A volterra filtering approach for the polynomial formulation of the constant modulus criterion

In this work, an extended polynomial formulation of the constant modulus (CM) criterion under quadratic constraints is presented. Based on the method of Lagrange Multipliers, this `Volterra-CM formulation´ brings very relevant information about the structure of the null-gradient CM solutions in the equalizer parameter space, including a conjecture regarding the relationship between the smallest multiplier and the optimal CM receiver. In the case of a two-tap filter, the proposed formulation allows that the solutions be obtained in terms of a single parameter, the corresponding Lagrange multiplier. For filters with more than two taps, the problem requires that a nonlinear system be solved, which is done with the aid of an iterative algorithm. The obtained global convergence rates show that the formulation is an effective tool to describe the structure of the optimal CM solution.