# OFDM synchronization using training symbols

In OFDM receivers, special OFDM training symbols for which the data content is known, can be used to perform the synchronization process. A correlation operation is performed between the received signal and the training symbols. From the correlation peaks, both symbol timing and frequency offset can be determined. I have two equestions.

1. Practically, how these OFDM symbols are generated at the receiver?
2. If these reference symbols are sufficient for both symbol tiiming and frequency offset determination, why differential detection is often employed? The information bits are modulatedon the subcarriers by differential QPSK. The reference phase and amplitude of each subcarrier have to be known in order to estimate the bits correctly. For this purpose differential detection is used.

# Claim

In OFDM receivers, special OFDM training symbols for which the data content is known, can be used to perform the synchronization process.

Be a bit careful about that statement.

There's basically four kinds of synchronization that I can think of right now:

• Frequency synchronization
• Timing synchronization
• Phase synchronization
• Clock synchronization

... as well as higher-level things such as frame sync, decoder sync.

## Frequency sync

Can be done in a number of ways. A very OFDM-typical way of doing so are autocorrelation methods.

With these methods, you don't actually use a known reference symbol, but send OFDM symbols that have a specific temporal structure.

For example, the well-known Schmidl&Cox synchronization is based on the idea that if you have two preamble symbols with certain symmetry, you can do both a fine frequency estimate as well as a timing estimate.

Rough frequency estimates are often done by exploiting the fact that OFDM systems usually don't use all subcarriers, but leave guard bands at the edges. So, for this, too, no known symbol is needed.

## Timing sync

... to expand on the above: It's very easy to build a timing estimator based on a fixed lag correlation, when you have a symbol that repeats itself. You just compare $$N$$ samples with $$N$$ samples a fixed delay $$\Delta T$$ later; when that correlation function sees a peak, you might be detecting your preamble symbol. Side effect is that the phase of that correlation (divided by $$\Delta T$$) serves as fine frequency estimate.

DAB (and DAB+), for example, use a non-Schmidl&Cox autocorrelation based frequency and timing estimator. WiFi uses S&C, for example.

## Clock Sync

That's a tough one with OFDM, as it's usually pretty bad if the receiver sampling clock is different from the transmitter's clock. It's solved by limited symbol length, or by coupling the carrier frequency to the sampling clock (so that you can correct the sampling clock by correcting the frequency), or by estimates based on the phase sync.

## Phase sync

This is really the only thing that is normally done through known data. But it's commonly not done by known symbols, but only by known pilots within distributed "ressource blocks", i.e. single subcarriers within payload symbols, as that has a lot of advantages by observing the channel as its being used.

Practically, how these OFDM symbols are generated at the receiver?

not at all. They are received, just like every other OFDM symbol. That's why it's called a receiver.

The known pilot subcarrier symbols are typically written in some standard document.

If these reference symbols are sufficient for both symbol timing and frequency offset determination,

They aren't. Frequency synchronization is usually done with autocorrelation methods, see above.

why differential detection is often employed?

Are they? Unbacked claim! I know that DAB does use OFDM with differential PSK internally, but that is kind of an odd duck: It's from the early 90s, so that OFDM was feasible on small systems, but proper channel estimates weren't. Generally, using OFDM says "need to use a wideband channel efficiently", and that usually means that you really want that non-differential modulation BER goodness.

The information bits are modulatedon the subcarriers by differential QPSK.

You're referring to some specific system, not to something that applies to OFDM in general. So, this is, in general, a false statement.

The reference phase and amplitude of each subcarrier have to be known in order to estimate the bits correctly. For this purpose differential detection is used.

This is self-contradictory. Either you need to know the phase of each subcarrier, or you do differential modulation. Never both.