: X = v, (5.2) Primary network ((9)) Information decoding Mutual interference Power split Decode S1 directly Energy harvesting Decode S1 then S2 Decode previous K-1 SU, then SK Secondary network Figure 5.1 (a) An illustration of the system model. (b) The power splitting architecture of SUs. 5.2 System and Energy Harvesting Models where Wk E CMX1 is the precoding vector for the k-th UE and Sk is the corresponding intended message. Furthermore, V ECMx1 is the energy vector allowing us to improve the energy harvesting efficiency at the SUs. We assume that Sk is unitary, i.e. E[|skl2] = 1, and V obeys the complex Gaussian distribution, i.e. V ~ CN (0, V), where V is the covariance matrix of V. Likewise, the extra interference arriving from the CBS to the n-th PU (5.3) where gh E CMx1 is the channel gain between the CBS and the n-th PU [236]. 5.2.2 Non-linear EH Model Most of the existing literature considered an idealized linear energy harvesting model, where the energy collected by the k-th SU is expressed the input power, where P is the power split- ting factor that controls the amount of received energy allocated to energy harvesting, 0<p< 1, while n is the energy conversion efficiency factor, 0  n < 1. However, measure- ments relying on real-world testbeds show that a typical energy harvesting model exhibits a non-linear end-to-end characteristic. To be specific, the harvested energy first grows almost linearly with the increase of the input power, and then saturates when the input power reaches a certain level. Several models have been proposed in the literature and one of the most popular ones is [22], which is formulated as follows: (5.4a) (5.4b) where is the actual energy harvested from the circuit. Furthermore, TP Practical rep- resents a function of the input power Ein Additionally, Mk is the maximum power that a receiver can harvest, while ak together with bk characterizes the physical hardware in terms of its circuit sensitivity, limitations, and leakage currents [22]. On the other hand, the signal receiv