In cognitive radio networks, for the robust joint optimization problem of multiuser admission control and power beamforming, a joint optimization scheme based on smooth approximation of entropy function was proposed. Firstly, the two optimization problems of admission control and transmit power beams were converted into a joint optimization problem by L ₀-norm minimization. Secondly, the method of smoothing approximation based on entropy function was used to optimize the non-convexity and discontinuity of L ₀-norm. Finally, since the objective function was smooth, differentiable and unimodal function, the problem was transformed into the Lagrange function, and Armijo gradient descent method was used to get the optimal solution. The numerical results show that by using the proposed algorithm, the number of admitted uses is not significantly increased when the Signal-to-Interference-plus-Noise Ratio (SINR) is relatively low, but the transmission power consumption is decreased and the number of admitted uses is increased when SINR is relatively high. The uncertain Channel State Information (CSI) of model is analyzed, which can make the network better adapt to the changes of the outside world and improve the reliability of the network. The proposed algorithm can effectively realize the optimal allocation of the network resources and improve the network performance.

Aiming at the resource allocation problem for the uplink in cognitive radio networks, a game-theoretic algorithm for joint power control and rate allocation adapted to multi-cell cognitive radio networks was proposed. To control user's power and rate more reasonably and reduce interference among Secondary Users (SUs), firstly, the different cost factors for power and rate were set respectively, so as to control user more reasonably and avoid user excessively increasing transmission power. Then, the existence and uniqueness of the Nash Equilibrium (NE) for the proposed algorithm were proved, the convergence demonstration of the proposed algorithm was given. Finally, for solving the optimization problem of the transmission power and transmission rate, the iterative updating flowchart of the proposed algorithm for the joint power control and rate allocation was presented. The theoretical analysis and simulation results show that, compared with the similar game algorithms, on the premise of guaranteeing the quality of communication, the proposed algorithm can make user acquire higher transmission rate and higher Signal to Interference plus Noise Ratio (SINR) at lower transmission power, reduce the interference among users, and improve the system capacity of SUs.