# Why does a higher bandwidth allow a higher data rate [duplicate]

I have not taken any signals processing classes yet but I am interning at ATnT in the RF department. I do not understand why higher bandwidth increases data rate and the other answers did not make sense to me. For instance, in FM, why does it matter if the frequency changes over 20kHz or 20MHz. The input waveform can still be represented in both frequency ranges, but the 20kHz band would have the same amount of information compressed into a smaller range. So my question is, why does the fact that the same amount of information can be contained in a wider range of frequencies mean that more information could be sent. Can't you send the same ammount of information on a 20kHz channel as a 20MHz channel as long as your electronic components can make very detailed modulations of the smaller bandwidth carrier so as to represent the exact same waveform over a smaller range?

• (there's really a lot of relevant questions that pop up when you search here for data rate bandwidth, I just picked one that was well-illustrated) Jun 1, 2020 at 20:37
• Three things allow a higher data rate. 1) Higher power. 2) lower noise and 3) higher bandwidth. This comes from the Shannon Theorem. It is to information theory what conservation of energy is to general physics. I don't think there is an easy way to understand it. Looking at your example, if my carrier frequency is 10 MHz, I can't really modulate it +/- 20 MHz. Theoretically, though, a noise free channel supports infinite data rate regardless of bandwidth (as long as BW is not zero). Jun 1, 2020 at 20:50
• I seem to remember typing out Shannon's (or shannon-hartly) out on this stackexchange at some point. Jun 2, 2020 at 7:54

Without noise, an arbitrarily high information rate can be transmitted over any narrow-band channel.

In general, the bandwidth depends on the symbol rate, i.e. how often the symbol is changed.If there were no noise, any number of bits could be transmitted with one symbol, since the receiver can reconstruct the signal as accurately as desired.

In the presence of noise, it is more difficult for the receiver to decide on the correct symbol. The more information (i.e. bits) a symbol contains, the more likely the receiver is to make a wrong decision.

Actually, any channel has a property, called channel capacity, that determines how many bits per second (or per channel usage) can be reliably transmitted. Claude Shannon proved in 1948 that as long as we stay below this threshold, an arbitrarily small bit error rate can be achieved (at least in principle).

When we are using FM with a higher deviation (and therefore a higher bandwidth), we actually use a channel with a higher capacity. In the presence of noise, it is easier for the receiver to reconstruct the signal and we will get a better signal-to-noise ratio at the output of the demodulator.

In general, the amount of bandwidth used is proportional to the amount of data transferred (analog or digital). However, if you have more than you need, there are tricks for converting it into additional SNR. In the most obvious case, you could send the signal on a number of different channels and add them together, but we can do better than that.

In the particular case of FM, the estimated required bandwidth is about twice your signal rate plus twice your deviation. Adding more deviation to an FM signal causes it to take up more bandwidth, but improves the range and noise performance.

This is taken to the extreme in direct sequence spread spectrum, where additional symbols (chips, not bits--bits carry data, but the chipping sequence is known to both transmitter and receiver) are added to increase the signal bandwidth. The lower rate data is superimposed on this stream to provide additional bandwidth to improve the error rate. It can also be used to fit more separate channels into that bandwidth. Cell phones do this.

It can then get really entertaining--if you've got more limited bandwidth, but you're the only one using it, you can get creative with forward error correction. I'll leave that for later.

So your signal needs a certain bandwidth but you have more, there are numerous approaches to trade it for power, performance, or more users.