Frequency Offset Estimation Algorithm with Amplitude and Phase Correction

Frequency offset estimation algorithms are crucial in wireless communication systems, primarily used to compensate for frequency deviations between received signals and local oscillators. Amplitude correction and phase correction are key steps in frequency offset estimation that effectively enhance system performance.

Amplitude Correction Amplitude correction adjusts signal power levels to ensure subsequent processing isn't affected by signal strength variations. Common methods include normalization or automatic gain control (AGC) based on signal statistical characteristics. In MATLAB implementation, amplitude correction can be achieved by calculating the signal's average power and applying appropriate scaling factors using functions like mean() and basic arithmetic operations.

Phase Correction Phase correction primarily eliminates phase shifts caused by frequency offsets. Widely used algorithms include maximum likelihood estimation (MLE) or FFT-based frequency offset estimation methods. In MATLAB, this can be implemented through phase difference calculations using angle() and diff() functions, or by detecting spectral peaks via FFT analysis followed by phase adjustment using complex exponent operations.

Complete Workflow Signal Preprocessing: Filter and denoise received signals to improve frequency offset estimation accuracy using functions like filter() or wavelet denoising tools. Frequency Offset Estimation: Calculate frequency offset values using appropriate algorithms (e.g., Costas loop or FFT methods) implemented with specialized functions or custom DFT code. Amplitude Adjustment: Perform power normalization or gain control based on estimation results using scaling operations and AGC simulation. Phase Compensation: Apply inverse phase adjustment using the estimated frequency offset value, typically implemented through complex multiplication with conjugate rotation factors.

Through MATLAB simulations, one can visually observe frequency offset estimation accuracy and post-correction signal quality, enabling algorithm parameter optimization for different application scenarios using plotting functions and performance metrics calculations.