Index Modulations, in the form of Spatial Modulation or Polarized Modulation, are gaining traction for both satellite and terrestrial next generation communication systems. Adaptive Spatial Modulation based links are needed to fully exploit the transmission capacity of time-variant channels. The adaptation of code and/or modulation requires a real-time evaluation of the channel achievable rates. Some existing results in the literature present a computational complexity which scales quadratically with the number of transmit antennas and the constellation order. Moreover, the accuracy of these approximations is low and it can lead to wrong Modulation and Coding Scheme selection. In this work we apply a Multilayer Feedforward Neural Network to compute the achievable rate of a generic Index Modulation link. The case of two antennas/polarizations is analyzed in depth, showing not only a one-hundred fold decrement of the Mean Square Error in the estimation of the capacity as compared with existing analytical approximations, but also a fifty times reduction of the computational complexity. Moreover, the extension to an arbitrary number of antennas is explained and supported with simulations. More generally, neural networks can be considered as promising candidates for the practical estimation of complex metrics in communication related settings.

Mutual Information is the metric that is used to perform link adaptation, which allows to achieve rates near capacity. The computation of adaptive transmission modes is achieved by employing the mapping between the Signal to Noise Ratio and the Mutual Information. Due to the high complexity of the computation of the Mutual Information, this process is performed off-line via Monte Carlo simulations, whose results are stored in look-up tables. However, in Index Modulations, such as Spatial Modulation or Polarized Modulation, this is not feasible since the constellation and the Mutual Information are channel dependent and it would require to compute this metric at each time instant if the channel is time varying. In this paper, we propose different approximations in order to obtain a simple closed-form expression that allows to compute the Mutual Information at each time instant and thus, making feasible the link adaptation.