An apparatus for generating an audio output signal is provided. The audio output signal has two or more audio output channels and is generated from an audio input signal having two or more audio input channels. The apparatus includes a provider and a signal processor. The provider is adapted to provide first covariance properties of the audio input signal. The signal processor is adapted to generate the audio output signal by applying a mixing rule on at least two of the two or more audio input channels. The signal processor is configured to determine the mixing rule based on the first covariance properties of the audio input signal and based on second covariance properties of the audio output signal, the second covariance properties being different from the first covariance properties.