g EP in SIC are (4.28) (4.29) Remark 4.1 The constraint for Theorem 4.3 to hold which has one additional constraint (as > ZIOBS) compared with Theorem 4.1. Similarly, Theorem 4.4 holds when>Ps>ma{4as,as}, which also posts another constraint. These additional constraints can potentially increase the outage probability. Remark 4.2 We show that power allocation factors impact the outage probability. Specif- ically, if the constraints in Remark 4.1 cannot be satisfied, the outage probability will always be 1 for both users, which indicates the failure of both schemes. The reason is that if X2 can- not be decoded in the first time slot, then the second or third time slot cannot proceed. If the maximum value of B's is less than where Superscript(1) = min {Z2(1 }, the outage probability under NOMA cooperative scheme is the same for both with EP or without EP cases. Likewise, for NOMA TDMA scheme, the outage probability is the same for user 1 in both EP or no EP cases when where S2 = min {Z4(1 }. The reason is that if we limit the value of Bs, the bottleneck of the data rate does not come from the first time slot transmission, which may be directly affected by the EP. However, for user 2, the outage probability is always identical with or with not EP since under this circumstance user 2 is not impacted by EP. 4.1 Outage Probability Study in a NOMA Relay System p out1 NC--ana p out2 NC--ana p out1 NT--ana p out2 NT--ana p out1 NC--sim p out2 NC--sim p out1 NT--sim p out2 NT--sim Transmission SNR of the AP in dB Figure 4.3 Theorem 4.1 and 4.2. as = 0.2, Bs = 0.8. R1 = R2 = 0.5 bps/Hz. 4.1.6 Numerical Results In this section, performance evaluation on the proposed schemes are provided based on both simulation and analysis. Some basic parameters are set as follows. The channel gains of hb,r1 and hb.r2 are 5 and 1, respectively, i.e. b,r1 = 5, of b,r2 = 1. The transmission SNR of the AP ranges from 10 to 50 dB, and the transmit power of both relays is set to half of the AP's power, which means there is a 3 dB difference betwe