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This paper studies the problem of pilot-aided cascaded channel estimation in amplify-and-forward (AF) relay transmissions over time- and frequency-selective channels. Different basis expansion models (BEMs) are used to represent the doubly selective cascaded AF relay channel. Then, a maximum-likelihood (ML) algorithm is developed for the destination to estimate the BEM coefficients of the cascaded doubly selective channel response from source to destination. Numerical results demonstrate that the use of BEMs can alleviate performance degradation due to the conventional block-fading assumption in cascaded channel estimation for AF relay networks with moving nodes.