Spatial modulation systems convey additional information bits over conventional MIMO systems. There are several papers on the mutual information and capacity of spatial modualtion systems, including hybird digital/analog beamforming, phase shifting, and antenna switching. What is the exact capcity of the spatial modulation systems?
The capacity of spatial modulation systems depends on several factors, including the number of transmit and receive antennas, the modulation scheme, the channel conditions, and the signaling scheme (i.e., whether hybrid digital/analog beamforming, phase shifting, or antenna switching is used).
The exact capacity formula for spatial modulation systems is generally complex and may not have a closed-form solution in many cases. However, some simplified capacity expressions have been derived for certain scenarios.
For example, in the case of spatial modulation with hybrid analog/digital beamforming, the capacity can be expressed as a sum of the capacity of a single-input single-output (SISO) channel and the mutual information of the modulation index (MI) bits. This expression assumes that the channel is sparse, meaning that the number of non-zero channel coefficients is much smaller than the total number of antennas.
In the case of antenna switching-based spatial modulation, the capacity can be expressed as a sum of the capacity of a SISO channel and a correction factor that accounts for the spatial diversity gain. This expression assumes that the channel is rich, meaning that the number of non-zero channel coefficients is comparable to the total number of antennas.
Overall, the capacity of spatial modulation systems is highly dependent on the specific system parameters and channel conditions, and a general closed-form expression may not be available.
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