Analysis of the prewhitened constant modulus cost function

We provide an analysis of the constant modulus (CM) cost function under the assumption of a white equalizer input. This can be achieved by means of an adaptive prewhitening all-pole filter and has been suggested in previous works as a means for both MSE improvement and DFE cold start-up. For white inputs, it is seen that CM -optimizing the spherical component of the equalizer parameter vector is equivalent to minimizing the fourth moment of its output, regardless of the value of the radial component. This leads to an eigenvector interpretation of prewhitened CM receivers, and to a blind initialization procedure from an eigenvector of the quadri-covariance matrix of the whitened data. Connections with iterative eigenvector-based schemes are also explored.