Mutual Information and Error Probability Analysis on Generalized Spatial Modulation System

Generalized spatial modulation (GSM) is an extended architecture to the spatial modulation multiple antenna system. The GSM system uses multiple activated transmit antennas to further exploit the system transmission capacity. In this paper, we consider the GSM systems with channel diagonalization (CD-) transmitter pre-coder (TPC), channel inversion TPC, and without TPC. For each TPC scheme, the pairwise activated antenna detection discriminant and closed-form antenna detection pairwise error probability (PEP) of the GSM system are derived. We use the antenna detection PEP to calculate the analytical antenna detection symbol error rate union bound and the mutual information lower bound. We use asymptotic methods to analyze antenna detection diversity and coding gains of GSM system with or without TPC when the signal-to-noise ratio is high. Together with complexity analysis on the pre-coders and antenna detectors, we discover the CD-TPC trades the antenna detection performance for complexity reduction, while the CD-TPC scheme achieves a balance between the performance and complexity. This paper introduces methods to the performance evaluation of the GSM system, and provides a guideline for the GSM system design such as antenna configuration and TPC schemes selection.