Discrete time-scale characterization of wideband time-varying systems

Wideband time-varying systems can be found in many applications, including underwater acoustics and ultra-wideband technologies. The time variation due to Doppler scaling effects, coupled with dispersive scattering due to multipath propagation, can severely limit the performance of wideband systems. Just as the discrete time-frequency model can efficiently improve narrowband processing, a discrete time-scale system characterization is important in processing wideband time-varying systems. In this paper, a time-scale model is proposed as a discrete characterization of wideband time-varying systems. This representation decomposes a wideband 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. The proposed transform-based approach uses the Mellin transform that is inherently matched to scalings to geometrically sample the scale parameter and the Fourier transform to arithmetically sample the time-delay parameter. Using this proposed 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. The simulation results demonstrate that, based on the proposed model, performance can be increased by exploiting the diversity intrinsically afforded by the wideband system.