Bits through ARQs: Spectrum sharing with a primary packet system

We study a problem motivated by cognitive radio in which the primary is a packet system that employs ARQ feedback. A secondary system is allowed to transmit in the same frequency band provided it ensures that the primary attains a specified target rate. That is, the secondary has a certain "interference budget." The crux of the problem is that the secondary does not know how much interference it creates on the primary and therefore is ignorant of its interference budget. Absent this knowledge, we propose a scheme in which the secondary eavesdrops on the primary's ARQ and uses this knowledge to stay within its interference budget. Under certain assumptions, we show there exists an optimal rate-interference budget (RIB) tradeoff. We compare how far fixed strategies are from this RIB function as we vary the interference budget. Further, we exhibit a strategy that is optimal beyond a threshold interference budget and within 1 bit per primary packet elsewhere.