 If the input signal power falls below the threshold, EH drops to zero and affects the sensitivity of the circuit [22]. 6.2.2 Nonlinear Energy Harvesting There are various seminal works on nonlinear harvesting models to characterize the practical EH circuits based on piece-wise linear function, rational function, a polynomial function, and a sigmoid functions. In piece-wise linear model, linear response is assumed up to the saturation level to capture the practical EH circuit saturation effect [23]. In rational model, seven parameters are used to characterize the nonlinear effect which are determined by curve fitting with measured data [24]. This model is analytically non-tractable. In polynomial model, the diode output is approximated with truncated Taylor expansion [25]. In sigmoid mode, the relation between input RF signal power and output energy harvested power is modeled with a sigmoid function to capture the saturation effect. However, this model fails to retain the sensitivity [26]. 6 Energy Harvested Device-to-Device MIMO Systems for Beyond 5G 6.3 Impact of Imperfect CSI 6.3.1 Mathematical Modeling Consider a three-terminal device which includes a source (S), relay (R), and the destination (D), where each of these terminal nodes is equipped with multiple anten- nas. At R node, amplify-and-forward relaying protocol is employed to broadcast the signal to D with the harvested energy [15]. S is considered as a base station, whereas the user equipment (UE) is taken as R and D, respectively. A channel matrix is considered from node P to node Q as HPQ with dimensions NQ X Np, where Np and No represent the antenna count at the P and Q nodes, respectively. It is highly deterrent to use multiple active antennas due to the requirement for active RF chains, which are cost, power, and size in efficient. Hence, to retain the MIMO gains, transmit antenna selection (TAS) is used at S and R nodes. Hence, the hardware complexity and cost are reduced; however, performance is retained. In TAS, at the node P, an ith transmit 