  Cognitive radio methodologies have the potential to dramatically increase the
throughput of wireless systems. Herein, control strategies which enable the
superposition in time and frequency of primary and secondary user transmissions
are explored in contrast to more traditional sensing approaches which only
allow the secondary user to transmit when the primary user is idle. In this
work, the optimal transmission policy for the secondary user when the primary
user adopts a retransmission based error control scheme is investigated. The
policy aims to maximize the secondary users' throughput, with a constraint on
the throughput loss and failure probability of the primary user. Due to the
constraint, the optimal policy is randomized, and determines how often the
secondary user transmits according to the retransmission state of the packet
being served by the primary user. The resulting optimal strategy of the
secondary user is proven to have a unique structure. In particular, the optimal
throughput is achieved by the secondary user by concentrating its transmission,
and thus its interference to the primary user, in the first transmissions of a
primary user packet. The rather simple framework considered in this paper
highlights two fundamental aspects of cognitive networks that have not been
covered so far: (i) the networking mechanisms implemented by the primary users
(error control by means of retransmissions in the considered model) react to
secondary users' activity; (ii) if networking mechanisms are considered, then
their state must be taken into account when optimizing secondary users'
strategy, i.e., a strategy based on a binary active/idle perception of the
primary users' state is suboptimal.
