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A method is proposed for enhancement of speech degraded by background noise and reverberation, which is collected simultaneously over several microphones. Each microphone signal is processed by the Linear Prediction (LP) analysis to extract the Hilbert envelope of the LP residual. The time-delays are estimated and the Hilbert envelopes of the LP residuals from all the microphones are added coherently. The coherently-added Hilbert envelope is processed by the the group delay analysis to derive a weight function. The LP residual of the coherently-added speech signal is multiplied with the weight function to produce a modi.ed LP residual in which the excitation part of speech is enhanced. The speech signal synthesized from the modi.ed LP residual is found to be perceptually enhanced signi.cantly.