Gardner Timing Synchronization Algorithm Simulation

In this document, we will conduct a comprehensive simulation of the Gardner timing synchronization algorithm. Through this MATLAB implementation, we generate signals using the Gardner algorithm, transmit them to the receiver, and achieve precise synchronization. The implementation covers key components including interpolation filter design, timing error detection, and loop filter configuration. The simulation demonstrates the algorithm's core functionality through MATLAB code that implements: - Signal generation with adjustable parameters for sampling rate and symbol timing offset - Interpolation using Farrow structure for efficient sample rate conversion - Timing error calculation using Gardner's non-data-aided approach - Loop filter implementation for stable synchronization convergence We provide detailed step-by-step explanations with corresponding code segments, including functions for calculating timing error (gardner_ted) and implementing the interpolation control loop. This approach helps users better understand and apply the Gardner synchronization algorithm in practical digital communication systems, particularly for symbol timing recovery in software-defined radios and modem designs. The code structure organizes the simulation into modular sections: signal generation module, transmitter chain, channel modeling, receiver processing, and synchronization loop. Key MATLAB functions used include resample for interpolation, filter for loop implementation, and custom functions for error calculation and timing adjustment.