Precoding decision for full-duplex X-relay channel with Decode-And-Forward

In this paper, we study a simple X-relay configuration where the shared relay operates in full-duplex (FD) mode. The relay node may have limited spatial degrees of freedom, and as a result, it may not be able to handle both the loop interference and the multiuser interference. Hence, a decision on the precoding scheme is necessitated. It is often the case that the relay does not have the option of real-Time switching between different precoding schemes, either due to hardware limitations of the relay or increased complexity of the problem. Hence, we investigate a 'static' precoding decision where the relay node decides on its precoding scheme based only on statistical knowledge of the channel conditions. To perform this decision, the behavior of the system is formulated as a Markov chain and the outage probability of the system is derived in a closed-form with the precoding decision as a parameter. The outage probability is minimized by optimally choosing the precoding scheme, using easily verifiable conditions on the statistical knowledge of the channel conditions. Simulations validate the investigated scheme.