Spatial Modulation Achieves Information-Theoretically Optimal Energy Efficiency

Spatial modulation (SM) is investigated for multiple-input single-output channels with perfect channel state information at the receiver. In spite of its low implementation complexity, SM with quadrature phase-shift keying is proved to achieve an information-theoretically achievable rate that is equal to the channel capacity up to second order as the signal-to-noise ratio tends to zero. This implies that SM is second-order optimal in terms of energy efficiency.