A microphone array signal processing system (100, 200), comprising: - a signal input (111,211) configured to receive a first digital audio signal from a first microphone of a microphone array and a second digital audio signal from a second microphone of the microphone array, - a digital buffer coupled to the signal input (111, 211) and configured to store the first digital audio signal and the second digital audio signal, - a voice trigger input indicating a first signal segment holding a first voice feature of the first digital audio signal in the digital buffer, - a beamformer analyser (117, 217) configured to, in response to the voice trigger input, determine noise statistics, such as an estimated noise covariance matrix S vv ( k), based on the first signal segment of the first digital audio signal and a first signal segment of the second digital audio signal aligned in time to the first signal segment of the first digital audio signal, wherein the first signal segment of the first digital audio signal represents a real-time period exceeding 500 ms and the first signal segment of the second digital audio signal represents a real-time period exceeding 500 ms, - a coefficients calculator (119, 219) configured to calculate a first set of fixed beamformer coefficients (w(k)) of a beamforming algorithm (121, 221) based on the first signal segment of the first digital audio signal, the first signal segment of the second digital audio signal and the determined noise statistics, and - the beamforming algorithm (121, 221) being configured for applying the first set of fixed beamformer coefficients ((w(k)) to at least: the first signal segment of the first digital audio signal and the first signal segment of the second digital audio signal retrieved from the digital buffer to produce a noise reduced digital audio signal (y enh (t)). - a signal input (111,211) configured to receive a first digital audio signal from a first microphone of a microphone array and a second digital audio signal from a second microphone of the microphone array, - a digital buffer coupled to the signal input (111, 211) and configured to store the first digital audio signal and the second digital audio signal, - a voice trigger input indicating a first signal segment holding a first voice feature of the first digital audio signal in the digital buffer, - a beamformer analyser (117, 217) configured to, in response to the voice trigger input, determine noise statistics, such as an estimated noise covariance matrix S vv ( k), based on the first signal segment of the first digital audio signal and a first signal segment of the second digital audio signal aligned in time to the first signal segment of the first digital audio signal, wherein the first signal segment of the first digital audio signal represents a real-time period exceeding 500 ms and the first signal segment of the second digital audio signal represents a real-time period exceeding 500 ms, - a coefficients calculator (119, 219) configured to calculate a first set of fixed beamformer coefficients (w(k)) of a beamforming algorithm (121, 221) based on the first signal segment of the first digital audio signal, the first signal segment of the second digital audio signal and the determined noise statistics, and - the beamforming algorithm (121, 221) being configured for applying the first set of fixed beamformer coefficients ((w(k)) to at least: