research article a new svm-based modeling...

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Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2013, Article ID 279070, 7 pages http://dx.doi.org/10.1155/2013/279070 Research Article A New SVM-Based Modeling Method of Cabin Path Loss Prediction Xiaonan Zhao, Chunping Hou, and Qing Wang School of Electronics and Information Engineering, Tianjin University, Tianjin 300072, China Correspondence should be addressed to Qing Wang; [email protected] Received 28 February 2013; Accepted 21 April 2013 Academic Editor: Yan Zhang Copyright © 2013 Xiaonan Zhao et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A new modeling method of cabin path loss prediction based on support vector machine (SVM) is proposed in this paper. e method is trained with the path loss values of measured points inside the cabin and can be used to predict the path loss values of the unmeasured points. e experimental results demonstrate that our modeling method is more accurate than the curve fitting method. is SVM-based path loss prediction method makes the prediction much easier and more accurate, which covers performance traditional methods in the channel propagation modeling. 1. Introduction While wireless mobile communication is consolidated on the ground, it is still missing inside cabin during flight. is issue has recently been addressed to establish a wireless channel suitable for the cabin environment, which can meet the demand for wireless transmission at anywhere and anytime. For the special environment in cabin, it is necessary to take the modeling according to the actual measurement data due to the restriction of current indoor and outdoor channel model to the cabin’s transmission environment. e path loss is one of the most important parameters to set up the channel model in the cabin environment. e state-of-art measurements of the path loss in large aircraſt were mostly applied in narrow band and low-frequency band including 1.8 GHz, 2.1 GHz, and 2.4 GHz [1]. e measurement in high- frequency band was confined to the single-input single- output (SISO) system [2, 3]. e large-scale parameters (path loss, shadow fading, and seat penetration loss) and the small- scale parameters (fading distribution, typical -factor values, and cabin wall penetration loss) and were related to the field strength [4, 5]. e theoretical prediction and field measurement are two different methods to obtain the radio propagation charac- teristics. e theoretical method, known as Computational Electromagnetic [6] based on the electromagnetic wave propagation theory, used the details of physical environment to make an accurate prediction. However, the calculation of cabin environment is limited by computation speed and memory size for the large and complex space of cabin. e field measurement, which needs to set the expensive and heavy equipment in the cabin, is limited by the narrow corridor space and the heavy equipment. erefore, changing the cabin environment was proposed, and improved mea- surement results [7] were carried out with removing some seats inside the cabin (to change the original cabin interior environment). In this case, the accuracy of the models is critical. e SVM, based on the statistical learning theory (SLT) and established on both the Vapnik Chervonenkis (VC) dimension theory and the minimum of the system risk [8], had a lot of applications in communication field recently [9, 10]. e optimal fitting between the complexity and the learning ability can be sought. A lot of problems, such as small sample, nonlinear and multiple dimensions, can be handled with SVM. In this paper, for the first time, we predicted the path loss values based on SVM. Firstly, we measured path loss values of some selected points, then put the values in the model for training, and finally used the model to predict the values of unknown points. e B-spine surface fitting method was also adopted to compare with the SVM prediction.

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Page 1: Research Article A New SVM-Based Modeling …downloads.hindawi.com/journals/ijap/2013/279070.pdfwhich permits unrestricted use, distribution, and reproductio n in any medium, provided

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2013 Article ID 279070 7 pageshttpdxdoiorg1011552013279070

Research ArticleA New SVM-Based Modeling Method ofCabin Path Loss Prediction

Xiaonan Zhao Chunping Hou and Qing Wang

School of Electronics and Information Engineering Tianjin University Tianjin 300072 China

Correspondence should be addressed to Qing Wang wqelainetjueducn

Received 28 February 2013 Accepted 21 April 2013

Academic Editor Yan Zhang

Copyright copy 2013 Xiaonan Zhao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A new modeling method of cabin path loss prediction based on support vector machine (SVM) is proposed in this paper Themethod is trained with the path loss values of measured points inside the cabin and can be used to predict the path loss valuesof the unmeasured points The experimental results demonstrate that our modeling method is more accurate than the curvefitting method This SVM-based path loss prediction method makes the prediction much easier and more accurate which coversperformance traditional methods in the channel propagation modeling

1 Introduction

While wireless mobile communication is consolidated on theground it is still missing inside cabin during flightThis issuehas recently been addressed to establish a wireless channelsuitable for the cabin environment which can meet thedemand for wireless transmission at anywhere and anytimeFor the special environment in cabin it is necessary to takethe modeling according to the actual measurement data dueto the restriction of current indoor and outdoor channelmodel to the cabinrsquos transmission environment The pathloss is one of the most important parameters to set up thechannel model in the cabin environment The state-of-artmeasurements of the path loss in large aircraft were mostlyapplied in narrow band and low-frequency band including18 GHz 21 GHz and 24GHz [1]Themeasurement in high-frequency band was confined to the single-input single-output (SISO) system [2 3]The large-scale parameters (pathloss shadow fading and seat penetration loss) and the small-scale parameters (fading distribution typical119870-factor valuesand cabin wall penetration loss) and were related to the fieldstrength [4 5]

The theoretical prediction and field measurement are twodifferent methods to obtain the radio propagation charac-teristics The theoretical method known as ComputationalElectromagnetic [6] based on the electromagnetic wave

propagation theory used the details of physical environmentto make an accurate prediction However the calculationof cabin environment is limited by computation speed andmemory size for the large and complex space of cabin Thefield measurement which needs to set the expensive andheavy equipment in the cabin is limited by the narrowcorridor space and the heavy equipmentTherefore changingthe cabin environment was proposed and improved mea-surement results [7] were carried out with removing someseats inside the cabin (to change the original cabin interiorenvironment) In this case the accuracy of the models iscritical

The SVM based on the statistical learning theory (SLT)and established on both the Vapnik Chervonenkis (VC)dimension theory and the minimum of the system risk [8]had a lot of applications in communication field recently[9 10] The optimal fitting between the complexity and thelearning ability can be sought A lot of problems such as smallsample nonlinear and multiple dimensions can be handledwith SVM

In this paper for the first time we predicted the path lossvalues based on SVM Firstly we measured path loss valuesof some selected points then put the values in the model fortraining and finally used the model to predict the values ofunknown pointsThe B-spine surface fittingmethod was alsoadopted to compare with the SVM prediction

2 International Journal of Antennas and Propagation

E

A

DC

B

EDC

E

A

DC

B

E

A

DC

BA

DC

B

01ndash03 04ndash25 26ndash32

Figure 1 Cabin seat distribution

This paper is organized as follows Cabin interior mea-surements and path loss estimations is introduced in Sec-tion 2 The traditional surface fitting method for path lossforecasting is introduced in Section 3 The SVM-based pathloss forecasting method is proposed in Section 4 Section 5analyzes the path loss prediction in cabin using SVM andcompares with the results achieved using surface fittingSection 6 comes to the conclusion

2 Cabin Interior Measurements and the PathLoss Calculation

The measurement equipment and data are provided byTsinghua University focusing on broadband (40MHz band-width) distributed and multiple antennas measurementThe equipment is a multiple-input single-output (MISO)system operating on 352GHz The measurement equipmentis 352Ghz MIMO radio channel sounder [11] A lot ofmeasurements have been done by students of TsinghuaUniversity with the help of this equipment [12 13] Themeasurement is located in an MD82 commercial passengeraircraft The transmitting node is equipped with distributedmultiple antennas while the receiving node with singleantenna This measure aims to analyze the field strengthlarge-scale and small-scale parameters

21 352 GHz MISO Measurement Configurations Transmit-ting terminal has seven 352GHz distributed antennas on thetop of cabin Receiving terminal is a single fixed 352GHzantenna The transmitter power is 0 dBm the gains oftransmitting and receiving antenna are 4 dbi

Two different locations of the receiving antenna arechosen to carry out the MISO measurement fixed point ofseat back and tables behind seat back The two positionsrepresent two main activities of the passengers phone calland network access with laptops The details of these twoconfigurations are as follows

(i) Scenario 1 fixed point of seat back the height ofseat back is 1077 cm and the width is 365 cm Thereceiving antenna is placed in the middle of the seatback and stays vertical

(ii) Scenario 2 fixed point of tables behind seat back theheight of the table is 61 cm and the length is 42 cm

Similar to the fixed point measurement of seat backthe receiving antenna is placed in the middle of thetable to keep the antenna vertical

In the economy class fixed point measurements arecarried out on the seat back and the table of seat 22 rowsfrom row 4 to row 25 are measured in economy class totallyThe 4th to the 25th rows have five seats marked as A B C Dand E The rest of the seats were not measured in this studyBlack dot represents distributed antenna position The cabinseat distribution is shown in Figure 1

22 MISO Path Loss Calculation

Step 1 Using the matrix of channel impulse response we cancompute instantaneous power firstly

119875 (119905 120591 119904 119906 119901) =1003816100381610038161003816ℎ (119905 120591 119904 119906 119901)

1003816100381610038161003816

2

(1)where 119905 is the time 120591 is the delay 119904 is the parameter ofthe transmitting antenna 119906 is the parameter of the receivingantenna 119901 is the power and ℎ is channel impulse response

Step 2 Average the instantaneous power in transmitting andreceiving antennas

119875 (119905 120591 119901) =1

119873119904119873119906

119873119904

sum

119904=1

119873119906

sum

119906=1

119875 (119905 120591 119904 119906 119901) (2)

Step 3 Average the instantaneous power in Snap-dimension-al and 119905-dimension

119875 (120591 119901) =1

119899119905

119899119905

sum

119894=1

119875 (119905 120591 119901) (3)

Step 4 Sum all clusters of the instantaneous power delay

119875 (120591 119901) =

119873119905

sum

119894=1

119875 (120591 119901) (4)

Step 5 Match the receiving power 119875 and the transmittingdistance

119875 (119901) 997888rarr 119875 (119889 119901) (5)Step 6 Calculate the path loss PL of each link

PL (119889 119901) = 119875119879119909

(119889 119901) + sum

119894

119866119894 minus sum

119894

119860119894 minus 119875 (119889 119901) (6)

where119866119894 is the gain of the antenna119860119894 is the line attenuation

International Journal of Antennas and Propagation 3

E

A

DC

B

E

A

DC

B

1ndash22

Figure 2 Renumbered rows

1Z

1K

2Z

2K

Figure 3 Position of table and seat back

Table 1 The path loss values of 16thndash20th rows dB

Row A B C D E16Z 6668 646 6593 6395 652716K 6403 6253 6083 629 627517Z 6561 6502 6449 6281 635517K 6365 6481 6165 6143 653718Z 63 6446 6242 6491 635118K 6201 622 6216 6103 629619Z 6384 6333 6331 6483 654719K 6487 6344 608 6318 618120Z 6371 6446 6279 6409 669320K 6158 6409 5953 6048 6606

As the measurements are carried out only in economyclass the 4thndash25th rows are renumbered as row 1 to row 22 tofacilitate the presentationsThus only A B C D and E of row1 to row 22 are considered The renumbered rows are shownin Figure 2

Besides we define K to present the scenario of seat backand Z for tables behind seat back Thus for example 1Kmeans the back of the seat of first row and 1Z means table offirst rowThus there are 220 data points in totalThe positionof table and seat back is shown in Figure 3

For example the path loss values of 16thndash20th rows arelisted in Table 1

3 The Traditional Surface Fitting Method forPath Loss Forecasting

The prediction of the path loss uses the method of fittingusually In order to compare with the SVM prediction theB-spline surface fitting method was adopted [14] Firstly weloaded cabin path loss values as input data to Matlab asshown in Figure 4

We removed some points which need to be predictedand got the fitting surface using the B-spline surface fittingmethod as shown in Figure 5

The comparison of the true values and the predictionvalues of the path loss values of the removed points is listedin Table 2 as well as the error analysis

4 SVM-Based Path Loss Forecasting

41 The SVM-Based Path Loss Forecasting Model The statis-tical learning theory (SLT) [15] is professional on the area ofthe machine learning especially for the small sample Thelinear regression is the basic idea of SVMHowever the linearregression is not suitable for some complex problems sothe linear SVM should be extended to the nonlinear SVMThrough the nonlinear regression we can get the regressiondecision function The K in the regression decision functionis called the kernel function which is very importantDifferent kernel functions will lead to different kinds of SVMalgorithm

411 The Linear Regression of the SVM Assume the trainingsample set (119909

119894 119910119894) 119894 = 1 119897 119909

119894isin 119877119899 is an 119899-dimension

input vector and 119910119894isin 119877119899 is the output vector Then the linear

regression problem can be converted to the optimal problembelow

min 1

2120596

2

st 1003816100381610038161003816120596 sdot 119909119894+ 119887 minus 119910

119894

1003816100381610038161003816 le 120576 119894 = 1 119897

(7)

where 120596 is the vector of weight 120596 isin 119877119899 and 119887 is the intercept

119887 isin 119877 As theremay be some estimating errors we introduce aparameter 119862 and two slack variables 120585

119894 120585lowast119894 Then the optimal

problem above can be modified as follows

min 1

21205962+ 119862

119897

sum

119894

(120585119894+ 120585lowast

119894)

st 1003816100381610038161003816120596 sdot 119909119894+ 119887 minus 119910

119894

1003816100381610038161003816 le 120585lowast

119894+ 120576

119910119894minus (120596 sdot 119909

119894) minus 119887 le 120585

lowast

119894+ 120576

120585119894 120585lowast

119894ge 0 119894 = 1 119897

(8)

Establish the Lagrange function and solve it under theKKT conditions The dual problem of the original one is asfollows

min

1

2

119897

sum

119894119895=1

(120572lowast

119894minus 120572119894) (120572lowast

119895minus 120572119895) (119909119894sdot 119909119895)

+120576

119897

sum

119894

(120572lowast

119894+ 120572119894) minus

119897

sum

119894

119910119894(120572lowast

119894minus 120572119894)

st119897

sum

119894

(120572119894minus 120572lowast

119894) = 0

0 le 120572119894 120572lowast

119894le 119862 119894 = 1 119897

(9)

4 International Journal of Antennas and Propagation

At last the regression decision function is as follows

119891 (119909) =

119897

sum

119894

(120572119894minus 120572lowast

119894) (119909119894sdot 119909) + 119887 (10)

412 The Nonlinear Regression When the dataset cannot belinearly regressed we can transform the original data intoa high dimension feature space using a nonlinear mapping120593(119909) where we can carry out the linear regression Bydefining the kernel function of the inner product of the highdimension feature space 119870(119909

119894 119910119894) = 120593(119909

119894)120593(119910119894) the inner

product of a variable in the high dimension space can beobtained by operating in the original space through the kernelfunction

min

1

2

119897

sum

119894119895=1

(120572lowast

119894minus 120572119894) (120572lowast

119895minus 120572119895)119870 (119909

119894sdot 119909119895)

+120576

119897

sum

119894

(120572lowast

119894+ 120572119894) minus

119897

sum

119894

119910119894(120572lowast

119894minus 120572119894)

st119897

sum

119894

(120572119894minus 120572lowast

119894) = 0

0 le 120572119894 120572lowast

119894le 119862 119894 = 1 119897

(11)

At last the regression decision function is as follows

119891 (119909) =

119897

sum

119894

(120572119894minus 120572lowast

119894)119870 (119909

119894sdot 119909) + 119887 (12)

413 The Selection of the Kernel Function Nowadays thewidely used kernel functions include the linear function thepolynomial kernel function the Gauss radial basis kernelfunction and the Sigmoid kernel function The performanceof the SVMhas no relationshipwith the selection of the differ-ent types of the kernel function but has a strong relationshipwith the parameters in the kernel function Nevertheless wecould select a good type of the kernel functions in order toreduce the calculation complexity

As for the polynomial kernel function (the linear kernelfunction is a special case of the polynomial kernel function)when the eigenspace has a high dimension the calculationamount could be huge and what is even worse we cannotobtain any correct solution under some certain situationsHowever the Gauss radial basis kernel function can over-come similar problems Furthermore the selection of Gausskernel function is connotative that is every support vectorwould produce a local Gauss function which is centered bythe vector itself We can find the global width of the basisfunction by structural risk minimization principle As statedabove we take the Gauss radial basis kernel function in thefollowing study

42 The Choice of Input and Output Variables We randomlyselect 5 rows (such as 16 to 20 rows) where only table data (Z)of the seats B and D are treated as unknown data (10 groupstotally) We use SVM model to forecast these 10 groups of

Raw data

0 510

15 2025 30

3540

45

5

5550606570

Cabin length

Cabin width

Path

loss

(dB)

152

253

354

45

1

Figure 4 Raw data

05

1015

2025

3035

4045

1

555606570

Cabin length

Cabin width

Path

loss

(dB)

60

61

62

63

64

65

66

67

68

B-spline surface fitting

152

253

354

45

Figure 5 B-spline surface fitting

Table 2 The error analysis of B-spline surface fitting dB

Point True value Fitted value Absolute error Relative error16ZB 646 6614 154 23816ZD 6395 6545 15 23517ZB 6502 6458 044 06817ZD 6281 6349 068 10818ZB 6446 6236 21 32618ZD 6491 6247 244 37619ZB 6333 6318 015 02419ZD 6483 6371 112 17320ZB 6446 6275 171 26520ZD 6409 6379 03 047The average of the relative error using B-spline surface fitting is 186

unknown data in order to verify the accuracy of the SVMprediction model The sample data of BCD is selected thereminder 30 rows (from 1K to 15Z and from 21K to 22Z)For one certain point the surrounding eight points path

International Journal of Antennas and Propagation 5

Table 3 An example of input and output variables in SVMmodel dB

Input data Output data6639 6577 6491 6258 6501 6451 655 6657 6426(1ZA) (1ZB) (1ZC) (1KC) (2ZC) (2ZB) (2ZA) (1KA) (1KB)6577 6491 6801 636 6583 6501 6451 6426 6258(1ZB) (1ZC) (1ZD) (1KD) (2ZD) (2ZC) (2ZB) (1KB) (1KC)6491 6801 6744 6661 6642 6583 6501 6258 636(1ZC) (1ZD) (1ZE) (1KE) (2ZE) (2ZD) (2ZC) (1KC) (1KD)

Table 4 The error analysis of the 45 groups back of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6248 212 32816ZD 6395 6192 203 31717ZB 6502 6213 289 44417ZD 6281 6181 1 15918ZB 6446 6256 19 29518ZD 6491 6183 308 47519ZB 6333 6203 13 20519ZD 6483 6177 306 47220ZB 6446 6256 19 29520ZD 6409 6163 246 384

Table 5 The error analysis of the 45 groups table of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6512 052 08016ZD 6395 6457 062 09717ZB 6502 6475 027 04217ZD 6281 6401 12 19118ZB 6446 6429 017 02618ZD 6491 637 121 18619ZB 6333 6435 102 16119ZD 6483 6416 067 10320ZB 6446 6446 0 020ZD 6409 6388 021 033

loss values are selected as the eight input variables 119909119894 119894 =

1 2 8 and the path loss value of this point is supposed asthe output variables 119910 The ninety sets of data included forty-five sets of seat back data and forty-five sets of table data Thefirst 8 values of each line are input variables the last data is theoutput variable Examples of the path loss samples selected asthe input data and the output data in SVMmodel are listed inTable 3

43 Path Loss Prediction Using SVM-Based Model in Cabin

431 Case 1 Training Table Data Using Seat Back DataFirstly the training samples of the forty-five back data areselected from ninety sets The data of forty-five groups are

trained using SVM The unknown data of row 16 to row 20are predicted using the trained model In order to verify thevalidity of the model the error analysis is caculated for thereal value and the predictive value such as absolute error andrelative error The result is described in Table 4 The relativeerror in the table refers to the ratio of the real value andabsolute error value

We average the relative error in Table 4 and conclude thatthe average relative error predicted is 337which shows thatthe forecast is not very accurate using the samples of back ofchair to train the table of chairs

432 Case 2 Training Table Data Using Table Data Then weselect the rest of the 45 groups of table samples to train themodel and send the 45 groups of data into SVM for trainingWe still forecast the 10 points mentioned above The result isdescribed in Table 5

The average relative error predicted is 092The conclu-sion is that when we use the samples of the tables to train asthe training samples and the predicted samples share morerelevance which means that their channel environments aremore similar the model is more accurate

433 Case 3 Training Table Data Using Both Seat Back andTable Data Finally we take all the 90 datasets includingsamples on back of the chair and the table into the SVMmodel for training We forecast the 10 points mentionedabove The result is described in Table 6

The average relative error predicted is 102 It can beconcluded that increasing training samples which share lessrelevance with the predicted samples makes no contributionto the accuracy of the prediction model

5 Further Discussion

It can be concluded that the accuracy forecasted by SVM isincreased greatly compared with the accuracy predicted bysurface fitting The relative average forecast error of SVMcan reach 092 in Case 2 The relative average forecasterror of surface fitting is 186 in this study using the samemeasurement data The accuracy of surface fitting and SVMfitting is compared in Figure 6

For the surface fitting method the plane is fitting ofsurface of these points with smooth surface connected fromfitting surface to find needed points The cabin environmentof plane is very complex with a lot of seats so the shadow

6 International Journal of Antennas and Propagation

Table 6 The error analysis of all the 90 groups training dB

Point True value Fitted value Absolute error Relative error16ZB 646 6514 054 08416ZD 6395 6495 1 15617ZB 6502 6434 068 10517ZD 6281 6392 111 17718ZB 6446 6394 052 08118ZD 6491 6348 143 22019ZB 6333 6381 048 07619ZD 6483 6438 045 06920ZB 6446 6443 003 00520ZD 6409 6437 028 044

1 2 3 4 5 6 7 8 9 10Data

Data comparison

Raw dataB-spline surface fitting

SVM

62

625

63

635

64

645

65

655

66

665

Path

loss

(dB)

Figure 6 Data Comparasion

fading will affect the signal strength greatly However mostthings in cabin are stable so it is very suitable to forecastusing SVM The environment information included in theSVM training data can avoid the influence of shadow fadingon predicting effectively

It can also be concluded that the more relevance of thetraining samples and the predicted samples can improve theaccuracy of the prediction model Besides more sampleswhich share less relevance with the predicted samples makeno contribution to the accuracy in statistical aspect

One of the purposes of this paper is to reduce the amountof measurements We need to reduce the measurementactivities as far as possible and predict the unknown pointusing SVM-based model at an acceptable error level

6 Conclusion

Although path loss can be obtained via theoretical predictionor field measurement the method of Computational Electro-magnetic and a lot of measurements without changing thecabin environment are very difficult to proceed because the

cabin is a big and complex space The principle challengesare to simplify the complicate measurement and to improvethe accuracy of prediction of the path loss In this paper anSVM-based path loss prediction method was first proposedto overcome the measurement challenges in complex andbig cabin environment We selected the path loss valuesaround the predicted points as the input data of the predictionmodel and used the trained model to predict points not beenmeasured The path loss prediction results demonstratedthat the proposed SVM-based prediction method is effectiveand accurate compared to the surface fitting method Therelevance of the training samples and the predicted samplescan affect the accuracy of the predictionmodelThe proposedSVM-based path loss prediction method can forecast thepoints inconvenient to be measured which can reduce theamount of measurement and provide supplement informa-tion in channel modeling

Acknowledgments

This work was supported by the National Science andTechnology Major Project of the Ministry of Science andTechnology of China (Grant no 2009ZX03007-003) theNational High Technology Research and Development Pro-gram of China (Grant no 2009AA011507) and the NationalNatural Science Foundation of China (Grant no 61101223)The authors would like to thank Tsinghua University forproviding the measurement data The first author also wouldlike to thank Associate Professor Yang Jinsheng and theproject team members Mao Xiangfang and Wu Xuzhao forthe helpful discussion

References

[1] N R Dıaz and J E J Esquitino ldquoWideband channel characteri-zation for wireless communications inside a short haul aircraftrdquoinProceedings of the IEEE 59thVehicular Technology Conferencepp 223ndash228 Milan Italy May 2004

[2] S Chiu J Chuang and D G Michelson ldquoCharacterization ofUWB channel impulse responses within the passenger cabin ofa boeing 737-200 aircraftrdquo IEEE Transactions on Antennas andPropagation vol 58 no 3 pp 935ndash945 2010

[3] K Chetcuti C J Debono R A Farrugia and S BruillotldquoWireless propagation modelling inside a business jetrdquo inProceedings of the IEEE Eurocon (EUROCON rsquo09) pp 1644ndash1649 St-Petersburg Russia May 2009

[4] J Jemai R Piesiewicz R Geise et al ldquoUWB channel modelingwithin an aircraft cabinrdquo in Proceedings of the IEEE Interna-tional Conference on Ultra-Wideband ICUWB 2008 pp 5ndash8Hannover Germany September 2008

[5] J Chuang N Xin H Huang S Chiu and D G MichelsonldquoUWB radiowave propagation within the passenger cabin ofa boeing 737-200 aircraftrdquo in Proceedings of the IEEE 65thVehicular Technology Conference pp 496ndash500 Dublin IrelandApril 2007

[6] C Cerasoli ldquoRF propagation in tunnel enviromentsrdquo in Pro-ceedings of the IEEEMilitary Communications Conference (OtL-COM rsquo04) pp 363ndash369 Monterey Calif USA November 2004

International Journal of Antennas and Propagation 7

[7] E Perrin F Tristant S Gouverneur et al ldquoStudy of electricfield radiated by wifi sources inside an aircraftmdash3D computa-tions and real testsrdquo in Proceedings of the IEEE InternationalSymposium on Electromagnetic Compatibility (EMC rsquo08) pp 1ndash5 Hamburg Germany September 2008

[8] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[9] Z Xiang X W Liu and R C Shangguan ldquoResearch on thechannel prediction algorithm of multiwavelet combined withsupport vector machines based on FPGArdquo in Proceedings of the6th International Conference on Natural Computation (ICNCrsquo10) pp 3614ndash3618 Yantai Shandong China August 2010

[10] J P Zhang Y N Zhuo and Y Zhao ldquoMobile location basedon SVM In MIMO communication systemsrdquo in Proceedings ofthe International Conference on Information Networking andAutomation (ICINA rsquo10) pp V2-360ndashV2-363 Kunming ChinaOctober 2010

[11] Y H Rui Y Zhang S J Liu and S D Zhou ldquo352GHz MIMOradio channel sounderrdquo in Proceedings of the InternationalConference on Communications Circuits and Systems (ICCCASrsquo08) pp 79ndash83 Fujian China May 2008

[12] X W Hu Y Zhang Y Z Jia S D Zhou and L MXiao ldquoPower coverage and fading characteristics of indoordistributed antenna systemsrdquo in Proceedings of the 4th Interna-tional Conference on Communications and Networking in China(CHINACOM rsquo09) pp 1066ndash1069 Xirsquoan China August 2009

[13] C H Zhuo S J Liu Y Zhang Y H Rui and S D ZhouldquoA simple broadband MIMO channel sounder prototyperdquo inProceedings of the International Conference on Wireless Mobileand Multimedia Networks pp 1ndash4 Hangzhou China 2006

[14] Y L Hu and M M Li ldquoSurface fitting by splines using matlabrdquoJournal of Yunnan University for Nationalities vol 14 no 2 pp168ndash171 2005

[15] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks vol 10 no 5 pp 988ndash9991999

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Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 2: Research Article A New SVM-Based Modeling …downloads.hindawi.com/journals/ijap/2013/279070.pdfwhich permits unrestricted use, distribution, and reproductio n in any medium, provided

2 International Journal of Antennas and Propagation

E

A

DC

B

EDC

E

A

DC

B

E

A

DC

BA

DC

B

01ndash03 04ndash25 26ndash32

Figure 1 Cabin seat distribution

This paper is organized as follows Cabin interior mea-surements and path loss estimations is introduced in Sec-tion 2 The traditional surface fitting method for path lossforecasting is introduced in Section 3 The SVM-based pathloss forecasting method is proposed in Section 4 Section 5analyzes the path loss prediction in cabin using SVM andcompares with the results achieved using surface fittingSection 6 comes to the conclusion

2 Cabin Interior Measurements and the PathLoss Calculation

The measurement equipment and data are provided byTsinghua University focusing on broadband (40MHz band-width) distributed and multiple antennas measurementThe equipment is a multiple-input single-output (MISO)system operating on 352GHz The measurement equipmentis 352Ghz MIMO radio channel sounder [11] A lot ofmeasurements have been done by students of TsinghuaUniversity with the help of this equipment [12 13] Themeasurement is located in an MD82 commercial passengeraircraft The transmitting node is equipped with distributedmultiple antennas while the receiving node with singleantenna This measure aims to analyze the field strengthlarge-scale and small-scale parameters

21 352 GHz MISO Measurement Configurations Transmit-ting terminal has seven 352GHz distributed antennas on thetop of cabin Receiving terminal is a single fixed 352GHzantenna The transmitter power is 0 dBm the gains oftransmitting and receiving antenna are 4 dbi

Two different locations of the receiving antenna arechosen to carry out the MISO measurement fixed point ofseat back and tables behind seat back The two positionsrepresent two main activities of the passengers phone calland network access with laptops The details of these twoconfigurations are as follows

(i) Scenario 1 fixed point of seat back the height ofseat back is 1077 cm and the width is 365 cm Thereceiving antenna is placed in the middle of the seatback and stays vertical

(ii) Scenario 2 fixed point of tables behind seat back theheight of the table is 61 cm and the length is 42 cm

Similar to the fixed point measurement of seat backthe receiving antenna is placed in the middle of thetable to keep the antenna vertical

In the economy class fixed point measurements arecarried out on the seat back and the table of seat 22 rowsfrom row 4 to row 25 are measured in economy class totallyThe 4th to the 25th rows have five seats marked as A B C Dand E The rest of the seats were not measured in this studyBlack dot represents distributed antenna position The cabinseat distribution is shown in Figure 1

22 MISO Path Loss Calculation

Step 1 Using the matrix of channel impulse response we cancompute instantaneous power firstly

119875 (119905 120591 119904 119906 119901) =1003816100381610038161003816ℎ (119905 120591 119904 119906 119901)

1003816100381610038161003816

2

(1)where 119905 is the time 120591 is the delay 119904 is the parameter ofthe transmitting antenna 119906 is the parameter of the receivingantenna 119901 is the power and ℎ is channel impulse response

Step 2 Average the instantaneous power in transmitting andreceiving antennas

119875 (119905 120591 119901) =1

119873119904119873119906

119873119904

sum

119904=1

119873119906

sum

119906=1

119875 (119905 120591 119904 119906 119901) (2)

Step 3 Average the instantaneous power in Snap-dimension-al and 119905-dimension

119875 (120591 119901) =1

119899119905

119899119905

sum

119894=1

119875 (119905 120591 119901) (3)

Step 4 Sum all clusters of the instantaneous power delay

119875 (120591 119901) =

119873119905

sum

119894=1

119875 (120591 119901) (4)

Step 5 Match the receiving power 119875 and the transmittingdistance

119875 (119901) 997888rarr 119875 (119889 119901) (5)Step 6 Calculate the path loss PL of each link

PL (119889 119901) = 119875119879119909

(119889 119901) + sum

119894

119866119894 minus sum

119894

119860119894 minus 119875 (119889 119901) (6)

where119866119894 is the gain of the antenna119860119894 is the line attenuation

International Journal of Antennas and Propagation 3

E

A

DC

B

E

A

DC

B

1ndash22

Figure 2 Renumbered rows

1Z

1K

2Z

2K

Figure 3 Position of table and seat back

Table 1 The path loss values of 16thndash20th rows dB

Row A B C D E16Z 6668 646 6593 6395 652716K 6403 6253 6083 629 627517Z 6561 6502 6449 6281 635517K 6365 6481 6165 6143 653718Z 63 6446 6242 6491 635118K 6201 622 6216 6103 629619Z 6384 6333 6331 6483 654719K 6487 6344 608 6318 618120Z 6371 6446 6279 6409 669320K 6158 6409 5953 6048 6606

As the measurements are carried out only in economyclass the 4thndash25th rows are renumbered as row 1 to row 22 tofacilitate the presentationsThus only A B C D and E of row1 to row 22 are considered The renumbered rows are shownin Figure 2

Besides we define K to present the scenario of seat backand Z for tables behind seat back Thus for example 1Kmeans the back of the seat of first row and 1Z means table offirst rowThus there are 220 data points in totalThe positionof table and seat back is shown in Figure 3

For example the path loss values of 16thndash20th rows arelisted in Table 1

3 The Traditional Surface Fitting Method forPath Loss Forecasting

The prediction of the path loss uses the method of fittingusually In order to compare with the SVM prediction theB-spline surface fitting method was adopted [14] Firstly weloaded cabin path loss values as input data to Matlab asshown in Figure 4

We removed some points which need to be predictedand got the fitting surface using the B-spline surface fittingmethod as shown in Figure 5

The comparison of the true values and the predictionvalues of the path loss values of the removed points is listedin Table 2 as well as the error analysis

4 SVM-Based Path Loss Forecasting

41 The SVM-Based Path Loss Forecasting Model The statis-tical learning theory (SLT) [15] is professional on the area ofthe machine learning especially for the small sample Thelinear regression is the basic idea of SVMHowever the linearregression is not suitable for some complex problems sothe linear SVM should be extended to the nonlinear SVMThrough the nonlinear regression we can get the regressiondecision function The K in the regression decision functionis called the kernel function which is very importantDifferent kernel functions will lead to different kinds of SVMalgorithm

411 The Linear Regression of the SVM Assume the trainingsample set (119909

119894 119910119894) 119894 = 1 119897 119909

119894isin 119877119899 is an 119899-dimension

input vector and 119910119894isin 119877119899 is the output vector Then the linear

regression problem can be converted to the optimal problembelow

min 1

2120596

2

st 1003816100381610038161003816120596 sdot 119909119894+ 119887 minus 119910

119894

1003816100381610038161003816 le 120576 119894 = 1 119897

(7)

where 120596 is the vector of weight 120596 isin 119877119899 and 119887 is the intercept

119887 isin 119877 As theremay be some estimating errors we introduce aparameter 119862 and two slack variables 120585

119894 120585lowast119894 Then the optimal

problem above can be modified as follows

min 1

21205962+ 119862

119897

sum

119894

(120585119894+ 120585lowast

119894)

st 1003816100381610038161003816120596 sdot 119909119894+ 119887 minus 119910

119894

1003816100381610038161003816 le 120585lowast

119894+ 120576

119910119894minus (120596 sdot 119909

119894) minus 119887 le 120585

lowast

119894+ 120576

120585119894 120585lowast

119894ge 0 119894 = 1 119897

(8)

Establish the Lagrange function and solve it under theKKT conditions The dual problem of the original one is asfollows

min

1

2

119897

sum

119894119895=1

(120572lowast

119894minus 120572119894) (120572lowast

119895minus 120572119895) (119909119894sdot 119909119895)

+120576

119897

sum

119894

(120572lowast

119894+ 120572119894) minus

119897

sum

119894

119910119894(120572lowast

119894minus 120572119894)

st119897

sum

119894

(120572119894minus 120572lowast

119894) = 0

0 le 120572119894 120572lowast

119894le 119862 119894 = 1 119897

(9)

4 International Journal of Antennas and Propagation

At last the regression decision function is as follows

119891 (119909) =

119897

sum

119894

(120572119894minus 120572lowast

119894) (119909119894sdot 119909) + 119887 (10)

412 The Nonlinear Regression When the dataset cannot belinearly regressed we can transform the original data intoa high dimension feature space using a nonlinear mapping120593(119909) where we can carry out the linear regression Bydefining the kernel function of the inner product of the highdimension feature space 119870(119909

119894 119910119894) = 120593(119909

119894)120593(119910119894) the inner

product of a variable in the high dimension space can beobtained by operating in the original space through the kernelfunction

min

1

2

119897

sum

119894119895=1

(120572lowast

119894minus 120572119894) (120572lowast

119895minus 120572119895)119870 (119909

119894sdot 119909119895)

+120576

119897

sum

119894

(120572lowast

119894+ 120572119894) minus

119897

sum

119894

119910119894(120572lowast

119894minus 120572119894)

st119897

sum

119894

(120572119894minus 120572lowast

119894) = 0

0 le 120572119894 120572lowast

119894le 119862 119894 = 1 119897

(11)

At last the regression decision function is as follows

119891 (119909) =

119897

sum

119894

(120572119894minus 120572lowast

119894)119870 (119909

119894sdot 119909) + 119887 (12)

413 The Selection of the Kernel Function Nowadays thewidely used kernel functions include the linear function thepolynomial kernel function the Gauss radial basis kernelfunction and the Sigmoid kernel function The performanceof the SVMhas no relationshipwith the selection of the differ-ent types of the kernel function but has a strong relationshipwith the parameters in the kernel function Nevertheless wecould select a good type of the kernel functions in order toreduce the calculation complexity

As for the polynomial kernel function (the linear kernelfunction is a special case of the polynomial kernel function)when the eigenspace has a high dimension the calculationamount could be huge and what is even worse we cannotobtain any correct solution under some certain situationsHowever the Gauss radial basis kernel function can over-come similar problems Furthermore the selection of Gausskernel function is connotative that is every support vectorwould produce a local Gauss function which is centered bythe vector itself We can find the global width of the basisfunction by structural risk minimization principle As statedabove we take the Gauss radial basis kernel function in thefollowing study

42 The Choice of Input and Output Variables We randomlyselect 5 rows (such as 16 to 20 rows) where only table data (Z)of the seats B and D are treated as unknown data (10 groupstotally) We use SVM model to forecast these 10 groups of

Raw data

0 510

15 2025 30

3540

45

5

5550606570

Cabin length

Cabin width

Path

loss

(dB)

152

253

354

45

1

Figure 4 Raw data

05

1015

2025

3035

4045

1

555606570

Cabin length

Cabin width

Path

loss

(dB)

60

61

62

63

64

65

66

67

68

B-spline surface fitting

152

253

354

45

Figure 5 B-spline surface fitting

Table 2 The error analysis of B-spline surface fitting dB

Point True value Fitted value Absolute error Relative error16ZB 646 6614 154 23816ZD 6395 6545 15 23517ZB 6502 6458 044 06817ZD 6281 6349 068 10818ZB 6446 6236 21 32618ZD 6491 6247 244 37619ZB 6333 6318 015 02419ZD 6483 6371 112 17320ZB 6446 6275 171 26520ZD 6409 6379 03 047The average of the relative error using B-spline surface fitting is 186

unknown data in order to verify the accuracy of the SVMprediction model The sample data of BCD is selected thereminder 30 rows (from 1K to 15Z and from 21K to 22Z)For one certain point the surrounding eight points path

International Journal of Antennas and Propagation 5

Table 3 An example of input and output variables in SVMmodel dB

Input data Output data6639 6577 6491 6258 6501 6451 655 6657 6426(1ZA) (1ZB) (1ZC) (1KC) (2ZC) (2ZB) (2ZA) (1KA) (1KB)6577 6491 6801 636 6583 6501 6451 6426 6258(1ZB) (1ZC) (1ZD) (1KD) (2ZD) (2ZC) (2ZB) (1KB) (1KC)6491 6801 6744 6661 6642 6583 6501 6258 636(1ZC) (1ZD) (1ZE) (1KE) (2ZE) (2ZD) (2ZC) (1KC) (1KD)

Table 4 The error analysis of the 45 groups back of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6248 212 32816ZD 6395 6192 203 31717ZB 6502 6213 289 44417ZD 6281 6181 1 15918ZB 6446 6256 19 29518ZD 6491 6183 308 47519ZB 6333 6203 13 20519ZD 6483 6177 306 47220ZB 6446 6256 19 29520ZD 6409 6163 246 384

Table 5 The error analysis of the 45 groups table of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6512 052 08016ZD 6395 6457 062 09717ZB 6502 6475 027 04217ZD 6281 6401 12 19118ZB 6446 6429 017 02618ZD 6491 637 121 18619ZB 6333 6435 102 16119ZD 6483 6416 067 10320ZB 6446 6446 0 020ZD 6409 6388 021 033

loss values are selected as the eight input variables 119909119894 119894 =

1 2 8 and the path loss value of this point is supposed asthe output variables 119910 The ninety sets of data included forty-five sets of seat back data and forty-five sets of table data Thefirst 8 values of each line are input variables the last data is theoutput variable Examples of the path loss samples selected asthe input data and the output data in SVMmodel are listed inTable 3

43 Path Loss Prediction Using SVM-Based Model in Cabin

431 Case 1 Training Table Data Using Seat Back DataFirstly the training samples of the forty-five back data areselected from ninety sets The data of forty-five groups are

trained using SVM The unknown data of row 16 to row 20are predicted using the trained model In order to verify thevalidity of the model the error analysis is caculated for thereal value and the predictive value such as absolute error andrelative error The result is described in Table 4 The relativeerror in the table refers to the ratio of the real value andabsolute error value

We average the relative error in Table 4 and conclude thatthe average relative error predicted is 337which shows thatthe forecast is not very accurate using the samples of back ofchair to train the table of chairs

432 Case 2 Training Table Data Using Table Data Then weselect the rest of the 45 groups of table samples to train themodel and send the 45 groups of data into SVM for trainingWe still forecast the 10 points mentioned above The result isdescribed in Table 5

The average relative error predicted is 092The conclu-sion is that when we use the samples of the tables to train asthe training samples and the predicted samples share morerelevance which means that their channel environments aremore similar the model is more accurate

433 Case 3 Training Table Data Using Both Seat Back andTable Data Finally we take all the 90 datasets includingsamples on back of the chair and the table into the SVMmodel for training We forecast the 10 points mentionedabove The result is described in Table 6

The average relative error predicted is 102 It can beconcluded that increasing training samples which share lessrelevance with the predicted samples makes no contributionto the accuracy of the prediction model

5 Further Discussion

It can be concluded that the accuracy forecasted by SVM isincreased greatly compared with the accuracy predicted bysurface fitting The relative average forecast error of SVMcan reach 092 in Case 2 The relative average forecasterror of surface fitting is 186 in this study using the samemeasurement data The accuracy of surface fitting and SVMfitting is compared in Figure 6

For the surface fitting method the plane is fitting ofsurface of these points with smooth surface connected fromfitting surface to find needed points The cabin environmentof plane is very complex with a lot of seats so the shadow

6 International Journal of Antennas and Propagation

Table 6 The error analysis of all the 90 groups training dB

Point True value Fitted value Absolute error Relative error16ZB 646 6514 054 08416ZD 6395 6495 1 15617ZB 6502 6434 068 10517ZD 6281 6392 111 17718ZB 6446 6394 052 08118ZD 6491 6348 143 22019ZB 6333 6381 048 07619ZD 6483 6438 045 06920ZB 6446 6443 003 00520ZD 6409 6437 028 044

1 2 3 4 5 6 7 8 9 10Data

Data comparison

Raw dataB-spline surface fitting

SVM

62

625

63

635

64

645

65

655

66

665

Path

loss

(dB)

Figure 6 Data Comparasion

fading will affect the signal strength greatly However mostthings in cabin are stable so it is very suitable to forecastusing SVM The environment information included in theSVM training data can avoid the influence of shadow fadingon predicting effectively

It can also be concluded that the more relevance of thetraining samples and the predicted samples can improve theaccuracy of the prediction model Besides more sampleswhich share less relevance with the predicted samples makeno contribution to the accuracy in statistical aspect

One of the purposes of this paper is to reduce the amountof measurements We need to reduce the measurementactivities as far as possible and predict the unknown pointusing SVM-based model at an acceptable error level

6 Conclusion

Although path loss can be obtained via theoretical predictionor field measurement the method of Computational Electro-magnetic and a lot of measurements without changing thecabin environment are very difficult to proceed because the

cabin is a big and complex space The principle challengesare to simplify the complicate measurement and to improvethe accuracy of prediction of the path loss In this paper anSVM-based path loss prediction method was first proposedto overcome the measurement challenges in complex andbig cabin environment We selected the path loss valuesaround the predicted points as the input data of the predictionmodel and used the trained model to predict points not beenmeasured The path loss prediction results demonstratedthat the proposed SVM-based prediction method is effectiveand accurate compared to the surface fitting method Therelevance of the training samples and the predicted samplescan affect the accuracy of the predictionmodelThe proposedSVM-based path loss prediction method can forecast thepoints inconvenient to be measured which can reduce theamount of measurement and provide supplement informa-tion in channel modeling

Acknowledgments

This work was supported by the National Science andTechnology Major Project of the Ministry of Science andTechnology of China (Grant no 2009ZX03007-003) theNational High Technology Research and Development Pro-gram of China (Grant no 2009AA011507) and the NationalNatural Science Foundation of China (Grant no 61101223)The authors would like to thank Tsinghua University forproviding the measurement data The first author also wouldlike to thank Associate Professor Yang Jinsheng and theproject team members Mao Xiangfang and Wu Xuzhao forthe helpful discussion

References

[1] N R Dıaz and J E J Esquitino ldquoWideband channel characteri-zation for wireless communications inside a short haul aircraftrdquoinProceedings of the IEEE 59thVehicular Technology Conferencepp 223ndash228 Milan Italy May 2004

[2] S Chiu J Chuang and D G Michelson ldquoCharacterization ofUWB channel impulse responses within the passenger cabin ofa boeing 737-200 aircraftrdquo IEEE Transactions on Antennas andPropagation vol 58 no 3 pp 935ndash945 2010

[3] K Chetcuti C J Debono R A Farrugia and S BruillotldquoWireless propagation modelling inside a business jetrdquo inProceedings of the IEEE Eurocon (EUROCON rsquo09) pp 1644ndash1649 St-Petersburg Russia May 2009

[4] J Jemai R Piesiewicz R Geise et al ldquoUWB channel modelingwithin an aircraft cabinrdquo in Proceedings of the IEEE Interna-tional Conference on Ultra-Wideband ICUWB 2008 pp 5ndash8Hannover Germany September 2008

[5] J Chuang N Xin H Huang S Chiu and D G MichelsonldquoUWB radiowave propagation within the passenger cabin ofa boeing 737-200 aircraftrdquo in Proceedings of the IEEE 65thVehicular Technology Conference pp 496ndash500 Dublin IrelandApril 2007

[6] C Cerasoli ldquoRF propagation in tunnel enviromentsrdquo in Pro-ceedings of the IEEEMilitary Communications Conference (OtL-COM rsquo04) pp 363ndash369 Monterey Calif USA November 2004

International Journal of Antennas and Propagation 7

[7] E Perrin F Tristant S Gouverneur et al ldquoStudy of electricfield radiated by wifi sources inside an aircraftmdash3D computa-tions and real testsrdquo in Proceedings of the IEEE InternationalSymposium on Electromagnetic Compatibility (EMC rsquo08) pp 1ndash5 Hamburg Germany September 2008

[8] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[9] Z Xiang X W Liu and R C Shangguan ldquoResearch on thechannel prediction algorithm of multiwavelet combined withsupport vector machines based on FPGArdquo in Proceedings of the6th International Conference on Natural Computation (ICNCrsquo10) pp 3614ndash3618 Yantai Shandong China August 2010

[10] J P Zhang Y N Zhuo and Y Zhao ldquoMobile location basedon SVM In MIMO communication systemsrdquo in Proceedings ofthe International Conference on Information Networking andAutomation (ICINA rsquo10) pp V2-360ndashV2-363 Kunming ChinaOctober 2010

[11] Y H Rui Y Zhang S J Liu and S D Zhou ldquo352GHz MIMOradio channel sounderrdquo in Proceedings of the InternationalConference on Communications Circuits and Systems (ICCCASrsquo08) pp 79ndash83 Fujian China May 2008

[12] X W Hu Y Zhang Y Z Jia S D Zhou and L MXiao ldquoPower coverage and fading characteristics of indoordistributed antenna systemsrdquo in Proceedings of the 4th Interna-tional Conference on Communications and Networking in China(CHINACOM rsquo09) pp 1066ndash1069 Xirsquoan China August 2009

[13] C H Zhuo S J Liu Y Zhang Y H Rui and S D ZhouldquoA simple broadband MIMO channel sounder prototyperdquo inProceedings of the International Conference on Wireless Mobileand Multimedia Networks pp 1ndash4 Hangzhou China 2006

[14] Y L Hu and M M Li ldquoSurface fitting by splines using matlabrdquoJournal of Yunnan University for Nationalities vol 14 no 2 pp168ndash171 2005

[15] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks vol 10 no 5 pp 988ndash9991999

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 3: Research Article A New SVM-Based Modeling …downloads.hindawi.com/journals/ijap/2013/279070.pdfwhich permits unrestricted use, distribution, and reproductio n in any medium, provided

International Journal of Antennas and Propagation 3

E

A

DC

B

E

A

DC

B

1ndash22

Figure 2 Renumbered rows

1Z

1K

2Z

2K

Figure 3 Position of table and seat back

Table 1 The path loss values of 16thndash20th rows dB

Row A B C D E16Z 6668 646 6593 6395 652716K 6403 6253 6083 629 627517Z 6561 6502 6449 6281 635517K 6365 6481 6165 6143 653718Z 63 6446 6242 6491 635118K 6201 622 6216 6103 629619Z 6384 6333 6331 6483 654719K 6487 6344 608 6318 618120Z 6371 6446 6279 6409 669320K 6158 6409 5953 6048 6606

As the measurements are carried out only in economyclass the 4thndash25th rows are renumbered as row 1 to row 22 tofacilitate the presentationsThus only A B C D and E of row1 to row 22 are considered The renumbered rows are shownin Figure 2

Besides we define K to present the scenario of seat backand Z for tables behind seat back Thus for example 1Kmeans the back of the seat of first row and 1Z means table offirst rowThus there are 220 data points in totalThe positionof table and seat back is shown in Figure 3

For example the path loss values of 16thndash20th rows arelisted in Table 1

3 The Traditional Surface Fitting Method forPath Loss Forecasting

The prediction of the path loss uses the method of fittingusually In order to compare with the SVM prediction theB-spline surface fitting method was adopted [14] Firstly weloaded cabin path loss values as input data to Matlab asshown in Figure 4

We removed some points which need to be predictedand got the fitting surface using the B-spline surface fittingmethod as shown in Figure 5

The comparison of the true values and the predictionvalues of the path loss values of the removed points is listedin Table 2 as well as the error analysis

4 SVM-Based Path Loss Forecasting

41 The SVM-Based Path Loss Forecasting Model The statis-tical learning theory (SLT) [15] is professional on the area ofthe machine learning especially for the small sample Thelinear regression is the basic idea of SVMHowever the linearregression is not suitable for some complex problems sothe linear SVM should be extended to the nonlinear SVMThrough the nonlinear regression we can get the regressiondecision function The K in the regression decision functionis called the kernel function which is very importantDifferent kernel functions will lead to different kinds of SVMalgorithm

411 The Linear Regression of the SVM Assume the trainingsample set (119909

119894 119910119894) 119894 = 1 119897 119909

119894isin 119877119899 is an 119899-dimension

input vector and 119910119894isin 119877119899 is the output vector Then the linear

regression problem can be converted to the optimal problembelow

min 1

2120596

2

st 1003816100381610038161003816120596 sdot 119909119894+ 119887 minus 119910

119894

1003816100381610038161003816 le 120576 119894 = 1 119897

(7)

where 120596 is the vector of weight 120596 isin 119877119899 and 119887 is the intercept

119887 isin 119877 As theremay be some estimating errors we introduce aparameter 119862 and two slack variables 120585

119894 120585lowast119894 Then the optimal

problem above can be modified as follows

min 1

21205962+ 119862

119897

sum

119894

(120585119894+ 120585lowast

119894)

st 1003816100381610038161003816120596 sdot 119909119894+ 119887 minus 119910

119894

1003816100381610038161003816 le 120585lowast

119894+ 120576

119910119894minus (120596 sdot 119909

119894) minus 119887 le 120585

lowast

119894+ 120576

120585119894 120585lowast

119894ge 0 119894 = 1 119897

(8)

Establish the Lagrange function and solve it under theKKT conditions The dual problem of the original one is asfollows

min

1

2

119897

sum

119894119895=1

(120572lowast

119894minus 120572119894) (120572lowast

119895minus 120572119895) (119909119894sdot 119909119895)

+120576

119897

sum

119894

(120572lowast

119894+ 120572119894) minus

119897

sum

119894

119910119894(120572lowast

119894minus 120572119894)

st119897

sum

119894

(120572119894minus 120572lowast

119894) = 0

0 le 120572119894 120572lowast

119894le 119862 119894 = 1 119897

(9)

4 International Journal of Antennas and Propagation

At last the regression decision function is as follows

119891 (119909) =

119897

sum

119894

(120572119894minus 120572lowast

119894) (119909119894sdot 119909) + 119887 (10)

412 The Nonlinear Regression When the dataset cannot belinearly regressed we can transform the original data intoa high dimension feature space using a nonlinear mapping120593(119909) where we can carry out the linear regression Bydefining the kernel function of the inner product of the highdimension feature space 119870(119909

119894 119910119894) = 120593(119909

119894)120593(119910119894) the inner

product of a variable in the high dimension space can beobtained by operating in the original space through the kernelfunction

min

1

2

119897

sum

119894119895=1

(120572lowast

119894minus 120572119894) (120572lowast

119895minus 120572119895)119870 (119909

119894sdot 119909119895)

+120576

119897

sum

119894

(120572lowast

119894+ 120572119894) minus

119897

sum

119894

119910119894(120572lowast

119894minus 120572119894)

st119897

sum

119894

(120572119894minus 120572lowast

119894) = 0

0 le 120572119894 120572lowast

119894le 119862 119894 = 1 119897

(11)

At last the regression decision function is as follows

119891 (119909) =

119897

sum

119894

(120572119894minus 120572lowast

119894)119870 (119909

119894sdot 119909) + 119887 (12)

413 The Selection of the Kernel Function Nowadays thewidely used kernel functions include the linear function thepolynomial kernel function the Gauss radial basis kernelfunction and the Sigmoid kernel function The performanceof the SVMhas no relationshipwith the selection of the differ-ent types of the kernel function but has a strong relationshipwith the parameters in the kernel function Nevertheless wecould select a good type of the kernel functions in order toreduce the calculation complexity

As for the polynomial kernel function (the linear kernelfunction is a special case of the polynomial kernel function)when the eigenspace has a high dimension the calculationamount could be huge and what is even worse we cannotobtain any correct solution under some certain situationsHowever the Gauss radial basis kernel function can over-come similar problems Furthermore the selection of Gausskernel function is connotative that is every support vectorwould produce a local Gauss function which is centered bythe vector itself We can find the global width of the basisfunction by structural risk minimization principle As statedabove we take the Gauss radial basis kernel function in thefollowing study

42 The Choice of Input and Output Variables We randomlyselect 5 rows (such as 16 to 20 rows) where only table data (Z)of the seats B and D are treated as unknown data (10 groupstotally) We use SVM model to forecast these 10 groups of

Raw data

0 510

15 2025 30

3540

45

5

5550606570

Cabin length

Cabin width

Path

loss

(dB)

152

253

354

45

1

Figure 4 Raw data

05

1015

2025

3035

4045

1

555606570

Cabin length

Cabin width

Path

loss

(dB)

60

61

62

63

64

65

66

67

68

B-spline surface fitting

152

253

354

45

Figure 5 B-spline surface fitting

Table 2 The error analysis of B-spline surface fitting dB

Point True value Fitted value Absolute error Relative error16ZB 646 6614 154 23816ZD 6395 6545 15 23517ZB 6502 6458 044 06817ZD 6281 6349 068 10818ZB 6446 6236 21 32618ZD 6491 6247 244 37619ZB 6333 6318 015 02419ZD 6483 6371 112 17320ZB 6446 6275 171 26520ZD 6409 6379 03 047The average of the relative error using B-spline surface fitting is 186

unknown data in order to verify the accuracy of the SVMprediction model The sample data of BCD is selected thereminder 30 rows (from 1K to 15Z and from 21K to 22Z)For one certain point the surrounding eight points path

International Journal of Antennas and Propagation 5

Table 3 An example of input and output variables in SVMmodel dB

Input data Output data6639 6577 6491 6258 6501 6451 655 6657 6426(1ZA) (1ZB) (1ZC) (1KC) (2ZC) (2ZB) (2ZA) (1KA) (1KB)6577 6491 6801 636 6583 6501 6451 6426 6258(1ZB) (1ZC) (1ZD) (1KD) (2ZD) (2ZC) (2ZB) (1KB) (1KC)6491 6801 6744 6661 6642 6583 6501 6258 636(1ZC) (1ZD) (1ZE) (1KE) (2ZE) (2ZD) (2ZC) (1KC) (1KD)

Table 4 The error analysis of the 45 groups back of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6248 212 32816ZD 6395 6192 203 31717ZB 6502 6213 289 44417ZD 6281 6181 1 15918ZB 6446 6256 19 29518ZD 6491 6183 308 47519ZB 6333 6203 13 20519ZD 6483 6177 306 47220ZB 6446 6256 19 29520ZD 6409 6163 246 384

Table 5 The error analysis of the 45 groups table of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6512 052 08016ZD 6395 6457 062 09717ZB 6502 6475 027 04217ZD 6281 6401 12 19118ZB 6446 6429 017 02618ZD 6491 637 121 18619ZB 6333 6435 102 16119ZD 6483 6416 067 10320ZB 6446 6446 0 020ZD 6409 6388 021 033

loss values are selected as the eight input variables 119909119894 119894 =

1 2 8 and the path loss value of this point is supposed asthe output variables 119910 The ninety sets of data included forty-five sets of seat back data and forty-five sets of table data Thefirst 8 values of each line are input variables the last data is theoutput variable Examples of the path loss samples selected asthe input data and the output data in SVMmodel are listed inTable 3

43 Path Loss Prediction Using SVM-Based Model in Cabin

431 Case 1 Training Table Data Using Seat Back DataFirstly the training samples of the forty-five back data areselected from ninety sets The data of forty-five groups are

trained using SVM The unknown data of row 16 to row 20are predicted using the trained model In order to verify thevalidity of the model the error analysis is caculated for thereal value and the predictive value such as absolute error andrelative error The result is described in Table 4 The relativeerror in the table refers to the ratio of the real value andabsolute error value

We average the relative error in Table 4 and conclude thatthe average relative error predicted is 337which shows thatthe forecast is not very accurate using the samples of back ofchair to train the table of chairs

432 Case 2 Training Table Data Using Table Data Then weselect the rest of the 45 groups of table samples to train themodel and send the 45 groups of data into SVM for trainingWe still forecast the 10 points mentioned above The result isdescribed in Table 5

The average relative error predicted is 092The conclu-sion is that when we use the samples of the tables to train asthe training samples and the predicted samples share morerelevance which means that their channel environments aremore similar the model is more accurate

433 Case 3 Training Table Data Using Both Seat Back andTable Data Finally we take all the 90 datasets includingsamples on back of the chair and the table into the SVMmodel for training We forecast the 10 points mentionedabove The result is described in Table 6

The average relative error predicted is 102 It can beconcluded that increasing training samples which share lessrelevance with the predicted samples makes no contributionto the accuracy of the prediction model

5 Further Discussion

It can be concluded that the accuracy forecasted by SVM isincreased greatly compared with the accuracy predicted bysurface fitting The relative average forecast error of SVMcan reach 092 in Case 2 The relative average forecasterror of surface fitting is 186 in this study using the samemeasurement data The accuracy of surface fitting and SVMfitting is compared in Figure 6

For the surface fitting method the plane is fitting ofsurface of these points with smooth surface connected fromfitting surface to find needed points The cabin environmentof plane is very complex with a lot of seats so the shadow

6 International Journal of Antennas and Propagation

Table 6 The error analysis of all the 90 groups training dB

Point True value Fitted value Absolute error Relative error16ZB 646 6514 054 08416ZD 6395 6495 1 15617ZB 6502 6434 068 10517ZD 6281 6392 111 17718ZB 6446 6394 052 08118ZD 6491 6348 143 22019ZB 6333 6381 048 07619ZD 6483 6438 045 06920ZB 6446 6443 003 00520ZD 6409 6437 028 044

1 2 3 4 5 6 7 8 9 10Data

Data comparison

Raw dataB-spline surface fitting

SVM

62

625

63

635

64

645

65

655

66

665

Path

loss

(dB)

Figure 6 Data Comparasion

fading will affect the signal strength greatly However mostthings in cabin are stable so it is very suitable to forecastusing SVM The environment information included in theSVM training data can avoid the influence of shadow fadingon predicting effectively

It can also be concluded that the more relevance of thetraining samples and the predicted samples can improve theaccuracy of the prediction model Besides more sampleswhich share less relevance with the predicted samples makeno contribution to the accuracy in statistical aspect

One of the purposes of this paper is to reduce the amountof measurements We need to reduce the measurementactivities as far as possible and predict the unknown pointusing SVM-based model at an acceptable error level

6 Conclusion

Although path loss can be obtained via theoretical predictionor field measurement the method of Computational Electro-magnetic and a lot of measurements without changing thecabin environment are very difficult to proceed because the

cabin is a big and complex space The principle challengesare to simplify the complicate measurement and to improvethe accuracy of prediction of the path loss In this paper anSVM-based path loss prediction method was first proposedto overcome the measurement challenges in complex andbig cabin environment We selected the path loss valuesaround the predicted points as the input data of the predictionmodel and used the trained model to predict points not beenmeasured The path loss prediction results demonstratedthat the proposed SVM-based prediction method is effectiveand accurate compared to the surface fitting method Therelevance of the training samples and the predicted samplescan affect the accuracy of the predictionmodelThe proposedSVM-based path loss prediction method can forecast thepoints inconvenient to be measured which can reduce theamount of measurement and provide supplement informa-tion in channel modeling

Acknowledgments

This work was supported by the National Science andTechnology Major Project of the Ministry of Science andTechnology of China (Grant no 2009ZX03007-003) theNational High Technology Research and Development Pro-gram of China (Grant no 2009AA011507) and the NationalNatural Science Foundation of China (Grant no 61101223)The authors would like to thank Tsinghua University forproviding the measurement data The first author also wouldlike to thank Associate Professor Yang Jinsheng and theproject team members Mao Xiangfang and Wu Xuzhao forthe helpful discussion

References

[1] N R Dıaz and J E J Esquitino ldquoWideband channel characteri-zation for wireless communications inside a short haul aircraftrdquoinProceedings of the IEEE 59thVehicular Technology Conferencepp 223ndash228 Milan Italy May 2004

[2] S Chiu J Chuang and D G Michelson ldquoCharacterization ofUWB channel impulse responses within the passenger cabin ofa boeing 737-200 aircraftrdquo IEEE Transactions on Antennas andPropagation vol 58 no 3 pp 935ndash945 2010

[3] K Chetcuti C J Debono R A Farrugia and S BruillotldquoWireless propagation modelling inside a business jetrdquo inProceedings of the IEEE Eurocon (EUROCON rsquo09) pp 1644ndash1649 St-Petersburg Russia May 2009

[4] J Jemai R Piesiewicz R Geise et al ldquoUWB channel modelingwithin an aircraft cabinrdquo in Proceedings of the IEEE Interna-tional Conference on Ultra-Wideband ICUWB 2008 pp 5ndash8Hannover Germany September 2008

[5] J Chuang N Xin H Huang S Chiu and D G MichelsonldquoUWB radiowave propagation within the passenger cabin ofa boeing 737-200 aircraftrdquo in Proceedings of the IEEE 65thVehicular Technology Conference pp 496ndash500 Dublin IrelandApril 2007

[6] C Cerasoli ldquoRF propagation in tunnel enviromentsrdquo in Pro-ceedings of the IEEEMilitary Communications Conference (OtL-COM rsquo04) pp 363ndash369 Monterey Calif USA November 2004

International Journal of Antennas and Propagation 7

[7] E Perrin F Tristant S Gouverneur et al ldquoStudy of electricfield radiated by wifi sources inside an aircraftmdash3D computa-tions and real testsrdquo in Proceedings of the IEEE InternationalSymposium on Electromagnetic Compatibility (EMC rsquo08) pp 1ndash5 Hamburg Germany September 2008

[8] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[9] Z Xiang X W Liu and R C Shangguan ldquoResearch on thechannel prediction algorithm of multiwavelet combined withsupport vector machines based on FPGArdquo in Proceedings of the6th International Conference on Natural Computation (ICNCrsquo10) pp 3614ndash3618 Yantai Shandong China August 2010

[10] J P Zhang Y N Zhuo and Y Zhao ldquoMobile location basedon SVM In MIMO communication systemsrdquo in Proceedings ofthe International Conference on Information Networking andAutomation (ICINA rsquo10) pp V2-360ndashV2-363 Kunming ChinaOctober 2010

[11] Y H Rui Y Zhang S J Liu and S D Zhou ldquo352GHz MIMOradio channel sounderrdquo in Proceedings of the InternationalConference on Communications Circuits and Systems (ICCCASrsquo08) pp 79ndash83 Fujian China May 2008

[12] X W Hu Y Zhang Y Z Jia S D Zhou and L MXiao ldquoPower coverage and fading characteristics of indoordistributed antenna systemsrdquo in Proceedings of the 4th Interna-tional Conference on Communications and Networking in China(CHINACOM rsquo09) pp 1066ndash1069 Xirsquoan China August 2009

[13] C H Zhuo S J Liu Y Zhang Y H Rui and S D ZhouldquoA simple broadband MIMO channel sounder prototyperdquo inProceedings of the International Conference on Wireless Mobileand Multimedia Networks pp 1ndash4 Hangzhou China 2006

[14] Y L Hu and M M Li ldquoSurface fitting by splines using matlabrdquoJournal of Yunnan University for Nationalities vol 14 no 2 pp168ndash171 2005

[15] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks vol 10 no 5 pp 988ndash9991999

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Page 4: Research Article A New SVM-Based Modeling …downloads.hindawi.com/journals/ijap/2013/279070.pdfwhich permits unrestricted use, distribution, and reproductio n in any medium, provided

4 International Journal of Antennas and Propagation

At last the regression decision function is as follows

119891 (119909) =

119897

sum

119894

(120572119894minus 120572lowast

119894) (119909119894sdot 119909) + 119887 (10)

412 The Nonlinear Regression When the dataset cannot belinearly regressed we can transform the original data intoa high dimension feature space using a nonlinear mapping120593(119909) where we can carry out the linear regression Bydefining the kernel function of the inner product of the highdimension feature space 119870(119909

119894 119910119894) = 120593(119909

119894)120593(119910119894) the inner

product of a variable in the high dimension space can beobtained by operating in the original space through the kernelfunction

min

1

2

119897

sum

119894119895=1

(120572lowast

119894minus 120572119894) (120572lowast

119895minus 120572119895)119870 (119909

119894sdot 119909119895)

+120576

119897

sum

119894

(120572lowast

119894+ 120572119894) minus

119897

sum

119894

119910119894(120572lowast

119894minus 120572119894)

st119897

sum

119894

(120572119894minus 120572lowast

119894) = 0

0 le 120572119894 120572lowast

119894le 119862 119894 = 1 119897

(11)

At last the regression decision function is as follows

119891 (119909) =

119897

sum

119894

(120572119894minus 120572lowast

119894)119870 (119909

119894sdot 119909) + 119887 (12)

413 The Selection of the Kernel Function Nowadays thewidely used kernel functions include the linear function thepolynomial kernel function the Gauss radial basis kernelfunction and the Sigmoid kernel function The performanceof the SVMhas no relationshipwith the selection of the differ-ent types of the kernel function but has a strong relationshipwith the parameters in the kernel function Nevertheless wecould select a good type of the kernel functions in order toreduce the calculation complexity

As for the polynomial kernel function (the linear kernelfunction is a special case of the polynomial kernel function)when the eigenspace has a high dimension the calculationamount could be huge and what is even worse we cannotobtain any correct solution under some certain situationsHowever the Gauss radial basis kernel function can over-come similar problems Furthermore the selection of Gausskernel function is connotative that is every support vectorwould produce a local Gauss function which is centered bythe vector itself We can find the global width of the basisfunction by structural risk minimization principle As statedabove we take the Gauss radial basis kernel function in thefollowing study

42 The Choice of Input and Output Variables We randomlyselect 5 rows (such as 16 to 20 rows) where only table data (Z)of the seats B and D are treated as unknown data (10 groupstotally) We use SVM model to forecast these 10 groups of

Raw data

0 510

15 2025 30

3540

45

5

5550606570

Cabin length

Cabin width

Path

loss

(dB)

152

253

354

45

1

Figure 4 Raw data

05

1015

2025

3035

4045

1

555606570

Cabin length

Cabin width

Path

loss

(dB)

60

61

62

63

64

65

66

67

68

B-spline surface fitting

152

253

354

45

Figure 5 B-spline surface fitting

Table 2 The error analysis of B-spline surface fitting dB

Point True value Fitted value Absolute error Relative error16ZB 646 6614 154 23816ZD 6395 6545 15 23517ZB 6502 6458 044 06817ZD 6281 6349 068 10818ZB 6446 6236 21 32618ZD 6491 6247 244 37619ZB 6333 6318 015 02419ZD 6483 6371 112 17320ZB 6446 6275 171 26520ZD 6409 6379 03 047The average of the relative error using B-spline surface fitting is 186

unknown data in order to verify the accuracy of the SVMprediction model The sample data of BCD is selected thereminder 30 rows (from 1K to 15Z and from 21K to 22Z)For one certain point the surrounding eight points path

International Journal of Antennas and Propagation 5

Table 3 An example of input and output variables in SVMmodel dB

Input data Output data6639 6577 6491 6258 6501 6451 655 6657 6426(1ZA) (1ZB) (1ZC) (1KC) (2ZC) (2ZB) (2ZA) (1KA) (1KB)6577 6491 6801 636 6583 6501 6451 6426 6258(1ZB) (1ZC) (1ZD) (1KD) (2ZD) (2ZC) (2ZB) (1KB) (1KC)6491 6801 6744 6661 6642 6583 6501 6258 636(1ZC) (1ZD) (1ZE) (1KE) (2ZE) (2ZD) (2ZC) (1KC) (1KD)

Table 4 The error analysis of the 45 groups back of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6248 212 32816ZD 6395 6192 203 31717ZB 6502 6213 289 44417ZD 6281 6181 1 15918ZB 6446 6256 19 29518ZD 6491 6183 308 47519ZB 6333 6203 13 20519ZD 6483 6177 306 47220ZB 6446 6256 19 29520ZD 6409 6163 246 384

Table 5 The error analysis of the 45 groups table of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6512 052 08016ZD 6395 6457 062 09717ZB 6502 6475 027 04217ZD 6281 6401 12 19118ZB 6446 6429 017 02618ZD 6491 637 121 18619ZB 6333 6435 102 16119ZD 6483 6416 067 10320ZB 6446 6446 0 020ZD 6409 6388 021 033

loss values are selected as the eight input variables 119909119894 119894 =

1 2 8 and the path loss value of this point is supposed asthe output variables 119910 The ninety sets of data included forty-five sets of seat back data and forty-five sets of table data Thefirst 8 values of each line are input variables the last data is theoutput variable Examples of the path loss samples selected asthe input data and the output data in SVMmodel are listed inTable 3

43 Path Loss Prediction Using SVM-Based Model in Cabin

431 Case 1 Training Table Data Using Seat Back DataFirstly the training samples of the forty-five back data areselected from ninety sets The data of forty-five groups are

trained using SVM The unknown data of row 16 to row 20are predicted using the trained model In order to verify thevalidity of the model the error analysis is caculated for thereal value and the predictive value such as absolute error andrelative error The result is described in Table 4 The relativeerror in the table refers to the ratio of the real value andabsolute error value

We average the relative error in Table 4 and conclude thatthe average relative error predicted is 337which shows thatthe forecast is not very accurate using the samples of back ofchair to train the table of chairs

432 Case 2 Training Table Data Using Table Data Then weselect the rest of the 45 groups of table samples to train themodel and send the 45 groups of data into SVM for trainingWe still forecast the 10 points mentioned above The result isdescribed in Table 5

The average relative error predicted is 092The conclu-sion is that when we use the samples of the tables to train asthe training samples and the predicted samples share morerelevance which means that their channel environments aremore similar the model is more accurate

433 Case 3 Training Table Data Using Both Seat Back andTable Data Finally we take all the 90 datasets includingsamples on back of the chair and the table into the SVMmodel for training We forecast the 10 points mentionedabove The result is described in Table 6

The average relative error predicted is 102 It can beconcluded that increasing training samples which share lessrelevance with the predicted samples makes no contributionto the accuracy of the prediction model

5 Further Discussion

It can be concluded that the accuracy forecasted by SVM isincreased greatly compared with the accuracy predicted bysurface fitting The relative average forecast error of SVMcan reach 092 in Case 2 The relative average forecasterror of surface fitting is 186 in this study using the samemeasurement data The accuracy of surface fitting and SVMfitting is compared in Figure 6

For the surface fitting method the plane is fitting ofsurface of these points with smooth surface connected fromfitting surface to find needed points The cabin environmentof plane is very complex with a lot of seats so the shadow

6 International Journal of Antennas and Propagation

Table 6 The error analysis of all the 90 groups training dB

Point True value Fitted value Absolute error Relative error16ZB 646 6514 054 08416ZD 6395 6495 1 15617ZB 6502 6434 068 10517ZD 6281 6392 111 17718ZB 6446 6394 052 08118ZD 6491 6348 143 22019ZB 6333 6381 048 07619ZD 6483 6438 045 06920ZB 6446 6443 003 00520ZD 6409 6437 028 044

1 2 3 4 5 6 7 8 9 10Data

Data comparison

Raw dataB-spline surface fitting

SVM

62

625

63

635

64

645

65

655

66

665

Path

loss

(dB)

Figure 6 Data Comparasion

fading will affect the signal strength greatly However mostthings in cabin are stable so it is very suitable to forecastusing SVM The environment information included in theSVM training data can avoid the influence of shadow fadingon predicting effectively

It can also be concluded that the more relevance of thetraining samples and the predicted samples can improve theaccuracy of the prediction model Besides more sampleswhich share less relevance with the predicted samples makeno contribution to the accuracy in statistical aspect

One of the purposes of this paper is to reduce the amountof measurements We need to reduce the measurementactivities as far as possible and predict the unknown pointusing SVM-based model at an acceptable error level

6 Conclusion

Although path loss can be obtained via theoretical predictionor field measurement the method of Computational Electro-magnetic and a lot of measurements without changing thecabin environment are very difficult to proceed because the

cabin is a big and complex space The principle challengesare to simplify the complicate measurement and to improvethe accuracy of prediction of the path loss In this paper anSVM-based path loss prediction method was first proposedto overcome the measurement challenges in complex andbig cabin environment We selected the path loss valuesaround the predicted points as the input data of the predictionmodel and used the trained model to predict points not beenmeasured The path loss prediction results demonstratedthat the proposed SVM-based prediction method is effectiveand accurate compared to the surface fitting method Therelevance of the training samples and the predicted samplescan affect the accuracy of the predictionmodelThe proposedSVM-based path loss prediction method can forecast thepoints inconvenient to be measured which can reduce theamount of measurement and provide supplement informa-tion in channel modeling

Acknowledgments

This work was supported by the National Science andTechnology Major Project of the Ministry of Science andTechnology of China (Grant no 2009ZX03007-003) theNational High Technology Research and Development Pro-gram of China (Grant no 2009AA011507) and the NationalNatural Science Foundation of China (Grant no 61101223)The authors would like to thank Tsinghua University forproviding the measurement data The first author also wouldlike to thank Associate Professor Yang Jinsheng and theproject team members Mao Xiangfang and Wu Xuzhao forthe helpful discussion

References

[1] N R Dıaz and J E J Esquitino ldquoWideband channel characteri-zation for wireless communications inside a short haul aircraftrdquoinProceedings of the IEEE 59thVehicular Technology Conferencepp 223ndash228 Milan Italy May 2004

[2] S Chiu J Chuang and D G Michelson ldquoCharacterization ofUWB channel impulse responses within the passenger cabin ofa boeing 737-200 aircraftrdquo IEEE Transactions on Antennas andPropagation vol 58 no 3 pp 935ndash945 2010

[3] K Chetcuti C J Debono R A Farrugia and S BruillotldquoWireless propagation modelling inside a business jetrdquo inProceedings of the IEEE Eurocon (EUROCON rsquo09) pp 1644ndash1649 St-Petersburg Russia May 2009

[4] J Jemai R Piesiewicz R Geise et al ldquoUWB channel modelingwithin an aircraft cabinrdquo in Proceedings of the IEEE Interna-tional Conference on Ultra-Wideband ICUWB 2008 pp 5ndash8Hannover Germany September 2008

[5] J Chuang N Xin H Huang S Chiu and D G MichelsonldquoUWB radiowave propagation within the passenger cabin ofa boeing 737-200 aircraftrdquo in Proceedings of the IEEE 65thVehicular Technology Conference pp 496ndash500 Dublin IrelandApril 2007

[6] C Cerasoli ldquoRF propagation in tunnel enviromentsrdquo in Pro-ceedings of the IEEEMilitary Communications Conference (OtL-COM rsquo04) pp 363ndash369 Monterey Calif USA November 2004

International Journal of Antennas and Propagation 7

[7] E Perrin F Tristant S Gouverneur et al ldquoStudy of electricfield radiated by wifi sources inside an aircraftmdash3D computa-tions and real testsrdquo in Proceedings of the IEEE InternationalSymposium on Electromagnetic Compatibility (EMC rsquo08) pp 1ndash5 Hamburg Germany September 2008

[8] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[9] Z Xiang X W Liu and R C Shangguan ldquoResearch on thechannel prediction algorithm of multiwavelet combined withsupport vector machines based on FPGArdquo in Proceedings of the6th International Conference on Natural Computation (ICNCrsquo10) pp 3614ndash3618 Yantai Shandong China August 2010

[10] J P Zhang Y N Zhuo and Y Zhao ldquoMobile location basedon SVM In MIMO communication systemsrdquo in Proceedings ofthe International Conference on Information Networking andAutomation (ICINA rsquo10) pp V2-360ndashV2-363 Kunming ChinaOctober 2010

[11] Y H Rui Y Zhang S J Liu and S D Zhou ldquo352GHz MIMOradio channel sounderrdquo in Proceedings of the InternationalConference on Communications Circuits and Systems (ICCCASrsquo08) pp 79ndash83 Fujian China May 2008

[12] X W Hu Y Zhang Y Z Jia S D Zhou and L MXiao ldquoPower coverage and fading characteristics of indoordistributed antenna systemsrdquo in Proceedings of the 4th Interna-tional Conference on Communications and Networking in China(CHINACOM rsquo09) pp 1066ndash1069 Xirsquoan China August 2009

[13] C H Zhuo S J Liu Y Zhang Y H Rui and S D ZhouldquoA simple broadband MIMO channel sounder prototyperdquo inProceedings of the International Conference on Wireless Mobileand Multimedia Networks pp 1ndash4 Hangzhou China 2006

[14] Y L Hu and M M Li ldquoSurface fitting by splines using matlabrdquoJournal of Yunnan University for Nationalities vol 14 no 2 pp168ndash171 2005

[15] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks vol 10 no 5 pp 988ndash9991999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 5: Research Article A New SVM-Based Modeling …downloads.hindawi.com/journals/ijap/2013/279070.pdfwhich permits unrestricted use, distribution, and reproductio n in any medium, provided

International Journal of Antennas and Propagation 5

Table 3 An example of input and output variables in SVMmodel dB

Input data Output data6639 6577 6491 6258 6501 6451 655 6657 6426(1ZA) (1ZB) (1ZC) (1KC) (2ZC) (2ZB) (2ZA) (1KA) (1KB)6577 6491 6801 636 6583 6501 6451 6426 6258(1ZB) (1ZC) (1ZD) (1KD) (2ZD) (2ZC) (2ZB) (1KB) (1KC)6491 6801 6744 6661 6642 6583 6501 6258 636(1ZC) (1ZD) (1ZE) (1KE) (2ZE) (2ZD) (2ZC) (1KC) (1KD)

Table 4 The error analysis of the 45 groups back of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6248 212 32816ZD 6395 6192 203 31717ZB 6502 6213 289 44417ZD 6281 6181 1 15918ZB 6446 6256 19 29518ZD 6491 6183 308 47519ZB 6333 6203 13 20519ZD 6483 6177 306 47220ZB 6446 6256 19 29520ZD 6409 6163 246 384

Table 5 The error analysis of the 45 groups table of chairs trainingdB

Point True value Fitted value Absolute error Relative error16ZB 646 6512 052 08016ZD 6395 6457 062 09717ZB 6502 6475 027 04217ZD 6281 6401 12 19118ZB 6446 6429 017 02618ZD 6491 637 121 18619ZB 6333 6435 102 16119ZD 6483 6416 067 10320ZB 6446 6446 0 020ZD 6409 6388 021 033

loss values are selected as the eight input variables 119909119894 119894 =

1 2 8 and the path loss value of this point is supposed asthe output variables 119910 The ninety sets of data included forty-five sets of seat back data and forty-five sets of table data Thefirst 8 values of each line are input variables the last data is theoutput variable Examples of the path loss samples selected asthe input data and the output data in SVMmodel are listed inTable 3

43 Path Loss Prediction Using SVM-Based Model in Cabin

431 Case 1 Training Table Data Using Seat Back DataFirstly the training samples of the forty-five back data areselected from ninety sets The data of forty-five groups are

trained using SVM The unknown data of row 16 to row 20are predicted using the trained model In order to verify thevalidity of the model the error analysis is caculated for thereal value and the predictive value such as absolute error andrelative error The result is described in Table 4 The relativeerror in the table refers to the ratio of the real value andabsolute error value

We average the relative error in Table 4 and conclude thatthe average relative error predicted is 337which shows thatthe forecast is not very accurate using the samples of back ofchair to train the table of chairs

432 Case 2 Training Table Data Using Table Data Then weselect the rest of the 45 groups of table samples to train themodel and send the 45 groups of data into SVM for trainingWe still forecast the 10 points mentioned above The result isdescribed in Table 5

The average relative error predicted is 092The conclu-sion is that when we use the samples of the tables to train asthe training samples and the predicted samples share morerelevance which means that their channel environments aremore similar the model is more accurate

433 Case 3 Training Table Data Using Both Seat Back andTable Data Finally we take all the 90 datasets includingsamples on back of the chair and the table into the SVMmodel for training We forecast the 10 points mentionedabove The result is described in Table 6

The average relative error predicted is 102 It can beconcluded that increasing training samples which share lessrelevance with the predicted samples makes no contributionto the accuracy of the prediction model

5 Further Discussion

It can be concluded that the accuracy forecasted by SVM isincreased greatly compared with the accuracy predicted bysurface fitting The relative average forecast error of SVMcan reach 092 in Case 2 The relative average forecasterror of surface fitting is 186 in this study using the samemeasurement data The accuracy of surface fitting and SVMfitting is compared in Figure 6

For the surface fitting method the plane is fitting ofsurface of these points with smooth surface connected fromfitting surface to find needed points The cabin environmentof plane is very complex with a lot of seats so the shadow

6 International Journal of Antennas and Propagation

Table 6 The error analysis of all the 90 groups training dB

Point True value Fitted value Absolute error Relative error16ZB 646 6514 054 08416ZD 6395 6495 1 15617ZB 6502 6434 068 10517ZD 6281 6392 111 17718ZB 6446 6394 052 08118ZD 6491 6348 143 22019ZB 6333 6381 048 07619ZD 6483 6438 045 06920ZB 6446 6443 003 00520ZD 6409 6437 028 044

1 2 3 4 5 6 7 8 9 10Data

Data comparison

Raw dataB-spline surface fitting

SVM

62

625

63

635

64

645

65

655

66

665

Path

loss

(dB)

Figure 6 Data Comparasion

fading will affect the signal strength greatly However mostthings in cabin are stable so it is very suitable to forecastusing SVM The environment information included in theSVM training data can avoid the influence of shadow fadingon predicting effectively

It can also be concluded that the more relevance of thetraining samples and the predicted samples can improve theaccuracy of the prediction model Besides more sampleswhich share less relevance with the predicted samples makeno contribution to the accuracy in statistical aspect

One of the purposes of this paper is to reduce the amountof measurements We need to reduce the measurementactivities as far as possible and predict the unknown pointusing SVM-based model at an acceptable error level

6 Conclusion

Although path loss can be obtained via theoretical predictionor field measurement the method of Computational Electro-magnetic and a lot of measurements without changing thecabin environment are very difficult to proceed because the

cabin is a big and complex space The principle challengesare to simplify the complicate measurement and to improvethe accuracy of prediction of the path loss In this paper anSVM-based path loss prediction method was first proposedto overcome the measurement challenges in complex andbig cabin environment We selected the path loss valuesaround the predicted points as the input data of the predictionmodel and used the trained model to predict points not beenmeasured The path loss prediction results demonstratedthat the proposed SVM-based prediction method is effectiveand accurate compared to the surface fitting method Therelevance of the training samples and the predicted samplescan affect the accuracy of the predictionmodelThe proposedSVM-based path loss prediction method can forecast thepoints inconvenient to be measured which can reduce theamount of measurement and provide supplement informa-tion in channel modeling

Acknowledgments

This work was supported by the National Science andTechnology Major Project of the Ministry of Science andTechnology of China (Grant no 2009ZX03007-003) theNational High Technology Research and Development Pro-gram of China (Grant no 2009AA011507) and the NationalNatural Science Foundation of China (Grant no 61101223)The authors would like to thank Tsinghua University forproviding the measurement data The first author also wouldlike to thank Associate Professor Yang Jinsheng and theproject team members Mao Xiangfang and Wu Xuzhao forthe helpful discussion

References

[1] N R Dıaz and J E J Esquitino ldquoWideband channel characteri-zation for wireless communications inside a short haul aircraftrdquoinProceedings of the IEEE 59thVehicular Technology Conferencepp 223ndash228 Milan Italy May 2004

[2] S Chiu J Chuang and D G Michelson ldquoCharacterization ofUWB channel impulse responses within the passenger cabin ofa boeing 737-200 aircraftrdquo IEEE Transactions on Antennas andPropagation vol 58 no 3 pp 935ndash945 2010

[3] K Chetcuti C J Debono R A Farrugia and S BruillotldquoWireless propagation modelling inside a business jetrdquo inProceedings of the IEEE Eurocon (EUROCON rsquo09) pp 1644ndash1649 St-Petersburg Russia May 2009

[4] J Jemai R Piesiewicz R Geise et al ldquoUWB channel modelingwithin an aircraft cabinrdquo in Proceedings of the IEEE Interna-tional Conference on Ultra-Wideband ICUWB 2008 pp 5ndash8Hannover Germany September 2008

[5] J Chuang N Xin H Huang S Chiu and D G MichelsonldquoUWB radiowave propagation within the passenger cabin ofa boeing 737-200 aircraftrdquo in Proceedings of the IEEE 65thVehicular Technology Conference pp 496ndash500 Dublin IrelandApril 2007

[6] C Cerasoli ldquoRF propagation in tunnel enviromentsrdquo in Pro-ceedings of the IEEEMilitary Communications Conference (OtL-COM rsquo04) pp 363ndash369 Monterey Calif USA November 2004

International Journal of Antennas and Propagation 7

[7] E Perrin F Tristant S Gouverneur et al ldquoStudy of electricfield radiated by wifi sources inside an aircraftmdash3D computa-tions and real testsrdquo in Proceedings of the IEEE InternationalSymposium on Electromagnetic Compatibility (EMC rsquo08) pp 1ndash5 Hamburg Germany September 2008

[8] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[9] Z Xiang X W Liu and R C Shangguan ldquoResearch on thechannel prediction algorithm of multiwavelet combined withsupport vector machines based on FPGArdquo in Proceedings of the6th International Conference on Natural Computation (ICNCrsquo10) pp 3614ndash3618 Yantai Shandong China August 2010

[10] J P Zhang Y N Zhuo and Y Zhao ldquoMobile location basedon SVM In MIMO communication systemsrdquo in Proceedings ofthe International Conference on Information Networking andAutomation (ICINA rsquo10) pp V2-360ndashV2-363 Kunming ChinaOctober 2010

[11] Y H Rui Y Zhang S J Liu and S D Zhou ldquo352GHz MIMOradio channel sounderrdquo in Proceedings of the InternationalConference on Communications Circuits and Systems (ICCCASrsquo08) pp 79ndash83 Fujian China May 2008

[12] X W Hu Y Zhang Y Z Jia S D Zhou and L MXiao ldquoPower coverage and fading characteristics of indoordistributed antenna systemsrdquo in Proceedings of the 4th Interna-tional Conference on Communications and Networking in China(CHINACOM rsquo09) pp 1066ndash1069 Xirsquoan China August 2009

[13] C H Zhuo S J Liu Y Zhang Y H Rui and S D ZhouldquoA simple broadband MIMO channel sounder prototyperdquo inProceedings of the International Conference on Wireless Mobileand Multimedia Networks pp 1ndash4 Hangzhou China 2006

[14] Y L Hu and M M Li ldquoSurface fitting by splines using matlabrdquoJournal of Yunnan University for Nationalities vol 14 no 2 pp168ndash171 2005

[15] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks vol 10 no 5 pp 988ndash9991999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 6: Research Article A New SVM-Based Modeling …downloads.hindawi.com/journals/ijap/2013/279070.pdfwhich permits unrestricted use, distribution, and reproductio n in any medium, provided

6 International Journal of Antennas and Propagation

Table 6 The error analysis of all the 90 groups training dB

Point True value Fitted value Absolute error Relative error16ZB 646 6514 054 08416ZD 6395 6495 1 15617ZB 6502 6434 068 10517ZD 6281 6392 111 17718ZB 6446 6394 052 08118ZD 6491 6348 143 22019ZB 6333 6381 048 07619ZD 6483 6438 045 06920ZB 6446 6443 003 00520ZD 6409 6437 028 044

1 2 3 4 5 6 7 8 9 10Data

Data comparison

Raw dataB-spline surface fitting

SVM

62

625

63

635

64

645

65

655

66

665

Path

loss

(dB)

Figure 6 Data Comparasion

fading will affect the signal strength greatly However mostthings in cabin are stable so it is very suitable to forecastusing SVM The environment information included in theSVM training data can avoid the influence of shadow fadingon predicting effectively

It can also be concluded that the more relevance of thetraining samples and the predicted samples can improve theaccuracy of the prediction model Besides more sampleswhich share less relevance with the predicted samples makeno contribution to the accuracy in statistical aspect

One of the purposes of this paper is to reduce the amountof measurements We need to reduce the measurementactivities as far as possible and predict the unknown pointusing SVM-based model at an acceptable error level

6 Conclusion

Although path loss can be obtained via theoretical predictionor field measurement the method of Computational Electro-magnetic and a lot of measurements without changing thecabin environment are very difficult to proceed because the

cabin is a big and complex space The principle challengesare to simplify the complicate measurement and to improvethe accuracy of prediction of the path loss In this paper anSVM-based path loss prediction method was first proposedto overcome the measurement challenges in complex andbig cabin environment We selected the path loss valuesaround the predicted points as the input data of the predictionmodel and used the trained model to predict points not beenmeasured The path loss prediction results demonstratedthat the proposed SVM-based prediction method is effectiveand accurate compared to the surface fitting method Therelevance of the training samples and the predicted samplescan affect the accuracy of the predictionmodelThe proposedSVM-based path loss prediction method can forecast thepoints inconvenient to be measured which can reduce theamount of measurement and provide supplement informa-tion in channel modeling

Acknowledgments

This work was supported by the National Science andTechnology Major Project of the Ministry of Science andTechnology of China (Grant no 2009ZX03007-003) theNational High Technology Research and Development Pro-gram of China (Grant no 2009AA011507) and the NationalNatural Science Foundation of China (Grant no 61101223)The authors would like to thank Tsinghua University forproviding the measurement data The first author also wouldlike to thank Associate Professor Yang Jinsheng and theproject team members Mao Xiangfang and Wu Xuzhao forthe helpful discussion

References

[1] N R Dıaz and J E J Esquitino ldquoWideband channel characteri-zation for wireless communications inside a short haul aircraftrdquoinProceedings of the IEEE 59thVehicular Technology Conferencepp 223ndash228 Milan Italy May 2004

[2] S Chiu J Chuang and D G Michelson ldquoCharacterization ofUWB channel impulse responses within the passenger cabin ofa boeing 737-200 aircraftrdquo IEEE Transactions on Antennas andPropagation vol 58 no 3 pp 935ndash945 2010

[3] K Chetcuti C J Debono R A Farrugia and S BruillotldquoWireless propagation modelling inside a business jetrdquo inProceedings of the IEEE Eurocon (EUROCON rsquo09) pp 1644ndash1649 St-Petersburg Russia May 2009

[4] J Jemai R Piesiewicz R Geise et al ldquoUWB channel modelingwithin an aircraft cabinrdquo in Proceedings of the IEEE Interna-tional Conference on Ultra-Wideband ICUWB 2008 pp 5ndash8Hannover Germany September 2008

[5] J Chuang N Xin H Huang S Chiu and D G MichelsonldquoUWB radiowave propagation within the passenger cabin ofa boeing 737-200 aircraftrdquo in Proceedings of the IEEE 65thVehicular Technology Conference pp 496ndash500 Dublin IrelandApril 2007

[6] C Cerasoli ldquoRF propagation in tunnel enviromentsrdquo in Pro-ceedings of the IEEEMilitary Communications Conference (OtL-COM rsquo04) pp 363ndash369 Monterey Calif USA November 2004

International Journal of Antennas and Propagation 7

[7] E Perrin F Tristant S Gouverneur et al ldquoStudy of electricfield radiated by wifi sources inside an aircraftmdash3D computa-tions and real testsrdquo in Proceedings of the IEEE InternationalSymposium on Electromagnetic Compatibility (EMC rsquo08) pp 1ndash5 Hamburg Germany September 2008

[8] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[9] Z Xiang X W Liu and R C Shangguan ldquoResearch on thechannel prediction algorithm of multiwavelet combined withsupport vector machines based on FPGArdquo in Proceedings of the6th International Conference on Natural Computation (ICNCrsquo10) pp 3614ndash3618 Yantai Shandong China August 2010

[10] J P Zhang Y N Zhuo and Y Zhao ldquoMobile location basedon SVM In MIMO communication systemsrdquo in Proceedings ofthe International Conference on Information Networking andAutomation (ICINA rsquo10) pp V2-360ndashV2-363 Kunming ChinaOctober 2010

[11] Y H Rui Y Zhang S J Liu and S D Zhou ldquo352GHz MIMOradio channel sounderrdquo in Proceedings of the InternationalConference on Communications Circuits and Systems (ICCCASrsquo08) pp 79ndash83 Fujian China May 2008

[12] X W Hu Y Zhang Y Z Jia S D Zhou and L MXiao ldquoPower coverage and fading characteristics of indoordistributed antenna systemsrdquo in Proceedings of the 4th Interna-tional Conference on Communications and Networking in China(CHINACOM rsquo09) pp 1066ndash1069 Xirsquoan China August 2009

[13] C H Zhuo S J Liu Y Zhang Y H Rui and S D ZhouldquoA simple broadband MIMO channel sounder prototyperdquo inProceedings of the International Conference on Wireless Mobileand Multimedia Networks pp 1ndash4 Hangzhou China 2006

[14] Y L Hu and M M Li ldquoSurface fitting by splines using matlabrdquoJournal of Yunnan University for Nationalities vol 14 no 2 pp168ndash171 2005

[15] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks vol 10 no 5 pp 988ndash9991999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 7: Research Article A New SVM-Based Modeling …downloads.hindawi.com/journals/ijap/2013/279070.pdfwhich permits unrestricted use, distribution, and reproductio n in any medium, provided

International Journal of Antennas and Propagation 7

[7] E Perrin F Tristant S Gouverneur et al ldquoStudy of electricfield radiated by wifi sources inside an aircraftmdash3D computa-tions and real testsrdquo in Proceedings of the IEEE InternationalSymposium on Electromagnetic Compatibility (EMC rsquo08) pp 1ndash5 Hamburg Germany September 2008

[8] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[9] Z Xiang X W Liu and R C Shangguan ldquoResearch on thechannel prediction algorithm of multiwavelet combined withsupport vector machines based on FPGArdquo in Proceedings of the6th International Conference on Natural Computation (ICNCrsquo10) pp 3614ndash3618 Yantai Shandong China August 2010

[10] J P Zhang Y N Zhuo and Y Zhao ldquoMobile location basedon SVM In MIMO communication systemsrdquo in Proceedings ofthe International Conference on Information Networking andAutomation (ICINA rsquo10) pp V2-360ndashV2-363 Kunming ChinaOctober 2010

[11] Y H Rui Y Zhang S J Liu and S D Zhou ldquo352GHz MIMOradio channel sounderrdquo in Proceedings of the InternationalConference on Communications Circuits and Systems (ICCCASrsquo08) pp 79ndash83 Fujian China May 2008

[12] X W Hu Y Zhang Y Z Jia S D Zhou and L MXiao ldquoPower coverage and fading characteristics of indoordistributed antenna systemsrdquo in Proceedings of the 4th Interna-tional Conference on Communications and Networking in China(CHINACOM rsquo09) pp 1066ndash1069 Xirsquoan China August 2009

[13] C H Zhuo S J Liu Y Zhang Y H Rui and S D ZhouldquoA simple broadband MIMO channel sounder prototyperdquo inProceedings of the International Conference on Wireless Mobileand Multimedia Networks pp 1ndash4 Hangzhou China 2006

[14] Y L Hu and M M Li ldquoSurface fitting by splines using matlabrdquoJournal of Yunnan University for Nationalities vol 14 no 2 pp168ndash171 2005

[15] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks vol 10 no 5 pp 988ndash9991999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 8: Research Article A New SVM-Based Modeling …downloads.hindawi.com/journals/ijap/2013/279070.pdfwhich permits unrestricted use, distribution, and reproductio n in any medium, provided

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of