# Symbol synchronization with unknown symbol rate

I'm learning about the early late gate symbol synchronization and understand that it needs to be given the symbol rate ahead of time.

How could a multi-symbol rate system use an early late gate?

It is my understanding that if the rate is known, the error is computed by going through the signal every samples-per-symbol and computing the error and eventually the timing offset converges.

But if the system has multiple symbol rates, how can a receiver know what the symbol rate without a control channel?

The one idea I have is to first use a symbol rate estimator, but the problem is that there will be some error from the estimator, then the error gets used in the symbol synchronization. Ideally, there is some synchronization method that don't need to know the symbol rate ahead of time or one that is resistant to small errors in the symbol rate estimate.

## Edit

This diagram is what I'm looking at:

The sampler block is the one which needs to know the symbol rate since it is taking samples every $$T_{sym}$$ seconds. But if the symbol rate estimator is off, then even if the timing offset $$\delta$$ is estimated correctly, the sampler will take samples like $$t=\delta$$, $$\delta+\hat{T}_{sym}$$, $$\delta+2\hat{T}_{sym}$$, ... . Is there a way to detect that the sampler is off and refine the symbol rate estimate?

• Just to add a bit onto the answer by @Marcus Müller , there are many ways you could conceive a system that supports multiple symbol rates automatically. One crude example is (assuming you're sufficiently sampled for your highest symbol rate), you could design an algorithm to inspect the observed occupied BW of the received signal which indicates the approximate symbol rate. In practice though as Marcus mentioned, usually it's easier to just throw this information as control info in the preamble. Ex in OFDM frames often the first OFDM symbol contains the mod/rate/coding of the rest of the frame Jul 20 '20 at 2:15

The one idea I have is to first use a symbol rate estimator, but the problem is that there will be some error from the estimator, then the error gets used in the symbol synchronization. Ideally, there is some synchronization method that don't need to know the symbol rate ahead of time or one that is resistant to small errors in the symbol rate estimate.

I mean, you need some tolerance anyways. No two oscillators in this universe are exactly the same frequency. And oscillator price pretty drastically scales with required long-term accuracy... so, you must assume that your receiver doesn't have perfect symbol rate knowledge, anyway.

Symbol timing recovery methods are typically resistant to small rate errors – look at the early/late gate, especially: You'll just see that you're a bit early more often than late if you're overestimating your symbol rate.

You just need to continuously run that.

This really isn't much different to phase recovery methods, which typically can also correct small frequency errors.

How could a multi-symbol rate system use an early late gate?

Uff, in such a system you'll often use a bit more complex synchronization methods, which take information from preambles, and, just as mentioned above, will keep tracking the symbol rate.

• Thank you for the answer. If my symbol rate estimate is off by too large of an amount, won't the sampling eventually drift away and ruin the synchronization? I mean if I consistently sample too early then I should expect the drift Jul 20 '20 at 11:11