Error probability and mutual information analysis on generalized precoded spatial modulation system

Generalized spatial modulation (GSM) is an extended architecture to the spatial modulation (SM) multiple antenna system. Multiple activated transmit antennas (TAs) are applied in the GSM system to further exploit the system transmission capacity. In this paper, we consider the transmitter pre-coding (TPC) GSM systems with channel diagonalization (CD) and channel inversion (CI) pre-coding schemes. The pairwise activated TA detection discriminant and closed-form pairwise error probability (PEP) function are derived. We use the TA detection PEP to calculate the analytical TA detection symbol error rate (SER) union bound and the mutual information lower bound. The analytical results are verified by numerical simulation over Rayleigh fading channels. We investigate the system with different number of antennas and TPC schemes to evaluate the error probability and mutual information performance of the GSM system. The results show that the CD-TPC GSM system with equal power allocation has the most TA detection mutual information, and the CD-TPC system with water-filling power allocation has the most joint APM domain and space domain mutual information.