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I have a channel bandwidth $B_c$ and a signal bandwidth $B_s$ with $B_s<<B_c$. What is the problem when the signal bandwidth is smaller than the channel bandwidth? For example, my channel bandwidth is $B_c=20$ kHz and my signal bandwidth is $B_s = 10$ Hz.

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    $\begingroup$ (there's a lot of context missing here: Why do you think it is a problem? Why should it?) $\endgroup$ – Marcus Müller Jul 23 at 14:24
  • $\begingroup$ There is no problem $\endgroup$ – Hilmar Jul 23 at 18:39
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No problem at all if $B_s \ll B_c$.

However, $B_s = 10\text{Hz}$ is considerably small that makes synchronization very difficult especially for low-cost receivers.

For example, Sigfox Ultra Narrow Band uses $10\text{Hz}$ bandwidth (are you studying the standard?) that requires precise but expensive oscillators like TCXO. Even with that, there must be random access enhancement to deal with the frequency imprecision.

There is also some effort to design transceivers without TCXO for such narrow bandwidth. Check e.g. Foxy.

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