1. Find the two-user broadcast channel capacity region under superposition coding for transmit power P = 10 mW, B = 100 kHz, and N0 = 10-9 W/Hz.
2. Show that the sum-rate capacity of the AWGN BC is achieved by sending all power to the user with the highest channel gain.
3. Derive a formula for the optimal power allocation on a fading broadcast channel to maximize sum-rate.