Phase-Equalizing Filter Design Employing Quadratic-Cone Programming
Tian–Bo Deng · 2023
Nonlinear-phase communication channels and digital signal processing (DSP) systems have the disadvantage to distort the transmitted as well as the processed signal waveforms. To avoid this type of undesirable waveform distortions, it is mandatory to equalize the nonlinear phase characteristics via employing a digital phase-equalizing filter (PEF). This paper targets at presenting a convex programming tactic for designing an allpass-type PEF. Originally, the PEF design problem can only be solved via employing a nonlinear programming technique. This paper reformulates an improved tactic that can reduce the PEF design to an approximated quadratic-cone (Qcone) programming (Qcone programming) problem, and thus can get an approximate convex programming solution. Although the solution is locally optimal, the design formulation is not only simple, but also needs no iterations for getting the solution. That is, this convex programming does not involve any iterative procedures. As compared to the existing Qcone design scheme, this improved tactic is able to enhance the PEF performance. A typical example is included, aiming to validate this improved Qcone programming tactic as well as show the performance improvement.