1 estimates its channel gain and uses the decoded signal X2. Therefore, the superposition signal for the next decoding symbol X1 will be updated to (4.24) where hb,r1 is the estimated channel gain for relay 1. Existing studies assume the perfect decoding and cancellation of X2, and thus we We argue that this is a strong assumption since neither the channel estimation nor signal decoding can be perfect. While we desire to let hk and SM as close to hk and SM as possible, factors such as synchronization, phase ambiguity, and deep fading can seriously degrade the SIC process and errors can be accumulated and affect the UE to be decoded afterwards. We refer this process as EP. 0 is defined as the EP factor in this chapter. Since there is a residual power when decoding the second signal, (4.4) and (4.6) can be updated to, (4.25) O represents the amount of residual power from the previous decoding and 0 < 1. When O = 0, the results agree with perfect cancellation. O = 1 is the worst case when SIC fails to decode the first signal and the second stage decoding has to treat the entire first signal as interference. Besides, O should be inversely proportional to the SNR of X2. In this chapter, we assume O is a constant for simplicity. Similarly, the outage probability analysis is given as follows. 4 NOMA in Relay and loT for 5G Wireless Networks 4.1.5.1 Outage Probability in NOMA Cooperative Scheme with EP Define i,NC' = as the outage event of user i in the NOMA cooperative scheme. Then, we have the following theorem for the outage probability. Theorem 4.3 The outage probabilities for users 1 and 2 in the NOMA cooperative scheme when considering EP in SIC are, respectively, derived as (4.26) (4.27) 4.1.5.2 Outage Probability in NOMA TDMA Scheme with EP Similarly, we also consider EP in SIC in the second scheme. Let = u2} be the event of an outage. We have the following theorem for the analytical results of outage prob- abilities. Theorem 4.4 The outage probabilities for users 1 and 2 in NOMA TDMA transmission when considerin