Oversampled Filter Banks and Redundant Signal Expansion

This project addressed several areas of time-frequency signal processing and wireless communications. We investigated the theory of oversampled filter banks and redundant signal expansions and their applications to image and subband coding as well as to the estimation and equalization of mobile radio channels. Other aspects of mobile radio communications related to multiple-antenna channels were considered as well. The project resulted in 3 book contributions, 5 papers in reviewed journals (1 more submitted, 1 more in preparation), and 11 conference papers. One journal paper received an IEEE Signal Processing Society Young Author Award. In the course of the project, informal contacts with the company Siemens Austria AG were maintained. The results obtained within the project can be grouped into four areas as discussed in the following. Oversampled Filter Banks and Redundant Signal Expansions We applied frame-theoretic methods to the analysis and design of oversampled filter banks. A new class of efficient oversampled cosine-modulated filter banks was introduced and applied to image coding. Oversampled filter banks were also used to develop oversampled predictive subband coders that allow the use of low-resolution quantizers. Theory of Linear and Quadratic Time-Frequency Analysis A unified theory of "covariant" linear and quadratic time-frequency signal representations that had been developed during a previous project was extended by introducing new operator classes (modulation and warping operators; affine operators). These operator classes underlie important linear and quadratic time-frequency signal representations such as the wavelet transform and the power classes. Estimation and Equalization of Mobile Radio Channels Mobile radio communications is a field of tremendous practical importance that allows a natural application of time-frequency methods. We developed a new time-frequency technique for estimating the statistical properties of a mobile radio channel. We also performed a time-frequency analysis of the systematic measurement errors of channel measurement devices (channel sounders). Finally, we developed efficient "blind" techniques for the equalization of mobile radio channels. These techniques do not require the transmission of training symbols and thus allow a substantial increase of data rates. Modulation and Equalization Techniques for Multiple-Antenna Channels The blind equalization techniques mentioned above led us to the development of new modulation and equalization techniques for multiple-antenna channels. The use of multiple transmit and receive antennas leads to significantly increased data rates. The proposed techniques allow the simultaneous transmission of several data streams such that these data streams can be demodulated/separated at the receiver without knowledge of the channel characteristics. We subsequently extended our techniques to the practically important case of multiple users.