Basic Simulation Models of Phase Tracking Devices Using MATLAB

Abstract

The Phase-Locked Loop (PLL), and many of the devices used for frequency and phase tracking, carrier and symbol synchronization, demodulation, and frequency synthesis, are fundamental building blocks in today's complex communications systems. It is therefore essential for both students and practicing communications engineers interested in the design and implementation of modern communication systems to understand and have insight into the behavior of these important and ubiquitous devices. Since the PLL behaves as a nonlinear device (at least during acquisition), computer simulation can be used to great advantage in gaining insight into the behavior of the PLL and the devices derived from the PLL.The purpose of this Synthesis Lecture is to provide basic theoretical analyses of the PLL and devices derived from the PLL and simulation models suitable for supplementing undergraduate and graduate courses in communications.The Synthesis Lecture is also suitable for self study by practicing engineers. A significant component of this book is a set of basic MATLAB-based simulations that illustrate the operating characteristics of PLL-based devices and enable the reader to investigate the impact of varying system parameters. Rather than providing a comprehensive treatment of the underlying theory of phase-locked loops, theoretical analyses are provided in sufficient detail in order to explain how simulations are developed. The references point to sources currently available that treat this subject in considerable technical depth and are suitable for additional study.

Limitations of the classical phase-locked loop analysis

“…But the attempts to justify analytically the reliability of conclusions, based on such engineering approaches, and to study the nonlinear models of PLL-based circuits are quite rare in the modern engendering literature [18]. One of the reasons is that "nonlinear analysis techniques are well beyond the scope of most undergraduate courses in communication theory" [3].…”

“…PLL is essentially a nonlinear control system and its real model is described by a nonlinear nonautonomous system of differential equations (mathematical model in the signal space). In practice, simulation and simplified mathematical models are widely used for the analysis of PLL-based circuits [1]- [3].…”

Efficient Phase Recovery System

“…The comparison shows that, the PLL response has a long settling (locking) time and ripples, and the proposed estimator locked the input phase quickly without any ripples. To remove the ripples from PLL it needs to use a higher order LPF, but unfortunately it increases the instability of the system [20][21].…”

Improved PLL-based MUSIC Algorithm for Single Receiver DF Systems

“…The QPSK case has a similar behavior, however, there are four stable operating points for each cycle of the input. It follows that the QPSK loop has a 2 ⁄ radian phase ambiguity [7].…”

“…The proper damping factor value depends on the PLL application. ) [7], with SNR fixed in 7dB for all cases. Hence, the greater value of , the lower the noise bandwidth.…”