Analysis of a multi-user cognitive radio network considering primary users return

• A complete distributed single-channel multi-user cognitive radio network with a common control channel is analyzed. To derive the necessary metrics, we exploit renewal reward theory by which we are able to carry out a continuous time analysis of the whole network. This approach can be used as a framework for some other scenarios with a few changes in the modeling of the renewal process.
• The imperfect behavior of secondary sensor as well as changes in the occupancy state of PU traffic during SU transmission is considered in deriving the probability of collision and it is introduced as a constraint for the problem of maximizing the network throughput. Consequently, the interference due to both primary user re-occupancy and sensing error in the detection of primary user are considered.
• We derive mathematical closed form expressions for the expected amount of interference and transmission time in a renewal cycle and hence for the collision and transmission rates as well as other performance measures, those which are important for network design and network planning.
• The analysis used in this paper can be easily extended to some other scenarios such as slotted transmission protocols. Furthermore, additional constraints such as energy can be easily included in the analysis since the complete continuous-time behavior of secondary and primary users in the spectrum access can be modeled.

Multi-user cognitive radio networks have been considered in the literature recently. However, there is no analytical framework which can provide a model in order to derive the system performance metrics. This paper presents an analytical continuous time framework for a multi-user cognitive radio in which secondary users (SUs) communicate on a single common control channel, the most common protocol discussed in the multi-user category. The proposed analysis method is based on the renewal theory. We prove that the spectrum access of SUs with respect to the primary user (PU) traffic behavior forms a renewal process. Furthermore, the corresponding renewal cycle is derived and metrics such as collision probability and interference time due to both sensing error and PU re-occupancy are formulated in the renewal cycle. Thanks to the proposed continuous time analyses, the transmission efficiency for the secondary network is formulated. Finally, some numerical analyses are provided on the derived equations to discuss the optimum transmission time for SUs in order to have the maximum efficiency under the prescribed collision constraint. As an example, for the sensor, probabilities of false alarm and miss-detection are taken to be equal to 0.1 and 0.01, respectively, with a primary network in which the idle and busy cycle rates are 0.1 and 0.3; also, the transmission time must be bounded to 500 ms in order for the collision probability to remain under 0.01. At the end, we show that simulation results are consistent with the numerical analyses.

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