n phase 2. For simplicity, we can consider the complementary event first. Specifically, we can derive the outage probability of UE 1 as follows. = 1-(1082(1a Notice that channel h CN (0,1) and |hb1|2 ~ exp(1).Definez2-122 = and Z3=22R3 - 1. =1-e-1, (4.41) where Note that the above outage probability is conditioned on 12>2211. Otherwise the outage occurs with probability 1. 4.2.3.2 UE 2 Outage Probability For UE 2, since the BS only transmits X2 via the relay. Thus the bottleneck of this trans- mission depends on the minimum data rate in two phases. The outage probability for UE 2 is P(OUE2)=1-P(OUB) = - (4.42) The following theorem provides an analytical result for the outage probability of UE 2. NOMA in Relay and loT for 5G Wireless Networks Theorem 4.5 The outage probability for UE 2 in the proposed non-linear energy harvest model is C1,C2,C3 and C4 are constants and defined in the following proof. Proof: Let C ==(1+d), = the outage probability becomes P(OUE2) = 1 - P(min (4.43) Let probability , Z2) be P for conciseness. Furthermore, let |hBR|2 =x and |hr212==. and y both follow an exponential distribution with parameter 1, and they are independent to each other. (4.44) where = a is conditioned on 22 M1Z2 Otherwise the outage probability will be always equal one, as already observed in the existing literature. Define f(x) = o2c(1+exp(-a(BPBro2x-b))) The above joint probability can be evaluated as (4.45) For notation simplicity, define C3 = 320-ceab and = appBRO2. Then P1 can be simplified as x)dx. (4.46) Let = XC4-C1,4,UE [0, oo]. According to ([65], 3.331-1) (4.47) F(M2,M1) is the lower incomplete gamma function, which is (4.48) where M2>0. 4.2 NOMA in a mmWave-Based loT Wireless System with SWIPT 4.2.3.3 Outage at High SNR In this section, we provide the approximation for the outage probability at high SNR region. Specifically, PBR 80, the outage probability for UE 1 becomes (4.49) since n X. For UE 2, the maximum charging power is M even when PC becomes infinity. Thus, the high approximation becomes (4.50) 