  A fundamental problem in cognitive radio systems is that the cognitive radio
is ignorant of the primary channel state and the interference it inflicts on
the primary license holder. In this paper we assume that the primary
transmitter sends packets across an erasure channel and the primary receiver
employs ACK/NAK feedback (ARQ) to retransmit erased packets. The cognitive
radio can eavesdrop on the primary's ARQs. Assuming the primary channel states
follow a Markov chain, this feedback gives the cognitive radio an indication of
the primary link quality. Based on the ACK/NACK received, we devise optimal
transmission strategies for the cognitive radio so as to maximize a weighted
sum of primary and secondary throughput. The actual weight used during network
operation is determined by the degree of protection afforded to the primary
link. We study a two-state model where we characterize a scheme that spans the
boundary of the primary-secondary rate region. Moreover, we study a three-state
model where we derive the optimal strategy using dynamic programming. We also
show via simulations that our optimal strategies achieve gains over the simple
greedy algorithm for a range of primary channel parameters.
