Full-Duplex Relaying with Half-Duplex Relays

We consider "virtual" full-duplex relaying by means of half-duplex relays. In this configuration, each relay stage in a multi-hop relaying network is formed by at least two relays, used alternatively in transmit and receive modes, such that while one relay transmits its signal to the next stage, the other relay receives a signal from the previous stage. With such a pipelined scheme, the source is active and sends a new information message in each time slot. We consider the achievable rates for different coding schemes and compare them with a cut-set upper bound, which is tight in certain conditions. In particular, we show that both lattice-based Compute and Forward (CoF) and Quantize reMap and Forward (QMF) yield attractive performance and can be easily implemented. In particular, QMF in this context does not require "long" messages and joint (non-unique) decoding, if the quantization mean-square distortion at the relays is chosen appropriately. Also, in the multi-hop case the gap of QMF from the cut-set upper bound grows logarithmically with the number of stages, and not linearly as in the case of "noise level" quantization. Furthermore, we show that CoF is particularly attractive in the case of multi-hop relaying, when the channel gains have fluctuations not larger than 3dB, yielding a rate that does not depend on the number of relaying stages. In particular, we argue that such architecture may be useful for a wireless backhaul with line-of-sight propagation between the relays.