| Summary: | In this paper, the uplink and downlink sum mean-squared error (MSE) duality for multi-hop amplify-and-forward (AF) multiple-input multiple-output relay channels is established, which is a generalization of several sum-MSE duality results. Unlike the previous results that prove the duality by calculatingthe MSEs for each stream directly, we introduce an interesting perspective to the relation of the uplink-downlink duality based on the Karush-Kuhn-Tucker (KKT) conditions. We address the transceiver design based on the minimization of sum-MSE subject to the power constraints at the relay and user nodes for both uplink and downlink channels. Based on the KKT conditions of the transceiver design optimization problems, the sum-MSE uplink-downlink duality is established.
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