To synchronize to a radio transmission in an OFDM transmission with Cyclic Prefix, there's only three variables needed to model in a software-defined radio.
- Frequency Offset
- Timing or Sampling Offset
The frequency offset can be corrected by multiplying the complex samples by the complement of the frequency offset.
Timing offset, also known as sampling offset can be divided into an integer and fractional part.
The integer part can be handled by skipping or adding an integer amount of samples between OFDM symbols.
The fractional timing offset is slightly trickier. A fractional delay over the whole frequency band is most easily implemented in the frequency domain (after the FFT). It is corrected by multiplying all the complex symbols by a complex number which adds or substracts phase.
For finding the offsets there are many creative ways available. There're many signal properties to deduce it from. Here's a few:
- Cyclic prefix
- Synchronization symbols
- Symbol length
- Subframe length