Optimal relay selections in two-way amplify-and-forward networks

Two-way amplify-and-forward (AF) relay network with both cooperative communication and analog network coding (ANC) has attracted great attention. In this paper, we formulate the fundamental issue, i.e., the optimal selection of multiple AF relays in a two-way dual-hop cooperative network, into linear fractional programming (LFP) problems. Firstly, in case of channel reciprocity, by minimizing the sum of the inverse of signal-to-noise ratios (SNR), the AF relays can be selected optimally by the LFP algorithms. Moreover, we derive a closed-form solution to this case, and prove that a node either participates relaying with full transmission power, or ceases relaying. Then, for the general (possibly channel non-reciprocity) case, by maximizing the weighted sum SNR, we show that the relay selection can be optimized by the sum-of-ratios LFP algorithms. Simulations are conducted to verify the proposed results.