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The effect of signal-to-noise ratio (SNR) mismatch on the bit error rate (BER) performance of log-MAP turbo detector is studied. It is shown that the sensitivity to the mismatched SNR depends on the channel loss and the encoder memory length. In particular, the sensitivity is more important for a "difficult-to-equalize" channel or, in other words, a high-loss channel. In fact, by affecting the equalizer and the decoder, a mismatched SNR (with an offset with respect to the true SNR) affects the convergence of the turbo detector. Using the asymptotic analysis tool of extrinsic information transfer (EXIT) charts, the effect of a positive or a negative SNR offset on the convergence of the log-MAP turbo detector is studied. When no information is available at the receiver on SNR, an online estimation of SNR is necessary in order to not lose the advantage of the log-MAP turbo detector over other suboptimal turbo detectors. In this view, a relatively simple SNR estimation method is proposed, which offers satisfying results.