This paper presents a method of adaptive microphone array beamforming using matched filters with signal subspace tracking, Our objective is to enhance near-field speech signals by reducing multipath and reverberation, In real applications such as speech acquisition in acoustic environments, sources do not propagate along known and direct paths. Particularly in hands-free telephony, we have to deal with undesired propagation phenomena such as reflections and reverberation, Prior methods developed adaptive microphone arrays for noise reduction after a time delay compensation of the direct path, This simple synchronization is insufficient to produce an acceptable speech quality, and makes adaptive beamforming unsuitable, In this contribution, we prove the identification of source-to-array impulse responses to be possible by subspace tracking, We consequently show the advantage of treating synchronization as a matched filtering step, Speech quality is indeed enhanced at the output by the suppression of reflections and reverberation (i.e., dereverberation), and efficient adaptive beamforming for noise reduction is applied without risk of signal cancellation, Evaluations confirm the performance achieved by the proposed algorithm under real conditions.