The performance of a Correlation Demodulator (CD) with Decision Feedback Carrier Recovery (DFCR) in a channel with an additive mixture of a speech signal and a Gaussian background noise as interference is analyzed. The MPSK modulation format is considered. Expressions of energy loss due to the influence of the speech signal and of the probability of error are obtained. For this purpose the speech signal is considered as a random combination of vowels, consonants and pauses. Moreover, the vowels as well as the consonants are modeled as the response of some Linear Time Invariant (LTI) systems to white Gaussian noise. An experiment was performed. Good agreement with the theoretical results was obtained.