Multi-objective optimization for information-energy transfer trade-offs in full-duplex multi-user MIMO cognitive networks

This paper considers simultaneous wireless information and power transfer enabled full-duplex multi-user multiple-input multiple-output cognitive networks. By taking into account imperfect channel state information (CSI) of the links toward primary users (PUs), this paper aims to simultaneously optimize two design objectives, namely the achievable sum-rate and sum harvested energy in the secondary network. Hence, the design problem is modelled as a multi-objective optimization problem (MOOP) subject to the transmit power constraint at the base station and robust harmful interference constraints at the PUs. Then, to find the Pareto set, the MOOP is rewritten to a single-objective problem (SOOP) by using the modified weighted Tchebycheff method. However, it is mathematically difficult to solve the transformed SOOP due to the non-concavity of the sum-rate function and the semi-infinite nature of the robust interference constraints. To overcome this challenge, we use the difference of two convex functions (DC) technique and S-procedure theory to recast the design optimization problem as the sequential convex programming. Various numerical simulations are conducted to illustrate the Pareto optimal solution sets, the robustness of interference constraints against CSI uncertainties, and trade-offs between the achievable sum-rate and harvested energy.