Two Contributions Derived from a Polynomial Formulation of the Constant Modulus Criterion

From the classical blind CM criterion, we derive a MSE-based polynomial formulation that lead to two contributions: a lower bound of the CM criterion, which works as an equalizability index, and an initialization heuristic for the CMA. The results indicate the validity of the index as an analytical tool and as a practical performance assessment metric in the context of inverse problems. For the heuristic, the results reveal that it is capable of outperforming the classical center-spike method and a random initialization approach.