ultiple pairs of users want to exchange information with each other via a shared relay on the same time-frequency resource [26-30]. The notations and assumptions remain the same. We now denote the user pair exchanging information as (Sk, Sk!) for k, k' = 1,..., K. We have in total K number of user pairs and therefore 2K number of users. During MAC phase, all the 2K users transmit their signal to the relay. The signal received at the relay is expressed as yr = V P Gs + zr, (4.23) where = define G=[g1, gi g2K], where gk E CNx1 denotes the channel between the kth user and the relay. The relay then amplifies and beamforms the received signal and then broadcasts it to all the users. 4 Full-Duplex Multi-Hop Communication for Beyond 5G The signal received at the kth user in the multi-pair scenario is as follows yk = agT Wy R (4.24) (4.25) Here (k, k') represents a user pair which exchange information. The first and second terms are the desired and the SI term. The third term, which was absent in the single- pair model, represents the interference coming from other K - 1 pairs and is termed as inter-pair interference. The fourth term is the amplified noise from the relay. 4.7.1 MRC/MRT Beamforming The received instantaneous SINR at the kth user, using (4.41), is given by SINRk = i#k,k' (4.26) where W = G*TGH with T = blkdiag{T1,..., TK}. Here permutation matrix (4.27) 4.7.2 ZFR/ZFT Beamforming Using (4.17), we can write gTWg = 8k,ii where Ski=1 = when k = i and 0 otherwise. The SI as well as interference tends to zero. The received signal in (4.41) is, therefore, simplified to (4.28) E. Sharma and P. Singh The received SINR at the kth user is given as (4.29) This is same as that obtained from its single-pair counterpart. The SE and EE, therefore, can be obtained, as explained earlier. 4.8 Full-Duplex Multi-Pair AF Massive MIMO Relay We now extend our understanding from previous sections to full-duplex multi-pair two-way massive MIMO relay [2, 24, 32]. There are few points to note multiple full-duplex user pairs with sing