The degrees of freedom region of the two-user interference channel with a cognitive relay under delayed feedback

Abstract

We derive the degrees of freedom (DoF) region of the two-user Gaussian fading interference channel with a cognitive relay (IC-CR) for three types of delayed feedback information - delayed channel state information at the transmitter (CSIT), delayed output feedback, and delayed Shannon feedback - and no CSIT. Firstly, we derive outer bounds of the DoF region of the two user multiple-input multiple-output (MIMO) IC-CR with delayed feedback information and without any feedback information, respectively. Then, focusing on the single-input single-output (SISO) case as a special case of the MIMO scenario, we propose the outer bound achieving schemes based on the retrospective IA for delayed CSIT, delayed output feedback, and delayed Shannon feedback, respectively. The derived DoF region shows that the sum DoF of the two-user SISO IC-CR is $4/3$ if we exploit delayed feedback information, but a cognitive relay is useless in terms of DoF if any kind of CSIT is not available. Extending the proposed retrospective IA schemes to the general MIMO scenario, we show that the three types of delayed feedback information result in the same achievable DoF region which is the optimal DoF region except when $M<N<M+K$ where $M$, $K$, and $N$ are the numbers of antennas at the transmitter, the relay, and the receiver, respectively. If the cognitive relay as well as the transmitters has the delayed feedback information, the three types of delayed feedback information can achieve the optimal DoF region for all antenna configurations through the proposed retrospective IA scheme.