Theorem

Given a fading channel where both $Y$ and $A$ are known at the receiver at each time instant (i.e. $(Y,A)$ is the channel output). Then we define the channel capacity with DSI, $C_{DSI}(P)$ as $$C_{DSI}(P)=E_{A}\left[\frac{1}{2}\log_{2}\left(1+ \frac{A^{2}P}{\sigma^{2}}\right) \right]$$

Note

Fading decreases capacity for the AWGN Channel $$C_{DSI}(P)\le C_{G}(P)$$