High-accuracy phase-equalizer design based on bi-linearized phase-error function

The phase response of a recursive all-pass digital phase-equalizer is inherently non-linear with respect to its coefficients. In this paper, we first derive an approximate phase-error function whose numerator and denominator are approximated as linear functions of the phase-equalizer coefficients. Then, we propose a new design algorithm for fitting the phase response of an all-pass digital phase-equalizer to a given ideal phase response in the minimax sense. This design scheme utilizes a modern optimization technique called rotated-cone (Rcone) programming, which is a relatively new optimization technique. Finally, we provide a phase-fitting example for demonstrating the design accuracy of the proposed Rcone-programming technique. Moreover, we also use a numerical example to demonstrate the Rcone-programming technique.