Wavelet Lifting Theory And Its Applications Study In The OFDM System

Wavelet analysis has more essential advantage than Fourier analysis such as wavelet analysis can abstract more useful information form the signal and the fast arithmetic of wavelet analysis bring more conveniences for us to settle actual problem. The wavelet lifting scheme were proposed by Sweldens and Daubechies to construct a new wavelet as a new method in 1990s. Lifting can improve a known wavelet to get a good feature and can give a good and efficient method to construct bi-orthogonal wavelet. All the traditional wavelet can be constructed through lifting scheme with Euclidean arithmetic. The dissertation proposed a method to improve the wavelet function vanishing moment, at the same time present an equation method to solve for the coefficients of the lifting scheme.M band wavelet not only has the wavelet feature but also can amplify high frequency narrow band part, so it could centralize more energy. The dissertation proposed a new lifting scheme to construct linear phase wavelet filter banks.It is well known that the OFDM (Orthogonal Frequency Division Multiplexing) system has a high ability to overcome the effect of multipath and can obtain high spectral efficiency in the wireless communication channel. However, to avoid interchannel interference (ICI) and intersymbol interference (ISI) in wireless channel, a guard interval longer than channel delay is used in conventional OFDM system, which cause the efficiency of bandwidth usage reduced. Due to the superior spectral containment of wavelets, this dissertation proposed a new OFDM system based on M band Lifting Wavelet Transform (LWMT-OFDM), which adopts M band lifting wavelet transform to replace the conventional Fourier transform. The new LWMT-OFDM system doesn抰need the Cyclic Prefix (CP) so its structure is more simply than FFT-OFDM and its algorithm is as simply as FFT-OFDM. The new LWMT-OFDM system can mitigates some disadvantages of FFT-OFDM system, such as a relatively large peak-to朼verage power ratio, more sensitive to carrier frequency offset and phase noise. Simulations show that the LWMT-OFDM system is more effective and attractive than conversional FFT-OFDM in wireless channel.The organization of the dissertation as follow: the first chapter focuses on the studying background and the relative technology. The second chapter focuses on wavelet and Multirate filter banks study. Given a conclusive of wavelet essential theory, essential feature and the relativity of Multirate filter banks. The third chapter focused on wavelet lifting structure study, proposed a new method to improve the wavelet function vanishing moment, at the same time present an equation method to solve for the coefficients of the lifting scheme. The fourth chapter focused on M band wavelet and M band filter banks lifting theory, proposed a new lifting scheme to construct linear phase wavelet filter banks. The fifth chapters based on M band lifting wavelet theory proposed a new OFDM system - M band lifting wavelet mutlicarrier system (LWMT-OFDM), at the same time gives the simulation result. In the end, the dissertation proposed a MC-CDMA system based on M band lifting wavelet and give the compare result of OFDM based MC-CDMA.