In this paper, we study two important transmission strategies in full-duplex two-way relaying in the presence of channel estimation errors. In analog network coding (ANC), the relay transmits the combined signals that were received from both sources, with the aim of achieving better spectral efficiency. However, due to imperfect channel-state information (CSI), sources cannot perfectly cancel their own data in the relayed signal. We derive an achievable information rate for ANC in imperfect-CSI conditions and show how the ANC performance can significantly be degraded as a result. Moreover, we derive cut-set bounds with channel estimation errors for traditional routing (TR), in which time sharing is used at the relay. Although it has been previously shown that ANC outperforms TR when the CSI is perfect, we find that it may not maintain its superiority in imperfect-CSI case at low signal-to-noise ratio (SNR) conditions. Next, we propose practical power allocation techniques that can be used in the sources and relay for both ANC and TR. The proposed power allocation schemes are relatively simple to compute and rely only on long-term channel statistics. Nevertheless, they are shown to be effective and close to optimal solutions for a wide range of SNRs, to different positions of the relay, and for both perfect-and imperfect-CSI conditions. By using the proposed power allocation techniques, it is possible to bring back advantages of ANC over TR for a wide range of SNRs in imperfect-CSI conditions.

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In a cooperative network, relays are often closer to the source than the destination and thus the source-relay links have a higher capacity than the source-destination one. In this paper, we investigate a hierarchical modulation-based cooperative scheme, where the relay is able to detect the whole signal, while the destination can only detect the rst layer of the modulation. We provide an error probability upper-bound for this scheme, which allows us to optimize the choice of the constellation parameter θ.

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