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The problem of cancellation of strong, potentially nonstationary, echoes in noise radars and passive radars utilizing digital transmissions is considered. The proposed solution is a multi-stage procedure. Initial clutter estimates, obtained using the least mean squares (LMS) algorithm, are refined using specially designed filters, “matched” to spectral densities of targets and clutter. When the postprocessing filters are noncausal, the performance of the proposed canceler is improved compared to the solution based on causal filters.