Синтез компенсаторов частотной дисперсии на основе цифровых фазовых цепей
Authors: Бугров В.Н. , Савельев Д.В. , Кудряшова О.Е. , Сатаев В.В. 
Published: February 2025

Рассматриваются вопросы решения задачи многофункционального синтеза цифрового фазового БИХ-фильтра с линейной дисперсионной характеристикой, необходимой для компенсации дисперсионных искажений в полосе радиоканала, методами нелинейного математического программирования в целочисленном пространстве восьмибитовых параметров. Приводятся характеристики и оптимальные параметры синтезированного цифрового компенсатора.
Introduction. Digital phase circuits or filters based on them are widely used in digital signal processing to correct for dispersion distortions in signal paths and communication links. Phase digital IIR filters have a unity gain modulus over the entire Nyquist zone and a tricky law of change in the phase-frequency characteristic, and, consequently, its derivatives - group delay and frequency dispersion. The feasibility of implementing the required law of change in the dispersion characteristic allows one to use such a phase filter to correct for dispersion distortions in a narrow-band radio channel. We shall note that when designing digital frequency dispersion compensators, the engineer deals with modest phase deviations when compensating for the frequency dispersion of a signal in a communication channel. This requires the most adequate representation of the phase-frequency characteristic and its derivatives (group delay and frequency dispersion) both at the stage of synthesis of a technical solution and at the stage of its implementation on a specific digital platform. However, the typical classical calculation of the phase IIR filter is characterized by both systematic errors in the analytical approximation of the characteristics of an analog prototype at the stage of synthesis of a technical solution, and quantization errors of the coefficients at the stage of practical implementation of a technical solution on a selected digital platform. These errors can be eliminated when designing a dispersion compensator with the use of a state-of-the-art numerical methods of discrete programming, which allow working not with an analytical, but with a discrete tabulated representation of the characteristics. This allows one to replace the analytical approximation procedure with a simple digitization of the required characteristics. Besides, the error in digitizing the phase characteristics of even a very complicated shape can be minimized by appropriate choice of frequency sampling step. The aim of the work was the usage of integer nonlinear programming for the efficient synthesis of integer digital dispersion compensator (DDC) with low number of bits and the maximum fulfillment of the requirements for the set of required characteristics of the compensator implemented on a digital phase circuit. When using calculations with the fixed-point format in the digital filtering algorithm, it is reasonable to discretize the parametric space of coefficients with an integer code. The ideology of integer programming allows to effectively design integer dispersion compensators with the complete fulfillment of the requirements for the set of required characteristics. Moreover, the use of dynamic coefficient quantization technology allows to obtain technical solutions with a minimum bit depth of data representation. Conclusion.It was shown that the application of the searching algorithm on a discrete grid of quantized parameters allows one to synthesize technical solutions with a zero implementation error on a digital platform or a crystal with a given coefficient word length. With the use of discrete search synthesis, we obtained a low bit depth compensator solution with a linearly increasing dispersion in the correction band and a minimum digital compensator inertia in terms of the impulse response delay. State-of-the-art discrete minimization algorithms allow to reliably and efficiently solve such design problems while meeting all external requirements and limitations on the operation of the DDC.