# RLS-Based Detection for Massive Spatial Modulation MIMO

## TL;DR

This paper analyzes the asymptotic performance of RLS-based detection algorithms in massive spatial modulation MIMO systems, providing theoretical insights and validation for various channel matrix types.

## Contribution

It derives the asymptotic mean squared error and error rate for RLS detection in SM, extending analysis to non-i.i.d. and non-Gaussian channel matrices.

## Key findings

- Performance characterization holds for non-Gaussian matrices.
- Analytical results match numerical simulations.
- Supports the validity of the box-LASSO approach.

## Abstract

Most detection algorithms in spatial modulation (SM) are formulated as linear regression via the regularized least-squares (RLS) method. In this method, the transmit signal is estimated by minimizing the residual sum of squares penalized with some regularization. This paper studies the asymptotic performance of a generic RLS-based detection algorithm employed for recovery of SM signals. We derive analytically the asymptotic average mean squared error and the error rate for the class of bi-unitarily invariant channel matrices. The analytic results are employed to study the performance of SM detection via the box-LASSO. The analysis demonstrates that the performance characterization for i.i.d. Gaussian channel matrices is valid for matrices with non-Gaussian entries, as well. This justifies the partially approved conjecture given in [1]. The derivations further extend the former studies to scenarios with non-i.i.d. channel matrices. Numerical investigations validate the analysis, even for practical system dimensions.