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In this paper, the authors consider an optimal power allocation scheme for a physical layer network coding relay based Secondary User (SU) communication in cognitive radio networks. SUs are located on two different Primary User (PU) coverage areas and they introduce an energy and spectrally efficient SU communication scheme. The sum rate of relay based two way communications for SUs is maximized under a total power constraint and Interference Power Threshold (IPT) constraints to PUs. The optimal power allocation schemes are illustrated for different cases of SUs and relay powers. Numerical results confirm that the power allocation scheme provides the optimal solution for the achievable sum rate and the IPT constraints have an effect on the sum rate variation with the total available power.
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