  This paper considers the scenario in which a set of nodes share a common
channel. Some nodes have a rechargeable battery and the others are plugged to a
reliable power supply and, thus, have no energy limitations. We consider two
source-destination pairs and apply the concept of cognitive radio communication
in sharing the common channel. Specifically, we give high-priority to the
energy-constrained source-destination pair, i.e., primary pair, and
low-priority to the pair which is free from such constraint, i.e., secondary
pair. In contrast to the traditional notion of cognitive radio, in which the
secondary transmitter is required to relinquish the channel as soon as the
primary is detected, the secondary transmitter not only utilizes the idle slots
of primary pair but also transmits along with the primary transmitter with
probability $p$. This is possible because we consider the general multi-packet
reception model. Given the requirement on the primary pair's throughput, the
probability $p$ is chosen to maximize the secondary pair's throughput. To this
end, we obtain two-dimensional maximum stable throughput region which describes
the theoretical limit on rates that we can push into the network while
maintaining the queues in the network to be stable. The result is obtained for
both cases in which the capacity of the battery at the primary node is infinite
and also finite.
