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This study improves the fading channel estimation in bit-interleaved coded modulation systems with iterative decoding (BICM-ID) and signal space diversity (SSD) by embedding a training sequence. Existing training schemes work well at high signal-to-noise ratio (SNR) or slowly time-varying channels whereas the applications of BICM-ID are beneficial at low SNR and fast time-varying fading channels. Motivated by the power/bandwidth efficiency of the SSD technique and the fact that superimposed training outperforms pilot symbol-assisted modulation (PSAM) training over relatively fast time-varying channels, a new superimposed training sequence is explored. The proposed training sequence inserts pilot bits into the coded bits prior constellation mapping and signal rotation. This becomes a superimposed training sequence in the rotated symbols and helps the estimator to track fast variation of the channel gains. A soft iterative channel estimator is developed to work with the superimposed training sequence. The performance of the proposed scheme, namely SSD-pilot, is shown to be superior to PSAM scheme. To gauge the performance improvement achieved with the proposed channel estimation, an analytical bound on the asymptotic bit error probability for BICM-ID using SSD over correlated fading channels is provided. The Cramer-Rao bound on the mean-square error of the channel estimator is also derived to evaluate the performance of the iterative channel estimator.