t the gNB. We assume that the receiver k has perfect and instantaneous knowledge of the channel matrix Hk. Note that the gNB is equipped with NTX transmit and NRX receive antennas. In the downlink, the received signal at the kth receiver can be written as yk=Hk+nkk=1,2, Nuser where is the downlink channel, and is the complex-valued additive Gaussian noise at the kth receiver. We assume that each receiver also has perfect and instantaneous knowledge of its own channel matrix Hk. The transmitted signal X is a function of the multiple users' information data, that is, X = New where Xk is the signal carrying kth user's message with covariance matrix Lk = E{X&XH}. The power allocated to the kth user is given by Pk = tr{Sk}. Under a Channel 1 User RX 1 w7 User1 data User 1 data Channel 2 User RX 2 User 2 data Linear User2 data Scheduler precoding Nuser S Nuser User Nuser data Channel NuserHN User RX Nuser WN User Nuser data Finite-Rate Feedback Channels Figure 4.61 MU-MIMO BC model [ 15]. New Radio Access Physical Layer Aspects (Part 2) 563 Maximum sum capacity Capacity region Near-far capacity region Capacity of user 1 Figure 4.62 An example illustration of capacity region. sum power constraint at the gNB, the power allocation needs to maintain Assuming a unit variance for the noise, it can be shown that the capacity region for a given matrix channel realization can be written as [15] CDL = where R +Nuser is the Nuser-dimensional set of positive real numbers. The preceding equation may be optimized over each possible user ordering. Although difficult to realize in practice, the computation of the capacity region can be simplified using the assumption that the downlink capacity region can be calculated through the union of regions of the dual MAC with all uplink power allocation vectors meeting the sum power constraint. The fundamental effect of the use of multiple antennas at either the gNB or the user terminals in increasing the channel capacity is best realized by examining how the sum capacity, that is, the point o