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## Main Question or Discussion Point

I'm sitting here with an interesting problem that I can't seem to figure out. I'm given two random variables

X=a*exp(j*phi)

Y=b

where both a and b are known constants.

phi is uniformly distributed on the interval [0,2pi)

a third random variable Z=X+Y.

My goal, is to find the magnitude of the resulting vector.

At first, I thought that this was an easy problem that could be solved by use of convolution. This doesn't work here since phi makes X a random vector. I tried using MATLAB to help solve it. I wrote an mfile that tried solving it using convolution, and it failed. I tried turning X into a toeplitz matrix and doing matrix multiplication to do the convolution, but that too, failed.

Can anyone help me out?

X=a*exp(j*phi)

Y=b

where both a and b are known constants.

phi is uniformly distributed on the interval [0,2pi)

a third random variable Z=X+Y.

My goal, is to find the magnitude of the resulting vector.

At first, I thought that this was an easy problem that could be solved by use of convolution. This doesn't work here since phi makes X a random vector. I tried using MATLAB to help solve it. I wrote an mfile that tried solving it using convolution, and it failed. I tried turning X into a toeplitz matrix and doing matrix multiplication to do the convolution, but that too, failed.

Can anyone help me out?