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A radial basis function (RBF) assisted turbo equaliser (TEQ) scheme, applied to various coded modulation schemes, is investigated. Specifically, trellis coded modulation (TCM), turbo trellis coded modulation (TTCM), bit-interleaved coded modulation (BICM) and BICM with iterative decoding (BICM-ID) are studied, when communicating over frequency selective fading channels. At a given complexity, the TTCM RBF-TEQ provides the best bit error ratio (BER) and frame error ratio (FER) performance. The RBF-TEQ structure is shown to provide an SNR performance improvement of about 5.5 dB at a BER of 10-4 in comparison to the conventional non-iterative DFE scheme.