This paper proposes an amplify-and-forward (AF) distributed relay network consisting of a one-source-one-destination pair and two-level N relays. Optimal relay amplifying matrices (or vectors) at the relays in the first and second levels are determined based on the minimum mean square error (MMSE) criterion. Power is globally, locally, and aggregately constrained at the relays in the first and second levels, independently or separately. With the derived optimal relay amplifying matrices, bit error rate (BER), mean square error (MSE) behavior, and the achievable rate are investigated. It is also proven that minimizing the MSE is equal to maximizing the signal-to-noise ratio (SNR) in a three-hop AF wireless relay network.
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