GUO Jing－hua，JI Hong，LI Yi，AN Chun－yan

郭惊华， 纪 红， 李 屹， 安春燕

（Key Lab of Universal Wireless Communication，Ministry of Education，Beijing University of Posts and Telecommunications，Beijing 100876，China）

In recent years，cognitive radio is a key technology to realize dynamic spectrum access（DSA）that enables the secondary users（SUs）to exploit the spectrum which is not used by primary users（PUs）in an opportunistic manner［1－2］.Cognitive radio networks（CRNs）bring spectrum access opportunities for secondary users to enhance the spectrum utilization.Spectrum sensing is the cornerstone of CR.To minimize the interference to primary users，secondary users need a reliable spectrum sensing mechanism to determine the availability of channels which belong to PUs in real time.

Much research has been done about how to sense spectrum hole effectively，in most of which the SUs are assumed to be able to sense the full spectrum band or randomly sense a few of them.However，it is impractical for SUs to sense all the channels in a short time due to hardware constraints.Besides，the considerable time and energy caused by sensing the busy spectrum channels can be reduced through spectrum prediction.U-sing a reliable prediction scheme，the SUs will sense only those channels which are predicted to be idle［3］.

An approach of single-SU prediction scheme based on modified HMM（Hidden Markov Model）has been proposed and tested in Refs.［4］and［5］，both in which response delays have been taken into account.A new spectrum-hole prediction model for cognitive radio systems based on the IEEE 802.11 wireless local areas networks was presented in Ref.［6］.As cognitive radio offers the promise of intelligent radios that can learn from and adapt to their environment，many machine learning algorithms have been introduced to solve the problem in CRNs［7］.A channel status predictor using the multilayer neural network model was designed in Ref.［3］，which did not require a prior knowledge of the traffic characteristics of the licensed user systems.An autoregressive channel prediction model was presented in Ref.［8］for cognitive radio systems to estimate spectrum holes，which adopts a second-order autoregressive process and a Kalman filter.

The previous studies in Ref.［4－6］are suitable for some specific situations，in which the PUs’traffic characteristics are known as a prior.Neural network based algorithm does not has the worries，but it needs a long series of data for neural network training.Besides，traditional neural network approaches have suffered difficulties with generalization，producing models that can over-fit the data.Meanwhile，the foundations of Support Vector Machines（SVM）are gaining popularity due to many attractive features，such as better generalization and good performance for small training samples ase，promising empirical performance，etc.

In this paper，we propose a novel spectrum prediction scheme based on SVM in cognitive radio networks.By learning from the history channel status，SVM model can predict the spectrum channels to be busy or idle in the next time slot.As the SU will not sense the full spectrum band but only the channels predicted to be idle，the proposed algorithm would obviously reduce the sensing energy and time.Besides，in order to get a better spectrum prediction result，a corporative mechanism is considered in multi-user condition.The simulation results show that the SVM algorithm has a very high predict accuracy，and the spectrum prediction scheme can obviously save the sensing energy，comparing with the normal spectrum sensing mechanism.

The remainder of this paper is organized as follows.Section 1 presents the system model.Section 2 proposes the novel prediction algorithm based on support vector machine.Section 3 describes the simulation results.The importantconclusionsare drawn in Section 4.

1 System Model

In this paper，we consider a cognitive radio network scenario with multi PUs and SUs，where SUs can opportunistically access licensed channels of PUs.The channel state is shown in Fig.1.

Channels A and B are two examples of independent channels based on different spectrum band.We use 1 to denote the busy state and 0 denote the idle state in every time slot.Then，the channel status prediction problem can be treated as a binary series prediction problem.It is supposed that SUs are aware of a short history of the states for every channel by storing or collected from neighbors over a common control channel.

We use the Support Vector Machine algorithm to formulate this problem.The input data of SVM algorithm are binary series，which represents the channel status for the last n time slots.U-sing the binary series，the SVM predictor is trained to predict the output Yi，which should be equal to the channel status in the next slot

2 Spectrum prediction Algorithm

In this section，we will present our proposed spectrum prediction algorithm.We firstly introduce the support vector machines，and then formulate support vector regression model to predict the spectrum channels.

2.1 Support Vector Machines

Support Vector Machines are gaining popularity due to many attractive features，and promising empirical performance after Vapnik developed the foundations in 1995.SVMs are currently used to solve the classification problem and regression problems.As a powerful computational intelligence theory，SVM is widely used in quadratic programming（QP）problems.Besides，many expert systems are organized based on SVM.The formulation of SVM embodies the Structural Risk Minimization principle（SRM），which has been shown to be superior to traditional Empirical Risk Minimization（ERM）principle employed by conventional neural networks.This is mainly because SRM minimizes an upper bound on the expected risk，as opposed to ERM that minimizes the error on the training data［9］.It is the difference which equips SVM with a greater ability to generalize，which is the goal in statistical learning.So the SVM model has better performance for small training sample case comparing to the traditional machine learning algorithms.

We choose Support Vector Regression（SVR）to formulate the spectrum prediction problem.And RBF（Radial Basis Function）is used to regress as the kernel function.The detail of the function and the regression algorithm will be given in the next part.

2.2 SVR Spectrum Prediction Algorithm

In this paper，we will use support vector regression to formulate the problem.SVM can be applied to regression problems by the introduction of an alternative loss function.The loss function must be modified to include a distance measure.We use ε-insensitive loss function which is an approximation to Huber’s loss function that enables a sparse set of support vectors to be obtained.

Considering the problem of approximating the set of training data，

with a function

where x is an n dimensional vector，such as）.In this paper，x is an n length binary series of one channel’s state;y is the next slot channel state，both of which have values 0 or 1.The optimal regression function is given by the minimum of the function［9］，

where C is a pre-specified value，andare slack variables representing upper and lower constraints on the outputs of the system.

Using an ε－insensitive loss function，

the solution is given by，

with constraints，

The Karush-Kuhn-Tucker（KKT）conditions that are satisfied by the solution are，

Therefore the support vectors（SV）are points where exactly one of the Lagrange multipliers is greater than zero.When ε=0，we get the L1loss function and the optimization problem is simplified［10］，

with constraints，

and the regression function is given by Eq.（2），where

Eq.（2）is a linear function，and a non-linear model is usually required to adequately model data.A non-linear mapping can be used to map the data into a high dimensional feature space where linear regression is performed.The kernel approach is employed to address the curse of dimensionality.

The non-linear SVR solution， using an ε－insensitive loss function is given by［9］，

with constraints of Eq.（6）.

Solving Eq.（12）with constraints Eq.（6）determines the Lagrange multipliersand the regression function is given by，

where

And we choose the radial basis function as the kernel function［10］，

The RBF kernel function produces a piecewise linear solution which can be attractive when discontinuities are acceptable.

After obtain the SVR model trained by plenty of history data，we can predict the channel state of the coming slot by using the former n states as input，the output y is the next time slot’s state.

2.3 Multi-user Prediction

The SVR predictor in the previous subsection is designed for single user to predict one spectrum channel’s state using the history data.However，practical cognitive radio networks often have multi-user and multi-channel，and the cooperation between different users will improve the system performance，which is also considered in this paper.Much research has been done in cooperative spectrum sensing，while in this paper，we focus on the sharing of history information and prediction results.

It is supposed that SUs are aware of short history information of multi-channel’s states.This is reasonable because SUs usually has the ability to store information，and new SU can collect history information from neighbor nodes over a common control channel once it enters in the cognitive radio network.

In most research work，SU is assumed to deal with full band channels，which is impossible due to the limitation of hardware and the large consumption of energy.Besides，single user’s predicting results may have errors for kinds of reasons，which lead to the unnecessary sensing energy consumption or the loss of spectrum access opportunity.In this paper，it is assumed that each node will broadcast its own message and receive the broadcast information from the neighbors after spectrum prediction.With the cooperation of neighbor SUs，every SU can be aware of most of the channels’state by predicting only a few channels.Moreover，if SU’s predicting result is not supported by its neighbors，it will adapt its result to arise the correct rate.

Suppose p SUs predict Channel A’s state in the next slot，and then the final result is shown as follows，

where fiis the prediction result of SUi;FAis a medium variation;YAis the final result.The certainty factor of the SU μidepends on its prediction accuracy in history，0≤μi≤1.

3 Simulation Results

In this section，we will evaluate the performance of the proposed spectrum prediction algorithm based on SVM in cognitive networks by simulations.As the Artificial Neural Network（ANN）algorithm is one kind of traditional machine learning algorithms，we will compare the prediction accuracy between SVM algorithm and the ANN algorithm in various scenarios.And then the performance of improving the spectrum utilization and reducing the sensing energy and time are simulated.

3.1 Predictive Accuracy

To simulate the algorithm performance，the primary users’traffic is assumed to follow Poisson process，and the busy/idle time of the channel is drawn from geometric distributions.For different traffic scenarios，we vary the traffic intensity λ and the average inter-arrival time tinterof the traffic bursts.The traffic intensity is related to the mean inter-arrival time as follows: where tbusyis the mean time that the primary user is active on the channel during each traffic burst.The training and testing data are generated by observing the channel’s occupancy.

The accuracy of the SVM spectrum predictor is evaluated in terms of the wrong prediction probability，denoted by Pe（all），which means the rate of condition that the prediction state is opposite to the real state.Our particular interest is the wrong prediction probability when the real channel status is busy，denoted by Pe（Busy）.Pe（Busy）is an important measure from the primary user’s perspective because it indicates the level of interference to the primary user.Pe（Busy）is analogous to the sensing error rate Pe（Miss Detect），while Pe（Idle）is like the Pe（False Alarm）.Pe（all）is an important measure from a secondary user’s standpoint because the goal of the SU is to minimize the interference to the PUs while maximizing its own transmission opportunities.

Fig.2 shows the performance of the SVM predictor and ANN algorithm for various traffic scenarios when the channel is busy.The ANN algorithm in this paper is based on three layered BP neural network［3］.

For a given traffic intensity λ，the predictors’performance improves when the mean inter-arrival time increases.Comparing with the artificial neural network predictor，the algorithm proposed in this paper has lower error rate and higher stability.

Fig.2 Prediction performance:Pe（Busy）in different scenarios

Fig.3 shows the SVM and ANN algorithms’average error rate for various traffic scenarios when the channel state is idle.From Figs.2 and 3，we can see that Pe（Idle）and Pe（Busy）are very close under the same traffic scenario.

Fig.3 Prediction performance:Pe（Idle）in different scenarios

During the simulation，the training data for SVM model is chosen as 200 slots as the inter-arrival time varies from 14 to 22 slots，while the ANN model needs 1000 observations.The results show that，without com-promising the prediction accuracy，the length of the training sequence is much shorter than that of the ANN algorithm.SVM model has better performance for small training examples comparing to the traditional machine learning algorithms.

As SVM algorithm has a high precision rate and stability，it can be well used in the cognitive networks to predict spectrum channel state.

3.2 Benefits of Spectrum Prediction

The benefits of spectrum prediction are manifold.We consider the improvement of spectrum utilization，the reduction of sensing energy and time in this paper.

Consider a cognitive radio network with Nchchannels，which belong to various primary users with differenttraffic distributions. There are normal SUs（SUnormal）and SUs who have ability to predict（SUpredict）in the system.SUnormalrandomly selects a channel in each slot to senses，while SUpredictpredicts the channel status before sensing.Each secondary user is able to sense only one channel during a slot due to the hardware constraint，but it can easily predict multichannels’status.The SUpredictcan randomly sense one of the channels which are predicted to be idle.

The improvement in spectrum utilization due to spectrum prediction can be expressed as

where Upredictand Unormalare spectrum utilization of the two kinds of SUs;Ipredictand Inormalare the number of idle channels sensed by them.

Fig.4 shows the improvement of spectrum utilization after implementing the proposed spectrum prediction scheme.Nsuis the number of secondary users.As the Nsuincreases，SUs can sense more channels in one time by cooperating with each other.The performance is more effective as the number of channel increase.

Fig.4 Benefits of spectrum prediction:spectrum utilization improvement

To simulate the reduction in sensing energy，and consider a single channel scenario（Nch= 1），in which a PU and SUshave worked for a period of time，a normal SU sensed the channel in every slot whereas a SUpredictsensed the channel only in the time slot when it is predicted to be idle.

The reduction in the sensing energy can be given by

where Enormaland Epredictare the energy used by the two kinds of SUs;Bpredictis the busy time slots predicted by the SUpredict;Sallis the total number of slots in the period of time.And it is assumed the same unit of energy is required to sense either slot.

Fig.5 shows the reduction of sensing energy.X axis means the PU’s traffic intensity，and Y is the energy reducing.The performance is more effective as the PU’s traffic intensity［10］increased，because of more busy time slot turn out and the SUpredictwould not waste energy to sense the channel.When Nsu=4，the SUswill bring higher traffic intensity to the network than the situation when Nsu=2.And with the cooperation between SUs，the Eredis higher as the number of SU increase.

Fig.5 Benefits of spectrum prediction:sensing energy reduction

SUswill sense spectrum channels all the time until an idle channel is found.So the use of spectrum prediction algorithm will also save the sensing time，which is similar to the energy.As aforementioned simulation results，the SVM predictor can help the SU to discover more idle slots and save sensing energy and time.

4 Conclusions

In this paper，we have proposed a novel spectrum predict scheme based on Support Vector Machine in CRNs.Firstly，we transform the channel status prediction problem into a binary series prediction problem.Then we introduce the SVM model to predict the states of spectrum channels by using history information.As the SU doesn’t need to sense all the channels，the algorithm can reduces the energy consumption.The sim-ulation results show that the novel prediction scheme based on SVM has a high predict accuracy and can obviously improve the spectrum utilization and reduce the sensing energy and time，comparing with the normal algorithms.

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