modeling and predictability analysis on channel spectrum

Received May 25, 2021, accepted June 7, 2021, date of publication June 11, 2021, date of current version June 21, 2021.

Digital Object Identifier 10.1109/ACCESS.2021.3088123

Modeling and Predictability Analysis on ChannelSpectrum Status Over Heavy WirelessLAN Traffic EnvironmentYAFEI HOU 1, (Senior Member, IEEE), JULIAN WEBBER 2, (Senior Member, IEEE),KAZUTO YANO 3, (Member, IEEE), SHUN KAWASAKI1,SATOSHI DENNO1, (Member, IEEE), AND YOSHINORI SUZUKI31Natural Science and Technology, Institute of Academic and Research, Okayama University, Okayama 700-8530, Japan2Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan3Wave Engineering Laboratory, Advanced Telecommunications Research Institute International, Kyoto 619-0288, Japan

Corresponding author: Yafei Hou ([email protected])

This work was supported in part by the Japan Society for the Promotion of Science (JSPS) KAKENHI under Grant 20K04484.

ABSTRACT Using the real wireless spectrum occupancy status in 2.4 and 5 GHz bands collected at arailway station as representative of a heavy wireless LAN (WLAN) traffic environment, this paper studiesthe modeling of durations of busy/idle (B/I) status and its predictability based on predictability theory.We first measure and model the channel status in the heavy traffic environment over almost all of the WLANchannels at 2.4 GHz and 5 GHz bands in a busy (rush hour) period and non-busy period. Then, using twoselected channels at 2.4 GHz and 5 GHz bands, we analyze the upper bound (UB) and lower bound (LB)of predictability of the busy/idle durations based on predictability theory. The analysis shows that the LBpredictability of durations can be easily increased by changing their probability distribution. Based on thisproperty, we introduce the data categorization (DC) method. By categorizing the busy/idle durations intodifferent streams, the proposed data categorization can improve the prediction performance of some streamswith large LB predictability, even if it employs a simple low-complexity auto-regressive (AR) predictor.

INDEX TERMS Spectrum usage model, heavy WLAN traffic environment, cognitive radio, predictabilitytheory, auto-regressive predictor, data categorization.

I. INTRODUCTIONWireless communication technology has become one ofindispensable and integral parts for our society. Withthe increase of requirements for high capacity and largenumber access to support the coming of beyond 5G andcoming 6G era [1], some efficient techniques have beenproposed to further improve the spectrum efficiency whichare being discussed in the standardizing process of the nextgeneration wireless LAN [2]. One of the most intensivelyresearched paradigms in wireless communications is cogni-tive radio (CR) system which configures dynamically to usethe best wireless channels in its vicinity to avoid congestionand interference in a smart way [3], [4].

To achieve efficient spectrum usage, two relative researchtopics are important for CR systems [5]. Firstly, the channel

The associate editor coordinating the review of this manuscript and

approving it for publication was Mauro Fadda .

usage status or pattern model of frequency bands needs to bemodeled. An accurate and realistic spectrum occupancy pat-tern is essential and extremely useful in domain of dynamicspectrum access (DSA) or CR research. The correct patternmodels can be utilized in design of the DSA system, sys-tem analysis, the implementation of simulation tools and thedevelopment of more efficient DSA techniques. The otherimportant but challenging research topic is that the chan-nel status of spectrum usage at allocated frequency bandsneeds to be correctly predicted using efficient predictionmethods [6], [7].

For the model of spectrum usage, there are many investiga-tions based on measurement campaigns in different real envi-ronments [8]–[11]. The busy and idle durations of an IEEE802.11bWLAN operated at 2.4 GHz band has been describedusing a continuous-time semi-Markov chain (CTSMC)modelwhere the data is obtained from measurements using a vectorsignal analyzer [12]. Some more realistic traffic sources

VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 85795

https://orcid.org/0000-0003-1227-6920

https://orcid.org/0000-0001-7796-2898

https://orcid.org/0000-0003-2752-7534

https://orcid.org/0000-0002-0615-6546

Y. Hou et al.: Modeling and Predictability Analysis on Channel Spectrum Status Over Heavy Wireless LAN Traffic Environment

such as File Transfer Protocol (FTP), Voice over Inter-net Protocol (VoIP) [13] and Hypertext Transfer Protocol(HTTP) [14] have been researched for the fitting of thespectrum occupancy model. They found that the idle sojourntime is fitted to a generalized Pareto distribution [13] ora hyper-Erlang distribution. However, they just consideredan interference-controlled environment. In [14], the authorsanalyzed the distribution of busy and idle durations in areal indoor office environment with several wireless devicesoperated in the 2.4 GHz band. In [15], the wireless envi-ronments which include one-pair, two-pair, or three-pair802.11 networks with a prefixed separation distance of 1 mover 2.4GHz band have been investigated. In [16], the authorsinvestigated the time-dimension models of spectrum usagefor large systems from amateur systems (144–146 MHz)to open bands and ISM band (2.4–2.5 GHz). The authorsof [17] researched the space-dimension models of spectrumusage and provided the closed-form relations between theaverage spectrum occupancy in terms of the duty circleand some simple operation parameters such as noise power,false-alarm probability. In [18], the authors have researchedthe deterministic-stochastic duty circle model for the empir-ical data captured in one university laboratory over the2.4 GHz and 834–845 MHz bands. In [19], the authorscharacterized the radio frequency spectrum opportunitiesavailable in a common GSM (Global System for MobileCommunications) channel to support the operation of aCR network which employed a discrete GeneralizedPareto (dGP) distribution. In [20], the 2.4 GHz spectrum in ahospital environment in whichmedical devicesmakewirelessaccess has been characterized and modeled as a generalizedextreme value (GEV) distribution.

These researches consider real environments and provideprofound and significant results and deep understanding ofspectrum access of CR networks. However, some researchesonly consider some specific traffic sources such as FTP, VoIP,HTTP, Video, etc., and cannot be directly used for somereal scenarios where collected channel data includes multi-ple applications. In addition, most measurement campaigns,however, consider the wireless traffic involved with a smallnumber of users or devices which generates amoderate or lowwireless traffic. Until now, there has been seldom researchconsidering heavy WLAN traffic environments. Comparedwith low WLAN traffic environments, for the heavy WLANtraffic environments, more spectrum resources are requiredand cognitive radio technique is extremely important anddifficult to be realized [3]. Therefore, it is very valuable toresearch the modeling of wireless spectrum usage over heavyWLAN traffic environments.

On the other hand, compared with capturing channel sta-tistical information, the prediction of channel status is moredifficult and sometimes impossible. A tutorial paper [21]has summarized most of the existing prediction methods foroptimization of wireless resource allocation. These researchresults have provided many efficient methods for usage ofthe cognitive radio system. However, these researches are,

in the most part, considering the prediction of some keyparameters such as channel occupancy ratio (COR) with atime resolution unit of either seconds, hours or days. If thesystem can correctly predict the start and end of channel busyor idle duration, the system can more efficiently utilize theavailable radio resources and improve spectrum efficiency.For example, a CR system can be designed to utilize idleperiods scattered in multiple frequency bands by splitting onetransmission packet into small sub-packets [22], [23] thentransmitting on the multiple bands. However, for the channelstatus prediction over heavyWLAN traffic environments, it ismore difficult than that of over low WLAN traffic environ-ments because the channels in unlicensed bands are occupiedby a huge number of different services such as audio, videoor file transfer etc. Such unstable and disordered traffic datamakes the prediction intangible and difficult.

Therefore, for the data captured from the heavy WLANtraffic environments, some fundamental questions for the pre-diction of busy or idle durations are that: to what degree is thetime-series data predictable?Whether canwe improve its pre-dictability using some simple methods? For the predictabilityresearch, the references [24], [25] have investigated suchissues for radio spectrum state over TV bands, ISM bands,cellular bands, GSM900 and GSM1800 downlink bands.However, until now, there have been no any researches onthe spectrum status over heavy WLAN traffic environmentsand how to improve their lower bound value.

In this paper, we investigate the modeling of durations ofbusy/idle (B/I) spectrum status over a heavy WLAN trafficenvironment at a major railway station and its predictabilitybased on predictability theory. The major contributions andnovelties of this paper are as follows.(1) This paper investigates the spectrum usage status and

modeling analysis of wireless traffic data obtained at arailway station over almost all of WLAN channels at2.4 GHz and 5 GHz bands. For each channel, we mea-sured the spectrum usage status over 30 minutes andobtain enough data samples for the statistical analysis.The fitting modeling can provide realistic parameters forusage considering a scenario over heavy WLAN trafficenvironments.

(2) Our measurement utilized a commercially availablewireless LAN frame acquisition and analysis tool. Thetool is capable of capturing radio frames transmitted byIEEE 802.11 wireless LAN devices, and can measurereceived power, frame size, frame type and informa-tion on the IEEE 802.11 wireless LAN frame etc. Thecaptured data information can provide more realisticparameters for modeling the spectrum status of heavyWLAN traffic environment.

(3) Using spectrum busy/idle duration data of two selectedWLAN channels, we analyze the predictability of spec-trum status over heavy WLAN traffic environment.The upper bound and lower bound of predictability areprovided based on predictability theory. Although itis still unknown how to find a method to realize the

85796 VOLUME 9, 2021


upper bound (UB) of prediction, the analysis showsthat the lower bound (LB) of partial data can be easilyincreased by changing the probability distribution ofbusy/idle durations.

(4) Based on predictability analysis, we introduce the datacategorization (DC) on the busy/idle durations. By set-ting the preceding status durations into different ranges,the upcoming status durations can be distributed intodifferent categorization with different range. This cat-egorization will change the value of the predictabilityof partial data. The proposed data categorization canimprove the prediction performance of some streamswhich has better predictability than that of withoutDC even if the system employs a simple low-complexityauto-regressive (AR) predictor.

This paper is organized as follows. Section II describes themethodology utilized to capture and process the empiricaldata used for the validation of the mathematical models. Themeasurement environment and channel information are alsointroduced in this section. Section III examines the probabil-ity distribution models and the goodness of fit (GOF) metricsutilized to assess their suitability in fitting the obtained data.The mathematical models of channel occupancy status forboth 2.4 GHz and 5 GHz bands will be also analyzed andexplained in Section III. Then we analyze the predictability ofthe busy/idle durations of two selected channels in Section IV.The proposed data categorization (DC), which separates thebusy/idle durations into several streams with different dis-tribution property to improve the predictability of partialbusy/idle data, is explained in Section V. The AR-basedpredictor with proposed data categorization method and itsprediction performance are presented in Section VI. Thepaper ends with conclusions presented in Section VII.

II. MEASUREMENTS SETUP AND DATA CAPTUREIn this section, we first explain how the busy/idle durationsare collected in a real heavy WLAN traffic environment.

A. MEASUREMENT SETUPMeasurements were carried out at a major railway sta-tion in Japan during peak hour periods, within boththe 2.4 and 5 GHz bands. We selected 12 channels for mea-surements each at 2.4 GHz and 5 GHz bands for comparisonas shown in Table 1.Measurements were conducted at the endof January 2017.

TABLE 1. Selected channels (CHs) for measurement.

The experiments were performed using commerciallyavailable wireless LAN frame acquisition and analysis soft-ware. The capture software is able to record radio frames

transmitted by IEEE 802.11 wireless LAN devices in real-time, and canmeasure received power, frame-size, andmodu-lation scheme. In order to simultaneously capture the data onall channels, we employed 5 PCs, each equipped with 3 wire-less LAN systems with the interfaces, devices and modules.Information on the IEEE 802.11 wireless LAN frame, such asMAC information, can also be obtained. The measurementequipment was positioned in an aisle near the ticket-gateof a mainline railway station. When busy (around 18:30)there were several hundred people and streams of passengersconstantly arriving and departing.

B. FRAME ESTIMATION PROCEDUREThe MAC addresses were first anonymized to an integernumber in order to remove the identity of each STA. Frameduration is determined by the PHY preamble, MAC headerand Data sections. Frame duration is the estimated over-the-air channel time which includes the PHY preamble,MAC header and Data sections. The Data section duration isestimated from the Length field (Bytes), data-rate, protocoltype (IEEE 802.11a/b/n/ac), bandwidth, number of spatial-streams, and modulation and code scheme (MCS) data. TheLength field is used to determine the number of OFDMsymbols in the frame. In some corrupted frames the Datarate is not available and it is assumed that the Type is thesame as the previous frame. The PHY header of 20µs wasappended for IEEE 802.11a/g frames and 32+(nss×4)µsfor IEEE 802.11n frames where nss is the number of spa-tial streams. A MAC header of 30Bytes and 34Byteswas appended for IEEE 802.11a/g and IEEE 802.11n framesrespectively.

When two or more uncoordinated STA attempt to trans-mit to different APs at the same time and same bandwith sufficient power, a frame collision will occur. If theinterfering transmissions originate from enough distancethe interference may be sufficiently low to not result in aframe check sequence (FCS) error. However, some trans-missions will be corrupted, and these are reported byan FCS error when the cyclic redundancy check (CRC)fails.

In normal operation with most network interface con-trollers (NICs), a packet received with an FCS error will notbe passed on to the operating system. However, the capturesoftware and wireless adapter in monitoring mode allowedthis data to be captured and processed. It should also be notedthat as the wireless adapter is in a different physical locationto the AP, it is possible that the particular packet was notactually corrupted at the AP.

As the wireless adapters can only capture one frameat a time, when two transmissions occur, only one isable to be captured. Therefore, in that respect the num-ber of transmissions is under-reported. However, the STAthat was unable to complete its transmission will retrya transmission later, and this should eventually be cap-tured by the wireless adapter and therefore included in thestatistics.

VOLUME 9, 2021 85797


C. NON-IEEE 802.11 FRAMES AND VERIFICATIONRadio signals other than the IEEE 802.11 wireless LANframe such as generated by a microwave oven, a weatherradar, a Bluetooth device or such like cannot be capturedwith the software. For this reason, radio data of the same fre-quency bandwas captured using a radiomeasuring equipment(I/Q data recorder) that has a maximum reception bandwidthup to 200 MHz. An RF circuit corresponding to 2.4 GHz,or 5 GHz band is connected to the measuring equipment soas to receive and record all the radio signals in the band.In addition, we visualized the radio resource usage statusby converting the recorded radio signal data into a spectro-gram. The configuration of the measuring device is depictedin Fig. 1 and a photograph of the measurement system onlocation is shown in Fig. 2.

FIGURE 1. The configuration of the RF power measuring device.

FIGURE 2. Measurement system set-up on location.

The captured signal was also used to validate the resultsobtained by the capture software. The channel occupancyratio was computed in 1 minute intervals and compared withthe results from the frame capture. It was confirmed thatthere was a high correlation between the occupancy resultsobtained using the two methods.

D. SPECTROGRAMS OF THE MEASURED DATAThe spectrograms of the measured data over the 2.4 GHz and5 GHz bands are shown in Fig. 3 and Fig. 4, respectively.

FIGURE 3. Spectrogram of the measured data at a railway stationover 2.4 GHz band.

FIGURE 4. Spectrogram of the measured data at a railway stationover 5 GHz band.

As shown in both figures, there are more wireless traffic overthe 2.4 GHz bands than over the 5 GHz bands. On the otherhand, even for the channels over the busy 2.4 GHz band, somechannels have more traffic than others. The results reflect thatthe existing channel allocation methods are not fully efficientand a new method need to be found to mitigate the usageimbalance.

III. MATHEMATICAL MODELS OF CHANNEL OCCUPANCYSTATUS FOR 2.4 GHz AND 5 GHz BANDSAfter capturing the empirical channel occupancy data,we converted all data into binary patterns and then calcu-lated the length of the continuous busy and idle durationswith a small resolution of 9µs which accords with IEEEWLAN Standard [26]. It should be noted that the durationsof busy and idle are continuous which cannot be an integralmultiplication of 9µs because of wireless channel multipathfading and reflection or other factors. The empirical cumu-lative distribution function (CDF) and probability densityfunction (PDF) of busy or idle durations are calculated for the

85798 VOLUME 9, 2021


TABLE 2. Probability distribution models for fitting.

fitting of the mathematical distribution models. In this paper,we will show the fitting results using some major simpledistribution models listed in Table 2.

A. PROBABILITY MODELS AND GOODNESS OF FIT (GOF)METRICSThemajor simple distributionmodels considered in this paperare exponential (EX), generalized Pareto (GP), Log-normal(LN), Logistic (LG), generalized extreme value (GEV),gamma (GM) andWeibull (WB) distribution. EX distributionis largely utilized to obtain the validity of the widely usedMarkov chain model for traffic analysis and system design.However, many researchers reported that EX model is notaccurate in many real environments because the wirelesstraffic appears to have some self-similarity with heavy-tailedtrend [27]. Therefore, GP distribution is largely employedfor traffic analysis. Similar to GP distribution, LN, GM andWB distributions can be used for fitting wireless traffic withheavy-tailed trend.

Pareto distribution, GP, GM and WB distributions havebeen used for modeling wireless traffic. In addition, extremevalue theory (EVT) has been used as a rational frameworkfor the problem of burst prediction which needs only a subsetof the data to work on. In the burst prediction based onEVT, GEV distribution is used for modeling different typesof traffic and throughput [28], [29]. Therefore, we also selectGEV distribution as one of candidates for model fitting. Thesignificance of parameters in each distribution can be foundin [30].

We utilize a technique based on maximum likelihoodestimation (MLE), which is widely adopted as an efficientinference technique to calculate the distribution parametersfrom empirical data. In Ref. [16], the authors have consideredmethods of moment (MOM) inference scheme for estimat-ing the distribution parameters and compared with that ofMLE-based method. The results showed that the MLE-basedmethod generally outperforms that of MOM scheme.

Therefore, in this paper, we choose MLE-based method forcalculating the distribution parameters.

To show the suitability of the fitting, we use threeGOF metrics as Kolmogorov-Smirnov (KS) distance,Kullback-Leibler (KL) divergence [31] and Bhattacharyyadistance [32]. These GOF metrics can provide some numeri-cal values to show the matched level for a certain probabilitymodel fitting for the whole range of busy or idle durations.The superscript of sym is to be B or I. That corresponds tobusy or idle duration data, respectively.

The KS distance DsymKS between the CDF model of busyor idle duration F symfit (L) and empirical CDF of busy or idleduration F symemp(L) with duration length L (L > 0) [point] canbe denoted as

DsymKS (Fsymfit (L),F symemp(L))=max

L{|F symfit (L)−F symemp(L)|}. (1)

KS distance is typically used in the context of anon-parametric test which performs a hypothesis test to checkthe test distribution is the same as the reference. KS distancehas a symmetric property that the distance from one distri-bution to another is equal to the distance from the latter tothe former. In addition, if DA, DB and DC are distributions,KS distance has a property of triangle inequality as

DKS (DB,DC ) ≤ DKS (DB,DA)+ DKS (DA,DC ). (2)

Those properties make the KS distance powerful and conve-nient for the fitting of distribution model.

Kullback-Leibler (KL) divergence can be given as

DsymKL =P∑k=1

f symemp (Lk ) ln

(f symemp (Lk )

f symfit (Lk )

)

+

P∑k=1

f symfit (Lk ) ln

(f symfit (Lk )

f symemp (Lk )

). (3)

f symemp (Lk ) and f symfit (Lk ) are empirical PDF and evaluatedPDF model of busy or idle duration data. P is the number

VOLUME 9, 2021 85799


FIGURE 5. GOFs results for the fitting of channel occupancy status using data over all channelsof 2.4 GHz and 5 GHz bands.

of different data. The KL divergence is typically used ininformation-theoretic settings, hypothesis testing, or evenBayesian settings, to measure the information cross entropychange between distributions before and after applying someinference. KL divergence provides the information entropyloss level when the wrong fitting model is selected. Thismetric is often utilized for machine learning and wirelesssystem capacity optimization.

The Bhattacharyya distance DsymB as the GOF metric forPDF model f symsit (Lk ) and empirical PDF f symemp (Lk ) can berepresented as

DsymB = − ln

(P∑k=1

√f symfit (Lk )f

symemp (Lk )

). (4)

Different with the KS distance, Bhattacharyya distance isusually used to measure the similarity of two probability dis-tributions. Different with KS distance, it grows depending onthe difference between the standard deviations. Using Eq. (3)and Eq. (4), it is easy to deduce the relationship between theKL divergence and Bhattacharyya distance as

DsymKL ≥ 2DsymB . (5)

Due to this property, compared with KL divergence, Bhat-tacharyya distances of several fitting distribution functionshave small difference among them.

From Eqs. (1), (3) and (4), we can find that a small value ofthese GOF metrics means that the probability distributions ofmathematical models are well-fitted to that of the empiricaldata. When the values are zero, both mathematical modelsand distribution of empirical data are totally identical.

B. MODELS FITTING USING GOF METRICS FOR ALLCHANNELS OVER 2.4 GHz AND 5 GHz BANDSIn this section, we discuss suitable probability models forfitting the busy and idle durations. The major process washandled as follows. First, each CDF/PDF model in Table 2 isfitted to the empirical CDF/PDF of busy and idle durationscaptured at each channel based on MLE. Then the resultingGOF metrics, i.e. KS distance, KL divergence and Bhat-tacharyya distance, are evaluated between each empiricalCDF or PDF model of busy and idle durations and all listedCDF or PDF models. Finally, the best fitting model with thesmallest GOFs are selected as the probability models of thebusy or idle durations.

Since a user can select any channels over 2.4 GHz bandor 5 GHz band, to get the correctness of our fitting mod-els for channel busy or idle durations, we utilize all useddata of channels over 2.4 GHz band and over 5 GHz bandto find general models. The results of three GOF metricsare shown in Fig. 5. For KS value, the largest values aresmaller than 0.08 which show good fitting results for data.On the other hand, the data obtained at busy period has sim-ilar well-fitted results. That is, both busy and idle durationsappear a Weibull distribution over 2.4 GHz and generalizedextreme value distribution over 5 GHz band. On the otherhand, over 5 GHz band, all results show that generalizedextreme value distribution is a generally well-fitted distribu-tion model for all busy and idle duration data. This is dueto the fact that compared with that of 2.4 GHz, the wirelesstraffic over 5 GHz is low regardless of the busy or non-busyperiod.

Table 3 concludes the fitting distribution models and theparameters of the distribution models using data from all

85800 VOLUME 9, 2021


TABLE 3. Parameters values of fitting results [point].

FIGURE 6. Fitting results of channel status using data over all channels of 2.4 GHz and 5 GHz bands.

channels at 2.4 GHz band and 5 GHz band. Based on theresults of Table 3, we use Fig. 6 to show the fitting resultsof channel status over 2.4 GHz and 5 GHz bands. As shownin Fig. 6, the selected distribution models are well-fitted tothat of empirical busy and idle durations, especially for thedata of idle durations which supports our proposed fittingmodels in Table 3.

IV. PREDICTABILITY ANALYSIS FOR TIME-SERIES BUSYAND IDLE DATAAfter we obtain the statistics of busy or idle durations,a fundamental question for the prediction of time-series datais that: to what degree is the time-series data predictable?Regarding to this question, a methodology of using sta-tistical entropy measures and Fano inequality have beenproposed to quantify the degree of predictability for thereal-world time-series data [24], [25]. In the following sec-tions, we selected the busy and idle durations of Channel 1over 2.4 GHz band and Channel 36 over 5 GHz band foranalyzing their predictability and showing how to improvetheir predictability.

First, we give a simple explanation for the concept ofpredictability which can decide the fundamental limitationssuch as the performance bounds of the prediction method.

Let us suppose there is a random variate X with M kind ofvalues. Therefore, its entropy S(X ) can be represented as

S(X ) = −M∑i=1

f (xi) log(f (xi)), (6)

where f (x) is the probability density function (PDF)of X . In addition, for an n-length time-series data X as[x1, x2, . . . , xn], its average entropy can be represented as

S(X) = limn→∞

1nS(x1, x2, . . . , xn). (7)

Let us also define a conditional entropy as S(X′) with equa-tion as

S(X′) = limn→∞

S(xn|xn−1, xn−2, . . . , x1). (8)

When n → ∞, the average entropy S(X) is usually equal toconditional entropy S(X′) which is represented as

S(X) = limn→∞

1nS(x1, x2, . . . , xn)

= limn→∞

S(xn|xn−1, xn−2, . . . , x1)

= limn→∞

1n

n∑i=1

S(xi|hi−1) = limn→∞

1n

n∑i=1

S(i). (9)

VOLUME 9, 2021 85801


Here hi−1 and S(i) are given as hi−1=[xi−1, xi−2, . . . , x1] andS(i) = S(xi|hi−1), respectively.The n-length average entropy S(X) is difficult to

be obtained because it is determined by the value of[x1, x2, . . . , xn] and their joint PDF. Usually, such entropy canbe approximately calculated as SReal(X) using an iterativemethod called as Lempel-Ziv algorithm [33]. On the otherhand, when the correlation property between the time-seriesdata is not considered, the n-length average entropy canbe simply calculated as SUnc(X) only using the PDF oftime-series data as

SUnc(X) = −∞∑i=1

f (xi) log(f (xi)). (10)

The SReal(X) and SUnc(X) are two different metrics of dataentropy. The value of SReal(X) considers the interrelation-ships on the timeline of time-series data which is shown asthe definition of hi−1. In other words, the entropy differenceas (SUnc(X) − SReal(X)) can be regarded as the additionalinformation certainty obtained from analyzing the correla-tion properties of time-series data. If data has no correlationamong the data, the value of SReal(X) will be the same to thevalue of SUnc(X).For the predictability of time-series data, we define Pr as

the accuracy probability of one prediction method which isrepresented as

Pr = Prob{x̂n = xn|hn−1}. (11)

We suppose that there exists all predictionmethods which canachieve different prediction accuracy Pr . Therefore, the pre-dictability of one time-series data is the maximum valueamong all prediction methods as

5(hn−1) = sup{Prob[x̂n = xn|hn−1]}. (12)

For n-length time-series data, the average predictability prob-ability 5 is represented as

5 = limn→∞

1n

n∑i=1

5(i), (13)

with 5(i) , f (hi−1)5(hi−1).Finally, we can build the relationship between the pre-

dictability probability and the entropy of time-series datausing Fano inequality. From the information theory, the rela-tionship between the conditional entropy and the predictionerror probability Pe = Prob{x 6= x̂} can be represented usingFano inequality as

S(xn|hn−1) ≤ S(Pe)+ Pe log2(M − 1), (14)

and S(Pe) can be represented as

S(Pe) = −Pe log2(Pe)− (1− Pe) log2(1− Pe). (15)

Let p as the value of 5(hn−1) (Eq. (12)) to represent theprediction accuracy of the best one among all predictionmethods. For the best prediction method, we can let Pe

as (1− p). Therefore, using Eq. (14), the following equationcan be obtained.

S(xn|hn−1) ≤ −[p log2 p+ (1− p) log2(1− p)]

+ (1− p) log2(M − 1)

, SF (p) = SF (5(hn−1)), (16)

whereM is the number of different value of x. SF (p) functionis concave and monotonically decreases with p. Using thisrelationship, the lower bound and upper bound of predictabil-ity probability for time-series data can be represented as

SReal ≤ SF (5Real)

= −[5Real log25Real+ (1−5Real) log2(1−5

Real)]

+ (1−5Real) log2(M − 1), (17)

SUnc ≤ SF (5Unc)

= −[5Unc log25Unc+ (1−5Unc) log2(1−5

Unc)]

+ (1−5Unc) log2(M − 1). (18)

Using Eqs.(17) and (18), it is easy to find the lower bound5Unc and upper bound 5Real of predictability probabilitywhen their entropy SUnc and SReal can be calculated. For thedetail process, readers can find further information in [24]and [25]. However, it should be noted that 5Unc and 5Real

just provide the level or degree of difficulty of predictabilityprobability but not the actual prediction method. For sometime-series data, it is perhaps impossible to find an efficientmethod to achieve the value as5Real .

In this paper, we use a low-complexity Lempel-Ziv (LZ)algorithm [33] to find the relation between the busy and idledurations and then calculate the value of SReal . LZ algorithmis based on the Lempel-Ziv compression algorithm. For a timeseries of length n, the entropy can be estimated as

S =

(1n

∑i

Li

)−1ln(n) (19)

where Li is the longness of the shortest substring starting atposition iwhich does not previously appear from position 1 toi − 1. The estimated entropy converges to the real entropyof the time series when n approaches to infinity. It shouldbe noted, that due to limited memory and huge size of data,the Lempel-Ziv algorithm just utilizes partial data for theSReal calculation. For SUnc, we just use the PDF of the busyand idle durations and Eq. (10) to calculate the value.

Table 4 shows the values of SReal , SUnc, 5Real , 5Unc andM of busy and idle durations for Channel 1 and Channel 36,respectively. 5Real and 5Unc show that the predictability

TABLE 4. The entropy and predictability probability.

85802 VOLUME 9, 2021


probability for Channel 36 over 5 GHz has larger valuethan that of Channel 1 over 2.4 GHz band. In addition, forboth idle and busy durations at Channel 1, the LB of pre-dictability for methods only using PDF information can reachabout 29%–35%.When using the relation information amongthe data, the predictability can be improved to 47%–53% asUB values. On the other hand, for busy and idle durationdata captured over 5 GHz band, both LB and UB valuesof predictability are larger than that of over 2.4 GHz band.From Fig. 4 and Fig. 5, it is easy to know that the spectrumusage over 5 GHz band is rarer than that of 2.4 GHz bandwhich makes the distribution properties of both idle andbusy durations at 5 GHz band more concentrated than thatof 2.4 GHz band. Therefore, the predictability is higher thanthat of over 2.4 GHz band.

V. PREDICTABILITY IMPROVEMENT WITH DATACATEGORIZATIONFrom the previous section, we can find that the correlationproperty highly decides the predictability of time-series data.If there is no correlation among the succeeding data, suchas time-series data of additive white Gaussian noise, it isnot possible to find a larger predictability than that of 5Unc.In other words, the predictability difference as (5Real-5Unc)is from the correlation property among the succeeding data.Therefore, how to exploit the correlation property becomesa challenging and difficult target which involves in the datavolume, dimensions and length of time-series data.

It is difficult to find the correlation property of data in anydimensions. However, it is possible to derive the relationshipamong data with limited length. In this section, we firstshow such relationship of the busy/idle duration data of theprevious section. Then amethod named as data categorizationis explained to improve the predictability of the partial busyand idle duration data.

A. ADAPTIVE KERNEL DENSITY ESTIMATIONTo find the relationship among succeeding status durations,here we use adaptive kernel density estimation (AKDE) tech-nique to estimate the joint probability distribution of suc-ceeding status durations. AKDE is an adaptive method toapproximate the joint distribution by adjusting its samplingresolution in order to reduce the approximation error. Here,we just give a brief introduction of AKDE. The reader canfind its tutorial introduction in reference [34]. In addition,more research results on the relation of joint distribution ofsucceeding busy/idle durations has been reported in our paperas [35].

For density estimation, usually a histogram graph can pro-vide its density result but with many discontinuous points.Therefore, some smooth symmetric functions are employedto interpolate the adjacent density points to make the curvemore smooth. These smooth symmetric functions are termedas kernel function. There are many types of kernel functionsuch as fisher kernel, polynomial kernel etc. These functionsprovide different approximate capability by adjusting the

smallest interpolation resolution which is termed as band-width H.

Let us consider the analysis of a L-variate data (x1, . . . , xL)from an unknown density function, f (x), where x ∈ <L .Usually, a normal kernel with Gaussian distribution is utilizedfor density estimate. For AKDE, it adaptively adjusts thesmooth bandwidth h to achieve the smallest distance betweenthe estimated density f̂ (x) and the true density f (x). Usually,the mean integrated square error (MISE) is used for thislikelihood criterion as

MISE(f̂ ) = E{∫ [

(f (x,H)− f̂ (x))2]dx}

(20)

where matrix H is a smooth bandwidth matrix for adaptiveadjustment, and E{.} is the mean function over all x.For multivariate density estimation with a normal ker-

nel, K ∼ N (0, 6), the AKDE with n samples xi ∈ <L

(i = 1, . . . , n) is given by

f̂ (x) =1

n(2π )L/2|6|1/2

n∑i=1

e[−12 (x−xi)

′6(x−xi)]. (21)

It should be noted that AKDE can find an approximatedensity function for the data but neglects some small valuesin a joint distribution to minimize the scale value of MISE.In addition, due to adjusting bandwidth H and interpolation,some parts of the density function may be out of the originaldata range.

Figures 7 and 8 show the 2-D probability distributionobtained by AKDE for estimating the joint density of thebusy and idle duration data captured on a railway station overChannel 1 at the 2.4 GHz band and over Channel 36 at the5 GHz band. To find the relationship between the busy andidle durations, we generate two distributions. The first one(xTypei = Busy, xTypei+1 = Idle) means that the first data is busyduration and the second data is idle duration following theprevious busy one. The other one (xTypei = Idle, xTypei+1 =Busy)is the similar process but the first data is idle duration andthe second data is the following busy duration. It should benoted that two types have different meanings. The first typereflects how long the channel will be idle after transmitting asignal with a specific busy duration, and the second one showsthe signal duration after a specific idle duration. Therefore,it is expected that there is some difference between the twodistributions.

From both figures, we can find that over Channel 1 at the2.4 GHz band, the joint density has more separated areas thanthat of over Channel 36 at the 5 GHz band. The reason ismainly due to that more wireless traffic and types of servicesutilize the channel over the 2.4 GHz band than that of the5GHz band. Different type of service diversifies the busy-idleor idle-busy durations and creates more patterns.

Another interesting result is that data categorization as{xi+1|xi} has different range. For example with Fig. 7(a),when busy duration is below 50 points, the idle durationis mainly below 240 points. On the other hand, when busyduration is between 150 points to 250 points, the idle duration

VOLUME 9, 2021 85803


FIGURE 7. Probability distribution of 2-D succeeding B/I durationobtained by AKDE (railway station @ Channel 1, 2.4 GHz band).

is mainly below 450 points which has a larger range on dataduration.

To further show the relationship of recent status durationsand the next status duration, we show the probability distri-bution of 3-D succeeding status duration obtained by AKDEin Fig. 9 for Channel 1 in the 2.4 GHz band and Fig. 10in Channel 36 in the 5 GHz band. We also generate twodistributions for each channel. The first one as (xTypei =Busy,xTypei+1 = Idle, xTypei+2 = Busy) is for two continuous channelstatuses (xi, xi+1) and the upcoming status (xi+2) is busy. The

other one is with (xTypei = Idle, xTypei+1 = Busy, xTypei+2 = Idle)for two continuous channel durations (xi, xi+1) with the nextone (xi+2) as idle. Both figures show the data categorizationas {xi+2|xi+1, xi} will have different range especially for thedata from Channel 1 in the 2.4 GHz band. For example withFig. 9(a), when busy duration (xi) is below 50 points and idleduration (xi+1) is below 100 points, the busy duration (xi+2)is mainly below 100 points. When increasing the range of xiand xi+1, the value of busy duration (xi+2) is distributed ina larger range. In addition, the value of idle duration (xi+2)in Fig. 9(b) mainly distributes a larger range in each data

FIGURE 8. Probability distribution of 2-D succeeding B/I durationobtained by AKDE (railway station @ Channel 36, 5 GHz band).

category than that of busy duration in Fig. 9(a). It should benoted that each categorized distribution in the 5 GHz bandusually has a smaller range compared with that of data in the2.4 GHz band.

From the relationships of 2-D and 3-D succeeding statusdurations, by setting the previous status durations into differ-ent ranges, the upcoming status durations can be distributedinto different categorization with different range. This datacategorization can be used for improving the prediction accu-racy for some categorizations where durations are distributedwith a smaller range.

B. DATA CATEGORIZATIONAlthough the predictability just provides ameasurement scaleto show whether data is easy to be predicted or not, it cannotprovide how to realize its upper bound or even lower boundwith a specific prediction method. For some data, it is notpossible to find one best prediction method to achieve itsupper bound. Usually, the lower bound of predictability onlydepends on the PDF of data, the higher LB means that data isseldom changed with large range. In this case, the data is easy

85804 VOLUME 9, 2021


FIGURE 9. Probability distribution of 3-D succeeding status durationobtained by AKDE (railway station @ Channel 1, 2.4 GHz band).

for prediction. Therefore, if the lower bound of predictabilityof time-series data is enlarged, the prediction accuracy ofsome prediction methods might be improved. However, forsome prediction methods which explore the time relationshipamong the time-series data, it is hard to further improve theirprediction accuracy.

From the previous sections, by setting the preceding statusdurations into different ranges, the upcoming status durationscan be distributed into different categorization with differ-ent range. This categorization will change the value of thepredictability of partial data. Based on this idea, we proposedata categorization to separate time-series data into differentstreams. The major idea is shown in Fig. 11 using busy/idleduration data as one example. The captured time-series busyor idle duration data xi can be divided into four streamsaccording to the sets (S1, S2) that the previous values xi−2and xi−1 belong to. As the example shown in Fig. 11, bothbusy and idle durations have two sets as (B_set1, B_set2)and (I_set1, I_set2) with different non-overlap ranges,

FIGURE 10. Probability distribution of 3-D succeeding status durationobtained by AKDE (railway station @ Channel 36, 5 GHz band).

FIGURE 11. Data categorization for busy and idle durations.

respectively. The busy duration Xi will be separated to thebusy stream # 4 if previous busy duration Xi−2 and idleduration Xi−1 belong to B_set2 and I_set2, respectively.The idea can be extended to K layers. The captured busy

and idle durations are firstly processed by a B/I duration cate-gorization with K layers and each layer has Si (i = 1, . . . ,K )sets. Therefore, there are Sall (Sall =

∏i=Ki=1 Si) different

streams. By setting the ranges of sets and number of layers

VOLUME 9, 2021 85805


and sets, the data categorization can separate all time-seriesdata into different streams with different statistical propertiesand predictability.

Figure 12 shows how the proposed method works for theprediction of partial time-series data (stream #1). When thecondition that (xi−1, xi) ∈ (Bset1, Iset1) is met, the predictionmethod is activated for the predicted busy duration xi+1. Theprevious n-length busy data ([xB#1k−n+1, x

B#1k−n+2, . . . , x

B#1k ])

which belongs to stream #1 has been saved for prediction inadvance. The prediction process includes two steps:

FIGURE 12. Example using data categorization for partial data prediction(stream # 1).

(1) update the n-length busy data as [xB#1k−n+2, xB#1k−n+3, . . . ,

xB#1k , xB#1k+1] with xB#1k+1 = xi−1.

(2) predict the next busy duration x̂i+1 using one specificprediction algorithm.

It should be noted that data categorization is not limited tothe continuous succeeding data such as using n-length dataXn([xi−n+1, xi−n+2, . . . , xi]) for estimating the data xi+1. It canbe upgraded to utilize Xn for predicting the l-th coming dataxi+l if the correlation between Xn and xi+l exists and thecorrelation property is clarified.

C. PREDICTABILITY IMPROVEMENT USING DATACATEGORIZATIONTo show the effectiveness of data categorization, we set thelayer number K as 2. Both busy and idle durations are cat-egorized with two sets which is similar to that of Fig. 11.We also consider two configurations of set ranges whichare shown in Table 5, and they are named as CASE I andCASE II, respectively. CASE II has the larger range thanthat of CASE I to show the impact on predictability fromthe different statistical property of each stream. After datacategorization, each busy/idle stream is calculated with thevalues of SReal , SUnc,5Real ,5Unc andM using LZ algorithmand their PDFs, respectively. In addition, to show how the DCchanges the values of SUnc and 5Unc, the PDF of each busyor idle stream after DC process is also provided.Figures 13 and 14 show the PDF of busy and idle dura-

tion captured from Channel 1 of 2.4 GHz band with DCfor CASE I and CASE II, respectively. For comparison,the PDF results of all busy or idle duration data with-out DC are also provided in each figure. From all figures,it can be found that DC diversifies the PDF of each stream.

TABLE 5. Set range settings [point].

FIGURE 13. PDF of busy / idle duration with and without DC (railwaystation @ Channel 1, 2.4 GHz band, CASE I).

From the Eq. (6), the concentrated PDF which distributedwith large values over a concentrated range usually has thesmaller entropy than that of non-concentrated one. UsingFig. 13(a) as an example, compared with that of busy durationwithout DC, the stream #1, which occupies about 17% of allbusy durations, shows a concentrated PDF property. There-fore, it should have a smaller SUnc and then a larger lowerbound 5Unc than that of busy durations without DC. Withthe same reason, it also can be found that DC deteriorates thelower bound5Unc of other three streams. On the other hand,when the range of each set is changed, the PDF of each streamis also adjusted as shown in both Figs. 13 and 14 whichmakesdifferent 5Unc for each stream.

Table 6 and Table 7 show the entropy and predictabil-ity probability of busy/idle duration data obtained fromChannel 1 after data categorization with CASE I andCASE II, respectively. As a comparison, the entropy andpredictability of busy and idle data without DC are listedin both tables. From both tables, which are in accord withthe previous figures and analysis, it can be found that the

85806 VOLUME 9, 2021


FIGURE 14. PDF of busy / idle duration with and without DC (railwaystation @ Channel 1, 2.4 GHz band, CASE II).

TABLE 6. The entropy and predictability probability with datacategorization (Channel 1, CASE I).

TABLE 7. The entropy and predictability probability with datacategorization (Channel 1, CASE II).

proposed method can increase lower bound 5Unc of the firststream, especially for busy data.

However, although DC can increase the lower bound5Unc

of some streams by adjusting their PDF properties, it ishard to improve their UB values 5Real . The major reason isthat the value of 5Real is mainly decided by the correlationproperties among the time-series data, and DC is difficult todeepen these correlation properties in each stream by settingdifferent layer number or set ranges. On the contrary, inap-propriate ranges of sets sometimes make the predictability oftime-series data decrease becauseDCweakens the correlationproperties among data in such case.

Figures 15 and 16 show the PDF of busy and idle durationcaptured fromChannel 36 of 5GHz bandwith DC for CASE Iand CASE II, respectively. These figures show the similarresults to that of Figs. 13 and 14. Table 8 and Table 9 showthe entropy and predictability probability of busy/idle dura-tion data obtained from Channel 36 after DC with CASE Iand CASE II, respectively. Compared with the busy data ofChannel 1 over 2.4 GHz band, busy durations are short whichare also shown in Figs. 13 and 14. The probability distributionof busy duration will be more concentrated than that of over2.4 GHz band. Therefore, both SReal and SUnc of busy datais smaller than that of data obtained over 2.4 GHz band.In addition, using data categorization, the similar results tothat of Table 6 and Table 7 are obtained.

FIGURE 15. PDF of busy / idle duration with and without DC (railwaystation @ Channel 36, 5 GHz band, CASE I).

From the results of all tables, we can find that the proposedDC can change the 5Real and 5Unc, especially for 5Unc,

VOLUME 9, 2021 85807


FIGURE 16. PDF of busy / idle duration with and without DC (railwaystation @ Channel 36, 5 GHz band, CASE II).

TABLE 8. The entropy and predictability probability with datacategorization (Channel 36, CASE I).

of selected partial data from all time-series data. Therefore,the proposed method improves the prediction accuracy ofthese partial data using some simple prediction methods.

VI. BUSY/IDLE DURATION PREDICTION USINGAUTO-REGRESSIVE PREDICTOR WITH DATACATEGORIZATIONIn this section, we will use a simple auto-regressive (AR)predictor to compare the prediction accuracy of time-seriesdata with and without the proposed data categorization.

A. AUTO-REGRESSIVE (AR) PREDICTORAuto-regressive (AR) model is a representation of a typeof random process [36]. The AR model specifies that the

TABLE 9. The entropy and predictability probability with datacategorization (Channel 36, CASE II).

FIGURE 17. Busy/idle duration prediction using the proposed method(railway station @ Channel 1, 2.4 GHz band, CASE I).

current value is only related to its own previous values and astochastic term; thus the model is in the form of a stochasticdifference equation.

The AR-based predictor with order p can be represented as

X̂i+1 = a1Xi + a2Xi−1 + . . . apXi−p+1. (22)

Here we use Xi to represent the duration of busy or idle status.The parameters [a1, . . . , ap] are calculated using training dataso that they give the solution as the least squares for linearregression. The reader can find more details of AR modelin [36].

85808 VOLUME 9, 2021


FIGURE 18. Busy / idle duration prediction using the proposed method(railway station @ Channel 1, 2.4 GHz band, CASE II).

TheAR predictor for the busy/idle duration prediction withdata categorization is almost identical structure as shownin Fig. 12. Here AR predictor is operated in each stream,independently. During the training process, k-th data streamutilizes its previous M durations to calculate the parameters[ak1, . . . , a

kp]. Then the following N durations are predicted

using the similar equation as Eq. (22) for each data stream.For comparison, we also provide the prediction performanceof busy or idle durations without data categorization, whichmeans only one data stream with all busy or idle durations areused for training and prediction process.

B. PREDICTION PERFORMANCE OF AR USING DATACATEGORIZATIONWe assume that the AR predictor uses the durations of theprevious 200 busy/idle durations to calculate a1 to ap oncefor predicting the durations of the upcoming 200 busy/idlestatues (M = 200,N = 200). In preliminary simulations,we have set the AR order p with different value and foundthat AR predictor with p = 2 can get the best predictionperformance. In this paper, we just provide the results ofAR predictor with p = 2. For data categorization, we uti-lize the same configurations of set ranges, which are shownin Table 5, as CASE I and CASE II. For the results of eachstream, we also provide the ratio of the data in this streamto all data to show the percentage of data with differentprediction performance.

FIGURE 19. Busy / idle duration prediction using the proposed method(railway station @ Channel 36, 5 GHz band, CASE I).

The evaluated prediction performances are shownin Fig. 17 for busy /idle duration prediction for CASE I andin Fig. 18 for CASE II on Channel 1 over the 2.4 GHz band.The x-axis shows the prediction error (Err) and y-axis showsthe complementary cumulative distribution function (CCDF)of prediction error which shows that the prediction error isnot smaller than Err.

Both figures show that the proposed method can differen-tiate the prediction performance of each stream, especiallyfor busy duration prediction. The proposed data catego-rization shows better prediction performance for the stream#1 with 17% and 26% total data for CASE I and CASE IIthan that of without categorization process, respectively. Forone example, the proposed DC of stream #1 can improveabout 37% and 32% prediction accuracy when Err is rangedamong [−15, 15] points. On the other hand, for idle durationprediction, two range settings cannot improve the predictionperformance. However, from Table 6 and Table 7, we canfind the prediction results match highlywith the predictabilityresults, especially with 5Unc. The proposed data categoriza-tion can improve the prediction accuracy of partial data evenif system employs a simple AR predictor.

The prediction performances are shown in Fig. 19 forbusy/idle duration prediction for CASE I and in Fig. 20for CASE II on Channel 36 over the 5 GHz band.For data captured from Channel 36 in 5 GHz band, generally,

VOLUME 9, 2021 85809


FIGURE 20. Idle duration prediction using the proposed method (railwaystation @ Channel 36, 5 GHz band, CASE II).

busy duration prediction performs reasonably well and ourproposed method can further improve its accuracy for thestream #1. The major reason is that the busy duration onChannel 36 distributes within a small range and data cate-gorization will further reduce its range. For idle duration pre-diction, the stream #1 of both CASE I and CASE II evidentlyshows better prediction performance than that of without DC.From the occurrence ratio of each stream, all figures showthat our proposed method can improve the prediction per-formance for over about 20% of the total idle data and overabout 12% of the total busy data. From Table 8 and Table 9,we can also find the prediction results match highly with thepredictability results. The proposed data categorization canimprove the prediction accuracy of a part of data.

It should be noted that it is still a challenge to find thesuitable parametersK , Si at the i-th layer and the range of eachset to optimize the predictability and prediction performancebecause the real-environment traffic data includes many ser-vice combinations and mixed traffic pattern. In addition, howto find the optimal prediction method to achieve the upperbound of predictability is still open issue. These issues areour ongoing research topics.

VII. CONCLUSIONThis paper first investigated the spectrum occupancy sta-tus and its modeling analysis for a heavy WLAN trafficenvironment at a major railway station. Our measurements

can provide more realistic parameters for considering sce-narios over heavy WLAN traffic environments. The fittingmodels of busy and idle duration can be used as a com-plement for building useful models such as interferencemodel, simple multi-band CR spectrum occupancy model forCR system research. We then analyzed the predictabilityanalysis on busy/idle durations of two selected channels at the2.4 GHz and 5 GHz bands. From the predictability analysis,we proposed a method called data categorization to separateall busy/idle durations into several streams with differentdistribution property. This separation facilitates some streamsto be more easily predicted. The results show that, evenusing a simple AR based predictor, data categorization canimprove the prediction accuracy of some streams with a highpredictability.

ACKNOWLEDGMENTThe authors would like to thank Ministry of Internal Affairsand Communications of Japan for providing the data forresearch purpose in this paper.

REFERENCES[1] A. Ijaz, L. Zhang, M. Grau, A. Mohamed, S. Vural, A. U. Quddus,

M. A. Imran, C. H. Foh, and R. Tafazolli, ‘‘Enablingmassive IoT in 5G andbeyond systems: PHY radio frame design considerations,’’ IEEE Access,vol. 4, pp. 3322–3339, 2016.

[2] E. Khorov, I. Levitsky, and I. F. Akyildiz, ‘‘Current status and direc-tions of IEEE 802.11be, the future Wi-Fi 7,’’ IEEE Access, vol. 8,pp. 88664–88688, 2020.

[3] R. Struzak, ‘‘Cognitive radio, spectrum, and evolutionary heuristics,’’IEEE Commun. Mag., vol. 56, no. 6, pp. 166–171, Jun. 2018.

[4] C. Jiang, H. Zhang, Y. Ren, Z. Han, K.-C. Chen, and L. Hanzo, ‘‘Machinelearning paradigms for next-generation wireless networks,’’ IEEEWirelessCommun., vol. 24, no. 2, pp. 98–105, Apr. 2017.

[5] M. Song, C. Xin, Y. Zhao, andX. Cheng, ‘‘Dynamic spectrum access: Fromcognitive radio to network radio,’’ IEEE Wireless Commun., vol. 19, no. 1,pp. 23–29, Feb. 2012.

[6] H. Sun, A. Nallanathan, C.-X. Wang, and Y. Chen, ‘‘Wideband spectrumsensing for cognitive radio networks: A survey,’’ IEEE Wireless Commun.,vol. 20, no. 2, pp. 74–81, Apr. 2013.

[7] C. Sun, G. P. Villardi, Z. Lan, Y. D. Alemseged, H. N. Tran, and H. Harada,‘‘Optimizing the coexistence performance of secondary-user networksunder primary-user constraints for dynamic spectrum access,’’ IEEE Trans.Veh. Technol., vol. 61, no. 8, pp. 3665–3676, Oct. 2012.

[8] M. H. Islam, C. L. Koh, S.W. Oh, X. Qing, Y. Y. Lai, C. Wang, Y.-C. Liang,B. E. Toh, F. Chin, G. L. Tan, and W. Toh, ‘‘Spectrum survey in singa-pore: Occupancy measurements and analyses,’’ in Proc. 3rd Int. Conf.Cognit. Radio Oriented Wireless Netw. Commun. (CrownCom), Singapore,May 2008, pp. 1–7.

[9] L. Stabellini, ‘‘Quantifying and modeling spectrum opportunities in a realwireless environment,’’ in Proc. IEEE Wireless Commun. Netw. Conf.,Sydney, NSW, Australia, Apr. 2010, pp. 1–6.

[10] S. Contreras, G. Villardi, R. Funada, and H. Harada, ‘‘An investigationinto the spectrum occupancy in japan in the context of TV white spacesystems,’’ in Proc. 6th Int. ICST Conf. Cognit. Radio Oriented WirelessNetw. Commun., Osaka, Japan, 2011, pp. 341–345.

[11] Y. Chen and H.-S. Oh, ‘‘A survey of measurement-based spectrum occu-pancy modeling for cognitive radios,’’ IEEE Commun. Surveys Tuts.,vol. 18, no. 1, pp. 848–859, 1st Quart., 2016.

[12] S. Geirhofer, L. Tong, and B. Sadler, ‘‘A measurement-based modelfor dynamic spectrum access in WLAN channels,’’ in Proc. MILCOM,Oct. 2006, pp. 1–7.

[13] S. Geirhofer, L. Tong, and B. M. Sadler, ‘‘Dynamic spectrum access inWLAN channels: Empirical model and its stochastic analysis,’’ in Proc. 1stInt. Workshop Technol. Policy Accessing Spectr. (TAPAS), 2006, pp. 1–10.

85810 VOLUME 9, 2021


[14] S. Geirhofer, L. Tong, and B. M. Sadler, ‘‘Dynamic spectrum access inthe time domain: Modeling and exploiting white space,’’ IEEE Commun.Mag., vol. 45, no. 5, pp. 66–72, May 2007.

[15] S. A. Rajab, W. Balid, and H. H. Refai, ‘‘Toward enhanced wirelesscoexistence in ISM band via temporal characterization and modellingof 802.11b/g/n networks,’’ Wireless Commun. Mobile Comput., vol. 16,no. 18, pp. 3212–3229, Nov. 2016.

[16] L. B. Miguel and F. Casadevall, ‘‘Time-domain model of spectrum usagefor the analysis, design, and simulation of cognitive radio networks,’’ IEEETrans. Veh. Technol., vol. 62, no. 5, pp. 2091–2104, Jun. 2013.

[17] L. B. Miguel and F. Casadevall, ‘‘Space-domain model of spectrum usagefor cognitive radio networks,’’ IEEE Trans. Veh. Technol., vol. 66, no. 1,pp. 306–320, Jan. 2017.

[18] K. Umebayashi, M. Kobayashi, and M. Lopez-Benitez, ‘‘Efficient timedomain deterministic-stochastic model of spectrum usage,’’ IEEE Trans.Wireless Commun., vol. 17, no. 3, pp. 1518–1527, Mar. 2018.

[19] M. O. Al Kalaa, W. Balid, H. H. Refai, N. J. LaSorte, S. J. Seidman,H. I. Bassen, J. L. Silberberg, and D.Witters, ‘‘Characterizing the 2.4 GHzspectrum in a hospital environment: Modeling and applicability to coex-istence testing of medical devices,’’ IEEE Trans. Electromagn. Compat.,vol. 59, no. 1, pp. 58–66, Feb. 2017.

[20] M. Luis, R. Oliveira, R. Dinis, and L. Bernardo, ‘‘RF-spectrum oppor-tunities for cognitive radio networks operating over GSM channels,’’IEEE Trans. Cognit. Commun. Netw., vol. 3, no. 4, pp. 731–739,Dec. 2017.

[21] N. Bui, M. Cesana, S. A. Hosseini, Q. Liao, I. Malanchini, and J.Widmer, ‘‘A survey of anticipatory mobile networking: Context-basedclassification, prediction methodologies, and optimization techniques,’’IEEE Commun. Surveys Tuts., vol. 19, no. 3, pp. 1790–1821, 3rd Quart.,2017.

[22] N. Egashira, K. Yano, S. Tsukamoto, J. Webber, M. Sutoh, Y. Amezawa,and T. Kumagai, ‘‘Integrated synchronization scheme for WLAN systemsemploying multiband simultaneous transmission,’’ in Proc. IEEE WirelessCommun. Netw. Conf. (WCNC), San Francisco, CA, USA, Mar. 2017,pp. 1–5.

[23] K. Yano, N. Egashira, J. Webber, M. Usui, and Y. Suzuki, ‘‘Achievablethroughput of multiband wireless LAN using simultaneous transmissionover multiple primary channels assisted by idle length prediction basedon PNN,’’ in Proc. Int. Conf. Artif. Intell. Inf. Commun. (ICAIIC), Naha,Okinawa, Feb. 2019, pp. 22–27.

[24] G. Ding, J. Wang, Q. Wu, Y.-D. Yao, R. Li, H. Zhang, and Y. Zou, ‘‘On thelimits of predictability in real-world radio spectrum state dynamics: Fromentropy theory to 5G spectrum sharing,’’ IEEE Commun. Mag., vol. 53,no. 7, pp. 178–183, Jul. 2015.

[25] J. Sun, L. Shen, G. Ding, R. Li, andQ.Wu, ‘‘Predictability analysis of spec-trum state evolution: Performance bounds and real-world data analytics,’’IEEE Access, vol. 5, pp. 22760–22774, 2017.

[26] IEEE Standard for Information Technology—Part 11: Wireless LANMedium Access Control (MAC) and Physical Layer (PHY) Specifications,Standard IEEE 802.11-2016, 2016.

[27] M. Wellens, J. Riihijärvi, and P. Mähönen, ‘‘Empirical time and frequencydomain models of spectrum use,’’ Phys. Commun., vol. 2, nos. 1–2,pp. 10–32, Mar. 2009.

[28] M. Uchida, ‘‘Traffic data analysis based on extreme value theory and itsapplications,’’ in Proc. IEEE Global Telecommun. Conf. (GLOBECOM),Nov. 2007, pp. 1–7.

[29] C. Liu, Y. Shu, J. Liu, and O. W. W. Yang, ‘‘Application of extreme valuetheory to the analysis of wireless network traffic,’’ in Proc. IEEE Int. Conf.Commun., Jun. 2007, pp. 486–491.

[30] P. Sahoo, Probability and Mathematical Statistics. Louisville, KY, USA:Univ. of Louisville, 2013.

[31] W. H. Press, S. A. Teukolsky, W. T. Vertterling, and B. P. Flannery,Numerical Recipes, The Art of Scientific Computing, 3rd ed. Cambridge,U.K.: Cambridge Univ. Press, 2007.

[32] A. Bhattacharyya, ‘‘On a measure of divergence between two statisticalpopulations defined by their probability distributions,’’ Bull. CalcuttaMath. Soc., vol. 35, no. 1, pp. 99–109, 1943.

[33] I. Kontoyiannis, P. H. Algoet, Y. M. Suhov, and A. J. Wyner, ‘‘Nonpara-metric entropy estimation for stationary processes and random fields, withapplications to English text,’’ IEEE Trans. Inf. Theory, vol. 44, no. 3,pp. 1319–1327, May 1998.

[34] D. Scott and S. Sain, ‘‘Multi-dimensional density estimation,’’ Hand-book of Statistics, vol. 24, pp. 229–261, Apr. 2005, doi: 10.1016/S0169-7161(04)24009-3.

[35] Y. Hou, K. Yano, S. Denno, and Y. Suzuki, ‘‘A study on joint prob-ability distribution property of busy/idle duration and its impact onthe performance of auto-regressive based predictor over real environ-mental channel,’’ IEICE Technique Rep., vol. 118, no. 475, pp. 89–96,Mar. 2019.

[36] R. Shumway and D. Stoffer, Time Series Analysis and Its Applications:With R Examples. New York, NY, USA: Springer-Verlag, 2010.

YAFEI HOU (Senior Member, IEEE) receivedthe dual Ph.D. degree from Fudan University,China, and the Kochi University of Technology(KUT), Japan, in 2007. He was a PostdoctoralResearch Fellow with Ryukoku University, Japan,from August 2007 to September 2010. He wasa Research Scientist with the Wave EngineeringLaboratories, ATR Institute International, Japan,from October 2010 to March 2014. He becamean Assistant Professor at the Graduate School of

Information Science, Nara Institute of Science and Technique, Japan, fromApril 2014 toMarch 2017. He became an Assistant Professor at the GraduateSchool of Natural Science and Technology, Okayama University, Japan,since April 2017. He was a Guest Research Scientist with the Wave Engi-neering Laboratories, ATR Institute International, from October 2016 toMarch 2021. His research interests include communication systems, wire-less networks, and signal processing. He is also a member of IEICE.He received the Institute of Electronics, Information and CommunicationEngineers (IEICE) Communications Society best paper awards in 2016 and2020, and the Best Tutorial Paper Award, in 2017.

JULIAN WEBBER (Senior Member, IEEE)received the M.Eng. degree from the Univer-sity of Bristol, U.K., in 1996, and the Ph.D.degree from the University of Bristol, in 2004.He worked with Texas Instruments Europe, fromSeptember 1996 to October 1998. He was aResearch Fellow with the University of Bris-tol, from November 2001 to August 2007, andwith Hokkaido University, Japan, from Septem-ber 2007 to March 2012. He was a Research Sci-

entist with the Wave Engineering Laboratories, ATR Institute International,Japan, from April 2012 to March 2018. He became an Assistant Professorwith Osaka University, since April 2018, and a Guest Research Scientistwith ATR. His research interests include signal processing, and wirelesscommunication systems design and implementation. He is also a memberof IEICE.

KAZUTO YANO (Member, IEEE) received theB.E. degree in electrical and electronic engineer-ing and the M.S. and Ph.D. degrees in commu-nications and computer engineering from KyotoUniversity, in 2000, 2002, and 2005, respectively.He was a Research Fellow with the Japan Soci-ety for the Promotion of Science (JSPS), from2004 to 2006. In 2006, he joined the AdvancedTelecommunications Research Institute Interna-tional (ATR). He is currently the Head of the

Department of Wireless Communication Systems, Wave Engineering Labo-ratories, ATR. His research interests include space-time signal processing forinterference suppression, MIMO transmission, and PHY/MAC cross-layerdesign of wireless communication systems for ISM bands. He is also a SeniorMember of IEICE. He received the Institute of Electronics, Information andCommunication Engineers (IEICE) Communications Society Best TutorialPaper Award, in 2017, and the ICAIIC 2019 Excellent Paper Award, in 2019.

VOLUME 9, 2021 85811

http://dx.doi.org/10.1016/S0169-7161(04)24009-3

http://dx.doi.org/10.1016/S0169-7161(04)24009-3


SHUN KAWASAKI received the B.S. andM.S. degrees from Okayama University, Japan,in 2019 and 2021, respectively. His research inter-ests include signal processing, and wireless com-munication systems.

SATOSHI DENNO (Member, IEEE) receivedthe M.E. and Ph.D. degrees from KyotoUniversity, Kyoto, Japan, in 1988 and 2000,respectively. He joined the NTT Radio Commu-nications Systems Laboratories, Yokosuka, Japan,in 1988. In 1997, he was seconded to the ATRAdaptive Communications Research Laborato-ries, Kyoto. From 2000 to 2002, he worked withNTT DoCoMo, Yokosuka. In 2002, he moved toDoCoMo Communications Laboratories Europe

GmbH, Germany. From 2004 to 2011, he worked as an Associate Professorwith Kyoto University. Since 2011, he has been a Full Professor with theGraduate School of Natural Science and Technology, Okayama University.From the beginning of his research career, he has been involved in theresearch and development of digital mobile radio communications. In par-ticular, he has considerable interests in channel equalization, array signalprocessing, space time codes, spatial multiplexing, and multimode reception.He received the Excellent Paper Award from IEICE, in 1995.

YOSHINORI SUZUKI received the B.E., M.E.,and Ph.D. degrees from Tohoku University,Sendai, in 1993, 1995, and 2005, respectively.He joined theNTTWireless Systems Laboratories,in 1995. Since then, he involved in researchingmicrowave signal processing techniques for satel-lite onboard applications and onboard multiplebeam antenna feed techniques. He worked as apart-time Lecturer with Niigata University, from2012 to 2014. From 2013 to 2014, he was in charge

of sales engineering of satellite communication services in NTT SoftwareCorporation (currently NTT TechnoCross Corporation). Since then, he wasa Research Engineer with the NTT Access Network Service Systems Lab-oratories working on future mobile satellite communication systems. SinceJune 2018, he has been involved in the research of innovative radio com-munication systems with the ATR Wave Engineering Laboratories, Kyoto,Japan.

85812 VOLUME 9, 2021

modeling and predictability analysis on channel spectrum

Documents