OFDM Implementation: Mapping, IDFT/DFT Operations, Time-Frequency Synchronization, Channel Estimation, and Frequency Offset Estimation

This collection of modular functions simulates and implements critical components of an OFDM communication system. The codebase includes implementation of subcarrier mapping algorithms, efficient IDFT/DFT operations using FFT algorithms, sophisticated synchronization routines incorporating preamble detection and correlation techniques for time synchronization, and pilot-based methods for frequency synchronization. The channel estimation module utilizes reference symbols and interpolation algorithms to characterize wireless channel properties, while the frequency offset estimator employs autocorrelation and phase-based methods to compensate for carrier frequency discrepancies. These implementations allow researchers to thoroughly analyze OFDM system performance, validate theoretical models against practical simulations, and develop enhanced communication protocols. The synchronization subsystem ensures robust signal recovery at the receiver through precise symbol timing alignment and carrier frequency correction. This comprehensive library serves as both an educational tool for understanding OFDM fundamentals and a development framework for advanced wireless communication research.