A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis

TL;DR

This paper surveys nonlinear models of the Costas loop, emphasizing the importance of rigorous derivation over simplified models and highlighting potential inaccuracies in traditional analysis methods.

Contribution

It provides a comprehensive review of nonlinear models for the BPSK Costas loop, discussing their derivation and limitations of classic analysis techniques.

Findings

Simplified models can lead to incorrect performance conclusions.

Rigorous derivation is essential for accurate analysis.

Traditional linearization methods may be insufficient.

Abstract

Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop physical model.