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Speech signals are often degraded by additive interference over single-channel communication systems. For stationary and well defined noise sources, effective solutions exist. However, it is often difficult to formulate a model for nonstationary and speechlike noise sources such as crosstalk or multispeaker babble, which exist in real scenarios. In this paper, we propose a solution to this problem under the assumption that we have access to the clean speech signal prior to transmission. A novel method for tracking transmission noise characteristics is described. Based on this noise estimate, a new speech enhancement technique is proposed. The enhancement method is evaluated for multispeaker babble noise, and shown to substantially improve both the quality and intelligibility of the processed speech signal.