Abstract: In the cognitive radio system, that the primary user (PU) has collision with the secondary user (SU) when the secondary user (SU) was detected properly was considered. The queuing theory was introduced and the PU’s appearance pattern was described by M/M/1 model. Considering the length of the transmitting slot, detection probability and transmitting collision, the function of spectrum usage and transmitting time were established based on the PU’s appearance pattern. The existence of the maximum value of spectrum usage in the definition domain of the transmitting time was proved by theoretical derivation in some condition. The simulation results provide support to the existence of the maximum value. Furthermore, the loss of spectrum usage caused by transmitting collision is more than 20%, which should be considered during the system design procedure.

Key words: cognitive radio, spectrum sensing, sensing period, transmission collision