predefined one. Outage probability is a good metric for QoS in the system design. A closed-form ana- lytical outage probability is derived for different users, based on which a high SNR approx- imation will also be presented. 4.1.3.1 Outage Probability in NOMA Cooperative Scheme Let R1 and R2 denote the predefined minimum rates for users 1 and 2, respectively. An outage occurs when the achievable data rate is less than the minimum data rate. Define OKLANG as the event of an outage at user 1. We first consider the complementary event of which is denoted as OUINC." The second time slot transmission relies on the successful decoding at the first time slot. For a DF relaying scheme, OULNC happens when relay 1 successfully decodes X1, and relay 2 successfully decodes X2, and user 1 successfully decodes X1. Thus, the outage probability can be calculated as = 1 > R1 and min {Rr1x2,R,2x2} R2). (4.15) Similarly, the outage probability for user 2 is = 1 - P (Rr1x1 > R1 and min R2) (4.16) Lemma 4.1 ([68], Theorem 2.3.18) Let H be a 2 x 2 matrix and its entries follow i.i.d. Gaussian distribution with zero mean and unit variance. If H = LQ, where L is a lower trian- gle matrix and Q is a semi-orthogonal matrix, then and 112.212 ~ exp(1). Theorem 4.1 The outage probabilities for users 1 and 2 in NOMA cooperative scheme can be expressed as (4.17) 4 NOMA in Relay and loT for 5G Wireless Networks (4.18) hee = max Proof: From equation (4.15), P(O1,1C) (min > R1 and min R2) - P * Here, all holds when Bs > max {Z2as,as}. = holds since both 1hb,r112 and 1hb,r212 follow an exponential distribution with parameter 1 while 14.1/2 follows a chi-squared distribution with a degree of freedom 4. Similarly, P(Ou2,NC) - P (Rr1,x1 R1 and = 1-P * Since lim-(1 - e-x) n X, in the high SNR regime, i.e. when Ps,Pr 8, user 2 outage probability at high SNR can be approximated as: (4.19) 4.1.4 Outage Probability in NOMA TDMA Scheme As previously stated the first time slot in this scheme also uses NOMA transmission from the AP to two relays. Afterwards