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Cognitive radio (CR) is an intelligent wireless communication system which can dynamically adjust the parameters to improve system performance depending on the environmental change and quality of service. The core technology for CR is the design of cognitive engine, which introduces reasoning and learning methods in the field of artificial intelligence, to achieve the perception, adaptation and learning capability. Genetic algorithm (GA) is good at multi-objective optimization, while RBF neural network has a strong learning ability. This paper effectively combines them and proposes a design of cognitive engine based on GA and RBF neural network (RBF_NN) to adapt the dynamical wireless environment and demands. The method adopts decision-making table produced by preprocessing perceptive information to train RBF learning model. GA is employed to adjust the operating parameters of RBF neural network, calculate the Pareto set, and select the appropriate configuration solution through the definition fitness function. After the model is trained, the performance is evaluated according to two benchmark functions. The simulation results demonstrate the effectiveness of the model and the proposed cognitive engine can effectively achieve the goal of learning and reconfiguration in cognitive radio.