  This paper addresses the achievable rate of single cell and sum rate of
multi-cell orthogonal frequency division multiplexing (OFDM) index modulation
(IM). The single cell achievable rate of OFDM-IM with Gaussian input is
calculated using a multi-ary symmetric channel. Then, the cumulative
distribution function (CDF) of multi-cell OFDM-IM is investigated by stochastic
geometry. Furthermore, it is proved in this paper that the probability density
function (PDF) of noise plus intercell-interference (ICI) in multi-cell OFDM-IM
with quadrature amplitude modulation (QAM) follows a mixture of Gaussians (MoG)
distribution. Next, parameters of the MoG distribution are estimated using a
simplified expectation maximization (EM) algorithm. Upper bound of sum rates of
multi-cell OFDM-IM is derived. Furthermore, analytic and simulated results are
compared and discussed.
