Methods and apparatus for blind channel estimation of a speech signal corrupted by a communication channel are provided. One method includes converting a noisy speech signal into either a cepstral representation or a log-spectral representation; estimating a correlation of the representation of the noisy speech signal; determining an average of the noisy speech signal; constructing and solving, subject to a minimization constraint, a system of linear equations utilizing a correlation structure of a clean speech training signal, the correlation of the representation of the noisy speech signal, and the average of the noisy speech signal; and selecting a sign of the solution of the system of linear equations to estimate an average clean speech signal in a processing window.