son is that it imposes the error propagation, which makes the utility function 3.15a hard to track. Besides, when cal- culating R, we also need to determine the precoding matrix W, for i = n,k. In Section 3.4, we propose a unified precoding matrix formation algorithm, and then we focus on the power allocation with residual interference. 3.4 Precoding and Power Allocation 3.4.1 Precoding Design Let tr(WW) = Pn and tr(W&WH) = Pk. The optimization problem can be revised as: max (Rn+Rk) (3.16) Wn,Wk subject to tr(WW) (3.17) (3.18) Rk R0. (3.19) The introduced error propagation model increases the complexity of the optimization problem. Basically it is a MIMO broadcast channel (BC) in the downlink. So it can be converted to multiple access channel (MAC) in the uplink using BC-MAC duality. But it requires extensive matrix calculation and is not easy to solve. Here in this chapter, we intro- duce the equivalent channel and its respective precoding solution. From (3.10), we denote Hnea as the equivalent channel of UE n and it can be expressed as (o21 + We then rewrite (3.10) in terms of the equivalent channel (3.20) Similarly, (3.11) can be expressed as, (3.21) where Hkea = Thus, we can treat the problem as two point-to-point MIMO UEs with a total power con- straint, which is already well known in the literature [63]. However, due to the imposed minimum data rate requirement for UE k, It is not necessarily the optimal solution. The sub- optimal precoding can be formed as follows. First, take the SVD of the equivalent channel, (3.22) 3 5G NOMA-Enabled Wireless Networks where Un is the unitary matrix and its columns are a set of orthonormal eigenvectors of E is a diagonal matrix. Therefore, the precoding matrix can be formed as, (3.23) where E is calculated from water-filling process with respect to the elements in the diagonal matrix En i.e. E = TANI - (E)-11+, here An is a parameter to ensure the power constraint tr(WW) = Pn, and [a]+ = max (a, 0). The precoding matrix for UE k can be formed in the same way. However, two