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A new form of multi-waveform space-time adaptive processing (MuW-STAP) is presented. The formulation provides additional training data for adaptive clutter cancellation for ground moving target indication after pulse compression. The pulse compression response is homogenized using stochastic phase filters to produce a smeared response that approximates identically distribution assumed by covariance estimation. Post pulse compression MuW-STAP (PMuW-STAP) is proposed to address clutter heterogeneity that causes degradation in detection performance of STAP similar to single-input multi-output MuW-STAP. Furthermore, the family of MuW-STAP algorithms are computationally expensive due to estimation of multiple covariance matrices and inversion of a single covariance for every range sample. Well-known partially adaptive techniques, previously implemented in STAP, are implemented with PMuW-STAP. Partial adaptation in element-space post-Doppler, beam-space pre-Doppler, and beam-space post-Doppler are presented. Each of these are examined on several simulated, controlled clutter scenarios. Fully adaptive PMuW-STAP is further evaluated on the high-fidelity knowledge aided adaptive radar architecture: knowledge-aided sensor signal processing and expert reasoning (KASSPER) dataset.