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This paper studies the interference channel with a cognitive relay (ICCR)under delayed feedback. Three types of delayed feedback are studied: delayedchannel state information at the transmitter (CSIT), delayed output feedback,and delayed Shannon feedback. Outer bounds are derived for the DoF region ofthe two-user multiple-input multiple-output (MIMO) ICCR with delayed feedbackas well as without feedback. For the single-input single-output (SISO)scenario, optimal schemes are proposed based on retrospective interferencealignment. It is shown that while a cognitive relay without feedback cannotextend the sum-DoF beyond $1$ in the two-user SISO interference channel,delayed feedback in the same scenario can extend the sum-DoF to $4/3$. For theMIMO case, achievable schemes are obtained via extensions of retrospectiveinterference alignment, leading to DoF regions that meet the respective upperbounds.

The Degrees of Freedom of the Interference Channel with a Cognitive Relay under Delayed Feedback