Consider a three-user fading downlink with bandwidth 100 kHz. Suppose the three users all have the same fading statistics, so that their received SNRs when allocated the full power and bandwidth are 5 dB with probability 1/3, 10 dB with probability 1/3, and 20 dB with probability 1/3. Assume a discrete-time system with i.i.d. fading at each time slot.
(a) Find the maximum throughput of this system if (at each time instant) the full power and bandwidth are allocated to the user with the best channel.
(b) Simulate the throughput obtained using the proportional fair scheduling algorithm for ic values of 1, 5, and 10.