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Analog network coding (ANC) is a promising technique of improving the throughput of relaying, especially when combined with both rate- and power-adaptation in the context of amplify-and-forward two-way relaying (AF-TWR ). In particular, the adaptation is employed both during the multiple access stage, when a pair of terminals transmit simultaneously to a relay, and during the broadcast stage, where the relay transmits to both terminals. Based on our bit-error-rate (BER) bounds, we formulate the explicit relationship amongst the data rates, transmit powers, and BERs. Then, we conceive a rate- and power-adaptation scheme, operating both under specific average power constraints and BER constraints both at the relay node and at the two terminals. We observe that the transmit power of nodes does affect the data rate and hence using a fixed transmit power is not always optimal. We then derive a closed-form solution for continuous-rate ANC aided quadrature amplitude modulation/phase shift keying (ANC-QAM/PSK) using the classic Karush-Kuhn-Tucker method and conceive discrete-rate ANC-QAM/PSK regimes for practical wireless systems. The performance of the proposed scheme is evaluated through extensive simulations. Our performance results confirm that the proposed ANC-QAM/PSK outperforms its counterpart operating without power adaptation in a broad range of scenarios.

Joint Rate and Power Adaptation for Amplify-and-Forward Two-Way Relaying Relying on Analog Network Coding