an analytic cognitive radio network

Our system model comprises an arbitrary number, , of homogeneous secondary users (SUs) that independently switch between active and idle states. The SU generates data at rate bits per second (bps) during the active periods, whether or not it has access to a channel for transmission. The transmission activities of SUs are modeled as Poisson processes, where the intervals between consecutive events (active and idle states) are independent and identically distributed exponential random variables. This model captures the burstiness of the data stream.

The channels can also be modeled as ON-OFF processes, because, when the PU returns to its given channel, that channel is essentially unavailable to the CRN. We model the PU network, comprising of Np homogenous PUs as a continuous time Markov Channel (CTMC) where, each channel can exist in one of two states: ON (corresponding to when the PU associated with it is OFF) or OFF (corresponding to when the PU associated with it is ON). The channel capacity is cp bps.

We assume that there exists a spectrum availability database through which the secondary devices can access perfect knowledge of spectrum availability. This assumption is reasonable as it is recommended approach for federally controlled spectrum [?]. When sensing based dynamic spectrum access is the only alternative, there can be imperfections in the sensing mechanisms leading to imperfect knowledge about spectrum bands. We leave this case for future work.

For a fixed access policy , let denote the queue size of the SU at time . Then, the buffer content of SU, , for the next seconds can be modeled as a Lindley process [?] satisfying the following equation [?, ?]:

(1)

where shows the output channel available to ...

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...effective bandwidth of the arrival and service processes separately. However, we can use the buffer overflow probability of the dependent systems in Eq. (5) to evaluate the effective bandwidth. The key point is that for the arrival process modeled by , with the buffer bound , and the QoS parameter that is the overflow probability, constant channel capacity should be at least , where is the solution to .

The objective of this paper is to obtain the maximum sustainable arrival rate which, by definition, is the effective bandwidth of the system calculated for a given value of buffer size, , and overflow probability defined as:

(6)

In the following section, we model the arrival and service processes in the CRN. Later, we find the closed-form expression for the buffer occupancy probability distribution function (pdf) to evaluate the effective bandwidth.