Estimation for Traffic Arrival Rate and Service Rate of Primary Users in Cognitive Radio Networks

（Communication Research Center，Harbin Institute of Technology，Harbin 150001，China）

Estimation for Traffic Arrival Rate and Service Rate of Primary Users in Cognitive Radio Networks

Xiaolong Yang and Xuezhi Tan∗

（Communication Research Center，Harbin Institute of Technology，Harbin 150001，China）

In order to estimate the traffic arrival rate and service rate parameters of primary users in cognitive radio networks，a hidden Markov model estimation algorithm（HMM-EA）is proposed，which can provide better estimation performance than the energy detection estimation algorithm（ED-EA）.Firstly，spectrum usage behaviors of primary users are described by establishing a preemptive priority queue model，by which a real state transition probability matrix is derived.Secondly，cooperative detection is utilized to detect the real state of primary users and emission matrix is derived by considering both detection and false alarm probability.Then，a hidden Markov model is built based on the previous two steps，and evaluated through the forward-backward algorithm.Finally，the simulations results verify that the HMM-EA algorithm outperforms the ED-EA in terms of convergence performance，and therefore the secondary user is able to access the unused channel with the least busy probability in real time.

cognitive radio；hidden Markov model；cooperative detection

1 Introduction

Cognitive radio has been widely considered as a promising technique to solve spectrum scarcity problem，which is caused by the fixed spectrum policy and the underutilization of the allocated spectrum at a time，frequency，or space［1］.Cognitive radio network（CRN）allows a secondary user（SU）to opportunistically access or share the licensed bands with the primary user（PU），thereby extremely improving the spectrum efficiency［2］.Specifically，in CRNs，a spectrum management framework includes four interrelated sections：spectrum sensing，spectrum decision，spectrum sharing，and spectrum mobility［3］. Spectrum sensing is interpreted as an action，by which SUs search for available spectrum holes among licensed spectrum bands for communication.Based on sensing information of spectrum holes，a SU selects the best channel for accessing by spectrum decision.Then，spectrum sharing will coordinate channel access among multiple SUs.As long as a PU reclaims a licensed channel temporarily occupied by a SU，spectrum mobility will immediately suspend the transmission，vacate the channel，and resume ongoing communication or retransmit data on another fallow channel.

Spectrum mobility mainly refers to spectrum handoff which has been widely considered as a challenge in different research programs related to heterogeneous networks and CRNs［4］.Up to now，the vast majority of researches on spectrum handoff focus on establishing handoff models and studying handoff strategies，which are generally divided into two categories：proactive spectrum handoff and reactive spectrum handoff［5］.In proactive spectrum handoff，the target channels prepared for future handoff have already been determined by intelligent prediction techniques or long-term statistics before a SU starts to establish a connection.In reactive spectrum handoff，as a SU is required to vacate a licensed channel，the SU will suspend the ongoing communication and execute spectrum sensing to seek for idle channel first，and then the available channel would be selected according to the sensing results.Essentially，both spectrum handoff schemes are aimed at resolving the same problem，i.e.the optimal approach to choose the target channel when more than one idle channel exists. Apparently，the SU gives preference to the channel with the lowest busy probability which depends on the traffic arrival rate and the traffic service rate of the PU. So，it is very important to estimate these parameters before data transmission.

In the existing works，the hidden Markov model（HMM）is widely applied to solve the spectrumprediction and parameter estimation problem in CRNs. Park proposed the HMM-based channel status predictor to implement a channel predictor and predict next channel status based on past channel states and analyze the disadvantage of the predictor［6］.In Ref.［7］，a modified HMM-based single SU prediction was proposed and examined based on two hardware platforms（the universal software radio peripheral 2 and the small form factor software defined radio development platform）.In addition，cooperative prediction with two stages was also proposed.In order to convince the theory results，real-world Wi-Fi signals are applied in simulation environment.In Ref.［8］，a HMM-based channel prediction algorithm was proposed as well as a channel allocation algorithm，resulting in the improvement of throughput in the frequencyhopping scheme.All these literatures above，however，predict the states of the PU（busy or idle）but do not estimate the traffic arrival rate and the traffic service rate of the licensed channels，further.Therefore，the SU may not be able to access the optimal channel，which directly results in more interruptions and longer handoff delay.

Additionally，Ref.［9］presented an analytical framework to study the proactive handoff strategies by evaluating the latency performance of spectrum handoffs in CRNs.Furthermore，the authors proposed a traffic-adaptive spectrum handoff strategy based on traffic parameters，i.e.the traffic arrival rate and the traffic service rate of the PU.But，they discussed little about how to obtain the traffic conditions.Similarly，Ref.［10］researched the handoff characteristics on the latency performance in the case of reactive handoff strategy.According to traffic parameters，the authors also provided an important insight to study the channel utilization.However，they still did not mention the way to get traffic parameters.In Ref.［11］，the CRN was modeled as a HMM，and the traffic arrival rate and the traffic service rate of the licensed channels were estimated by energy detection estimation algorithm（ED-EA）.However，the SUs could not accurately detect the real state of the PU in the case of low signal to noise ratio or hidden terminal problem.In order to solve aforementioned problems，a hidden Markov model estimation algorithm（HMM-EA）based on cooperative detection was proposed to estimate the traffic arrival rate and service rate parameters of the PU，which is better than ED-EA algorithm in terms of convergence performance.

2 Cognitive Radio System Model

In this paper，it assumes that the CRN hasMSUSUs，and each SU equips with two sets of antenna，one is directional antenna for transmitting or receiving signals while the other one is omnidirectional antenna for spectrum detection.In addition，each channel is considered with its own high-priority and low-priority queues as discussed in Ref.［12］.In order to transmit data，PUs and SUs enter the high-priority and lowpriority queues，respectively.Then，the primary connection and secondary connection are established，respectively.Here，in spite of uplink or downlink，the connection with the same priority is considered to follow the first-come-first-served（FCFS）scheduling policy in a centralized manner.The CRN is supposed to adopt time-slotted scheme as implemented in Refs.［13-14］.

In order to avoid interfering with PUs，the SU must sense the operation state of current channel at the beginning of every time slot.In single-user spectrum detection process，energy spectrum detection is adopted and licensed channel state is directly determined by the SU according to its detection result. In multiple-user spectrum detection process，cooperative energy spectrum detection is applied and licensed channel state is judged by fusion center based on detection results from cooperative SUs.If the state is busy，the SU has to execute spectrum handoff to retransmit its unfinished data.Otherwise，the SU is allowed to transmit data in remaining duration of this time slot.

Spectrum usage behaviors of PUs are analyzed byM／M／1／Nqueuing network model，which requires the following traffic parameters.It is assumed that the arrival processes of primary connection on the queue of each channel are Poisson.Furthermore，the corresponding service time follows exponential distribution.Nrepresents the cache capacity of each channel，namely queue length.Letndenote the number of PU in high-priority queues，andn∈｛0，1，2，…，N｝．

Fig.1 shows the schematic diagram ofM／M／1／Nqueuing network model，whereλ（n）（arrivals／slot）denotes the arrival rate of transition from staten ton+1，andμ（n）（slots／arrival）denotes the service rate of transition from staten ton+1．From the point of SU，when queuing network model satisfiesn＝0，the channel stays idle，presented byS0．Otherwise，the channel stays busy，presented byS1．

Define the probability functionPn（t）as the steady-state probability that the given process is in statenat timet.Based on the above assumptions andanalysis，the equilibrium equations of the given process can be written as follows，

When the process goes steady，for alln（n∈｛0，1，2，…，N｝），the limit of the steady-state probability astapproaches to infinity exists.That is，Then，the equilibrium equations can be solved and the solutions are expressed as follows：

From the point of SU，we define the real state transition probability aswhich denotes the probability that high-priority queue transfers from stateSitoSjbetween two time slots.For∀i，j∈｛0，1｝，Thus，the real state transition probability matrix can be expressed as，

LetPnn′（t；Δt）denote the probability that given that the high-priority queue stays in staten at timet，and then a time slot Δtlater，it will stay staten′．That is，

Therefore，the state transition probabilitycan be expressed as follows，

3 Spectrum Detection Methods

3.1 Single User Energy Detection

In the existing research on cognitive radio，energy detection is primarily applied to detect whether if the licensed channel is busy.But，in this paper，we will further study the energy detection to adequately utilize the relationship between the detection result and the real state of licensed channel.LetD0，D1present the detection consequences which are respectively nonpresence and presence of PUs，and letdescribe the relationship between the detection result and the real state of licensed channel. Specifically，donates the probability that the channel stays statewith the detection result．ForAccording to the definitions of the detection probabilityand the false alarm probability

So，the matrixBcan be written as，

In the following，the concrete expression will be derived.Firstly，we suppose that the licensed channels are additive white Gaussian noise（AWGN）channels. During the energy detection period，Letr′（t）present the received RF signal，which is first pre-filtered by anideal filter.Then，r（t），the output of the filter is sampled，squared，and summed over a sensing time interval to finally produce a measure of the energy of the received waveform.That is，

where finally hasNsterms to sum over，andYacts as a test statistic to test the two hypothesesS1andS0．It then follows that underS1，Yhas a non-central chi-square distribution.Likewise，givenS0，will be central chisquare distribution.With varianceσ2，non-centrality parameter 2γ，andNsdegrees of freedom，the probability density function ofYcan be expressed as follows［15］，

Therefore，the detection probability and the alarm false probability of themth SU can be written asrespectively.Set the parameterηmas the energy detection threshold of themthcan be expressed as follows，

3.2 Cooperative Energy Detection

Recalling aforementioned assumptions about system model，for each sensing slot，multiple SUs，at the same time，perform distributed cooperation detection，in which each SU adopts energy detection，and then delivers the detection consequence to fusion center.Afterward，the fusion center judges whether the primary channel is busy or not based on a certain fusion criterion.Assuming that report channels are perfect，and OR criterion is employed，for improving the detection performance of cognitive radio networks，as well as reducing the detection accuracy requirement of single SU.Based on the OR criterion，the final detection probability and the false alarm probability can be expressed as follows，

Obviously，the cooperation detection probability is higher than single SU energy detection with the same channel situation.However，the false alarm probability is becoming higher，too.Although this will increase the possibility that SU has to perform handoff，it is absolutely necessary to guarantee the quality of service of PU.Based on the aforementioned analysis，the expression ofBcan be got as follows，

Then，substituting Eqs.（12）and（13）into Eq.（16），we can get the final expression ofB．That is，

This is a very useful conclusion.The matrixBwill be viewed as an important element of HMM in the following discussions.

4 HMM-EA Algorithm

It is well-known that the hidden Markov process is a doubly embedded stochastic process with an underlying stochastic process.This process is not observable，but can only be observed through another stochastic process which can produce a sequence of observations.In this paper，from the perspective of SU，the variation process of the real state（S1orS0）of channel is viewed as an underlying stochastic process which cannot be obtained directly.But，the channel detection will produce a sequence of observations（D1orD0）so as to judge the real states.Consequently，it has definite physical significance to describe the aforementioned cognitive radio system as a HMM.

Fig.2 shows the schematic diagram of the HMM，which perfectly describes all possible variation.From the schematic diagram，we can see three basic elements in the HMM.As one of the basic elements，the real state transition probability matrixAdepicts the probability that the licensed channel transfers from one state to another state between two time slots and it has been obtained in section 2.The matrixB，another basic element，presents the relationship between hidden states（i.e.real states）and observations（i.e. detection results）and it is called emission matrix，derived in detail in section 3.Thus，the HMM can be formulated asψ＝（A，B，π）．Among the compact notation，π＝｛πi｝denotes the initial real state distribution probability.

Fig.2 The relationship between the basic elements in the HMM

Generally speaking，there are three basic problems which need to be solved in practical applications.The first one，evaluation problem，is to compute the probability of the observed sequence，given a model and a sequence of observations.The second one，decoding problem，is to find out the unobservable part of the HMM to discover the real state sequence.The third one，learning problem，is to optimize the model parameters so that it can accurately describe how a given observation comes out.In this paper，the last problem will be solved to optimally adapt model parameters to observed sequence，namely to estimate best modelψfor a detection sequence of SU.Therefore，the arrival rate and the service rate of PU can be obtained by estimating the state transition matrixAand the emission matrixB．In order to solve this problem，firstly considering such a known observed sequence obtained by spectrum detection，

whereTdenotes the number of time slots，anddt（dt∈｛D0，D1｝）is the detection consequence of SU in thetth time slot.Letst（st∈｛S0，S1｝）present the real state of PU in thetth time slot.As shown in Fig.3，the arrows indicate the direction from one state to another state between two time slots.

Fig.3 Diagram of the HMM along time slots

In order to solve learning problem，the forwardbackward procedure will be firstly introduced. Considering the forward valuableϑt（i）defined as the probability of the partial observation sequence，d1d2…dt，（until timet）and statestat timet，given the modelψ，namely，

The forward valuable can be inductively solved，as follows

Therefore，the backward valuable can be inductively solved as follows，

Based on the definitions above，ξt（i，j）can be defined as the probability of being in stateSiat timet，and stateSjat timet+1，given the model and observation sequence，expressed as，

So，given the observation sequence and the model，the probability of being in stateSiat timetcan be written ascan be obviously interpreted as the expected number of transitions made fromcan be viewed as the expected number of transitions fromSitoSj．By maximizing the Baum’s auxiliary function，

It has been proved in Refs.［16-17］that the maximization of the Baum＇s auxiliary function leads to increased likelihood，namely modelis more likely than modelψ＝（A，B，π）．Through iteratively usingin place ofψand repeating the reestimation calculation，the most likely model will be found and the parameters of the HMM will be estimated，i.e.the traffic arrival rate and service rate of PU will be obtained by solving the equation sets as follows，

The proposed HMM-EA algorithm’s complexity consists of two parts.One is the complexity of HMM model estimation and can be written as（6H1Z1Z2Z3+2H2Z1Z2Z3）［8］，whereZ1means the number of states；Z2is the number of observation；Z3is the total number of transitions divided by the total number of states；H1means dimension of the observation vector andH2is maximum number of observations for a single transition. The other one is the complexity of cooperative detection and can be written asmO（Z），whereO（Z）means the complexity of every SU’s energy detection，andZis the number of sample andmis the number of cooperative SUs.According to Ref.［11］，the ED-EA algorithm’s complexity can be written as（14Z1Z2Z3+O（Z））．In the following section，we will compare algorithm complexity between the HMM-EA algorithm and EDEA algorithm by simulations.

5 Simulation and Result Analysis

In section 4，we do the analysis about the HMMEA algorithm.In this part，the convergence performance will be discussed by simulations.We suppose that the licensed channels are additive white Gaussian noise channels and set degrees of freedom of chi-square distribution to be 5，signal to noise ratio of the detected channelSNR＝γ／σ2＝8 dB，detection thresholdTH＝η／σ2＝10 dB，convergence tolerance of likelihood estimation Δδ＝1e-6，and the maximum number of iterationsNUM＝500.In addition，only one licensed channel is detected at a time and the real traffic arrival rate and the traffic service rate of the PU queue are set to beλ＝0.3 andμ＝0.5，respectively. Simulation results and analysis are as follows.

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Fig.4 shows that，for constant channel conditions，the estimation values of real state transition probability matrixAgradually converge to the real values with the increase of number of detection time slots.Because more detection results can more accurately reflect the transformation law of licensed channel state.Letj）present the estimation value ofA（i，j）．Specifically，when Tadds up to 2 000，the estimation erroris only 0.032 andis 0.017.Additionally，it is found that the curve ofand the curve ofare symmetrical because ofas well as the curve ofand the curve of

Fig.5 shows that，for constant channel conditions，the estimation values of traffic arrival rate and service rate gradually converge to the real values with the increase of number of detection time slots.Because these two parameters are obtained by solving Eq.（28）. Especially，whenTadds up to 2 000，the estimation erroris only 0.018 andis 0.007. Hence，the traffic parameters can be estimated accurately by HMM-EA algorithm.

In order to describe the convergence performance of traffic parameters，letdenote estimation error ofA（i，j）．Fig.6 shows that the estimation error ofA（1，1）converge to zero with theincrease of number of detection time slots.Furthermore，the convergence rate gradually accelerates when the channel condition becomes better.Obviously，whenSNR＝8 dB，the estimation error converges to zero faster than that ofSNR＝4dB andSNR＝0 dB.Based on the above theoretic analysis，as the channel condition is better，the detection result will be more accurate.Consequently，the HMM model will be estimated more accurately by solving learning problem. In addition，for convenience，the estimation error curve is fitted by exponential function.Similarly，Fig.7 shows the same law.

Fig.4 Convergence ofaccording to the number of detection time slots by HMM-EA（m＝2）

Fig.5 Convergence ofaccording to the number of detection time slots by HMM-EA（m＝2）

Fig.6 Estimation performance ofA（1，1）compared with differentSNR，that is，SNR＝8 dB，SNR＝4 dB andSNR＝0 dB

In order to compare the convergence performance of HMM-EA and ED-EA algorithm，we set channel conditionSNR＝4 dB.Then，letdenote the estimation error of traffic parameterλandμ，respectively.For convenience，the estimation error curves are also fitted by using exponential function. The simulation results are shown in Figs.8 and 9.From these two figures，it can be seen that the convergence performance of HMM-EA algorithm is better than that of ED-EA algorithm.Furthermore，the convergence rate of HMM-EA gradually accelerates with the increase of the number of cooperative users.However，with the increase of the number of cooperative users，signaling overhead and complexity also increase.It is worth mentioning the optimal number of cooperative users is studied in Ref.［18］.

Fig.7 Estimation performance ofA（2，2）compared with differentSNR，that is，SNR＝8 dB，SNR＝4 dB andSNR＝0 dB

Fig.8 Estimation performance ofλ，compared between HMM-EA and ED-EA algorithm

Fig.9 Estimation performance ofμ，compared between HMM-EA and ED-EA algorithm

Based on the previous analysis about HMM，Z1＝H1＝2，Z2＝TandH2＝1．In addition，Zis set to be5 000 andZ3can be obtained from the statistical results within evaluating HMM process.Therefore，the simulation results are shown as Fig.10.As is seen，with the increase of number of detection time slots，the complexity of the HMM-EA and ED-EA algorithm are both becoming more and more complex.Furthermore，the complexity of the HMM-EA algorithm is more complex than that of the ED-EA algorithm.From previous simulation pictures，we know that more detection time slots lead to better convergence performance.That means the HMM-EA algorithm sacrifices algorithm complexity performance to improve the convergence performance.

Fig.10 Complexity comparison between the HMM-EA and ED-EA algorithm

6 Conclusions

In this paper，we build the cognitive radio system as a preemptive priority queue，and then derive the real state transition probability matrix.Subsequently，the emission matrix is derived based on cooperative energy detection.According to these two matrixes，we build the HMM and thereby propose the HMM-EA algorithm，which sufficiently utilizes the inner collection among detection results to estimate traffic parameters of licensed channels.Due to the fact that cooperative energy detection can overcome the low signal to noise ratio or hidden terminal problem，the proposed HMM-EA algorithm has better convergence performance than ED-EA algorithm.Therefore，SUs can estimate busy probability of licensed channels，and access the optimal target channel.In this paper，the cooperative energy detection is discussed based on perfect report channel.So，in our future work，we will focus on imperfect report channel，which seriously impacts detection results.

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TN929.5

：

：1005-9113（2015）05-0061-08

10.11916／j.issn.1005-9113.2015.05.010

2014-08-01.

Sponsored by the National Natural Science Foundation of China（Grant No.61071104）.

∗Corresponding author.E-mail：tanxz1957＠hit.edu.cn.