In this paper, we apply the data-dependent superimposed training (DDST) in amplify-and-forward (AF) relay networks with cyclic-prefix single carrier (CPSC) modulation. We consider various issues such as channel estimation, training design and data detection. A sub-optimal training sequence that can minimize the upper bound of the mean square error of the estimator is derived. Since the DDST estimator can only find the overall channel information, we further propose a doubly cooperative estimator (DCE) to track the individual channel knowledge at the cost of some performance loss. Simulations are then provided to corroborate the proposed studies.