Discrete characterizations of wideband and dispersive time-varying systems

Discrete characterizations of linear time-varying systems have been successful in improving narrowband processing in various applications. In this dissertation, discrete characterizations and processing techniques are developed using matched analysis tools for wideband and dispersive time-varying systems. The proposed discrete models are used to exploit inherent diversity for systems suffering from wideband or dispersive transmission degradations. Also, system design techniques are investigated to estimate unknown system parameters, to exploit the potential diversity and to improve receiver performance.; When the narrowband assumptions are not valid, wideband time-varying systems are characterized by time shifts and Doppler scale changes, instead of constant frequency shifts, to describe the effect of the system on the transmitted signal. For characterizing wideband time-varying systems, a discrete time-scale representation is proposed to decompose the system output into discrete time shifts and Doppler scalings on the input signal, weighted by a smoothed and sampled version of the wideband spreading function. A transform-based methodology is developed to derive the proposed model: the Mellin transform that is inherently matched to scalings is used to geometrically sample the scale parameter and the Fourier transform is used to arithmetically sample the time delay parameter. Using this proposed discrete wideband model, and by properly designing the signaling and reception schemes using wavelet techniques, a joint multipath-scale diversity can be achieved over a dyadic time-scale framework in wideband wireless systems. Simulation results demonstrate that the proposed model can indeed increase system performance by exploiting the diversity intrinsically afforded by the wideband system.; Time-varying signal processing techniques are also investigated to estimate wideband system parameters and to design modulation schemes. Specifically; linear frequency-modulated chirps are used as pilot signals to estimate wideband communication channel parameters by exploiting time-frequency methods such as the Radon-Wigner transform and the modified matching pursuit decomposition. Also, modulation schemes are designed using linear frequency-modulated chirps to derive orthogonality conditions for suppressing interference between paths.; Time-varying systems can be characterized by dispersive signal transformations such as nonlinear shifts in the phase of the propagating signal, causing different frequencies to be shifted in time by different amounts. A discrete time-frequency model is proposed to decompose the dispersive system output into discrete dispersive frequency shifts and generalized time shifts, weighted by a smoothed and sampled version of the dispersive spreading function. The discretization formulation is obtained from the discrete narrowband model through a unitary warping relation between the narrowband and dispersive spreading functions. This warping relation depends on the nonlinear phase change on the input signal caused by the dispersive system. In order to demonstrate the effectiveness of the proposed discrete characterization, acoustic transmission over shallow water acoustic environments that suffers from severe degradations as a result of model frequency dispersions and multipath fading is considered. Numerical results demonstrate that the discrete dispersive model can lead to a joint multipath-dispersion diversity. Transmitted waveforms and reception schemes are designed to snatch the environment dispersive characteristics.