Find the sum-rate capacity for a two-user broadcast fading

Question

1. Find the sum-rate capacity of a two-user fading BC, where the fading on each user's channel is independent. Assume that each user has

(i) a received power of 10 mW and

(ii) an effective noise power of 1 mW with probability .5 or 5 mW with probability .5.

2. Find the sum-rate capacity for a two-user broadcast fading channel where each user experiences Rayleigh fading. Assume an average received power of P = 10 mW for each user, bandwidth B = 100 kHz, and N₀ = 10^-9 W/Hz.