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Orthogonal frequency division multiplexing- (OFDM-) based amplify-and-forward (AF) cooperative communication is an effective way for single-antenna systems to exploit the spatial diversity gains in frequency-selective fading channels, but the receiver usually requires the knowledge of the channel state information to recover the transmitted signals. In this paper, a training-sequences-aided linear minimum mean square error (LMMSE) channel estimation method is proposed for OFDM-based cooperative diversity systems with multiple AF relays over frequency-selective fading channels. The mean square error (MSE) bound on the proposed method is derived and the optimal training scheme with respect to this bound is also given. By exploiting the optimal training scheme, an optimal low-rank LMMSE channel estimator is introduced to reduce the computational complexity of the proposed method via singular value decomposition. Furthermore, the Chu sequence is employed as the training sequence to implement the optimal training scheme with easy realization at the source terminal and reduced computational complexity at the relay terminals. The performance of the proposed low-complexity channel estimation method and the superiority of the derived optimal training scheme are verified through simulation results

A Low-Complexity LMMSE Channel Estimation Method for OFDM-Based Cooperative Diversity Systems with Multiple Amplify-and-Forward Relays