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The goal of radar space-time adaptive processing (STAP) is to detect slow moving targets from a moving platform, typically airborne or spaceborne. STAP generally requires the estimation and the inversion of an interference-plus-noise (I+N) covariance matrix. To reduce both the number of samples involved in the estimation and the computational cost inherent to the matrix inversion, many suboptimum STAP methods have been proposed. We propose a new canonical framework that encompasses all suboptimum STAP methods we are aware of. The framework allows for both covariance-matrix (CM) estimation and range-dependence compensation (RDC); it also applies to monostatic and bistatic configurations. Finally, we discuss a taxonomy for classifying the methods described by the framework.