| Recently, wireless mobile communication has been the hot topic in the domain of communication. Nowadays, many techniques have been comprehensively considered as the major candidates of the future radio communication architecture, including OFDM and MIMO. Supported by the National High Technology Research and Development Program of China under Grant No.2003AA12331005 and National Science Foundation of China under Grant No.60496315, our research work concentrates on the severe communication circumstances, for example, under multi-antenna and multi-carrier scenarios, we focus on the transmitter design of adaptive transform techniques with imperfect channel state information. First, we overview the current impulsive response model of multi-path fading channel.Then we analyze the self-similar characters of multi-path fading channel via fractional geometry and fractional metrics. As a time sequence, the multiple outdated estimates can be mapped into Euclid space to reduce uncertainty of the actual channel estimation. Experiments results show that the channel estimation sequence has some self-sililar character. Second, the transmitters acquire the channel state information (CSI) from the feedback of receivers in TDD systems. Unfortunately, system performance degrades due to imperfect CSI, caused by noisy channel estimation and delay. To improve the average spectral efficiency of adaptive OFDM system, we propose to use multiple outdated estimates and extended self-similar process to reduce the uncertainty of current channel estimate.Simulation results show that the novel method can track the actual channel state, so the average spectral efficiency of time-varying fast fading channels is significantly improved. The number of outdated estimates can be reduced significantly, which also means that the system can tolerate larger channel estimation error with reasonable complexity. For multi-antennae OFDM system, an identical scheme is applied to improve performance based on equated channel design, which provide theory guidance for their practical applications.The signal processing literature has traditionally been dominated by the Gaussian assumption. Unfortunately, Non-Gaussianity often results in significant performance degradation for systems optimized under the Gaussian assumption. Thus, more realistic statistical models must be used. There is a trade-off between model complexity and accuracy. The parameter estimation for multi-path fading channel estimations is calculated via method of maximum likelihood, method of sample quantiles and method of sample characteristic functoins, respectively. Analysed results show that Generalied Gaussian distribution assess stable fits to data sets. The data set of channel estimations is only slightly deviate from the Gaussian, so the performance changes little. But the outliers of fast fading cause infinite variance. So, the data set of multiple estimations is statistically processed via fractional low order moments. Simulation results show signal processing based on generalized Gaussian can improve generalized SNR and average spectrum efficiency with more robusticity than the Gaussian.In order to track the time-varying fast fading channel, LMS adaptive filtering is a very popularalternative technique to reduce quantity of pilots in real wireless systems. We introduce fractional Fourier transform (FRFT) and part of its properties, and then present its interpretation as a rotation of the timefrequency plane. The FRFT's relationships with timefrequency representations have a very simple and natural form and supports LMS adaptive time-frequency filtering in the FRFT domain. The simulation results indicate that the novel method can speed convergence effectively with low complexity, which can benefit adaptive channel tracking.
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