Iterative SOCP scheme for designing digital phase-networks

In digital communications, the non-linear phase characteristic of a digital communication channel must be equalized by using a phase-network in such a way that the whole communication channel has nearly linear-phase and does not distort the waveform of the transmitted signal. This paper proposes an improved iterative second-order-cone-programming (iSOCP) technique for designing an all-pass (AP) phase-network such that a given ideal phase response can be well fitted in the minimax error sense. This AP phase-network design approach first approximates the highly non-linear constraint of the SOCP-based minimax design as a quadratic cone (Qcone) constraint and then iteratively solves the approximated SOCP problem. We will use an example to illustrate that this improved iSOCP design yields smaller maximum errors (peak errors) of the phase response and frequency response (FR) of the resulting AP phase-network than other existing designs such as linear-programming (LP) design and non-iterative SOCP and iSOCP designs.