In this paper we analyze a cognitive radio network with one primary and one secondary transmitter, in which the primary transmitter has bursty arrivals while the secondary node is assumed to be saturated (i.e. always has a packet waiting to be transmitted). The secondary node transmits in a cognitive way such that it does not impede the performance of the primary node. We assume that the receivers have multipacket reception (MPR) capabilities and that the secondary node can take ad- vantage of the MPR capability by transmitting simultaneously with the primary under certain conditions. We obtain analytical expressions for the stationary distribution of the primary node queue and we also provide conditions for its stability. Finally, we provide expressions for the aggregate throughput of the network as well as for the throughput at the secondary node.