AFC Algorithm: Automatic Frequency Control

This page explains the basics of the Automatic Frequency Control (AFC) algorithm, focusing on frequency offset estimation and correction within a wireless receiver.

Frequency offset is a common issue in wireless systems. It arises because the transmitting and receiving ends use separate clocks and oscillators in their digital and analog circuits. AFC, short for Automatic Frequency offset correction, is employed in wireless communication to synchronize the oscillator frequencies between the transmitter and receiver.

The AFC algorithm’s primary function is to estimate the frequency offset and then apply a correction to compensate for it.

AFC algorithms, or frequency offset estimation/correction algorithms, generally fall into two main categories:

1. Coarse Frequency Offset Estimation/Correction: This deals with larger frequency offsets, providing an initial, rough correction.
2. Fine Frequency Offset Estimation/Correction: This refines the initial correction, providing a more precise frequency synchronization.

Various algorithms are designed based on specific system requirements to estimate and correct the frequency offset. This algorithm is a crucial part of the signal processing chain in a wireless receiver.

Frequency Offset Estimation

Multiple methods exist for frequency offset estimation, and the specific approach varies depending on factors such as whether the system uses single carrier (SC), OFDM, OFDMA, or other system parameters.

• Coarse Frequency Offset Estimation: A wider range of frequency offset is estimated. Typically, this involves correlating the received preamble with a known, reference preamble in the frequency domain.

• Fine Frequency Offset Estimation (for OFDM): A common technique is based on the Schmidl and Cox algorithm. This algorithm uses the complex conjugate multiplication of cyclic prefix (CP) samples from the beginning and end of an OFDM symbol to determine the angular frequency. More detailed information can be found in the IEEE publication: ieeexplore.ieee.org/iel3/26/14182/00650240.pdf

Frequency Offset Correction

Frequency-corrected samples are obtained by multiplying the received signal with a complex exponential term:

Y[n] = X[n] \* exp(-jΘ)

Where:

• X[n] represents the frequency-impaired data samples.
• Y[n] represents the frequency-corrected data samples.
• Θ represents the estimated frequency offset.

This process is known as frequency offset correction.