| In order to cope with the challenges from the scarce spectrum resources and the mobile radio channels, advanced signal processing techniques must be exploited in the future high-data-rate communication systems to improve the spectral efficiency and the reliability of information transmission. From the perspective of time-frequency signal analysis and processing, this dissertation focuses on the research of principle, performance, characteristic, system design and detection techniques of wireless digital communications in various fading channels. The main contributions are summarized as follows:1. By considering the characteristic of multicarrier signals, it is proved that the assumptions that the fading of the subcarrier is frequency flat (non-selective) and independent of one another are incompatible. Based on this result, we develop a simulation algorithm for Rayleigh fading channels in multicarrier systems via frequency-domain correlation function.2. Based on the function space theory, the general framework of time-frequency transmission is given, showing that the signal transmission problem can be viewed as tiling of the time-frequency plane. Furthermore, a time-frequency transmission scheme on hexagonal/quincunx lattice is proposed.3. From the viewpoint of time-frequency transmission, the optimization and design of system parameters of communication systems in time-frequency doubly dispersive channels, such as modulation pulses, lattice parameters, are addressed, under the criterion of minimum symbol energy perturbation.4. The equalization and detection for multicarrier digital transmission in time-frequency dispersive channels are dealt with in this study. By employing the matrix inversion lemma and the block-partitioned matrix inversion lemma, two kinds of iteratively sequential time-frequency equalization are proposed to combat the inter-symbol interference and inter-carrier interference caused by the dispersive and fading channels. Moreover, by exploiting the time-frequency concentration ofthe optimized transmission pulses and the underspread property of the mobile radio channels, a parallel maximum likelihood detector is presented, as well as its quantitative analysis of performance and computational and memory complexity.5. By expressing the decision variable of the transmission symbol in time-varying multipath channels as a complex Gaussian quadratic form, the analytic expression for its characteristic function is obtained. Furthermore, the matched filter bound for time-varying discrete multipath channels is derived, which serves as the lower bound for the performance of the best detector.6. From the function space theory, it is proved that for the transmission of digital symbols taken from discrete and finite alphabet, the orthogonality or biorthogonality constraint of the modulation waveforms can be relaxed. Namely, correlated pulses can also be employed to construct a perfect transmultiplexing system. Based on this observation, communication systems that employ Weyl-Heisenberg frames and hexagonal Gabor frames as the modulation waveforms are proposed. They can be viewed as an important generalization of the conventional orthogonal/biorthogonal frequency division multiplexing to the oversampled case, with a signaling rate larger than the Nyquist rate.7. The above transmission systems based on the Weyl-Heisenberg frames and hexagonal Gabor frames are generalized to the case of general frames. Its transmission capacity in the band-limited additional white Gaussian noise (AWGN) channels is considered from the information theoretic point of view. By analyzing the relationship between the Shannon capacity and Nyquist rate and exploiting the large dimensional random matrix theory, it is demonstrated that the digital transmission system based on frames can achieve the Shannon capacity of band-limited AWGN channel asymptotically.
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