Consider the following idealized LTE scenario. The downstream channel (see
Figure \(6.20\) ) is slotted in time, across F frequencies. There are four
nodes, \(\mathrm{A}, \mathrm{B}, \mathrm{C}\), and \(\mathrm{D}\), reachable from
the base station at rates of \(10 \mathrm{Mbps}\), \(5 \mathrm{Mbps}, 2.5
\mathrm{Mbps}\), and \(1 \mathrm{Mbps}\), respectively, on the downstream
channel. These rates assume that the base station utilizes all time slots
available on all F frequencies to send to just one station. The base station
has an infinite amount of data to send to each of the nodes, and can send to
any one of these four nodes using any of the F frequencies during any time
slot in the downstream sub-frame.
a. What is the maximum rate at which the base station can send to the nodes,
assuming it can send to any node it chooses during each time slot? Is your
solution fair? Explain and define what you mean by "fair."
b. If there is a fairness requirement that each node must receive an equal
amount of data during each one second interval, what is the average
transmission rate by the base station (to all nodes) during the downstream
sub-frame? Explain how you arrived at your answer.
c. Suppose that the fairness criterion is that any node can receive at most
twice as much data as any other node during the sub-frame. What is the average
transmission rate by the base station (to all nodes) during the subframe?
Explain how you arrived at your answer.