A low complexity decision feedback equalizer for single-carrier amplify-forward MIMO relay system

In this paper, we introduce a block iterative frequency domain decision feedback equalizer with noise prediction (NP-BI) for single-carrier (SC) multiple input multiple output (MIMO) relay systems. Firstly, we derive the minimum mean-squared error (MMSE) equalizer at the destination node. Then the decision feedback equalizer coefficients can be calculated according to the error covariance matrix of the MMSE equalizer and the equivalent channel frequency-domain (FD) response. Then, we combine the spatial precoding matrix with the decision feedback equalizer at the source node, which performs better than the frequency domain equalization with noise prediction (FDE-NP), especially when the number of antennas is large. In addition, NP-BI has a lower computational complexity than FDE-NP.