I really appreciate an answer or any hint how to approach this problem:
Problem:
A receiver has two antennas. The first antenna receives $Y_1=hx+n_1$, where $x\in\{-A,+A\}$, $h$ estimated channel, and $n_1$~$N(0,\sigma^2)$. The second antenna receives $Y_2=n_1+n_2$, where $n_1$ is identical to the noise at antenna 1, $n_2$~$N(0,\sigma^2)$ and two noise are iid.
The question is whether $Y_2$ can be used to improve the performance of system? If yes, how?
I think yes, because $I(Y_1;Y_2)\neq 0$, but I don't know how to combine them linearly.