A New Achievable Rate for Decode-Forward-Based Gaussian Relay Channel with Hybrid-Duplex

Combining half-duplex (HD) and full-duplex (FD) has shown great potential to improve the transmission rate of relay channels. To approach the channel capacity of Gaussian relay channel, a novel three-phase hybrid-duplex (HyD) scheme was proposed based on decode-forward (DF) relaying. Apart from the pure FD mode, the relay works in receive-only and transmit-only modes for a fraction of time, respectively. The achievable rate of the proposed scheme is characterized. Furthermore, a joint time division and power allocation problem is formulated, aiming at maximizing the achievable rate of the proposed HyD relaying scheme. In particular, a two-step optimization method is raised to solve the formulated problem. Firstly, the local optimal power allocation is obtained for given time division factors. Then, the maximization of the achievable rate is addressed by finding the optimal time division factors, leading to a new achievable rate of the DF-based Gausian relay channel. A degenerated two-phase hybrid-duplex (D-HyD) scheme is also studied to reduce the implementation complexity. Additionally, the maximal achievable rate of the D-HyD scheme is derived in closed-form for specific scenarios. Numerical results demonstrate that, when using optimal parameters, the proposed three-phase HyD scheme and its two-phase variant can significantly enhance the rate performances of Gaussian relay channel, outperforming pure HD, pure FD, and other benchmark DF-based relaying schemes.