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Passengers communication inside a car can be improved by using a speech reinforcement system. This system picks up the speech of each passenger, amplifies it and plays it back into the cabin through the loudspeakers of the car. Due to the electro-acoustic coupling between loudspeakers and microphones, a closed-loop system is created. To avoid the risk of instability due to the acoustic feedback, acoustic echo cancellation must be performed. Using the Minimum Mean Square Error (MMSE) criterion to adapt the filter, what is very common in acoustic echo cancellation, leads to inaccurate estimates of the Loudspeaker-Enclosure-Microphone (LEM) path due to the closed-loop operation of the system. In this paper, the solution obtained with the MMSE criterion for a Finite-length Impulse Response (FIR) causal adaptive filter is derived, showing that the identification error depends on the amplification factor of the system, the delay of the loop and the spectral characteristics of the excitation signal. The use of whitening filters is proposed and justified to improve the acoustic echo cancellation in speech reinforcement systems for cars. Results obtained for a one-channel speech reinforcement system are presented.