Abstract—In spectrum sharing systems, a secondary user (SU) is permitted to share frequency bands with primary user (PU) as long as its transmission does not interfere with the PU’s communication. In this paper, the outage probability is investigated for the physical-layer network coding (PNC) based cognitive two-way relay network over Nakagami-m fading channel. By applying the interference temperature (IT) constraints at the transceiver nodes and relay nodes in secondary systems, we analyze the outage performance in underlay spectrum sharing with the best relay selection criterion. The cumulative distribution function (CDF) of the signal to noise ratio (SNR) for each link is derived to obtain the tight upper bound on the outage probability of the secondary relay system. Simulations results demonstrate the validity and accuracy of the theoretical analysis