This paper studies the large-system performance of Least Square Error (LSE)
precoders which~minimize~the~input-output distortion over an arbitrary support
subject to a general penalty function. The asymptotics are determined via the
replica method in a general form which encloses the Replica Symmetric (RS) and
Replica Symmetry Breaking (RSB) ans\"atze. As a result, the "marginal
decoupling property" of LSE precoders for b-steps of RSB is derived. The
generality of the studied setup enables us to address special cases in which
the number of active transmit antennas are constrained. Our numerical
investigations depict that the computationally efficient forms of LSE precoders
based on "ℓ1-norm" minimization perform close to the cases with
"zero-norm" penalty function which have a considerable improvements compared to
the random antenna selection. For the case with BPSK signals and restricted
number of active antennas, the results show that RS fails to predict the
performance while the RSB ansatz is consistent with theoretical bounds.Comment: 5 pages; 2 figures; to be presented at ISIT 201