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What is the maximum duration of a preamble for underwater acoustic communications? For example, can we have a preamble $>10 \textrm{ sec}$?

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In communications, no matter whether it's radio, underwater acoustics or say powerline comms, there's multiple influences on the permissible duration of a symbol.

If you consider your preamble to be kind of a "super symbol" that you use for detection and equalization / phase correction, then you'd typically want to make sure that the channel coherency time is larger than that symbol's length; otherwise, your channel will change while you're still transmitting that preamble, and thus you will lose sensitivity detecting the preamble, or you'll learn about a channel state that simply is already "gone" the moment your preamble finishes.

However, if your receiver does e.g. OOK/power detection, then you can basically not go "too long" with your preamble – the longer it is, the more gain you'll have.

Now, I'm no expert in underwater communications, but all I know indicates that you might be dealing with a heavy multipath channel, and thus, frequency selectivity. Thus, your preamble detector might not only serve the purpose of detecting the start of a transmission, but also use the preamble to estimate the channel and feed the equalizer. In that case, as said above, a preamble that's longer than your channel coherency makes no sense.

Whether 10 s is longer than your channel is coherent is something I can't say. If you're doing communications in a container of liquid that doesn't change, then your coherency is probably "forever" and there's no upper limit. If you're doing communication across a stream with a lot of large debris rushing through quickly, then 10s might be far too long.

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