SNR Decomposition for Full-Duplex Gaussian Relay Channel

A relay channel (RC), consisting of a source, a relay, and a destination, is a basic transmission unit of cooperative communication networks. The capacity of an RC is not known in general. In this paper, an SNR decomposition (SD) strategy is presented to implement time sharing, which provides a new tractable and achievable rate for a full-duplex Gaussian RC. More specifically, we first expand the SNR of a relay destination channel (SNR-RD) into two terms under the relay power constraint and divide the system into two subbands. Then, we assign the obtained SNR-RD for each subband and employ decode-forward (DF) or compress-forward (CF) according to the assigned SNR-RD. It is shown that the achievable rate of the SD strategy is competitive with that of superposing CF on DF. As the superposition structure requires a sophisticated codeword design, the SD strategy provides another practical combination structure of DF and CF strategies. Approximations for the SNR-RD and bandwidth allocation for subbands are also given. Based on the obtained results, two application scenarios, i.e., mobile relay and quasi-static fading RCs, are also considered. Finally, various numerical results are shown to support our developed theoretical results.