This paper studies the problem of pilot-aided cascaded channel estimation in amplify-and-forward (AF) relay transmissions over time- and frequency-selective (doubly selective) channels. In the literature, most of existing studies on relay systems have assumed either perfect channel estimation has been established or imperfect channel estimation is implemented in two separated links: (i) source-to-relay (sr) and (ii) relay-to-destination (rd). Furthermore, the channels are usually assumed to be block-fading (i.e., the channel responses are time-invariant within a transmission burst). In practice, such a channel estimation strategy under the conventional block-fading assumption would incur several drawbacks in relay transmissions, especially in AF networks with moving nodes (e.g., mobile users in moving cars and trains). Addressing the AF transmission scenario, this paper considers the use of different basis expansion models (BEMs) for capturing time- and frequency-selective cascaded channels in broadband relay networks with moving nodes. Then, the cascaded doubly selective channel response from source to destination is estimated by the maximum likelihood (ML) technique at the destination only (instead of performing two separated sr and rd channel estimation processes). Numerical results demonstrate that the deployment of BEMs is able to alleviate performance degradation due to the conventional block-fading assumption in cascaded channel estimation for AF relay networks with moving nodes.
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