Optimal Power Allocation Strategies in Two-Hop X-Duplex Relay Channel

We consider a dual-hop, decode-and-forward network, where the relay can operate in full-duplex (FD) or half-duplex (HD) mode (X-duplex relay). We model the residual self-interference as an additive Gaussian noise with variance proportional to the relay transmit power, and we assume a Gaussian input distribution at the source. Unlike previous work, we assume that the source is only aware of the transmit power distribution adopted by the relay, but not of the symbols that the relay is currently transmitting. This assumption better reflects the practical situation, where the relay node forwards data traffic but modifies physical-layer or link-layer control information. We then identify the optimal power allocation strategy at the source and relay, which in some cases coincides with the HD transmission mode. We prove that such strategy implies either FD transmissions over an entire time frame or FD/HD transmissions over a variable fraction of the frame. We determine the optimal transmit power level at the source and relay for each frame, or fraction thereof. We compare the performance of our scheme against reference FD and HD techniques, which assume that the source is aware of the symbols instantaneously transmitted by the relay, and show that our solution closely approaches such strategies.