Generalized SOCP scheme for designing all-pass digital phase circuits

In digital communications, the non-linear phase characteristic of a digital communication channel distorts the waveform of the transmitted signal. To avoid this problem, a phase circuit must be cascaded to the communication channel such that the whole communication channel has nearly linearphase. This paper presents a generalized iterative second-order-cone-programming (SOCP) method for designing an all-pass (AP) phase circuit that approximates a given ideal phase specification. The highly non-linear design constraints of the minimax design are iteratively approximated as second-order-cone (SOC) constraints and then the minimax design problem is iteratively solved by utilizing the SOCP technique. We will use an example to demonstrate that this iterative SOCP design can further reduce the maximum errors (peak errors) of the phase response and frequency response (FR) of the designed AP phase circuit as compared with the existing linear-programming (LP) design and other SOCP designs.