A method for a multi microphone noise reduction in a complex noisy environment is proposed. A left and a right noise power spectral density for a left and a right noise input frame is estimated for computing a diffuse noise gain. A target speech power spectral density is extracted from the noise input frame. A directional noise gain is calculated from the target speech power spectral density and the noise power spectral density. The noisy input frame is filtered by Kalman filtering method. A Kalman based gain is generated from the Kalman filtered noisy frame and the noise power spectral density. A spectral enhancement gain is computed by combining the diffuse noise gain, the directional noise gain, and the Kalman based gain. The method reduces different combinations of diverse background noise and increases speech intelligibility, while guaranteeing to preserve the interaural cues of the target speech and directional background noises.