Maximum Likelihood Synchronization Algorithm for OFDM Systems

This program implements the Maximum Likelihood (ML) synchronization algorithm for OFDM systems, using a Rayleigh fading channel model with Doppler frequency shift. The implementation involves several key computational steps: first, the received signal undergoes sampling at appropriate intervals to capture OFDM symbol characteristics. The algorithm then computes the spectral characteristics of the received signal using Fast Fourier Transform (FFT) operations. Core to the ML synchronization approach is the likelihood function calculation, which compares the received signal statistics with the known channel model parameters. The Rayleigh fading model with Doppler shift is implemented through complex channel coefficients that vary over time, simulating real-world wireless propagation effects including frequency offset and signal attenuation. The ML estimation process involves maximizing the likelihood function through iterative optimization techniques, potentially using gradient descent or grid search methods to find optimal time and frequency synchronization parameters. The final output is a synchronized signal where timing offsets and carrier frequency deviations are corrected, ensuring proper alignment with the reference channel model for subsequent demodulation and decoding operations.