Second-Order Optimality of Generalized Spatial Modulation for MIMO Channels With No CSI

Generalized spatial modulation (GSM) is investigated for Rayleigh block-fading multiple-input multiple-output (MIMO) channels with no channel state information (CSI). Under a condition for coherence time, GSM with quadrature phase-shift keying (QPSK) is proved to achieve a transmission rate that is equal to the capacity of the MIMO channels up to second order in the low signal-to-noise ratio regime, regardless of the number of simultaneously activated transmit antennas and of whether CSI is available at the receiver or not. This implies that QPSK GSM is second-order optimal for the MIMO channels in terms of information-theoretical energy efficiency.