Recently, the difficulty of placing multiple antennas onto a mobile terminal to exploit more diversity has been solved by using the cooperative communication technique, in which several relay nodes with a single antenna partner with each other to serve as virtual multiple antennas for providing the spatial diversity. Many existing researches in cooperative communication focuses on designing relay strategies to achieve better communication performance. However, most of their designs require the channel state information (CSI) being perfectly known. Unfortunately, CSI is generally unknown in practice. Therefore, before getting benefits brought by the relay-assisted network, it is necessary to obtain accurate channel state information (CSI) at the destination or relays. In this thesis, we also consider the training design for channel estimation in the AF relay network. The involvement of multiple relay nodes to exploit space diversity in cooperative communications requires sophisticated and complicated protocols, which poses a difficulty in avoiding all possible misbehaving relay nodes. Therefore, the channel estimation scheme in cooperative communication network needs to be robust against the possible relay misbehaviors. However, most prior works focused on developing channel estimation schemes by assuming perfect relayassisted communication protocol. By contrast, this work focuses on designing robust channel estimation schemes to combat the possible presence of the relay misbehaviors. Besides considering the robust design against relay misbehaviors, this work also considers more general channel model when designing the training sequence and channel estimation scheme. Specifically, in contrast to assume independent channels across relays, this thesis considers the correlated channels in both phases and the correlated noises in the first phase. Overall, the main problem of this work is to design robust channel estimation and training sequences against relay misbehaviors when the communication channels within the cooperative network are not restricted to be independent.