Symbol Timing Recovery

Overview

This repository contains MATLAB scripts focusing on symbol timing recovery algorithms. The implementation is based on the material from the book "Digital Communications: A Discrete-Time Approach" by Michael Rice. If you are new to the topic, you can check out chapter 8 from this book or access the introductory tutorial in my blog.

The main script of this repository (file main.m) is a simulator of symbol timing recovery applied to a pulse-shaped PAM/QAM signal under additive white Gaussian noise (AWGN). This script generates the pulse-shaped Tx sequence and feeds it into a receiver with the following blocks:

The symbol timing recovery loop is implemented by the symbolTimingSync function and combines the timing error detector (TED), interpolator, controller, and loop filter blocks. The adopted loop filter is a proportional-plus-integrator (PI) controller, while the interpolator controller is a modulo-1 counter. Meanwhile, you can choose the TED and interpolator implementation from various alternative methods.

When running the simulation, ensure to tune the parameters of interest at the top of the main.m file. For instance, choose the TED scheme and the interpolation method from the supported options summarized in the table below. Alternatively, experiment with filter parameters such as the loop bandwidth and damping factor, or play with plotting and debugging options by enabling the debug_tl_static and debug_tl_runtime flags at the top of main.m.

Supported TEDs	Supported Interpolators
Maximum-likelihood TED (MLTED)	Polyphase filterbank interpolator
Early-late TED (ELTED)	Linear polynomial interpolator
Zero-crossing TED (ZCTED)	Quadratic polynomial interpolator
Gardner TED (GTED)	Cubic polynomial interpolator
Mueller and Müller TED (MMTED)

Code Organization

File	Description
calcSCurve.m	Function to compute the TED's S-curve analytically.
calcTedKp.m	Function to compute the timing error detector gain.
derivativeMf.m	Function to compute the derivative matched filter.
genTestVector.m	Function to generate input/output test vectors.
main.m	Main simulation.
piLoopConstants.m	Function to compute the PI controller constants.
plotTedGain.m	Function to plot the TED gain vs. the rolloff factor.
polyDecomp.m	Function to decompose a filter into a polyphase bank.
polyInterpFilt.m	Function to design a polyphase interpolator.
sCurveDemo.mlx	A demonstration of TED S-curve and gain evaluations.
simSCurve.m	Function to simulate the TED's S-curve.
symbolTimingSync.m	Function implementing the symbol timing recovery loop.

Experiments

Please refer to the documentation page covering relevant experiments with the symbol timing recovery simulator.

Contact

If you have any questions or comments, please feel free to e-mail me or open an issue.