Channel is the most important part in communication system, especially for wireless radio channel. It poses a severe challenge as a medium for reliable high-speed communication. It is not only susceptible to noise, interference and fading, but the impediments change over time in unpredictable ways due to the user movement. For high-speed movement, channel becomes more complexity. To counterpart these impediment, diversity techniques are the most common solution. In various diversity techniques, time diversity and frequency diversity are frequently used. Besides these diversity techniques, multipath diversity and antenna diversity also adopted in wireless radio channel. All these diversity techniques are based on the same assumption that the signal experiences slow fading. The application of diversity techniques in fast fading originated by the Sayeed’s works, in which a novel concept: Doppler diversity is proposed. The core idea is to decompose the received signal into a basis. In the thesis, we propose a new framework termed as multi-resolution framework to study fast fading channel (time selective and doubly selective channel). In this framework, Doppler diversity is reviewed in a total new viewpoint, and at the same time an optimal receiver—wavelet receiver is proposed. Firstly，we establish the multi-resolution analysis framework for doubly-selective channel. The core of diversity techniques is to decompose signal into statistical independent branches. The orthogonality of wavelet provides intrinsic independence between branches, and the multi-resolution property can capture any variation in any time scale. Further more, this framework unites the signaling of slow fading and channel and fast fading channel. We can view the multi-path diversity as a special case of Doppler diversity. Secondly，a kind of 2D RAKE receiver, termed as wavelet receiver is proposed. We separate the wavelet receiver into two classes, one for coherent detection and the other is used for noncoherent detection. Theoretical analysis and simulations show that the wavelet receiver promises great system performance gain.
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