W2f=F*TGH. (4.35) HereFF(F"F)and(Gg)1 We can observe by iteratively substituting (4.32) into (4.33) that the relay transmit signal is an iterative function of user transmit signal. XR(n)=sX(n-1)+x(n-2) - - + ZR(n - ZR(n + . . ], (4.36) where s[.] is some function. The recent full-duplex studies, e.g., in [18, 23, 24], demonstrate that the SI can be significantly suppressed using the SI suppression techniques mentioned in Sect. 4.8.1. After employing SI suppression techniques, E. Sharma and P. Singh the strong SI gets significantly suppressed, and the residual SI can be regarded as additional noise [24]. The Gaussian assumption holds due to the various sources of imperfections in the cancellation process (i.e., using central limit theorem). Also this can be considered to be worst-case assumption [25], [42, Prop. 1]. The term GRRXR in (4.32) which represents the SLI at the relay can be rewritten as GRRXR ~ CN(0, PROZIRIN) be the corresponding residual SLI. We, therefore, = Gx(n)+GRRR(n)R(n), (4.37) XR(n) = aWyr(n 1). (4.38) We observe from (4.38) that the vector XR(n) is only a function of x(n-1), and therefore we drop the time labels as rewritten (4.38) as follows: (4.39) Using (4.39) and = Tr (E[XRX#]], the amplification factor a can be written (4.40) The received signal at the user Sk in (4.31), using (4.39), is given by = aWGWGRRWZ desired signal self-interference inter-pair interference + f/ aWGRRXR + amplified SI from relay amplified noise from relay AWGN at Sk SI at user and IUI (4.41) Here (k,k') denotes the user pair exchanging information. 4 Full-Duplex Multi-Hop Communication for Beyond 5G The instantaneous SINR of user Sk can be written using (4.41) as SINRk (4.42) Recall that a E {amrc, azf}. The sum rate of the considered system model can be written as (4.43) 4.10 Performance Analysis We now provide the SE results for considered multi-pair two-way full-duplex and half-duplex AF relay system model. For this study, we consider the following settings: Noise = = system SNR is defined as SNR = PR/o2. K = 1