Impact of imperfect channel estimation on the performance of amplify-and-forward relaying

In this paper, we investigate the error rate performance of amplify-and-forward (AF) relaying with imperfect channel estimation. We consider a single-relay scenario with orthogonal and non-orthogonal AF (OAF and NAF) cooperative protocols. Two pilot-symbol-assisted receiver architectures are studied: in the mismatched-coherent receiver, the complex fading channel coefficients (i.e., both phase and amplitude) are estimated based on a linear minimum-mean-squared-error estimation approach and fed to a coherent sub-optimal maximum likelihood decoder as if the channels were perfectly known. In the partially-coherent receiver, channel amplitude is ignored and phase is estimated by a phase locked loop. For both receiver types, we analyze the achievable diversity orders for cooperative protocols under consideration and quantify the impact of channel estimation through the derivation of pairwise error probability. Our performance analysis reveals that a second order diversity order is obtained for the considered single-relay scenario indicating that full diversity is extracted. Our simulation results demonstrate that the performance degradation due to channel estimation with respect to the genie bound (i.e., perfect channel state information) is as small as 1.1 dB based on the employed detector. Performance results further show that partially-coherent receiver presents a similar performance to mismatched-receiver for sufficiently large loop SNRs although channel amplitude is completely ignored.