MATLAB Code Implementation for Time Delay Estimation

This document discusses how to implement time delay estimation using MATLAB. Time delay estimation is a technique used to measure propagation delays in signal transmission. In our experiment, we utilize Gaussian white noise signals with specific signal-to-noise ratios (SNR) for time delay estimation. SNR represents the ratio between signal power and noise power, which significantly impacts the accuracy of delay estimation. The implementation involves several key steps: First, we generate Gaussian white noise signals using MATLAB's randn() function and add controlled noise levels to achieve target SNRs. Then we apply time delay estimation algorithms such as cross-correlation methods (implemented via xcorr() function) or phase-based approaches. The cross-correlation method works by computing the correlation between the original and delayed signals, where the position of the maximum correlation coefficient corresponds to the time delay. For enhanced accuracy, we may incorporate preprocessing techniques like signal filtering and windowing functions. The algorithm calculates the time delay by analyzing peak detection in the correlation output, with MATLAB's max() and find() functions helping to locate the precise delay point. Through systematic signal analysis and processing, we can estimate propagation delays with high precision, which is crucial for applications like radar systems, underwater acoustics, and communication networks. The MATLAB implementation includes error analysis metrics such as mean squared error (MSE) calculations to evaluate estimation performance under different SNR conditions. This comprehensive approach ensures reliable time delay estimation results in our experimental framework.