Capacity Analysis of Index Modulations over Spatial, Polarization and Frequency Dimensions

Determining the capacity of a modulation scheme is a fundamental topic of interest. Index modulations (IM), such as spatial modulation (SMod), polarized modulation (PMod), or frequency index modulation (FMod), are widely studied in the literature. However, finding a closed-form analytical expression for their capacity still remains an open topic. In this paper, we formulate closed-form expressions for the instantaneous capacity of IM, together with its second- and fourth-order approximations. We show that, in average, the second-approximation error tends to zero for low signal to noise ratio (SNR) and is o(SNR). Also, a detailed analysis of the ergodic capacity over Rayleigh, Rice, and Nakagami-m channel distributions is provided. As application of the capacity analysis, we leverage the proposed expressions to compute the ergodic capacities of SMod for different antenna configuration and correlations, PMod for different channel components and conditions, and FMod for different frequency separations.Grant numbers : This work has received funding from the Spanish Ministry of Economy and Competitiveness (Ministerio de Economia y Competitividad) under project ELISA (TEC2014-59255-C3-1-R) and from Satellite Network of Experts (SatNEx) IV of European Space Agency (ESA).© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works