On the achievable rates of full-duplex Gaussian relay channel

In full-duplex Gaussian relay channels, neither Decode-and-Forward (DF) nor Compress-and-Forward (CF) can achieve a larger rate than the other for all the channel gain combinations. Combining DF and CF strategies, we show that a new achievable rate, which is the concave envelop of the maximal rate achieved by DF and CF with respect to the source power, is achievable. To this end, we actively adjust the transmission power of the source for different time and switch the transmission strategy between DF and CF according to the source power. It is proved that when the signal to noise ratio (SNR) of the source-destination link falls into a certain range, the new achievable rate is strictly larger than that achieved by pure DF and pure CF. The optimal power allocation and corresponding time proportions are also obtained. Numerical results show that the new achievable rate is also competitive with the rate achieved by superposing CF on DF. As strategy switching avoids complex codeword constructions, it is more practical than superposition structures to be implemented in relay systems.