The BOX-LASSO with application to GSSK modulation in massive MIMO systems

The BOX-LASSO is a variant of the popular LASSO that includes an additional box-constraint. We propose its use as a decoder in modern Multiple Input Multiple Output (MIMO) communication systems with modulation methods such as the Generalized Space Shift Keying (GSSK) modulation, which produces constellation vectors that are inherently sparse and with bounded elements. In that direction, we prove novel explicit asymptotic characterizations of the squared-error and of the per-element error rate of the BOX-LASSO, under iid Gaussian measurements. In particular, the theoretical predictions can be used to quantify the improved performance of the BOX-LASSO, when compared to the previously used standard LASSO. We include simulation results that validate both these premises and our theoretical predictions.