# RF Wireless World

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## AFC algorithm-Automatic Frequency Control

This page describes Automatic Frequency Control(AFC) algorithm basics which covers frequency offset estimation and correction in wireless receiver.

Frequency offset is introduced between transmit and receive end of wireless systems as both uses different clocks and oscillators in digital and analog circuits.

AFC stands for Automatic Frequency offset correction, used in wireless communication systems to synchronize frequency of oscillators between Transmit and Receive end.AFC algorithm is used to estimate frequency offset and to correct the same.

AFC algorithms or frequency offset estimation/correction algorithm is categorized into two main parts viz. 1. Coarse frequency offset estimation/correction and 2. Fine frequency offset estimation/correction.

There are various algorithms designed based on system requirements, which can estimate frequency offset and later correct the same. The algorithm is used in signal processing chain of wireless receiver.

### Frequency offset Estimation

There are various methods for frequency offset estimation and will vary based on single carrier (SC), OFDM, OFDMA and other system parameters.

In coarse frequency offset estimation , frequency offset in more range is determined. This is estimated by correlating received preamble with reference preamble in frequency domain.

In fine frequency offset estimation for OFDM based system in done as per schmidl and cox algorithm, where complex conjugate multiplication of CP samples of front and end of the OFDM symbol gives angular frequency. The same can be purchased from IEEE, the details are mentioned below.

ieeexplore.ieee.org/iel3/26/14182/00650240.pdf

### Frequency offset correction

Frequency corrected samples are obtained by multiplying with exp(-jΘ). X[n] vector is frequency impaired data samples and Y[n] vector is frequency corrected data samples.
Y[n]=X[n] * exp(-jΘ)
This process is called as frequency offset correction.