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The purpose of this study is to investigate the performance of speech presence (SP) microphone array beamforming. When the presence uncertainty of the desired speech is considered, noise reduction is greatly achieved while preserving low speech distortion level. Furthermore, we propose a novel model based speech presence probability (SPP) estimator, exploring both the sinusoid structure of speech and signal-to-noise ratio (SNR). Finally, experiments verify the effectiveness of the proposed SP-beamformer, resulting in a better trade-off between speech distortion and noise leakage, and a corresponding higher output segmental SNR, when compared with the classical beamformers.