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On the Time-Frequency Localization of the Wavelet Signals, with Application to Orthogonal Modulations Marius Oltean, Alexandru Isar, Faculty of Electronics.

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Presentation on theme: "On the Time-Frequency Localization of the Wavelet Signals, with Application to Orthogonal Modulations Marius Oltean, Alexandru Isar, Faculty of Electronics."— Presentation transcript:

1 On the Time-Frequency Localization of the Wavelet Signals, with Application to Orthogonal Modulations Marius Oltean, Alexandru Isar, Faculty of Electronics and Telecommunications, Timisoara, Romania

2 ISSCS Iasi 2009 ETC Timisoara Contents Conclusions Results OFDM and WOFDM Time-frequency localization Orthogonal modulations concept

3 ISSCS Iasi 2009 ETC Timisoara Objectives  To prove that the time-frequency localization of the wavelet functions is better than the one of OFDM’s windowed complex exponentials  To highlight the meaning of the above remark for an orthogonal modulation system

4 ISSCS Iasi 2009 ETC Timisoara Orthogonal Modulations  The transmitted symbol composed as a sum of orthogonal “carriers”:  a k : data symbols, x k (t): orthogonal carriers  Advantage: information distributed along low-rate carriers, less affected by ISI  The orthogonality allows demodulation: (1)

5 ISSCS Iasi 2009 ETC Timisoara Radio channels  The radio channels are frequency - selective (multipath propagation) and time-variants (Doppler effect)  A “time-frequency” localization of the channel can be introduced  The carriers used in transmission should be localized as the channel itself Time-frequency localization

6 ISSCS Iasi 2009 ETC Timisoara Effective bandwidth and duration  Two measures are introduced:  There isn’t “perfect” localization in time and frequency simultaneously: Time-frequency localization (4)

7 ISSCS Iasi 2009 ETC Timisoara OFDM and WOFDM Properties & Representations OFDM WOFDM The signal The carriers p: rectangular window, m: subcarrier index The signal The carriers

8 ISSCS Iasi 2009 ETC Timisoara OFDM  Balyan-Low theorem: for all the time windows p(t) that gate complex exponential to generate orthonormal basis of L 2 (R), we have: Time-frequency localization

9 ISSCS Iasi 2009 ETC Timisoara WOFDM ….When time meets frequency Cardinal sine Daub20 Daub4 Haar Time-frequency localization

10 ISSCS Iasi 2009 ETC Timisoara Results  The effective duration and bandwidth are normalized to unity  The effective duration has a sharper evolution with N  Numerically, the best time-frequency compromise is provided by Daubechies- 4  The choice of the wavelets mother must be dependent on the channel’s characteristics

11 ISSCS Iasi 2009 ETC Timisoara Orthogonal modulation chain  The channel is flat, and time-variant  The variability in time is related to the maximum Doppler shift  IFFT implements the OFDM modulator and IDWT implements the WOFDM modulator Orthogonal modulation in flat, time-variant channels [w est ] IDWT/ IFFT DWT/ FFT Decision s[n] ray[n] p[n] [w] Baseband implementation of an orthogonal modulation system. r[n]

12 ISSCS Iasi 2009 ETC Timisoara BER results  WOFDM has better results than OFDM  For WOFDM, the time-localization of the carriers is the predominant factor which determines the BER performance Orthogonal modulation in flat, time-variant channel BER performance in various Doppler shift scenarios. Wavelets mother comparison in a WOFDM system.

13 ISSCS Iasi 2009 ETC Timisoara BER Results  Daubechies-12 has better results than Haar  This time, the frequency-selectivity is predominant for the errors Orthogonal modulation in frequency-selective & time-variant channel  It = the number of IDWT iterations  Two ray channel model, with equal power of the two paths  BER is computed independently at the third and the fourth scales

14 ISSCS Iasi 2009 ETC Timisoara Conclusions  Daubechies wavelets time-frequency localization is better than the time-frequency localization of OFDM’s windowed exponentials  In flat, time-variant channels, WOFDM performs better than OFDM  Wavelets with short compact time support are the best choice (e.g. Haar)  In frequency-selective & time variant channels, wavelets with short compact frequency support provide better results  The choice of the carrier family in an orthogonal modulation must be dependent on the channel characteristics

15 Click to edit company slogan. Marius Oltean & Alexandru Isar


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