Let f(z) = ztAz+2Re{z`b} +c, where A E HN, b E CNx1 CER, and z ~ CN (0, I). For any E E (0,1], an approximate and convex form for [13] (6.8) can be written as Tr(A) + (6.9a) vec(A) (6.9b) U2I-A>0,02>0, (6.9c) where 01 and 02 are slack variables. We apply Bernstein-type Inequality II to (6.2e), and let Agn = G1/2g where ~ CN(0,1) is a standard Gaussian vector. We can have the following convex-form approximation. Tr(G-n((0 (6.10a) 6 Robust Beamforming in NOMA Cognitive Radio Networks: Gaussian CSI (6.10b) (6.10c) (6.10d) where 11,n and V2,n are slack variables. Lastly, we relax P4 by dropping the constraint that Wk should have rank 1 for now, since it is not a convex one. The relaxed version of the problem is (6.11a) s.t. (6.5), (6.7), (6.10), (6.2e), (6.2f), (6.2g). (6.11b) Likewise, the coupling variables in (6.5b) and (6.7b) make P2 a non-convex problem. Thus we can still use the transformation in (5.17), which converts P2 into an equivalent optimiza- tion problem. 6.3 Maximum Harvested Energy Problem Formulation In contrast to Section 6.2, where the minimum transmission power problem is considered, in the following we consider the optimization problem of maximizing the total harvested energy. This problem has important real-world applications, since most of the consumer electronics products are battery-driven and thus their energy efficiency is critical. In this section, we first formulate the problem, then we transform it in a convex way SO that an existing software package can solve it efficiently. A one-dimensional search algorithm will be used. Furthermore, we also consider our previous pair of channel models. In this section, we formulate the maximum harvested energy under the Gaussian CSI error model formulated is as follows: (6.12a) s.t. (6.2b), (6.2e), (6.2e), (6.2f), (6.2g), (6.2h). (6.12b) We first simplify the objective function and then a new approximation will be formulated based on the Bernstein-type Inequality [13, 194]. By involving a simple transformation, we arrive at: maxk{Meepab (6.13a) s.t.