From non-causality to causality: degrees of freedom of the interference relay channel

The achievable degrees of freedom (DOF) in an interference relay channel are examined. We highlight some differences between two relaying strategies in two different setups. Namely, we study the DOF achieved using interference alignment and interference cancellation in a cognitive relay setup and in a half-duplex relay setup. The difference between the two setups is causality, which leads to a difference in the achievable DOF. We show that 3/2 DOF are achievable almost surely in a 3-user complex Gaussian interference relay channel with quasistatic channel coefficients and with one antenna at each node. This result holds for both the cognitive as well as for the more practical half-duplex non-cognitive relay. However, while this is achieved in the cognitive relay setup using one symbol duration, it needs two symbol extensions in the half-duplex case. On the other hand, we show that in the cognitive case, interference cancellation performs better than interference alignment, since it achieves 2 DOF almost surely. Moreover, interference cancellation achieves full, i.e. K DOF for a family of K-user interference channels with a cognitive relay. Interestingly, for the half-duplex setup the outcome is swapped. Here, interference alignment outperforms interference cancellation, since the latter achieves less than 3/2 DOF almost surely in the 3 user case.