Communications systems that use multicarrier modulation techniques are highly sensitive to non-linear distortions due to relatively high values of a peak-to-average power ratio (PAPR). In order to improve the performance of these systems, schemes using sub carrier index modulation techniques are being proposed. This paper presents analytical expressions that allow evaluating the bit error rate performance of a multicarrier system such as the Orthogonal Frequency Division Multiplexing (OFDM) using a particular type of sub carrier index modulation know as Enhanced sub carrier Index Modulation (ESIM) and operating over a non-linear channel with memory. Numerical results obtained for a specific case allow verifying the performance improvement of ESIM-OFDM systems when compared with classic OFDM systems.