Impact of maximum transmit power limit on the first-order and second-order performance of cognitive opportunistic relaying

This paper focuses on the first-order and second-order performance of dual-hop underlay cognitive radio systems with opportunistic relaying (UCR-OR) over independent and non-identically distributed (i.ni.d) Rayleigh fading channels. For the UCR-OR systems, the tolerable maximum interference power (TMIP) Q at primary users (PUs) and the allowable maximum transmission power limit (AMTP) P_max at secondary users (SUs) are considered, simultaneously. We first obtain the closed-form solutions to the first-order performance such as outage probability, average symbol error ratio (SER), and ergodic capacity (EC). Secondly, we investigate the second-order statistical performance, i.e., average outage rate (AOR) and average outage duration (AOD). With the consideration that in practice implementation the receiver performance is primarily influenced by the signal-to-noise ratio (SNR) (not the signal envelope), the second-order statistical performance is investigated based on the equivalent instantaneous end-to-end SNR. Finally, we present the detailed performance comparison analysis of UCR-OR systems by defining a random variable μ=P_max/Q. The results show that the effect of μ on the first-order and second-order performances is different greatly. For the first-order performance, the performance gap is negligible when the value of μ is relatively large. However, for the second-order one, the gap is distinct.