Robust Power Control with Distribution Uncertainty in Cognitive Radio Networks

In cognitive radio networks, it is often impossible to have regular information exchange between PUs and SUs. This implies that SUs are unable to obtain up-to-date channel information at the PU side, and will face technical challenges in accurately controlling their interference to PUs through power control. In this paper, we assume that SUs can estimate the channel information in the reciprocal channel, and study the channel uncertainty due to estimation errors and its impact on SUs' performance and PUs' protection. Specifically, we model the uncertain channel gain to be a random variable following a state-dependent distribution function, and propose a power control mechanism that is robust against the channel uncertainty. We study the robust power control in two cases. In the first case, all SU transmitters (e. g., secondary base stations) transmit with the same power, while in the second case each SU transmitter may choose distinct transmit power based on its own preference. In either case, we formulate the power control problem as a chance constrained robust optimization problem and design an iterative algorithm, respectively. Numerical results show that our robust power control mechanism can provide better protection for PUs than existing methods that overlook the uncertainty in channel measurement, and the second-case power control generally provides better Quality of Service (QoS) for SUs than that in the first case.