SVM-based Fuzzy Inference System (SVM-FIS) for Frequency Calibration in Wireless Networks

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1 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON COMMUNICATIO AND INFORMATION TECHNOLOGY SVM-based Fuy Inference System SVM-FIS for Frequency Cabraton n Wreess Networks Wang-Hsn Hsu, Y-Yuan Chang, Wen-Yen Ln, We-Chen Ta, and Jung-Shyr Wu Abstract To guarantee the connectvty n wreess networks s an mportant ssue. For ths purpose, we have to provde precse frequency for the network such that t can meet the varous requrements of future appcatons. In ths paper, we not ony propose a nove frequency cabraton methodoogy based on SVM-based fuy nference system SVM-FIS n wreess networks, but aso aganst temporary faure of wreess connecton. There are two modes norma mode and handover mode n the cabraton system. In norma mode, the prmary cock can perodcay devers the controng sgnas to steer the remote staton s oven-controed crysta oscator OCXO through the wreess connecton. Once the wreess connecton was temporary crashed, the staton swtches to hodover mode whch the SVM-FIS controer takes over sendng the controng sgnas from prmary cock to steer ts OCXO. Expermenta resuts ndcate that performance of frequency stabty of the OCXO can be mproved from a few parts n 0 9 to 0 3 for averagng tmes of one day, and the performance can be mantaned wthn a few parts n 0 over a day n hodover mode. Keywords Frequency cabraton, frequency stabty, fuy Modes, hodover, OCXO, SVM. I. INTRODUCTION To guarantee the connectvty n wreess networks s an mportant ssue. For exampes, wreess mesh networks WMNs are dynamcay sef-organed and sef-confgured wth the nodes n the network automatcay estabshng an ad hoc network and mantanng the mesh connectvty []; wreess networks such as CDMA, 3GPP, WBro and WMAX [8], [4], [9], [0] have strct requrements of connectvty to meet the end user s quaty of servce QoS for rea tme voce, vdeo and gamng appcatons. In partcuar, WMAX has a profound effect on today s wreess networks. Tme and frequency accuracy s crtca to the effcency of the WMAX base staton. For the purpose of assurng the connectvty of wreess networks, we not ony have to mantan tme synchronaton, but aso have to preserve frequency syntonaton. There have been a ot of studes on tme synchronaton. The Insttute of Eectrca and Eectroncs Engneers IEEE 588 standard defned a precson tme protoco PTP enabng precse synchronaton of cocks n measurement and Manuscrpt receved December 5, 009. Wang-Hsn Hsu s wth the Dept. of CSIE, Vanung Unversty, Chung, Taoyuan, Tawan and the Dept. of EE, Natona Centra Unversty, Chung, Taoyuan, Tawan e-ma: kmbe@vnu.edu.tw. Y-Yuan Chang s wth the Dept. of CSIE, Vanung Unversty, Chung, Taoyuan, Tawan phone: ext. 765; e-ma: yychang@vnu.edu.tw Wen-Yen Ln s wth the Dept. of EE, Vanung Unversty, Chung, Taoyuan, Tawan e-ma: qqnce@vnu.edu.tw We-Chen Ta s wth the Dept. of DP, Ku-Pao home economcs & commerca hgh schoo, Tape, Tawan e-ma: dgf530@ms.hnet.net Jung-Shyr Wu s wth the Dept. of EE, Natona Centra Unversty, Chung, Taoyuan, Tawan e-ma: jswu@wreess.ee.ncu.edu.tw contro systems mpemented usng dstrbuted archtectures comprsed of evovng technooges n network communcaton [7]. In [9], Sar et a. consdered the jont maxmum kehood JML estmaton of cock offset and skew under exponenta nose mode n the Reference Broadcast Synchronaton RBS protoco to deveopng hghy accurate cock synchronaton protocos on, the more unstabe, ADSL network. On the other hand, for frequency syntonaton, the technques whch base on G Dscpned Oscators GDOs s one of the prncpa approaches for mantanng frequency dssemnaton gobay [3], [5], [5], [6]. These scheme can acheve the traceabty of frequency dssemnaton and obtan hgh frequency stabty. However, the weather condton s an essenta factor to affect stabe communcaton from the satete to statons n a G system. Therefore, t s worthwhe to fnd another approach that can avod the weather factor and mantan the frequency syntonaton n an acceptabe naccuracy. In [6], Hsu et a. frst adopted soft computng approach for frequency syntonaton. They uted adaptve neura-fuy nference systems ANFIS [0] to earn the behavor of a prmary cesum cock and to adjust a ow-cost oven-controed crysta oscator OCXO for frequency cabraton. However, the gradent-decent-based ANFIS controer may ead to a oca mnmum probem so that the performance of the controer s nhbted. In order to resove the oca mnmum probem, the support vector machne SVM s an vabe aternatve. SVMs have been recenty ntroduced as a technque for sovng pattern cassfcaton probems [7], [8]. It can be seen as an approxmaton mpementaton of what Vapnk defned as structure rsk mnmaton, as an nductve prncpe that ams at mnmng an upper bound on the generaaton error of a mode. Durng structure rsk mnmaton, an optma pane coud be found wthout encounterng the oca mnmum probems such as neura networks [0]. Therefore, SVMs have been recogned as a superor method for modeng [3]. In ths paper, we adopt SVM-based fuy modeng for frequency syntonaton n a cabraton system whch contans a master server and n remote statons. The master server conssts of a prmary cesum cock as we as a sgna sender. In a remote staton, a ngustc fuy controer [4], an SVM- FIS controer, and a ow-cost crysta oscator are but. The ngustc fuy controer aong wth the SVM-FIS controer have to mprove the performance of the ow-cost crysta oscator utng the sgna of cesum cock perodcay. There are two modes norma mode and handover mode n the cabraton system. In norma mode, the performance of the crysta oscator s mproved by more than three orders of ISBN: ISSN:

2 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON COMMUNICATIO AND INFORMATION TECHNOLOGY magntude stabty mprovement under the fuy controer. In ths mode, the contro messages from the output of the fuy controer are coected for tranng the SVM-FIS. When the nput frequency source ost the wreess connecton goes down, the system enters hodover mode, n whch the SVM- FIS then repaces the roe of the fuy controer to generate contro sgnas for steerng the oscator. Expermenta resuts ndcate that performance of frequency stabty of the OCXO can be mproved from a few parts n 0 9 to 0 3 for averagng tmes of one day, and the performance can be mantaned wthn a few parts n 0 over a day n hodover mode. The rest of ths paper s organed as foows. The SVMbased fuy nference system s descrbed n Secton. Then, the proposed system archtecture s shown n Secton 3. The effectveness of ths scheme s demonstrated through expermenta resuts and anayss n Secton 4 foowed by Concusons n Secton 5. II. SVM-BASED FUZZY INFERENCE SYSTEM In what foows, we frst gve the basc dea of support vector machnes, and then expan how to extract a fuy system from a SVM and show the functona equvaence between SVMs and fuy systems. Suppose we are gven a set of tranng data: {x, y, x, y,..., x, y } X R, where X denotes the space of the nput patterns. In ε support vector regresson [7], the goa s to fnd a functon fx that has at most ε devaton from the actuay obtaned targets y for a the tranng data, and at the same tme s as fat as possbe. That s, the errors woud be gnored as ong as they are ess than ε, but any devaton arger than ths woud not be accepted. For near regresson cases, we want to fnd near functons f, takng the form fx = w, x + b wth w X, b R where, denotes the nner product n the nput space X. In order to acheve the crteron of ε support vector regresson, an ε-nsenstve oss functon [3] s ntroduced: { 0 f ξ ε ξ ε =. 3 ξ ε otherwse Then, the task can be wrtten as a convex optmaton probem: mnme w + C subject to ξ + ξ y w, x b ε + ξ w, x + b y ε + ξ. 4 ξ, ξ 0 The constant C > 0 determnes the trade-off between that fatness of f and the amount up to whch devatons arger than ε are toerated [3]. The key dea to sove 4 s to construct a Lagrangan functon from the objectve functon and the correspondng constrants, by ntroducng a dua set of varabes. The dua quadratc programmng regresson probem s α α α j αj x, x j,j= maxme 5 ε α + α + y α α subject to α α = 0 and α, α [0, C]. The vector w has the form and f can be wrtten as fx = w = α α x 6 α α x, x + b. 7 For the cases of nonnear regresson, the tranng patterns x are preprocessed by a mappng Φ : X F nto some feature space F and appyng the standard SV regresson agorthm. The mappng Φ need not to be known snce t s mpcty defned by the choce of kerne functons K: Kx, x j = Φx, Φx j. 8 The decson functon f n 7 becomes fx = α α Kx, x + b. 9 The nput ponts x wth α α 0 are caed support vectors. The dfference to the near case s that w s no onger gven expcty. Besdes, the task becomes to fnd fattest functon n feature space, not n the nput space. Equatons 8 and 9 can be graphcay depcted as shown n the efthand-sde of Fg.. The steps from top to bottom s expaned as foows: a fattest regresson curve that has at most ε devaton error from the actuay obtaned targets y for a the tranng data s obtaned; support vectors x, =,,..., that wth α α 0 are extracted; 3 each x s mapped nto a feature space va a nonnear functon Φ; 4 nner product Φx, Φx s substtuted by a kerne functon K as equaton 8; 5 weghted summaton of Kx, x assocated wth weght α α pus a bas b generate the fna output fx. On the other hand, a fuy system s a set of IF-THEN rues n the foowng form: R j : If x s A j then y s B j for j =,,..., M, 0 where x, y X R; A j and B j are ngustc terms charactered by membershp functons µ A j x and µ B j y, respectvey. Notaby, µ A j x s a membershp functon defned on a mut-dmentona vector whch s defned as µ A j x = Π n µ A j x. ISBN: ISSN:

3 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON COMMUNICATIO AND INFORMATION TECHNOLOGY u3, v3 sncx+0.5 sncx-0.5 approxmaton u, v u, v u4, v4 u, v support vectors φ : N R R k φ x, φ x u u u3 u4 φ x φ x φ x3 φ x4 u φ x Σ output Support vector machne equvaent u u u3 u4 u p x p x p x p x 3 4 p x 3 Σ output 4 Gaussan membershp functons x x µ x = exp σ fuy bass functons n p x = Π µ x / Πµ x j j j = A = A j= j= Fuy nference system M j x u j = v j exp[ ] σ n Fg.. SVMs and Fuy Modeng The nference process s shown as beow: membershp vaues actvaton. The membershp vaues of nput varabes are computed as t-norm operator and the center of Gaussan membershp functons are seected as j = α α. 7 Π n µ A j x. the fna output can be computed as M j= fx = j µ A j x M j= µ. 3 Aj x In order to et equaton 9 and 3 are equvaent, at frst we have to et the kerne functons n 9 and membershp functons n 3 are equa. The most frequenty used membershp functons are trange, trapeoda, Gaussan, and Be-shaped. Among these membershp functons, ony the Gaussan membershp functons can be chosen as the kerne functons snce the Mercer condton [] shoud be satsfed. Besdes, the bas term b of the expresson 9 shoud be 0. Whe the Gaussan functons to be chosen as the kerne functons and membershp functons, and the number of rues equas the number of support vectors, then 9 and 3 becomes fx = α α exp x x 4 and fx = σ j= j exp xj x j= exp σ j xj x. 5 σ j The nference of fuy systems can be modfed as [] fx = j exp xj x, 6 j= σ j Then, the output of fuy system 3 s equa to the output of SVM 9. However, the equvaence has some shortcomngs: the modfed fuy mode removes the normaaton process; therefore, the modfed fuy mode sacrfces the generaaton. the nterpretabty cannot be provded durng the modfcaton. An aternatve approach s to set the kerne functon of SVMs as Kx, x = exp x x σ. 8 exp x x σ Consequenty, the output of SVMs becomes j= α α exp xj x σ j fx =. 9 j= exp xj x σ j We ony have to set the center of membershp functons to α α, then we can assure the output fuy systems 9 and the output of the SVMs 4 are equa. Notaby, the expresson 8 ony can be acheved when the number of support vectors,, s known prevousy. The SVM approach utes a nonnear mappng to transform the orgna tranng data nto a hgher dmenson feature space. Wthn the new dmenson t searches for a near optma hyperpane wth owest error measure w + C ξ + ξ 0 ISBN: ISSN:

4 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON COMMUNICATIO AND INFORMATION TECHNOLOGY RSn Prmary Cock RS _ Frequency Offsets Estmaton K yτ K y τ Lngustc Fuy Controer Kout D/A OCXO RS SVM-FIS Controer Sgna Sender Wreess Network Fg. 3. The fuy contro bock dagram. Fg.. System archtecture. Remote Staton to each cass. The geometrca nterpretaton of the method s to fnd a maxma separaton between subsets of the convex hus of the data. Whe the data of dfferent casses cannot be ceary separated, a hyperpane wth east ntersectons of the convex hus s found. Support vectors are ponts beng ocated at the edges of convex hus wth east dstances to the hyperpane. Therefore, support vectors can be extracted as the centers of membershp functons such that the extracted fuy rues can separate the dfferent data set wth smaest error measures. III. THE PROPOSED SYSTEM ARCHITECTURE Fg. dspays a functona bock dagram of the proposed system. There s one master server and n remote statons denoted by RS, RS,..., RS n n the ad hoc wreess envronment. The master server contans a prmary cesum atomc cock and software sgna sender nstaed on PC. The sgna sender encapsuate frequency sgna nto a packet and the sgna coector decapsuate the packet nto orgna frequency sgna. Every remote staton contans software sgna coector, TIC, an oven-controed crysta oscator OCXO and a D/A converter. The frequency offsets between the prmary cock and the OCXO are measured by the TIC. The offsets y τ and ts change y τ are fed nto a fuy controer as presented n Fg. 3. The frequency of ow-cost oscator can typcay be fney tuned by controng the votage. Envronmenta effects such as vbraton, temperature, pressure and humdty cause the desred frequency to be output not aways wth a constant votage. In the proposed system, the frequency offset wth respect to tme y τ t and ther change y τ = y τ t y τ t are the nput varabes of the fuy controer. An ncrementa votage V t generated by the fuy controer s used to update the votage for steerng the oscator as beow: V + = V + V t The system has two modes. In the norma mode, the save cock s synchroned wth the prmary cock under the fuy contro va wreess connecton. The contro messages are coected smutaneousy to tran the SVM-FIS. When the Fg. 4. y τ y τ Fuy rues tabe. sgna of the prmary cock s ost, the system enters hodover mode. The votage that s predcted by the SVM-FIS controer, rather than the orgna votage s used as the contro message to steer the OCXO n ths mode. The fuy controer n the proposed system attempts to generate a contro message to steer the OCXO. Fg. dspays the bock dagram of the fuy controer apped n our system. The nference engne part s the knowedge-base of a fuy controer, whch has two components, the data base and the fuy contro rue base. The nput space s dvded nto fve sets: negatve bg, negatve sma, ero, postve sma and postve bg for a frequency offset or ts change. The tabe of fuy rues s shown n Fg. 3. In ths work, tranguar-shaped membershp functons MFs are used as the contro nput varabes because of ther smpcty and ease of computaton. The sets were desgned to be coser to the desred vaue of ero to provde precse contro. The contro output s determned by the center-average method, whch s formuated as foows: where u 0 = K out n w u, n u K out : output contro gan; w : grade of th output MF; u : output abe for vaue contrbuted by the th MF; n : number of contrbutons from the rues. The rues of the fuy controer are based on the process frequency offset and ts changes y τ. These rues are expressed as foows and FIG.. 4 presents the fuy rues tabe. ISBN: ISSN:

5 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON COMMUNICATIO AND INFORMATION TECHNOLOGY a x a x x 0-3 b x x 0-3 b x c x c x 0 4 Fg. 5. a The desred data. b The predcted data. c The predcton error. Fg. 6. a The desred data. b The predcted data. c The predcton error. IV. EXPERIMENTAL RESULTS AND ANALYSIS Fg. 5 presents the expermenta setup for testng. A 0 MH of a cesum atomc cock HP507A s used as the prmary cock. An OCXO FTS30 s uted as the save cock. The D/A converter ADLINK PCI-608 apped n the system has a 6-bt resouton wth the b-poar output votage rangng from -0V to +0V. The software that runs the fuy controer n norma mode, the SVM-FIS controer n hodover mode and coects the data s desgned n MATLAB. The Sgna Sender and the Sgna Coector as a socket program s desgned n C/C++. Ths study chose about fve-day nput-output data pars of the foowng format: [xt 3τ, xt τ, xt τ, xt; xt + τ] The frst four-day pars were used for tranng the SVM-FIS whe the remanng about one-day pars were used for vadatng the dentfed mode. After 00 epochs, RMSE chk = V was acheved. Fg. 5 pots the desred data, the predcted data and the predcton error. In Fg. 6, the frst four-day pars were used for tranng the SVM-FIS whe the remanng about one-day pars were used for vadatng the dentfed mode. In ths experment, the connecton between the sgna sender and the sgna coector may crash temporary, the connecton recover from faure after a coupe mnutes. In Fg. 6c, the predcton error means the system runnng under the norma mode. After 00 epochs, RMSE chk =. 0 4 V was acheved. Fg. 6 pots the desred data, the predcted data and the predcton error. Ths work examned the performance of the free runnng OCXO used n the proposed system n order to compare the resuts wth the performance of the OCXO under the fuy and the SVM-FIS contro. These frequency anayes are shown n Fg. 7. The Free Runnng ne n Fg. 7 shows the frequency nstabty, especay over the ong term. The Norma ne shows the typca resuts of a frequency stabty anayss of the OCXO under contro va wreess communcaton sendng contro message perodcay. The Hodover Temporary ne presents the system swtch between norma and hodover mode due to the connecton some tme up and some tme down. The Modfed Aan devaton Modσ y τ Frequency stabty Free Runnng Averagng tme seconds, τ Hodover Hodover Temporary Norma Fg. 7. Frequency stabty anayss of the free runnng OCXO Free runnng ne, the hodover mode Hodover ne, Hodover temporary Hodover temporary ne, and the norma mode Norma ne. ast Hodover ne ndcates the performance of the OCXO coud be mantaned better than the free runnng OCXO at east one order. The performance of the free runnng used n the proposed system, OCXO, was examned under the fuy controer, whe the SVM-FIS controer was apped to predct the contro messages n hodover mode. Fg. 7 presents the frequency anayses. The free runnng ne ndcates that the OCXO runs freey wthout any contro messages. The norma ne reveas that the OCXO was steered usng the prmary cock va n a manner controed by fuy controer. The frequency stabty of the OCXO coud be mproved from a few parts n 0 0 to 0 3 for averagng tmes of one day n norma mode. The hodover temporary ne reveas that the OCXO was steered usng the prmary cock va n a manner controed by fuy controer underng the connecton n wreess network. It s sometmes connected and sometmes dsconnected n ad hoc envronment. Therefore, the hodover temporary mode consders unreabe stuaton. The frequency stabty of the OCXO coud be mproved from a few parts n 0 0 to 0 ISBN: ISSN:

6 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON COMMUNICATIO AND INFORMATION TECHNOLOGY for averagng tmes of one day n norma mode. Fnay, the Hodover ne shows that the system oses reference frequency from the prmary cock; the SVM-FIS controer takes over to predct contro message and send wth the contro message to OCXO. The performance of the OCXO s mantaned a few parts n 0 over 4 hours. The SVM-FIS controer exhbts hgh frequency stabty not ony over the short term, but aso over the ong term. V. CONCLUSIO The connectvty n wreess mut-hop networks such as ad hoc and sensor networks cannot be guaranteed. Each node acts as a reay for other nodes, the hosts are free to eave out or jon nto the communcatons system. It s mportant to provde a hodover capabty when the connecton temporary crashed. Ths study estabshes not ony the feasbty of usng SVM- FIS for frequency cabraton n hodover mode but aso a save cock foow by a master server wth hgh accuracy n norma mode va wreess connecton. The presented expermenta resuts demonstrate that the frequency stabty of the OCXO can be mproved from a few parts n 0 0 to a few parts n 0 3 for averagng tmes of one day n norma mode, and the frequency stabty can be mantaned at around a few parts n 0 over one day n hodover mode. [5] Kun-Yuan Tu, Fan-Ren Chang, Cha-Shu Lao, and L-Sheng Wang, Frequency Syntonaton Usng G Carrer Phase Measurements, IEEE Transactons on Instrumentaton and Measurement pp , 00. [6] K. Y. Tu, W. H. Hsu, J. S. Wu, and C. S. Lao, Frequency Cabraton Based on Adaptve Neura-Fuy Inference System, The CPEM 008, Broomfed, Coorado, June 8-3, 008. [7] V. N. Vapnk, The Nature of Statstca Learnng Theory, 995. [8] V. N. Vapnk, Statstca Learnng Theory, 998. [9] A. J. Vterb, CDMA: Prncpes of Spread Spectrum Communcaton, Addson Wesey, 995. [0] 3GPP TS 5.33: Requrements for support of rado resource management FDD, Reease 6, V 6..0, December 005. REFERENCES [] Akyd, I.F., Xudong Wang, A survey on wreess mesh networks, IEEE Communcatons Magane, Vo. 43, Issue 9, pp. S3 - S30, Sept [] J.-H. Chang and P.-Y. Hao, Support vector earnng mechansm for fuy rue-based modeng: a new approach, IEEE Trans. on Fuy Systems, vo., pp., 004. [3] J. A. Davs, B. Rougeaux, The deveopment of a computer mode of a G dscpned oscator to ad error budget determnaton, Frequency and Tme Forum, 999 and the IEEE Internatona Frequency Contro Symposum, vo., pp. 9-95, 3 Apr 999. [4] D. Dranko, H. Heendoorn, and M. Renfrank, An Introducton to Fuy Contro, New York: Sprnger-Verag, 99. [5] P. Eskenen, Observatons on stabty measurements of commerca atomc cocks, Frequency and Tme Forum, 999 and the IEEE Internatona Frequency Contro Symposum, vo., pp , 3 Apr 999. [6] Wang-Hsn Hsu, Kun-Yuan Tu, Jung-Shyr Wu, and Cha-Shu Lao, Frequency Cabraton based on the Adaptve Neura-Fuy Inference System, IEEE Transacton on Instrumentaton and Measurement, vo. 58, no. 4, 009. [7] IEEE Std , IEEE Standard for a Precson Cock Synchronaton Protoco for Networked Measurement and Contro Systems, 00. [8] IEEE Std. 80.6e TM -005 and IEEE 80.6 TM -004/Cor-005, IEEE, New York, USA. [9] Ikay Sar, Erchn Serpedn, Kyoung-Lae Noh, Qasm Chaudhar, and Bruce Suter, On the Jont Synchronaton of Cock Offset and Skew n RBS-Protoco, IEEE Transactons on Communcatons, vo. 56, no. 5, May 008. [0] J.-S. R. Jang, ANFIS: Adaptve Network-based Fuy Inference System, IEEE transactons on Systems, Man, and Cybernetcs, vo. 3, no. 3, pp , June 993. [] C. W. T. Nchos, G. C. Careton, Adaptve OCXO drft correcton agorthm, IEEE Frequency Contro Symposum and Exposton, pp , 004. [] J. Shawe-Tayor and N. Crstann, Kerne Methods for Pattern Anayss. U.K.: Cambrdge Unversty Press, 004. [3] A. J. Smoa and B. Schoekopf, A tutora on support vector regresson, Statstcs and Computng, vo. 4, pp. 99, 004. [4] TTA Std. Specfcatons for.3 GH Band Portabe Internet Servce Physca Layer, TTA, Korea, June 004. ISBN: ISSN: