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Radar pulse compression involves the extraction of an estimate of the range profile illuminated by a radar in the presence of noise. A problem inherent to pulse compression is the masking of small targets by large nearby targets due to the range sidelobes that result from standard matched filtering. This paper presents a new approach based upon a minimum mean-square error (MMSE) formulation in which the pulse compression filter for each individual range cell is adaptively estimated from the received signal in order to mitigate the masking interference resulting from matched filtering in the vicinity of large targets. The proposed method is compared with the standard matched filter and least-squares (LS) estimation and is shown to be superior over a variety of stressing scenarios.