Time-scale canonical model for wideband system characterization

In this paper, we propose a time-scale canonical model as a discrete characterization of wideband linear time-varying systems. This representation decomposes a system output into discrete time shifts and Doppler scalings on the input, weighted by a smoothed discrete version of the wideband spreading function. We base this formulation on the Mellin transform that is matched to scalings. We also demonstrate that our proposed model inherently affords a joint multipath-scale diversity in wideband communication channels. By properly designing the signaling and reception schemes using wavelet techniques, we can achieve this diversity over a dyadic time-scale framework.