  We introduce a class of nonlinear least square error precoders with a general
penalty function for multiuser massive MIMO systems. The generality of the
penalty function allows us to consider several hardware limitations including
transmitters with a predefined constellation and restricted number of active
antennas. The large-system performance is then investigated via the replica
method under the assumption of replica symmetry. It is shown that the least
square precoders exhibit the "marginal decoupling property" meaning that the
marginal distributions of all precoded symbols converge to a deterministic
distribution. As a result, the asymptotic performance of the precoders is
described by an equivalent single-user system. To address some applications of
the results, we further study the asymptotic performance of the precoders when
both the peak-to-average power ratio and number of active transmit antennas are
constrained. Our numerical investigations show that for a desired distortion at
the receiver side, proposed forms of the least square precoders need to employ
around %35\%$ fewer number of active antennas compared to cases with random
transmit antenna selection.
