Improved linear-programming design of all-pass digital phase-networks

In this paper, we present an improved iterative linear-programming (iLP) technique for designing an all-pass digital phase-network (PN). The phase-error function used in the design is an improved version of the existing bi-linear phase-error function with its numerator and denominator expressed as linear functions of the all-pass PN coefficients. Although the original minimax design is a constrained non-linear optimization problem, we reduce it to an iLP problem by iterating the denominator of the improved bi-linear phase-error function. A design example is included in the paper for proving the performance improvement through using the improved phase-error function.