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One of the biggest problems in phase modulated communication is discovering when your signal has arrived. High accuracy in this area is important, as even a quarter wavelength error can cause the estimated data bit to be completely wrong. One solution to this problem is to use a preamble code, which is a waveform whose autocorrelation has a very tight mainlobe and low sidelobes.

My question is, are preamble codes actually used in practice? If so, which ones? How is it that such a high accuracy of quarter wavelength is achieved in the real world using a preamble code? If this bound isn't correct, what bound do we really need to achieve synchronization using say BPSK?

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Not only are you dealing with the uncertain delay or phase but also importantly there will be frequency offsets; inevitably your transmitter will not be at the exact frequency of your receiver. Carrier and symbol timing recovery loops are common receiver implementations. A preamble code is not necessarily required as such recovery and synchronization schemes can be done using the data directly, but having known sequences can aid the recovery to be faster and operate in a lower SNR condition. For a example of a carrier recovery implementation that is suitable for BPSK/QPSK/QAM see

Recovering signal for psk

For timing recovery the Gardner Loop and Mueller &Mueller synchronizer are commonly used. I posted some information on the Gardner Loop here:

Gardner Loop

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