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Well-established fact shows that the fixed spectrum allocation policy conveys to the low spectrum utilization. The cognitive radio technique promises to improve the low efficiency. This paper proposes an optimized access strategy combining overlay scheme and underlay scheme for the cognitive radio. We model the service state of the system as a continuous-time Markov model. Based on the service state, the overlay manner or/and the underlay manner is/are used by the secondary users. When the primary user is not transmitting and only one secondary user has the requirement to transmit, the secondary system adopts the overlay scheme. When the primary user is transmitting and the secondary users want to transmit simultaneously, an underlay scheme with an access probability is adopted. We obtain the optimal access probability in a closed form which maximizes the overall system throughput.

The wireless spectrum resource has become the major bottleneck for the development of the future wireless communications. Recent researches in spectrum-sharing techniques have enabled different wireless communication technologies to coexist and cooperate towards achieving a better gain from the limited spectrum resources. This started when spectrum utilization measurements showed that most of the allocated spectrum experiences low utilization [

In spectrum sharing systems, the secondary user can adopt two types of access schemes: overlay scheme and underlay scheme. In underlay scheme, the licensed spectrum band can be accessed without considering the primary user’s activities, but with strict power constraint. In overlay scheme, the secondary user senses the spectrum bands and accesses the unused spectrum spots. The secondary users must be ceased when the primary user appears in the band and resumed when the primary user finishes its service.

The different features of these two schemes enable them to make up with each other. In [3,4], the papers give a mixed access strategy: When the channel is being used by the primary user, the secondary users access the channel with a probability in underlay manner. When the channel is idle, they choose to access in overlay manner.

There have been several previous efforts addressing these two schemes from different points of view. In [

In [

Based on [

The optimized access strategy proposed in this paper is similar in spirit to the work done in [

The rest of this paper is organized as follows. Section 2 introduces the system model and assumptions. In Section 3, the maximal throughput expressions for the two schemes are given. The optimal access strategy for equiprobability case is introduced in Section 4. While Section 5 introduces the case of unlike access probability. Performance analysis and simulation results are given in Section 6. Finally, the paper is summarized in Section 7.

vice state indicates a user’s requirement for transmitting at specific time. The primary user can employ the channel without considering secondary users’ service state.

The traffic pattern of the primary and the two secondary users is modeled as independent Poisson processes with arrival rates, and, respectively.

The service times are assumed to be exponentially distributed with rates, and, respectively. We define service state of the system as the sum service state of all the users in the system at a moment. Based on the individual’s service state, we get the service state set for the system as. State

“0” represents there is no user tends to transmit on the channel; State “P” represents only the primary user is transmitting on the channel; State “A” represents only user A wants to transmit on the channel; State “B” represents only user B wants to transmit on the channel; State “AB” represents both cognitive users want to transmit on the channel at the same time; State “PA” represents user A wants to transmit on the channel while the primary is transmitting; State “PB” represents user B wants to transmit on the channel while the primary user is transmitting; State “PAB” represents both A and B want to transmit on the channel while the primary user is transmitting. These states in the cognitive radio system can be modeled as an eight-state continuous time Markov model, as shown in

The rate at which transitions take place out of state s_{i} equals to the rate at which transitions take place into state s_{j}. The normalization equations governing this flow balance can be written as

where represents the steady-state probability of being in state and. Also we have

The steady state probabilities for all the states can be found by solving the set of the linear Equations (1) and (2).

In the overlay scheme, the secondary users can only ac-

cess the spectrum hole which is currently not used by the primary user. They can not co-exist on the same spectrum band. If one secondary user is transmitting, the only interference is the background noise. The user A or B accesses the channel with power. Since in the overlay manner, only one user can transmit, the maximal data rate for each of them individually is

where is noise power. These rates can be achievable with the following corresponding probabilities:

respectively.

Unlike the overlay scheme, in the underlay system, secondary users are allowed to share the channel simultaneously with the primary user pledging not to violate the limit of interference which is assumed as.

Since the secondary users A and B can get the service state of the system with the help of their base station, A and B make access decision based on the service state of the system. Here, there are two possible service state sets. When the service state is, which indicates the primary user P is not transmitting and only one secondary user has the requirement to transmit. The other case is when the service state

, which indicates that the primary user is transmitting or both secondary users want to transmit at the same time. User A and B have to adopt their powers to access the channel with probabilities and, respectively in the underlay scheme. In order to protect the primary user and decrease the mutual interference between secondary users, we assume that

satisfies the minimum SINR requirement.

These probabilities and determine the sum throughput of the secondary users and the interference on the primary user. When and/or are large, the sum throughput may be large and the chance to coexist with primary user is large, too. Our goal is to obtain optimal access probabilities to maximize the total secondary throughput, while limit the interference on the primary user. The service state set of the system in the underlay manner is. Hence the actual access state set is. The users’ maximal data rates under each state in the underlay manner is given in as

where denotes the i’s maximal data rate for the underlay case. The term

is the channel power gain between the transmitter of the user i and the receiver j as shown in

The corresponding probabilities of these rates are:

In this section we introduce an optimal access strategy which makes the cognitive network to operate in both schemes. During primary user’s idle periods, the network employs the overlay scheme; while in primary user’s busy periods, the network permits the secondary users to use the channel with probability subject to satisfying the interference threshold constraint. The parameter is a secondary service parameter which has to be adjusted based on the spectrum status to achieve maximum throughput.

Based on Equations (3) to (5), we can get the average throughput for the secondary users as

The total throughput of the cognitive network is

Using Equaions (6)-(8), can be written in the quadrature form as

where and are given as follows

To maximize the secondary throughput, we take the first derivative of with respect to and equate it to zero.

Solving for leads to the optimal access probability.

We can note from Equation (12) that is always positive. Since is a probability value (i.e.,

), the value of is always negative. The throughput function of the secondary network in Equation (9) is concave down. Thus it must have a unique maximum value, it can be expressed as

where denotes the absolute value.

In this section, a similar approach will be followed as in the previous section expect that it is assumed that each user A and B has its own access probability (and) respectively. The goal here is to optimize these parameters. So the best access probability for each secondary user is found to achieve the highest possible throughput.

User A and B have to adopt their powers to access the channel with probabilities and, respectively in the underlay scheme. In order to protect the primary user and decrease the mutual interference between secondary users, we assume again that satisfies the minimum SINR requirement.

These probabilities and determine the sum throughput of the secondary users and the interference on the primary user. When and/or are large, the sum throughput may be large and the chance to coexist with primary user is large, too. Our goal is to obtain optimal access probabilities to maximize the total secondary throughput, while limit the interference on the primary user.

Same service state set

exists. The users’ maximal date rate under each state in the underlay manner is given in Equation (5).

The corresponding probabilities of these rates given in Equation (6) can be written now as

Using Equations (7), (8) and (14), can be written in a nonlinear equation form as

where, is given as follows

To find an optimization solution for Equation (15), we bring up the following theorem:

Theorem 1 Let f be a function with two variables with continuous second order partial derivatives, and at a critical point. Let D is the determinant of the Hessian matrix of the function f, i.e., , thus

Using Theorem 1, it is forward to conclude that the possible maximum of the utility function (i.e., Equation (15) occurs at the saddle point of this function which appears at. Then the maximum secondary throughput can be found by substituting this point into Equation (15), this yields

In this section, a simulation example will be carried to illustrate the proposed algorithm. The following powers are set: and. The arrival rates are set as,

and with equal average times,. The wireless channel bandwidth. It is assumed that the loss of power in propagation follows the exponential propagation law with exponent loss 3.5. The position of the primary user’s transmitter and receiver are and respectively. The user A’s transmitter and receiver location are at and, and for User B’s transmitter and receiver are located at and respectively. The interference constraint is assumed double the background noise;.

In

This is because B’s transmitter and receiver are located closer than those of A. As the arrival rate of B increases, the throughput of B gets better, which can be understood intuitively. The throughput of A decreases because the user B transmitting creates more interference to it.

In

user, since the condition is always guaranteed.

In

In

, note that.

To study the effect of changing the arrival rate of the far user A, is fixed at 110 ms, while is varied in

The two dominant access schemes in the cognitive radio architecture, underlay and overlay, are studied. It is found by some literatures that these two schemes can make up with each other to enhance the system’s performance. This paper proposes a mixed access strategy combining these two schemes. It is assumed that secondary users

access the spectrum with certain access probabilities. It is focused on the service state and model the service state of the system as a continuous-time Markov chain. Finally, optimal access probabilities and optimal throughput for this mixed strategy are introduced in closed forms to maximize the overall capacity of the cognitive network. The simulation results show that the proposed access strategy can achieve much better performance for the secondary uses, compared with the single scheme strategies.