The perception of consonants in background noise has been investigated in various studies and was shown to critically depend on fine details in the stimuli. In this study, a microscopic speech perception model is proposed that represents an extension of the auditory signal processing model by Dau, Kollmeier, and Kohlrausch [(1997). J. Acoust. Soc. Am. 102, 2892-2905]. The model was evaluated based on the extensive consonant perception data set provided by Zaar and Dau [(2015). J. Acoust. Soc. Am. 138, 1253-1267], which was obtained with normal-hearing listeners using 15 consonant-vowel combinations mixed with white noise. Accurate predictions of the consonant recognition scores were obtained across a large range of signal-to-noise ratios. Furthermore, the model yielded convincing predictions of the consonant confusion scores, such that the predicted errors were clustered in perceptually plausible confusion groups. The large predictive power of the proposed model suggests that adaptive processes in the auditory preprocessing in combination with a cross-correlation based template-matching back end can account for some of the processes underlying consonant perception in normal-hearing listeners. The proposed model may provide a valuable framework, e.g., for investigating the effects of hearing impairment and hearing-aid signal processing on phoneme recognition.