member that MRC/MRT cannot completely suppress the self-interference and therefore perform inferior than ZFR/ZFT at high SNR. 4.6.1.2 ZFR/ZFT Precoder The ZFR/ZFT precoder is formulated as W G*TGH, (4.10) where G=G(G4G)-1 The computational complexity is O(N2K+NK2+K3), which is higher as compared to the MRC/MRT beamforming design. 4.6.2 Performance Analysis of Single-Pair Relay Model: MRT/MRC Beamforming In this subsection, we calculate the SE and EE of the single-pair AF two-way half- duplex relay model considering MRC/MRT beamforming matrix. Using (4.8), the 4 Full-Duplex Multi-Hop Communication for Beyond 5G received signal in (4.6) and (4.7) can be further simplified as (4.11) (4.12) The received instantaneous signal-to-noise ratio (SNR) is given as a2PsgGTG4gsao (4.13) SINR2 (4.14) The sum SE of the system, in bps/Hz, is therefore SINRk)]. (4.15) We also define the EE of the system, in bits/Joule, as the ratio of the sum SE to the total power consumed by it B x SE (4.16) where B denotes the bandwidth and MR and Ms denote the inverse transmit power amplifier efficiency of the relay and users, respectively. The scalar Pc.k denotes the circuit power consumption. 4.6.3 Performance Analysis of Single-Pair Relay Model: ZFR/ZFT Beamforming In this subsection, we calculate the SE and EE of the single-pair AF two-way half- duplex relay model considering ZFR/ZFT beamforming matrix. Using (4.35), we can write (4.17) (4.18) E. Sharma and P. Singh which implies that g7 Wg2 gTWg = 1 and Wg1 = gTWg2 = 0. Using (4.17), the received signal in (4.6) and (4.7) can be further simplified as (4.19) (4.20) The received instantaneous signal-to-interference-noise ratio (SINR) at the kth user (for k = 1, 2) is given as SINRA (4.21) The sum SE of the system, in bps/Hz, is therefore (4.22) The EE of the system can be defined similar to (4.16) by substituting the value of SE of ZFR/ZFT. 4.7 Multi-Pair Half-Duplex Two-Way Relay: Mathematical Model We now generalize the single-pair model results to its multi-pair counterpart, wherein now m