This study 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 of multi-cell OFDM-IM is investigated by stochastic geometry. Furthermore, it is proved in this study that the probability density function of noise plus inter-cell interference in multicell OFDM-IM with quadrature-amplitude modulation follows a mixture of Gaussians (MoGs) distribution. Next, parameters of the MoG distribution are estimated using a simplified expectation maximisation algorithm. Upper bound of sum rates of multi-cell OFDM-IM is derived. Furthermore, analytic and simulated results are compared and discussed
