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Comparison of Wavelet Families with Application to WiMAX Traffic Forecasting

This study compares different wavelet families for accurate forecasting of WiMAX traffic. The research proposes a selection strategy for mother wavelets and evaluates prediction accuracy using various types of wavelets.

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Comparison of Wavelet Families with Application to WiMAX Traffic Forecasting

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  1. Comparison of Wavelet Families with Application to WiMAX Traffic Forecasting Cristina Stolojescu, Ion Railean, Sorin Moga and Alexandru Isar Faculty of Electronics and Telecommunications, Timisoara, Romania TELECOM Bretagne, Brest, France OPTIM 2010

  2. Contents Subject.Objectives Wavelets. The Stationary Wavelet Transform Time-frequency localization Results Conclusions OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  3. Subject ARIMA based forecasting ANN based forecasting OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  4. Objectives • to propose a strategy for the selection of the mother wavelet used in one of the steps of our algorithm. • to evaluate the WiMAX traffic prediction accuracy by using different types of mother wavelets. OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  5. Wavelets • Provide a useful decomposition of the time series, in terms of both time and frequency. • One of the main properties of wavelets is that they are localized in time (or space) which makes them suitable for analyzing non-stationary signals. OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  6. The Stationary Wavelet Transform (SWT) • two parameters: • the mother wavelet which generates the decomposition. • the number of decomposition levels. • The Multi-resolution • Analysis (MRA) • the à trous algorithm, • which corresponds to • the computation of • the SWT. The SWT decomposition tree OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  7. Time-frequency localization • Two measures are introduced: • A measure of the time-frequency localization of a given signal can be obtained by the product : OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  8. Time-frequency localization • In the case of the SWT, both time and frequency localizations depend on the scale factor. • One may notice that the time localization is getting worse with the increase of the scale factor, while frequency localizationimproves with the increase of the scale factor. OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  9. Results • wavelet families: Daubechies, Coiflet, Symmlet, Biorthogonal and Reverse Biorthogonal. OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  10. Conclusions • Mother wavelets selection must be done by searching the best time localization (e.g. Haar). • Mother wavelets with good time-frequency localization, meaning reduced number of vanishing moments, (e.g rbio1.1 or db3) are also a good choice. OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  11. Thank You ! OPTIM 2010 ETC Timisoara – TELECOM Bretagne

  12. Quality Evaluation • Mean absolute error (MAE): • the analysis of variance (ANOVA), • Symmetric Mean Absolute Percent Error (SMAPE): • Root Mean Square Error (RMSE). • Mean Square Error (MSE). OPTIM 2010

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