Presented is a simple two-way amplify-and-forward relay selection criterion for the more general case that all terminals' transmit powers can be unequal, in which the optimal relay can be selected in a distributed manner requiring local channel knowledge and the terminals' transmit powers, and a closed-form lower bound of outage probability is obtained over Nakagami-m fading channels. Simulation results show that the proposed scheme is outage-optimal.Introduction: To overcome the loss in the spectral efficiency due to half-duplex transmission in conventional cooperative communication networks [1,2], two-way relaying (TWR) based on both decodeand-forward (DF) and amplify-and-forward (AF) has attracted much attention [3,5]. In view of the implementation of the two-way opportunistic relaying amplify-and-forward (TWOR-AF) scheme, it can be accomplished in a centralised or distributed manner. In [4], a tight closed-form approximation has been derived over Nakagami-m fading channels in the case of all the terminals having the same transmit powers. In [5], it is shown that a proposed TWOR-AF scheme can be performed in a distributed manner without requiring global channel state information (CSI), but, in the process of analysis, the amplification factor is assumed to be a constant. In [6], outage probability and power allocation are analysed by using given lower and upper bounds of instantaneous signal-to-noise ratio (SNR) in the case that two terminals transmit powers that are equal as well. In [7], a low-complexity distributed relay selection criterion was proposed, however it did not consider the effect of every relay node's transmit power. Unfortunately, all the terminals' transmit powers are usually unequal for practical two-way relaying systems. So in this case, we will fail to select the optimal relay if we use these methods mentioned above again.In this Letter, we give tight upper bounds of the end-to-end SNRs received by two sources for the more general case of all terminals having different transmit powers. Furthermore, based on the approximation to the SNR, we give a relay selection criterion which can be performed in a distributed manner without requiring global CSI and maybe wide application in practical two-way relaying systems. Simulation results corroborate our proposed.

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