Digital PLLs for phase noise channels: a concept based on the Tikhonov distribution

We explore the concept of a digital phase-locked loop (PLL) of the first type, derived as an alternative solution to Kalman's estimation problem by employing the Tikhonov distribution rather than the traditional Gaussian model. The resulting Tikhonov PLL is a complex-valued nonlinear filter that is simple to implement and demonstrates interesting features in channels affected by strong phase noise. We present a comparative analysis including the classical PLL and Kalman filter to highlight the strengths of the Tikhonov PLL in such contexts.