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In this paper, we present a robust hybrid transceiver design for millimeter-wave communication systems operating in amplify-and-forward multiple-input multiple-output relay channels. Unlike most of current works that assume the perfect or partial channel state information (CSI) at the transceivers in the design, the CSI uncertainty is taken into consideration to design a robust transceiver. To achieve that end, the average received signal-to-noise ratio (SNR) is adopted as the objective function. To produce a tractable expression, an accurate approximation of the average received SNR is derived and used as the design criterion. An alternating maximization algorithm is proposed to optimize the design criterion, in which an orthogonal matching pursuit-based algorithm is utilized to design the transceiver at the relay. Simulations show that the algorithm takes a few iterations to produce converged transceivers for the source, relay, and destination nodes. Numerical results demonstrate the substantial performance gains of the proposed scheme, compared with the existing non-robust designs.

Robust Hybrid Transceiver Design for AF Relaying in Millimeter Wave Systems Under Imperfect CSI