Accurate Forecasting of Underground Fading Channel Based on Improved LS-SVM Anyi Wang1, a, Xi Xi1, b

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1 nd Workshop on Advanced Research and echnology n Industry Applcatons (WARIA 06) Accurate Forecastng of Underground Fadng Channel Based on Improved LS-SVM Any Wang, a, X X, b College of Communcaton and Informaton Engneerng, X an Unversty of Scence and echnology, X an, 70054, Chna a emal: wangany@xusteducn, bemal: @qqcom Keywords: Channel Forecastng; LS-SVM; Fadng Channel; Abnormal Data Abstract Amng at the shortcomngs of tradtonal fadng channel forecastng algorthms, least square support vector machne(ls-svm) s appled to predctng underground fadng channel In lght of complcated and changeable underground envronment, the measured data may be abnormal hus, an mproved LS-SVM wth abnormal data detecton s proposed n ths paper to forecast underground fadng channels hs algorthm utlzes ampltude of the fadng channel as observed values to establsh studyng model and then mplements nonlnear predcton wth the help of learnng and judgment ablty of LS-SVM he experment shows that the predcton algorthm based on mproved LS-SVM rases the predcton accuracy of fadng channels and s an effectve and feasble nonlnear fadng channel forecastng method Introducton In a communcaton system, t s crucal for recever to obtan channel characterstcs n advance, whch s helpful to acheve adaptve modulaton and demodulaton and adaptve power control technology radtonal predcton algorthms of fadng channel are manly based on lnear ones [][] However, due to the complcated nonlnear characterstcs of the channel, lots of nonlnear algorthms attract much more attenton, such as neural network and support vector machne (SVM) [3] eural network has slow convergence rate and s easy to fall nto the local mnmum LS-SVM s an mproved algorthm of standard SVM, whch s a machne learnng method based on structural rsk mnmzaton prncple and overcomes the problems of neural network It has been successfully appled to varous felds In ths paper the LS-SVM s used to construct underground akagam fadng channel predcton model And consderng the abnormal underground data, LS-SVM s mproved durng data processng to detect and elmnate the abnormal data he feasblty and effectveness of the method are verfed by expermental results akagam Dstrbuton he underground tunnel dffers from ndoor multpath envronment, wth well-observed roughness and many obstacles whch lead to severe reflecton, dffracton and scatterng phenomena herefore, the receved sgnal s syntheszed by multpath sgnals akagam dstrbuton, Raylegh dstrbuton and Rce dstrbuton can be used to descrbe the multpath fadng n hgh frequency (HF) channel he Raylegh dstrbuton s often used to smulate fast fadng n HF channel of short dstance In lght of long dstance channel, t s qute rough to adopt the Raylegh dstrbuton [4] akagam dstrbuton can descrbe dfferent characterstcs through changng the parameter m Raylegh and Rce are specal cases for certan values herefore t s reasonable to adopt akagam dstrbuton to descrbe the small scale multpath fadng n underground mne akagam dstrbuton s also known as m-dstrbuton whose probablty densty functon s as follows [5]: 06 he authors - Publshed by Atlants Press 449

2 m m m r mr pr ( ) = exp( ) m Γ( m) Ω Ω () In the equaton, m x m x e dx Γ ( ) = s Gamma functon Ω=E[r ] s second-order central moments, 0 average power m = E [ r ] Var [ r ] represents fadng factor, whch ndcates fadng severty of transmtted sgnal resulted from multpath effects he smaller the value m s, the more serous the fadng; otherwse, the less serous the fadng When m=05 and m=, the dstrbuton transforms nto unlateral Gauss dstrbuton and Raylegh dstrbuton separately When m>, t s very smlar to Rcan dstrbuton And the relatonshp between the two dstrbutons s shown n equaton () ( K + ) m = ( K + ) () Among the equaton, K s the Rcan factor Compared to Raylegh or Rcan, akagam can descrbe dstrbutons of dfferent statstc characterstcs by changng the value m herefore, akagam fadng channel model s more flexble and convenent to characterze the dfferent degrees of fadng of multpath sgnals under the mne [6] Improved LS-SVM Based on Abnormal Data Detecton LS-SVM algorthm LS-SVM ntroduced least square method nto SVM he correspondng Lagrange functon s defned Wth the KK condtons a set of lnear equatons are acheved and by solvng the equatons the resoluton of the problem s ganed n For a gven tranng data set: ( x, y),,, lx, R, y R he tranng data of orgnal space R n s mapped to feature space φ ( x ) by takng advantage of nonlnear mappng functon φ() he optmal decson functon n the hgh-dmenson feature space s as follows [7]: yx ( ) = ωφ ( x) + b (3) hus, nonlnear regresson estmaton functon n orgnal space transformed to lnear functon n feature space o search for the parameters ω and b by usng structural rsk mnmzaton prncple s to mnmze R= ω + γ R emp (4) Among the Eq, ω s the ncredble rsk whch ndcates the complexty of model, Remp s the emprcal rsk and the value γ s regularzaton parameter whch controls the penalty degree of error sample he optmzaton problem of LS-SVM s presented n Eq 5 l γ mn J ( wx, ) = w + x (5) st y = w φ( x) + b+ x, =,, l Lagrange functon s defned as Eq 6[8]: L( ω, be,, α) = ωω+ γ ζ α( ωφ( x) + b+ ζ y) (6) Among the equaton, α are the Lagrange factors Accordng to KK condtons, partal dervatve s calculated: 450

3 L = 0 ω= αφ ( x) ω L = 0 α = 0 b (7) L = 0 α = γx x L = 0 ω φ( x) + b+ x y = 0 α For =,, l, ω and ξ are elmnated and then get 0 b 0 K( x, x) + K( x, xn ) c α y (8) = αn yn K( xn, x ) K( xn, xn) + c Among the Eq 6, K s a square matrx of whch K ( ) j = φ x φ( xj ) = K( x, xj ) for the element at row and column j K(,) s the kernel functon α and b can be obtaned by least square method and the predcted output s shown n Eq 9 l y = αφ( x) φ( x ) + b l = α Kxx (, ) + b j LS-SVM Predcton wth Abnormal Data Detecton In underground envronment, electromagnetc wave has refracton, reflecton and dffracton phenomenon durng propagaton [9] and due to the mne equpment, vehcles and personnel, nose jammng could be hgh herefore, the ampltude of the receved sgnal may be greatly changed, resultng n undesrable samplng data In LS-SVM model, data are dvded nto support vectors, whch are dvded nto boundary support vectors and non boundary support vectors, and non support vectors Only part of α resolved from Eq 9 are not zero and ther correspondng tranng samples are support vectors[0] So, the correspondng to abnormal data meet the condtons that α = γ Combned wth the analyss of the LS-SVM, the procedure of abnormal data detecton s as follows[] ) Establsh LS-SVM model wth the orgnal data ) When usng the model to regresson estmatng, fnd the samples whch meet the condtons that α = γ Calculate the resduals between predcton values and orgnal values hat s to calculate E = y yˆ, where y s orgnal value and y ˆ predcton value 3) Accordng to the actual needs and accuracy of the data, the constant ε s defned If E (9) α > ε, the y wth the same subscrpt s an abnormal sample and elmnate y A new estmated value y s reganed for ( x, y ) to replace the abnormal one 4) Rebuld the LS-SVM model wth the revsed data, comparng the performance wth the former one Smulaton Experment and Dscusson In the experment, the parameters of the akagam channel model are set as follows Carrer frequency s 3GHz Maxmum Doppler frequency shft s 06Hz m parameter of akagam dstrbuton s set to tranng samples and 400 test samples are generated on ths bass In 45

4 order to verfy the accuracy of the method n ths paper, the abnormal data s added to replace the orgnal samples he nserton method s as follows o avod the concentraton phenomenon of random nserton data, the tranng set are dvded nto four groups [,00], [0,00], [0,300] and [30,400] Four ponts are selected randomly to modfy n each group and sxteen abnormal data are obtaned he abnormal data of testng set are produced n the same way Radal bass functon s used and embedded dmenson d=3 n LS-SVM model he wavelet neural network(w) regresson forecastng method s also appled for comparson he hdden layer of the network structure contans 6 nodes, and the number of teratons s 00 tmes Fg shows the comparson between predcton curve and orgnal curve when the samples don t contan abnormal data It can be seen that although W has a larger float at some ponts, the predcton values of two algorthms ft wth the orgnal values to a large degree Fg LS-SVM and W predcton wthout abnormal data When there are abnormal data n the samples, use the method n ths paper to detect and elmnate abnormal data and rebuld LS-SVM model Fg shows the comparson between standard LS-SVM and method n ths paper wth abnormal data It can be seen that regresson curve wth LS-SVM s devated from the orgnal data to some degree but the method n ths paper s not affected by abnormal data bascally and mantan good predcton accuracy Fg 3 shows the comparson between W and method n ths paper wth abnormal data It ndcates that the predcton curve of W has a larger offset from orgnal one because of the nterference of abnormal data whle the method whch s that LS-SVM based on abnormal data detecton and elmnaton keep good robustness and s less affected by the random fluctuaton Fg 4 represents the predcton error curves of standard LS-SVM, W and the method n ths paper he predcton error of the other two algorthms s apparently larger than the mproved LS-SVM method n ths paper Fg Comparson between LS-SVM and method n ths paper wth abnormal data 45

5 Fg 3 Comparson between W and method n ths paper wth abnormal data Performance Analyss of the Model Fg 4 Predcton error of three algorthms hree ndcators are used to measure the performance of two dfferent models hey are mean absolute error (MAE), root mean square error (RMSE) and correlaton coeffcent he MAE between predcton values and orgnal values s defned as follows: MAE = y yˆ (0) = he RMSE s defned as follows: ( y ˆ y) RMSE = And the correlaton coeffcent s defned as follows: r = ( y y)( yˆ yˆ ) ( y ) ( ˆ ˆ y y y) Among the equatons, y s the orgnal value y ˆ s predcton value y s the average of orgnal values and ŷ s the average of predcton values he smaller the MAE and RMSE s, the better the performance s And r shows the smlarty degree of orgnal data and predcton data able shows the performance of three algorthms from these three aspects Compared to standard LS-SVM or W, the mproved LS-SVM that detects and elmnates abnormal data has a better performance he MAE and RMSE are smaller than the other two algorthms and the correlaton coeffcent s larger he superorty of the proposed method can be dsplayed n the presence of abnormal data () () 453

6 able Performance Comparson of three algorthms Predcton Method MAE RMSE r W LS-SVM Method n ths paper Concluson Forecastng of fadng channel s vtal for moble communcaton In ths paper, n lght of underground akagam fadng channel, an mproved LS-SVM method that used to detect abnormal data s mplemented From the smulaton experments, the method n ths paper can detect the abnormal data and at the same tme, the correct regresson predcton s carred out whch has an mportant sgnfcance for mprovng nonlnear fadng channel forecastng Acknowledgement hs research was supported fnancally by atural Scence Basc Research Plan n Shaanx Provnce of Chna (Program o S05YFJM734) References [] ung Sheng Yang, Duel Hallen A, Hallen H Long Range fadng predcton to enable adaptve transmsson at another carrer [C] 4th IEEE Workshop on Sgnal Processng Advances n Wreless Communcaton USA: orth Carolna State Unversty, 003:95-99 [] X M Gao, J M A anskanen, S J Ovaska Comparson of lnear and neural network - based power predcton schemes for moble DS/CDMA system [C] IEEE press, 996:6-65 [3] Hao He Predcton of Jakes Fadng Channel Based on Least Square Support Vector Machnes [J] MICROELECROICS & COMPUER, 00, 7(7):-4 [4] Yanfen Wang Study on Channel Models of the Ultra-wdeband Wreless Communcaton Under the Specal Envronment of Mnes [M] Xu Zhou: Chna Unversty of Mnng and echnology Press, 0, [5] akagam M he m-dstrbuton A general formula of ntensty dstrbuton of rapd fadng[j] In: Hoffman WG,edtor Statstcal methods n rado wave propagaton Oxford: Pergamon; 960 [6] Changsen Zhang, Yanfang Zhang Research of akagam fadng channel model n mne moble communcaton[j] Computer Engneerng and Applcatons, 04, 50(7):38-4 [7] JAK Suykens, J Vandewalle Least Squares Support Vector Machne Classfers [J] eural Processng Letters,999,9(3): [8] JAK Suykens onlnear Modelng and Support Vector Machnes [C]IEEE Instrumentaton and Measurement echnology Conference, Budapest, Hungary,00 [9] Changsen Zhang, Yanfang Zhang Research of akagam fadng channel model n mne moble communcaton [J] Computer Engneerng and Applcatons, 04, 50(7):38-4 [0] ZHU Yong-Sheng, WAG Cheng-Dong, ZHAG You-Yun Expermental study on the Performance of Support Vector Machne wth Squared Cost Functon [J] Chnese Journal of Computers, 003, 6(8): [] Wu Jn-Pe, Sun De-Shan Modern Data Analyss [M] Pekng: Chna Machne Press,006: