er MU-MIMO channel. The maximum capacity for user 1 is achieved 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 pos- sible power distribution, there is an achievable information rate, which results in the New Radio Access Physical Layer Aspects (Part 2) 561 capacity regions depicted in the figure. Two regions are shown in Fig. 4.60, 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 user. For Nuser users, the capacity region is characterized by an Nuser-dimensional hyper-region. Let us use a simple MU-MIMO system model to demonstrate how the sum rate of the sys- tem is calculated. As shown in Fig. 4.61, the transmit vector X can be expressed as the weighted sum (precoded) of the input data symbols Sklk=1,2,...,Nusser as follows X = = Ph where Nuser X1 vectors2denotes the data symbols from Nuser users and P = (P1,P2,. PNuser) is the precoding matrix comprising Nuser precod- ing vectors. It is assumed that the finite transmit power at the transmitter can be calculated as follows PTX = =E{x"x}. The kth complex-valued output of the system can be written as Yk HkX + nk ECN where N denotes the dimension of vector y. The kth branch user data can be detected using a linear minimum mean squared error (MMSE) receiver as follows Sk = WTXKEC in which the MMSE weighting matrix is given by It can be further shown that the SINR at the kth output is given by w/H&Pkl2 The sum rate of the system is given as In the uplink of a multi-user MIMO system, the received signal at the gNB can be written as = where Xk is the NTX X 1 transmitted signal vector of the kth UE with NTX transmit antennas, denotes the flat-fading channel matrix from the kth user to the gNB and n = (n1,N2,..., Nk N(0,1) is an independent and identically distributed additive white Gaussian noise vector a