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In a cooperative network, relaying nodes transmit to the destination information that is related to the message sent by the source. In literature the performance of such networks is usually studied under the (unrealistic) assumption of perfect channel knowledge at the destination. In this paper we consider the Amplify-and-Forward protocol and assume time-varying Rice fading components. Based on pilot symbols an initial estimate of the channel parameters that correspond to the actual channel realizations is obtained, and is subsequently refined in an iterative way by also exploiting the information contained in the data part of the received signals. The iterative estimator gives rise to substantial improvements in terms of error performance and bandwidth efficiency as compared to the initial pilot-based estimate.