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The spectral efficiency of practically oriented vector precoding schemes for the Gaussian Multiple-Input Multiple-Output (MIMO) broadcast channel is analyzed in the large system limit. Considering discrete complex input alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the transmit energy penalty imposed by the linear front-end. The energy penalty is minimized by relaxing the input alphabet to a larger alphabet set prior to precoding. The so-called "Replica method" of statistical physics is employed to derive the limiting empirical distribution of the precoder's output, as well as the limiting energy penalty.
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