Simplified linear-programming method for designing all-pass phase-compensation network

In this paper, we propose a new method for designing all-pass (AP) digital filters for equalizing the nonlinear phase characteristics of non-linear digital communication channels. Once a desired phase response is given, we first derive an approximate phase error function that is a linear function with respect to the coefficients of the AP digital filter. Then, we propose a non-iterative scheme for minimizing the approximated maximum phase error so as to minimize the maximum phase error by employing a linear-programming (LP) technique. In other words, the resulting AP filter is aimed to minimize the worst-case phase error, which is a minimax phase error design. The coefficients of the AP digital filter can be obtained through using the approximately formulated LP design. As compared with the existing LP design, the proposed new LP scheme reduces the total number of the LP constraints by one half (50%) and thus reduces the computational complexity required in the LP design, whereas the design errors are slightly smaller. An example is given for demonstrating the effectiveness of the proposed LP-based design scheme.