Optimal Transmission Strategy in Full-duplex Relay Networks

In this work, we consider a dual-hop, decode-and- forward network where the relay can operate in FD mode. 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, however, we assume that the source is only aware of the transmit power distribution adopted by the relay over a given time horizon, not of the symbols that the relay is currently transmitting. This scenario better reflects practical situations in which the relay node may also have to forward signaling traffic, or data originated by other sources. Under these conditions, we show that the optimal communication strategy that source and relay can adopt is a time-division scheme, and, for each slot, we determine the optimal transmit power level that source and relay should adopt depending on the channel gains. Interestingly, the distribution of the optimal transmit power turns out to be discrete with two probability masses.