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This paper studies the problem of channel estimation in amplify-and-forward (AF) multi-relay transmissions over time- and frequency-selective (doubly selective) channels. To avoid two separate channel estimation processes of source-to-relay and relay-to-destination links, a cascaded doubly selective channel model is formulated to characterize the source-to-relay-to-destination (SRD) channel. Time-varying SRD channel gains are projected onto different basis expansion functions to attain dimension reduction in the formulated channel model. In estimating the cascaded SRD channel responses at the destination, the presence of multiple relays gives rise to the ambiguity problem due to the use of a single pilot signal transmitted from the source. To circumvent this problem, time-variant amplifying factors at relays are introduced to be used in maximum-likelihood-based cascaded multi-relay channel estimation …