On the Capacity of Index Modulation

Index modulation represents the transmitted information in two parts: by selecting a subset of available transmission dimensions (antennas, sub-carriers, or time-slots) whose selection index carries information, and by modulation symbols transmitted in the selected dimensions. Index modulation is motivated by reducing the transmitter hardware complexity and has attracted significant research attention in the past decade. In practice, knowing the spectral efficiency or capacity is essential for setting the parameters of modulation and coding for index modulation, but approximations and bounds thus far have not been accurate enough for that purpose. We calculate close lower and upper bounds for the spectral efficiency of index modulation. Our lower and upper bounds meet at high-SNR when the number of receive antennas is greater than or equal to the number of transmit antennas, thus the high-SNR capacity of index modulation in these cases has been fully characterized. A catalog of results is provided for spatial modulation, generalized spatial modulation, time and frequency index modulation. Extensive simulations illustrate the usefulness and accuracy of our results. For example, for spatial modulation with
$4\times 2$
antennas at 8 bits/s/Hz, our results are 2dB tighter than the best available bounds in the literature.