Derivations of decoder and beamforming vector for amplify-and-forward relays based on the Cauchy-Schwartz inequality

Abstract

For multiple amplify-and-forward (AF) relays, optimal decoder and beamforming vector have been presented [3], [4]. The derivations of these optimal ones have been based on the generalized eigenvalue problem. In this work, we show the derivations using the Cauchy-Schwartz inequality. Moreover, the intimate relation between decoder and beamforming vector is analyzed.