TABLE OF CONTENTS The MAC consists of K transmitters, each with power P k, sending to a receiver over a channel with power gain g k . We assume that all transmitters and the receiver have a single antenna. The received signal is corrupted by AWGN with PSD N 0 /2 . The two-user MAC capacity region is the closed convex hull of all vectors (R 1, R 2 ) satisfying the following constraints [35, Chap. 14.1]:
The first constraint (14.38) is just the capacity associated with each individual channel. The second constraint (14.39) indicates that the sum of rates for all users cannot exceed the capacity of a superuser with received power equal to the sum of received powers from all users. For K users, the region becomes
Thus, the region described by (14.40) demonstrates that the sum of rates for any subset of the K users cannot exceed the capacity of a superuser with received power equal to the sum of received powers associated with this user subset.
The sum-rate capacity of a MAC is the maximum sum of rates 
, where the maximum is taken over all rate vectors (R 1, , R K ) in the MAC capacity region. As with the like capacity for the BC, the MAC sum-rate also measures the maximum throughput of the system regardless of fairness and is easier to characterize...
