Spatial Modulation vs. Single-Antenna Transmission: When is Indexing Helpful?

In spatial modulation, even though only one antenna is active in each transmission interval, the receiver needs channel estimates with respect to all transmit antennas at all times. Thus, spatial modulation is more sensitive to the cost of the estimation of channel state information (CSI) compared with conventional single-antenna transmission. Despite its importance, an accurate, joint characterization of the impact of CSI cost and CSI imperfections on the capacity of spatial modulation has been unavailable thus far. As a result, the marginal cost/benefit of each additional antenna, and hence the optimal antenna alphabet, has been unclear. This work calculates the spectral efficiency of spatial modulation subject to training through a tight characterization of the dependence of the achievable rate on the power and degrees of freedom dedicated to pilots. Our results reliably characterize the cases when conventional single-antenna transmission is superior to spatial modulation or vice versa.