The Federal Communications Commission (FCC) allocates the majority of spectrum for specific systems with a specific use. To prevent systems from interfering with one another, the FCC divides spectrum into bands and prevents different systems from sharing the same band. However, it turns out many of these allocated bands are underutilized.

A proposed solution to this problem is to use software defined radios to dynamically sense and use available frequency bands. These cognitive radios must therefore use a band in such a way that a primary system for which said band was originally allocated continues to function. Given this restriction, a secondary system wants to achieve the maximum allowable throughput.

Thus, the goal is to define policies that enable cognitive radios to coexist with primaries oblivious of their presence.

The starting point for our work comes from observing that many communications systems use feedback to acknowledge the receipt of packets. In a wireless environment, cognitive radios may be able to overhear this feedback and may may look as follows:

We develop a model to study the capacity of a cognitive radio system in the presence of such a primary. The primary sends packets across an erasure channel and employs simple ACK/NAK feedback (ARQs) to retransmit erased packets. Furthermore, its erasure probabilities are influenced b the cognitive radio's activity. While these erasure probabilities are unknown to the cognitive radio, the cognitive radio can eavesdrop on the primary's ARQs. The model leads to strategies in which the cognitive radio adaptiely adjusts its transmissions based on the primary's ARQs, thereby guaranteeing the primary exceeds a target packet rate. Tools from the theory of martingales are used to show that the primary meets its packet rate for arbitrary parameters and determine what rates the cognitive radio can achieve under these different interference conditions.