btained by the maximum NISE Rk in the capacity region, scales with the number of active users (see Fig. 4.62). An efficient UE pairing scheme is required at the gNB to choose the correct pair of UEs for transmission in MU-MIMO systems. This pairing scheme is required to maintain minimal interference among scheduled UEs in MU-MIMO transmission. A proper pairing scheme can be designed by maximizing the chordal distance¹5 between the feedback precoding The asymptotic performance of a coding scheme is dominated by the shortest distance between any pair of codewords. The relevant distance measure between two codewords xjandx2 of an orthogonal code for a non- coherent MIMO system is the chordal distance defined as d2(x1,X2) = - x 564 Chapter 4 matrices of the UEs. The chordal distance between two matrices is given in [15] and repre- sented by where II.I.F denotes the Frobenius norm of the matrix. The chordal distance generalizes the distance between two points on the unit sphere through an isometric embedding from complex Grassmann manifold Gr(Nrx,N1) to the unit sphere. Assuming an infinite number of UEs served by the current gNB, the kth UE with reported precoding matrix Pk will be paired with the mth UE, where the mth UE reports pre- coding matrix Pm and the chordal distance between precoding matrices is maximized. With the maximized chordal distance criterion, Pm stays in the anti-polar position of Pk; hence, is minimized, yielding the minimized inter-user interference. Therefore, the UE pairing scheme for MU-MIMO transmission in practical systems is designed to find the best match between two UEs (e.g., the mth UE and the kth UE) based on the reported precoding matrices and the following criterion Pm = arg de(p), Pk) with PUE representing the pool containing all reported precoding matrices at a certain gNB. 4.1.9.3 Analog, Digital, and Hybrid Beamforming Large antenna arrays and beamforming play an important role in 5G implementations since both base stations and devices can accommodate a larger number of antenna 