Joint Implementation of Symbol Timing Synchronization and Carrier Synchronization Simulation Using Maximum Likelihood Method

1) This study implements joint symbol timing synchronization and carrier synchronization simulation using the Maximum Likelihood (ML) method. The implementation typically involves developing algorithms that simultaneously estimate timing offset and carrier phase by maximizing the likelihood function of received signals. Building upon this foundation, we further investigate the impact of Poisson distribution on simulation outcomes and conduct an analysis of Bayesian estimation. Finally, we employ the RANSAC (Random Sample Consensus) method to validate and optimize the simulation results, which involves iterative random sampling to handle outliers in parameter estimation.

2) Poisson distribution is a probability distribution widely used in probability theory for modeling the number of random events occurring within a fixed interval. In code implementation, this distribution can be simulated using probability mass functions to generate random event counts. Our research reveals that Poisson distribution significantly influences the simulation results of symbol timing synchronization and carrier synchronization, necessitating careful consideration during experimental design and parameter configuration.

3) Bayesian estimation is a statistical method that combines prior knowledge with observed data to estimate parameters. In algorithmic terms, this involves updating posterior probabilities using Bayes' theorem. In this study, we analyze the theoretical framework of Bayesian estimation and explore its application in symbol timing synchronization and carrier synchronization systems, where it can improve estimation accuracy by incorporating historical channel information.

4) RANSAC method is an iterative parameter estimation technique particularly effective for identifying and removing outliers from datasets. The algorithm works by randomly selecting minimal data subsets to form hypotheses and then evaluating consensus across the entire dataset. In our research, we utilize RANSAC to validate and optimize simulation results, ensuring the accuracy and reliability of synchronization performance metrics through robust outlier rejection mechanisms.