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Abstract The finite length absolute minimum vectors of the Constant Modulus (CM) criterion with an arbitrary source and a single output linear regression model are shown to equal the Wiener filter or one of its phase shifted versions. The exact equations for these vectors are also provided and depend on the second and the fourth order statistical moments of the sample sequence only. These expressions describe the behavior of the Constant Modulus Algorithm (CMA) when it operates at the desired global minimum and expose key characteristics of the CM minimization approach. These characteristics include the existence conditions, the persistency of excitation, the computational complexity, the excess CM cost, the robustness to an additive noise, and the tolerance to the length variations. Moreover, several computer simulation experiments are included to validate our findings. [ABSTRACT FROM AUTHOR]