Robust power control for underlay cognitive radio networks under probabilistic quality of service and interference constraints

In cognitive radio networks, conventional power control algorithms (PCAs) based on instantaneous perfect channel gain may lead to performance degradation in practical systems, since channel uncertainties are inevitable because of quantisation errors and estimation errors. As a result, robustness of the algorithms becomes an important issue. However, traditional robust PCAs with probabilistic models require to perfectly know the distribution information of the estimation error (e.g. Gaussian distribution) which is difficult to obtain. Moreover, the distribution function of the actual error may not be Gaussian distribution. In this study, instead of using deterministic distribution model, a robust PCA based on a distribution-free method is designed to minimise total transmit power of secondary users subject to probabilistic interference and signal to interference plus noise ratio constraints. Based on the minimax probability machine, the original problem is reformulated as a second order cone programming problem solved by interior-point method. An adaptive estimation scheme is proposed to estimate the actual mean and covariance matrix of uncertain parameters. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm by comparing with the robust algorithms under worst-case constraints and probabilistic constraints, respectively.