Abstract
The outage performance of cognitive opportunistic relaying (COR) systems with the interference at secondary user (SU) from primary user (PU) is analyzed over Nakagami-m fading channels. Specially, we derive an exact closed-form expression for the outage probability of the interested COR systems under the joint impact of the maximum transmission power P M at SU and the maximum interference power Q at PU. Based on the derivations, the impact of system parameters on outage performance is investigated. We first investigate the outage probability versus Q under different fading severity factors. Results show that all curves of outage probability pass through a common crossing point (the corresponding value of Q be Q *) only when the all fading severity factors are equal. In this case, the outage probability is decreasing with the fading severity factors when Q > Q *, while it is increasing when Q < Q*. Furthermore, the formation of the crossing point only dependents on the fading severity factors, but not on other system parameters such as the average fading power and the number of relays. At the same time, we also investigate the impact of P M on outage performance by defining μ = Q/P M . It is achieved that the maximum transmit power constraint P M can be neglected with very little error of performance estimation when \(\mu > 1.5\). This would result in the decrease of complexity in performance analysis and system design. Otherwise, the impact of the maximum transmit power constraint P M must be considered in order to avoid the estimation error.
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Acknowledgments
The authors would like to thank the editors and the anonymous reviewers for their constructive comments and suggestions, which helped to improve the quality of this paper. This work was supported by the Natural Basic Research Program of China (973 Program) under Grant 2013CB329104, the National Natural Science Foundation of China under Grant 61561043, 61372124, 61427801, 61261015, 61363059, and 61302100, and by the Foundation Research Funds for the University of Gansu Province: ‘Massive MIMO channels modeling and estimation over millimeter wave band for 5G’.
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Appendix: Proof of Lemma 1
Appendix: Proof of Lemma 1
Using the assumption that the RVs X and Y obey Nakagami-m fading with parameters \(\omega_{A}\) and \(m_{A} ,\;A \in \{ X,Y\}\), conditioned on Y we have the conditional probability [20]
Using Eq. (8.352.2) in [19], Eq. (37) can be written as
Taking the integral of (38) with respect to Z and using (3.381.4) in [19], the result in Lemma 1 can be obtained.
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Wang, W., Jia, X., Yang, L. et al. Study on Cognitive Opportunistic Relaying with the Interference from Primary User over Nakagami-m Fading Channels. Wireless Pers Commun 91, 793–810 (2016). https://doi.org/10.1007/s11277-016-3497-0
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DOI: https://doi.org/10.1007/s11277-016-3497-0