l-rank matrix and it can be decomposed as H = LQ, where L is a 2 x 2 lower triangular matrix and Q is a semi-orthogonal matrix, QQH I2. Thus, let W = QHG and G is given as (4.9) where lij is the (i,j)-th entry of matrix L. The received signals at two users can be expressed as y=HX+n=HWx+n (4.10) 4 NOMA in Relay and loT for 5G Wireless Networks hr1,u1 Relay 1 User 1 Relay 1 User 1 'r2,u2 Relay 2 User 2 Relay 2 User 2 First phase Interference Second phase Figure 4.1 NOMA cooperative scheme. Therefore, SINRs for users 1 and 2 can be written as (4.11) An illustration of NOMA cooperative scheme is shown in Figure 4.1. For a fair comparison, the user sum rate achieved in one round communication is nor- malized with respect to the number of time slots in each round. Thus the achievable sum rate for users 1 and 2 is expressed as (4.12) where the factor 1/2 is used to account for two time slots needed to complete one round transmission. 4.1.2.2 NOMA TDMA Scheme NOMA TDMA scheme needs three time slots to complete one round communication. The first slot does the same as the first time slot in the NOMA cooperative scheme. Afterwards, relay 1 sends X1 to user 1 in the second time slot, while relay 2 sends X2 to user 2 in the third time slot, as shown in Figure 4.2. Figure 4.2 NOMA TDMA scheme. hr1,u1 Relay 2 User 1 r2,u2 Relay 2 User 2 First phase Second phase Third phase 4.1 Outage Probability Study in a NOMA Relay System By receiving messages separately in time slots 2 and 3, users 1 and 2 will not experience interference from each other. As a result, the achievable sum rate is (4.13) where i = {u1,u2},j= {r1,r2}. Likewise, we use the factor 1/ 1 to indicate three time slots in this scenario. Note that when calculating the first time slot data rate, we also need to use the factor 1/3, (4.14) where i = {r1,r2},j = {x1,x2}. 4.1.3 Outage Probability Analysis In this section, we analyze the system performance in terms of outage probability, which represents the probability of an event that the achieved data rate is less than a 