 when 100% of the power is allocated to user 1, and for user 2, the maximum capacity is also obtained when it is allocated the full power. For every possible power distribution there is an achievable information rate, which results in the capacity regions depicted in the figure. Two regions are shown in Figure 10- 33, the larger one for the case where both users have roughly the same maximum capacity (similar channel conditions), and the other region for a case where one of the users has much better channel condition than the other. For Nu users, the capacity region is characterized by a Nu-dimensional hyper-region. 10.4 Multi-antenna transmission schemes Figure 10-25 illustrates a generic multi-user MIMO scenario where Nu users, each having NtNu transmit antennas, transmitting simultaneously to the BS in the uplink. The maximum achievable throughput of the system is determined by the point on the Nu-dimensional hyper-region that maxi- mizes the sum of all the users' information rates and is referred to as the sum capacity of the channel (see Figure 10-33). In the case of a near-far problem where one user has a more strongly attenuated channel than other users or some users are closer to the BS than others, obtaining the sum capacity would cause the user with the worse channel to achieve a lower rate. As shown in Figure 10-32, in the uplink of a multi-user MIMO system, the received signal at the BS can be written as y = n where Xk is the Ntk X 1 of the kth user complex-valued TX Antenna TX Antenna Port 1 Port 1 TX Antenna TX Antenna Port 2 Port 2 TX Antenna TX Antenna Port Nt1 Port Nr1 TX Antenna TX Antenna Port 1 Port 1 RX Antenna TX Antenna Port 1 TX Antenna Port 1 TX Antenna Port 2 Port 2 RX Antenna TX Antenna Port 2 Port 2 TX Antenna TX Antenna Port N12 Port Nr2 RX Antenna TX Antenna Port Nr Port Nt TX Antenna TX Antenna Port 1 Port 1 TX Antenna TX Antenna Port 2 Port 2 TX Antenna TX Antenna Port NtNu Port NrNu Uplink Downlink FIGURE 10-32 A generic multi-user MIMO transmission scheme 572 CHAPTER 10 The IEEE 