On the generalized degrees-of-freedom of the phase fading Z-interference channel with a relay

We study the generalized degrees of freedom (GDoF) of the phase fading Z-interference channel with a relay in the weak interference regime. We consider the scenario in which the relay node receives transmissions only from one of the sources but its transmissions are received at both destinations. We first derive two upper bounds on the achievable GDoF: the first bound is based on the genie-aided approach, and the second bound is based on the cut-set theorem. We then derive an achievable GDoF by employing the decode-and-forward strategy at the relay and by treating interference as noise at each receiver. Lastly, we derive conditions on the gains of the links, under which this simple scheme is GDoF-optimal. Our results support the application of relaying in scenarios in which the interference is weak.