Consider an FDMA system with K = 2 users, in an AWGN channel, where user 1 is assigned a...

Consider an FDMA system with K = 2 users, in an AWGN channel, where user 1 is assigned a bandwidth W1 = αW and user 2 is assigned a bandwidth W2 = (1 − α)W, where 0 ≤ α ≤ 1. Let P1 and P2 be the average powers of the two users.

a. Determine the capacities C1 and C2 of the two users and their sum C = C1 +C2 as a function of α. On a two-dimensional graph of the rates R2 versus R1, plot the graph of the points (C2,C1) as α varies in the range 0 ≤ α ≤ 1.

b. Recall that the rates of the two users must satisfy the conditions

Determine the total capacity C when P1/α = P2/(1−α) = P1 + P2, and, thus, show that the maximum rate is achieved when α/(1 − α) = P1/P2 = W1/W2.