Index Modulation With Channel Training: Spectral Efficiency and Optimal Antenna Alphabets

Index modulation is a MIMO technology where some transmit antennas are idle during each transmission interval, but the receiver requires knowledge of all link gains at all times. Even though index modulation is particularly sensitive to the cost of estimating the channel state information (CSI), the impact of CSI cost and imperfections on the capacity of index modulation has not been adequately characterized until now. As a result, the marginal cost/benefit of each additional antenna, and the optimal antenna alphabet have remained unclear. This study computes the spectral efficiency of index modulation subject to training and determines optimal antenna alphabets. Our approach involves a comprehensive examination of the influence of pilot power and degrees of freedom on the achievable rate of index modulation. The results include 2.5dB improvement over the best previously known bound for
$4\times2$
spatial modulation at 6b/s/Hz. Additionally, we determine the conditions under which single-antenna transmission is superior to spatial modulation, and vice versa. Moreover, this training-based spectral efficiency analysis is extended to the multiuser uplink, identifying the number of users that can be accommodated while maximizing the uplink sum-rate under spatial modulation.