  The use of $N$ cognitive relays to assist primary and secondary transmissions
in a time-slotted cognitive setting with one primary user (PU) and one
secondary user (SU) is investigated. An overlapped spectrum sensing strategy is
proposed for channel sensing, where the SU senses the channel for $\tau$
seconds from the beginning of the time slot and the cognitive relays sense the
channel for $2 \tau$ seconds from the beginning of the time slot, thus
providing the SU with an intrinsic priority over the relays. The relays sense
the channel over the interval $[0,\tau]$ to detect primary activity and over
the interval $[\tau,2\tau]$ to detect secondary activity. The relays help both
the PU and SU to deliver their undelivered packets and transmit when both are
idle. Two optimization-based formulations with quality of service constraints
involving queueing delay are studied. Both cases of perfect and imperfect
spectrum sensing are investigated. These results show the benefits of relaying
and its ability to enhance both primary and secondary performance, especially
in the case of no direct link between the PU and the SU transmitters and their
respective receivers. Three packet decoding strategies at the relays are also
investigated and their performance is compared.
