<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$</tex-math></inline-formula> Minimization Based Symbol Detection for Generalized Space Shift Keying

Abstract

Generalized space shift keying (GSSK), as one simplified version of spatial modulation (SM), has attracted plenty of interest in the study of large-scale multiple-input multiple-output (MIMO). In this letter, we propose a low-complexity symbol detector for GSSK based on $\ell_\infty$ minimization. Via a bijective transformation, the symbol detection for GSSK can be converted into the reconstruction of a binary symbol, of which the entries are selected from $\{-1, 1\}$ . The reconstruction is done by solving an $\ell_\infty$ minimization problem, which is convex and can be solved by many off-the-shelf optimization tools. The new detection scheme is capable of detecting GSSK symbols under overdetermined and underdetermined MIMO systems and only requires a polynomial complexity. Numerical simulations are further performed to substantiate the performance of the proposed detector.