ssage is not decoded [158]. However, DRS can be affected by error propa- gation, and we will show this concept below. 3.3 SIC and Problem Formulation 3.3.1 SIC with Error Propagation Sequential decoding can be affected by error propagation. Consider a simpler system with one BS and two UEs, in which UE 1 and UE 2 form a NOMA pair. The power of the BS is P and the channel gains for UE 1 and UE 2 are h1 and h2, respectively. Without loss of generality, let h1 > h2- The transmitted signal can be expressed as (3.4) where O1 and O2 are power allocation factors, A1 < O2 for QoS consideration, and A1 + O2 = 1. S1 and S2 are normalized signals. At the receiver side, the signal for UE 2 has a larger power than that for UE 1, thus, at the first stage, UE 1 will decode UE 2's signal. Let R1,2 denote the achievable data rate for UE 1 to detect UE 2's message, it can be expressed as, (3.5) UE 1 then reconstructs this message according to a prior known constellation and channel gain. After that UE 1 will subtract UE 2's signal and decode its own, and the data rate is given by, (3.6) The received signal for UE 2 = the desired signal has a larger power, SO it can be detected directly. The achievable data rate for UE 2 is simply (3.7) The above procedure, however, depends on the perfect DRS of UE 2's signal at UE 1, which is a strong assumption, since various factors such as deep fading can affect the signal detection and decoding. Assuming at UE 1 side, the DRS procedure is not perfect, there will be residual signal power at stage 2 when decoding its own message. As a result, the data rate for UE 1 becomes, (3.8) where B is the error propagation factor, which is inversely proportional to the signal-to- noise-plus-interference-ratio (SINR) of (3.5), i.e. B & 01P|h1|2+n2 02P|h1/2 and 1. B = 0 repre- sents the perfect decoding, which is the same as (3.6). While B=1 is the worst case that the DRS of UE 2 is totally unsuccessful and UE 1 has to treat its entire signal as interference. (In this case, it has the same result as without 