Optimal Linear Precoder for Multiuser MIMO for Discrete Alphabets

Abstract—In this paper we study the effect of discrete constellation alphabets on linear precoding for the downlink of multiuser (MU) MIMO. We underline the fundamental difference in the approach of precoding if the alphabets are assumed to be discrete constellations rather than the idealized Gaussian assumption. We derive the optimal linear precoder by maximizing the sum rate taking into account discrete inputs. For Gaussian alphabets, pre-interference subtraction (dirty paper coding DPC) is the optimal nonlinear precoding strategy while interference cancellation (Channel Inversion CI) and interference attenuation (Regularized Channel Inversion RCI) are the recommended strategies for linear precoding. However we show that the optimal linear precoder for realistic discrete constellations does not attenuate, subtract or cancel the MU interference. Rather it allows MU interference to be propagated so as to be subsequently exploited by the users in the detection process thereby improving the error resilience. We further propose in this paper a viable linear precoding strategy of controlled interference combined with a low complexity MU detector which outperforms the existing approaches of linear precoding both in performance and complexity.