Peak power and interference outage probability constrained optimal transmission policy for underlay cognitive radios

In an underlay cognitive radio (CR) system, a secondary user (SU) can transmit even when the primary is on but under stringent constraints on the interference that it causes at the primary receiver (PRx). The interference constraint fundamentally influences and changes how the SU transmits. We develop a novel and optimal transmit power policy for an SU that minimizes its symbol error probability (SEP) when it is subject to two practically motivated constraints, namely, a peak transmit power constraint and an interference outage probability constraint. We derive new expressions for the SEP of the optimal transmit power policy for MPSK. Our results bring out the impact of several system parameters such as the peak transmit power, the target outage probability, the interference threshold, and the constellation size on the SEP of the CR system.