  We propose in this work to employ the Box-LASSO, a variation of the popular
LASSO method, as a low-complexity decoder in a massive multiple-input
multiple-output (MIMO) wireless communication system. The Box-LASSO is mainly
useful for detecting simultaneously structured signals such as signals that are
known to be sparse and bounded. One modulation technique that generates
essentially sparse and bounded constellation points is the so-called
generalized space-shift keying (GSSK) modulation. In this direction, we derive
high dimensional sharp characterizations of various performance measures of the
Box-LASSO such as the mean square error, probability of support recovery, and
the element error rate, under independent and identically distributed (i.i.d.)
Gaussian channels that are not perfectly known. In particular, the analytical
characterizations can be used to demonstrate performance improvements of the
Box-LASSO as compared to the widely used standard LASSO. Then, we can use these
measures to optimally tune the involved hyper-parameters of Box-LASSO such as
the regularization parameter. In addition, we derive optimum power allocation
and training duration schemes in a training-based massive MIMO system. Monte
Carlo simulations are used to validate these premises and to show the sharpness
of the derived analytical results.
