Penalty Function Based Detector for Generalized Space Shift Keying Massive MIMO Systems

Generalized space shift keying (GSSK) has recently attracted much interest in the study of emerging massive MIMO systems. The maximum likelihood (ML) detection of GSSK can be posed as a 0-1 quadratic program with an equality constraint. The penalty function method is a common way to transform a constrained programming into an unconstrained one. However, determining an ideal penalty factor is not a trivial problem and has not been addressed adequately. In this letter, we prove a lemma to show that the ML detection of GSSK can be converted into an equivalent 0-1 quadratic program if the penalty factor is greater than a small constant. Based on the proposed lemma, we also present an algorithm to determine the penalty factor and finally recover the transmitted signals of GSSK. Simulation results substantiate the performance of the proposed detector.