nce X is a composite signal consisting of all SUs' messages, SIC is applied at the receiver side to detect the received signal. The detection is carried out in the same order of channel gains, i.e. the SUs with lower channel gain will be decoded first. A pair of imper- fect CSI error models are considered, namely a bounded and a gaussian model. We adopt both of these in this chapter and assume that all SUs have a perfect knowledge of their own CSI. 5.3 Power Minimization-Based Problem Formulation 5.3.1 Problem Formulation In this section, we seek to find the precoding vectors Wk, k E KC, the energy vector V, and the power split ratio p, which altogether achieve a satisfactory QoS for all users, and at the same time, they can harvest part of the energy for their future usage. Thus, the problem can be formulated as follows: (5.8a) s.t. C1 (5.8b) 2Epract (5.8c) C3 gn (5.8d) C4 Tr (5.8e) C5 0<p<1 (5.8f) (5.8g) C7 : Rank(Wi)=1, vk e K. (5.8h) Our goal is to minimize the total transmitted power. The constraint C1 ensures that SU k does attain the predefined minimum data rate; C2 allows each SU to harvest the amount of energy that at least compensates the static power dissipation Pkss C3 is the interference limit for the n-th PU; C4 represents the maximum transmit power constraint of the BS; in C5, the power split factor should be in the range of (0,1). The optimization problem P1 is hard to solve due to its non-convexity constraints C1 and C2. Moreover, the realistic imperfect CSI imposes another challenge on the original problem. In the following, we transform the variables. Let us introduce Yk,min Ill -1). Then C1 in (5.8b) becomes Yk,min (5.9) where i = (k,k+1,...,K), E K. For the notational simplicity, we denote the above con- straint as Eik Thus, P1 becomes (5.10a) s.t. C1 Ei.k (5.10b) (5.10c) 5 Robust Beamforming in NOMA Cognitive Radio Networks: Bounded CSI C3 : On, (5.10d) (5.8e) - (5.8h). (5.10e) Here, C6 comes from the fact that both V and Wk are positive semi-definite matrices. The extra constraint that the 