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In this paper, the authors study the effect of discrete constellation alphabets on linear pre-coding for the downlink of Multi-User (MU) MIMO. They underline the fundamental difference in the approach of pre-coding if the alphabets are assumed to be discrete constellations rather than the idealized Gaussian assumption. They derive the optimal linear pre-coder by maximizing the sum rate taking into account discrete inputs. For Gaussian alphabets, pre-interference subtraction (Dirty Paper Coding - DPC) is the optimal nonlinear pre-coding strategy while interference cancellation (Channel Inversion - CI) and interference attenuation (Regularized Channel Inversion - RCI) are the recommended strategies for linear pre-coding.
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