  This paper investigates the design of access policies in spectrum sharing
networks by exploiting the retransmission protocol of legacy primary users
(PUs) to improve the spectral efficiency via opportunistic retransmissions at
secondary users (SUs) and chain decoding. The optimal policy maximizing the SU
throughput under an interference constraint to the PU and its performance are
found in closed form. It is shown that the optimal policy randomizes among
three modes: Idle, the SU remains idle over the retransmission window of the
PU, to avoid causing interference; Interference cancellation, the SU transmits
only after decoding the PU packet, to improve its own throughput via
interference cancellation; Always transmit, the SU transmits over the
retransmission window of the PU to maximize the future potential of
interference cancellation via chain decoding. This structure is exploited to
design a stochastic optimization algorithm to facilitate learning and
adaptation when the model parameters are unknown or vary over time, based on
ARQ feedback from the PU and CSI measurements at the SU receiver. It is shown
numerically that, for a 10% interference constraint, the optimal access policy
yields 15% improvement over a state-of-the-art scheme without SU
retransmissions, and up to 2x gain over a scheme using a non-adaptive access
policy instead of the optimal one.
