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 transmit/peak interference power constraints and peak transmit/average interference power constraints for general fading distributions. A low-complexity optimal power control algorithm is proposed. Also, the optimal power control policy in the low-power regime is analyzed. In particular, by considering gamma distributed channel power gains of the interference link between the secondary transmitter and the primary receiver and the transmission link between the secondary transmitter and the secondary receiver, closed-form expressions for the maximum achievable rate attained with the optimal power control strategy 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 constellations and Gaussian signals are investigated.