The present invention relates in one aspect to a microphone array signal processing system comprising a digital buffer coupled to a signal input and configured to store first and second digital audio signals. A beamformer analyzer is configured to, in response to a first voice trigger, determine noise statistics based on the first signal segment of the first digital audio signal and a first signal segment of the second digital audio signal. A coefficients calculator is configured to calculate a first set of fixed beamformer coefficients of a beamforming algorithm. The beamforming algorithm is configured for applying the first set of fixed beamformer coefficients to the first signal segments of the first and second digital audio signals retrieved from the digital buffer to produce a noise reduced digital audio signal.