In this letter, we propose the reactive relay selection scheme based on cumulative distribution function (CDF) of SNRs for two-way relay networks over Nakagami-m fading channels. We analyze average relay fairness by deriving the exact integral and asymptotic expressions for relay selection probability.

Also, we obtain diversity order by deriving outage probability. Numerical results show that the analytical results of the proposed scheme match the simulation results well. It is shown that the proposed scheme guarantees strict fairness among relays and achieves full diversity.