This paper studies a two-user single-input single- output (SISO) interference channel with a cognitive relay (ICCR) under delayed feedback. We consider three types of feedback: delayed channel state information at transmitter (CSIT), delayed output feedback, and no feedback. For each feedback information, we derive the optimal degrees of freedom (DoF) region of the two-user ICCR where delayed feedback information is available at all transmitters. We show that while a cognitive relay with no feedback cannot improve the sum DoF beyond 1 in the two-user interference channel, delayed feedback can increase the sum DoF to 4/3.

This paper studies the interference channel with a cognitive relay under delayed feedback. Three types of delayed feedback are studied: delayed channel state information at the transmitter, delayed output feedback, and delayed Shannon feedback. Outer bounds are derived for the degrees of freedom (DoF) region of the two-user multiple-input multiple-output interference channel with a cognitive relay with delayed feedback as well as without feedback. For the single-input single-output scenario, optimal schemes are proposed based on retrospective interference alignment. It is shown that while a cognitive relay without feedback cannot improve the sum-DoF in the two-user single-input single-output interference channel, delayed feedback in the same scenario can increase the sum-DoF to 4/3. For the multiple-input multiple-output case, achievable schemes are obtained via extensions of retrospective interference alignment, leading to the DoF regions that meet the respective upper bounds.