  We investigate a cognitive radio system with two secondary users who can
cooperate with the primary user in relaying its packets to the primary
receiver. In addition to its own queue, each secondary user has a queue to keep
the primary packets that are not received correctly by the primary receiver.
The secondary users accept the unreceived primary packets with a certain
probability and transmit randomly from either of their queues if both are
nonempty. These probabilities are optimized to expand the maximum stable
throughput region of the system. Moreover, we suggest a secondary multiple
access scheme in which one secondary user senses the channel for $\tau$ seconds
from the beginning of the time slot and transmits if the channel is found to be
free. The other secondary user senses the channel over the period $[0,2\tau]$
to detect the possible activity of the primary user and the first-ranked
secondary user. It transmits, if possible, starting after $2\tau$ seconds from
the beginning of the time slot. It compensates for the delayed transmission by
increasing its transmission rate so that it still transmits one packet during
the time slot. We show the potential advantage of this ordered system over the
conventional random access system. We also show the benefit of cooperation in
enhancing the network's throughput.
