phase base on value of x and y. But I do not know x and y.

When I rotate the antenna, can I define the position, amplitude and phase?

I hope any one can give me suggestions.

Thank you.