Include any computer code that you use to solve the non-linear equations that may appear.
1. Consider a flat fading channel in which, for a fixed transmit power $P$, the received SNR is a continuous
random variable that is uniformly distributed between 0 and 1000.
(a) Find the capacity of the channel assuming that the transmitter has no CSI but the receiver has
full CSI.
(b) Find the capacity of the AWGN channel with the same average received SNR (for a fixed trans-
mitter power $P$) and compare it with the capacity in (a).
(c) In (c)-(d), assume the transmitter has perfect CSI as well, and assume $P$ is the long tern power
constraint. Find the optimal power adaptation policy $P[i]/P$ for this channel and its corresponding
Shannon capacity. Here, $P[i]$ represents the power used for channel state with index $i \in \{1,2,3,4\}$.
(d) Find the channel inversion power adaptation policy for this channel and associated zero-outage
capacity.