 4 Full-Duplex Multi-Hop Communication for Beyond 5G Self-loop Slot-I Slot-II interference at relay Slot-I Self-loop Self-loop interference Inter-user interference at user interference at relay Fig. 4.5 Full-duplex relay. (a) One-way relay. (b) Two-way relay side of the relay will interfere with each other, resulting in the inter-user interference (IUI). Also due to multiple pairs of users accessing the same channel, there will be co-channel (inter-pair) interference [24]. E. Sharma and P. Singh Transmit Receive Self-loop Self-loop interference Inter-user interference at user interference at relay Fig. 4.6 Multi-pair full-duplex two-way relay system 4.6 Single-Pair Half-Duplex Two-Way Massive MIMO Relay: Mathematical Model Consider a single-pair (i.e., two-user) two-way AF half-duplex relaying system [26- 30]. Let N denote the number of antennas at relay, and each user is equipped with a single antenna. The direct link between the two users is absent due to large path loss and heavy shadowing. The channels between the relay and the users are reciprocal; this implies that the users and relay operate in time-division duplex (TDD) mode. We assume that all the users have the same transmit power Ps and relay power is PR. The communication takes place in two phases: (1) multiple access (MAC) phase and (2) broadcast (BC) phase. During the MAC phase, the user-1 and user-2 transmit signal /Pssi and VPss2, respectively, to the relay. The signal received at the relay is expressed as (4.1) We define = [S1, s2]T, and G=[g1, g2], where CNx1 denotes the channel between the kth user and the relay. The channel matrix G = HD 1/2, where D is the diagonal matrix representing the large-scale fading coefficients as follows: 4 Full-Duplex Multi-Hop Communication for Beyond 5G D = The matrix H ~ CN(0, IN) represents the small-scale fading. Remember the elements of the matrix H ~ CN(0, IN) are all independent and identically distributed (i.i.d.) random variables. The vector ZR ~ CN(0, ONIN) represents the additive white Gaussian noise (A