Fundamental Applicability of Spatial Modulation: High-SNR Limitation and Low-SNR Advantage

Abstract

Spatial modulation (SM) is viewed as a promising multi-antenna technology for future communications. Numerous works on SM have been done on the specific optimized designs and performance analysis mainly based on high signal-to-noise ratio (SNR) union bound approximation. However, the existing information-theoretical investigation indicates that SM is more efficient in low SNR regimes. Therefore, the most prominent potential of SM with respect to the error performance is still not well understood. As a first step to filling this void, we consider the fundamental applicability of SM in multi-antenna channels. On the one hand, for high SNR regimes, by developing the optimal structure of multi-input single-output (MISO) and proposing efficient multiple-input multiple-output (MIMO) transmission schemes, we prove that the performance limits of SM-MISO and SM-MIMO with respect to the received minimum Euclidean distance (MED) can be outperformed even by single radio-frequency chain transmission. On the other hand, for the low-SNR regimes, we show the respective optimality of: 1) SM for single-user energy-based noncoherent massive MIMO (ED-MaMIMO) channels; and 2) dual SM of multi-user ED-MaMIMO which collaboratively modulates data onto both the indexes of transmitter antennas and those of the users. In addition, the dual SM for multiuser ED-MaMIMO has a practically important property that partial coordination via user index modulation can be as useful as full one. Our analytical findings and numerical results strongly suggest that more attention should be paid to the low-SNR behavior and designs of SM rather than the currently popular MED optimization in high-SNR regimes. This paper points out a direction, towards which SM should evolve, and also shows that combination of SM with the users' index modulation can be very useful for designing the optimal finite-alphabet nonorthogonal multiple-access.