On-Grid Equivalence of Continuous-Time Doubly Selective Channels: A Revisit of Bello's Models (2510.03626v1)

Abstract: Significant studies on communications over doubly selective channels have utilized on-grid DD channel models, which are previously investigated in Bello's seminar paper in 1963. The DD grid is typically specified by the bandwidth and time duration of the transmission frames. However, the physical channels are determined by the propagation environments and they are typically off-grid. Hence, there is often a gap between an actual physical channel and the on-grid model. This paper revisits the on-grid modeling of practical physical channels. We study the associated on-grid DD-domain representations for continuous-time, doubly selective channels with off-grid delay and Doppler shifts, accounting for practical time/frequency-domain windowing at the transceivers. The universal models obtained are applicable under the mild assumption that the windows have finite supports, and they extend Bello's classical results to account for more general windows. We also discuss the features and implications of the equivalent on-grid models.