few, we list two methodologies here. 1. Eigen-decomposition. Let us denote two eigenvalues of W K by X1 and A2, where X1 > 22 > 0. Clearly, WK = M1WW +A2W2kWT Wik, i = {1,2} are the corresponding eigenvec- tors. To get the rank 1 approximation from a rank 2 matrix, we can let the solution of the original problem be Wk= provided it is feasible. 2. Randomization technique. Similar to eigen-decomposition, we first decompose Wt according to W* = U T U . Then, = we let UkT1/2ek where the m-th element of ek is [eklmekmand0k.mobeysan = independent and uniform distribution within [0, 2). The above two methods are essentially the same. If we want to get a more precise result, another scaling factor can be added. Specifically, let us define Ck as the scaling factor yet to be determined. Certainly, the problem can be transformed in terms of Wk and Ck, once we get the optimal value, we can apply either one of the above methods to get a better result. Another point worth noting here is that when the rank of Wk is 2, there only exists the approximation result of W*, and this approximation always provides an upper bound. 5 Robust Beamforming in NOMA Cognitive Radio Networks: Bounded CSI 5.4 Maximum Harvested Energy Problem Formulation In contrast to Section 5.3, 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. Upon considering the imperfect CSI model used in (5.6), the maximum total harvested energy of all SUs can be formulated as follows: (5.18a) s.t. (5.11), (5.13), (5.8e), (5.8f), (5.8g), (5.8h), (5.18b) i.k.Pn.Ok 0, Ak K, i = {k,k+1,...,K}, , In E K. (5.18c) The 