Optimal Power Control for Underlay Cognitive Radio Systems With Arbitrary Input Distributions

This paper studies optimal power control policies that maximize the achievable rates of underlay cognitive radio systems with arbitrary input distributions under both peak/average transmit power and peak/average interference power constraints for general fading distributions. In particular, optimal power adaptation schemes are formulated and low-complexity optimal power control algorithms are proposed. Additionally, simpler approximations of optimal power control policies in the low-power regime are determined. By considering gamma distributed channel power gains of the interference link between the secondary transmitter and the primary receiver and of the transmission link between the secondary transmitter and the secondary receiver, closed-form expressions for the maximum achievable rate attained with optimal power control in the low-power regime are provided. Through numerical results, the impact of the fading severity of both interference and transmission links and transmit power and interference power constraints on the maximum achievable rate of the cognitive user for different practical constellations and Gaussian signals are investigated.