Abstract
In this study, we consider a multi-input-single-output (MISO) orthogonal frequency division multiplexing (OFDM) underlay cognitive radio system with channel uncertainty. In order to solve the multi-objective secondary user’s QoS enhancement and primary user’s interference mitigation problem in this system, a multi-objective beamforming design method is introduced for cognitive radio systems to guarantee optimal secondary user’s QoS performance and primary user’s interference power simultaneously. First, a quadratic constrained optimization problem is derived to represent the cognitive radio system. Then, based on the mini-max formulation, the beamforming design for both secondary user’s QoS enhancement and primary user’s interference mitigation are formulated as a multi-objective optimization problem (MOP) to minimize the worst case of the negative signal-to-interference-plus-noise ratio (SINR) of secondary users and the interference temperature (IT) of primary users for the cognitive radio system at the same time. Since it is not easy to solve the MOP directly, an indirect method is proposed to solve this MOP for multi-objective beamforming design, by minimizing the corresponding upper bounds of two objectives. For the convenience of design, the multi-objective beamforming design problem is transformed to a linear matrix inequalities (LMIs)-constrained multi-objective optimization problem. Further, a LMIs-constrained multi-objective evolutionary algorithm (LMIs-constrained MOEA) is developed to efficiently solve the set of Pareto optimal solutions for the MOP, and an improvement optimization process is provided for designer to select one unique design according to his own preference. Finally, a numeric simulation is given to illustrate the design procedure and to demonstrate the performance of the proposed multi-objective beamforming design for cognitive radio system.