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We introduce a class of nonlinear least square error precoders with a generalpenalty function for multiuser massive MIMO systems. The generality of thepenalty function allows us to consider several hardware limitations includingtransmitters with a predefined constellation and restricted number of activeantennas. The large-system performance is then investigated via the replicamethod under the assumption of replica symmetry. It is shown that the leastsquare precoders exhibit the "marginal decoupling property" meaning that themarginal distributions of all precoded symbols converge to a deterministicdistribution. As a result, the asymptotic performance of the precoders isdescribed by an equivalent single-user system. To address some applications ofthe results, we further study the asymptotic performance of the precoders whenboth the peak-to-average power ratio and number of active transmit antennas areconstrained. Our numerical investigations show that for a desired distortion atthe receiver side, proposed forms of the least square precoders need to employaround %35\%$ fewer number of active antennas compared to cases with randomtransmit antenna selection.

Nonlinear Precoders for Massive MIMO Systems with General Constraints