# Calculating average power of a discrete random signal with complex values

I have a Rayleigh channel that transmits discrete values according to the following: $$y(n) = h(n) * s_n + \omega_n$$ Where $$y$$ is the received message, $$s_n$$ is the symbol sent (constellation 2-PSM), $$\omega_n$$ is a white noise and $$h(n)$$ is a Gaussian circular random variable of mean 0 and variance 1. The first thing I am asked to do is determine an $$A(n)$$ such that, by sending $$s_n/A(n)$$, I am able to keep the instantaneous power constant. To find this value, I did the following:

• Did not consider the noise, because it is impossible to know its value each time.
• Then: $$P = |y(n)|^2$$. This means that P = $$|h(n)|^2 |s_n|^2/P$$, where $$P$$ is the instantaneous power. From there I obtained $$A$$.

I don't know if this the correct approach but it seems logical to me. Now the part I am stuck at is calculating the average power of the signal. I tried going via the correlation formula: $$P_a = R(0) = \mathbb{E}[|y(n)|^2]$$ But I don't know where to follow from here. I could try integration but I'm not sure on how to do that in a discrete signal. Also, should I take the noise into consideration when calculating the average power?

Reference: This is an exercise from Chapter 9 of Principles of Digital Communications, by R. Gallegher.