In this paper, we study multi-hop non-regenerative multiple-input multiple-output (MIMO) relay communications with any number of hops. We design the optimal source precoding matrix and the optimal relay amplifying matrices for such relay network where a nonlinear decision feedback equalizer (DFE) based on the minimal mean-squared error (MMSE) criterion is used at the destination node. We show that when the composite objective function is Schur-convex, the MMSE-DFE receiver together with the optimal source and relay matrices enable an arbitrary number of source symbols to be transmitted at one time, and yield a significantly improved performance compared with non-regenerative MIMO relay systems using linear receivers at the destination.
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