Described is a audio signal processing technology in which an adaptive beamformer processes input signals from microphones based on an estimate received from a pre-filter. The adaptive beamformer may compute its parameters (e.g., weights) for each frame based on the estimate, via a magnitude-domain objective function or log-magnitude-domain objective function. The pre-filter may include a time invariant beamformer and/or a non-linear spatial filter, and/or may include a spectral filter. The computed parameters may be adjusted based on a constraint, which may be selectively applied only at desired times.