Hi everyone and thanks in advance.
Let's say we have a random variable Y which can be expressed as the sum of two other complex random variables X and W, i.e. $ Y = X + W $. $X$ and $W$ are independent. $X$ variable stands for the user signal and has the following statistics:
$$ E[X] = 0 $$ $$ Var[X] = E[(X-E[X])·(X-E[X])^*] = E[|X|^2] = P_x $$
Where $X^*$ is the conjugate transpose of X.
$W$ variable stands for a zero mean white noise with normal distribution and variance $\sigma_w^2$:
$$ W \sim \mathcal{CN} (0,\sigma_w^2)$$
$E[Y]$ and $Var[Y]$ can be easily computed, but my question is referring to $|{Y}|$. How should I compute the expected value $E[|Y|]$ ?