How does UWB enable higher positioning accuracies than Narrowband?


literature and internet articles often only explain UWB’s much higher positioning accuracies with its much higher bandwidth compared to the bandwidth of other narrowband technologies such as WiFi/Bluetooth.
For me the bandwidth is only a very good indicator for how much data can be transmitted over a second but I don’t understand how this could help to determine positionins more accurately. It seems that high bandwidth enables us to make use of ToF whereas ToF isn’t available in narrowband systems. But why is that the case?

In APS006 Part 1 of Decawave docs there is this graphic which should explain this situation. Essentially the signal level in narrowband systems rises slower which is subject to higher interference of other signals. I get that but then my question is why does this slow rise only happen in narrowband systems? Is it because UWB makes use of impulse radio (IR) and narrowband makes use of continuous waveforms? But why doesn’t a narrowband system use IR then, too?

Please notice that I am not coming from a radio transmission engineering background so my knowledge isn’t that big in this field.

Cheers, Max

Hi Max,

UWB is a pulse based RF technology. you can imagine a transmitter, which emits a series of short pulses with a certain pattern. On the receiver side you have a correlation of these pulses and because of the property of the pattern you can synchronize the tx and rx side precisely.
For more information you can search “Ipatov sequences” in the internet, as these sequences is the core of the tech. Also in 802.15.4-2015/2020 you have a section which describes the UWB PHY.

Hi @alliv,
thanks for your response. I gained some more insight in this topic now and actually understood my problem better as well.
I knew that ToF yields better results than RSSI and for ToF measurements you have to emit pulses rather than continuous waves. But I wondered Why is that only available for UWB communication? Why do traditional WiFi/Bluetooth RTLS do not make use of IR as well? And where is the connection to the bandwidth?

As I found out, the pulse width is in relation to the bandwidth due to Heisenberg’s uncertainty which you can read more of here:

So the greater the bandwidth is, the smaller the possible pulse width becomes and as such, UWB can make use of much smaller pulses than WiFi/Bluetooth. So essentially WiFi/Bluetooth could also emit IR pulses as well, but since these pulses would last much longer, they’d be much more subject to multipath interference. That’s why for WiFi/Bluetooth RSSI measurements make more sense.

I’d like to hear your feedback to this argumentation!

Cheers, Max

If you want to learn more about RTLS/IPS Systems take a look to this university thesis.

3 Indoor Positioning Technologies.pdf (3.5 MB)

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The uncertainty principle has nothing to do with it. It’s simple AM modulation.
If you have an Carrier wave with AM modulation the required bandwidth is proportional to the modulating frequency. If you turn the signal on and off again (which is just an extreme form of AM modulation) then the bandwidth of the resulting signal will be related to how long the signal was on for. You turn the transmitter on and off in 1 ns and you’ll get a bandwidth in the 1 GHz region.

The chip is doing something a little more complicated but the basic relationship between bandwidth and pulse duration still holds true and can be explained without resorting to quantum theory.

You can do accurate ToF with continuous waves. That’s how GPS works and it can give 2 cm accuracies. With the added benefit that since you have a carrier you can accurately measure the Doppler on it and also get velocity. However as anyone who’s familiar with accurate GPS could tell you, while it works great in a big open area it doesn’t work indoors.

UWB and the short pulses are good for indoor ToF because the short pulses and their reflections don’t mix together in the same way that a constant modulated signal does and so reflections are a lot easier to ignore.

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@DonQuijote thanks for the document, I’ll have a look into it.

@AndyA I know there is that relationship of bandwidth and pulse widths so maybe I had to ask my question in a different way: Why does a higher bandwidth result in shorter time impulses? That is what I didn’t understand. What you just told me that this realtion exists but I was already aware of that.
Your argument

the bandwidth of the resulting signal will be related to how long the signal was on for.

does not answer the question why this is the case. And I am pretty sure that your argument can be explained by the below lines.
I was looking for an answer to where the connection between higher bandwidths and shorter pulses is and it surely does base on Gabor’s principle (see the link of pozyx I’ve posted above) which in turn bases on Heisenberg’s uncertainty principle. You’re right it is a little deep to dig out Heisenberg’s principle but that’s the kind of answer I was looking for because with Gabor it is easy to show off the relation between bandwidth and pulse width in a mathematical way. I don’t think that’s wrong, it’s just very low level.
Correct me please please if that’s totally wrong but I didn’t find any other explanation other than that.

Cheers, Max

this is a typical problem from communication signal processing, rect signal R(a t)'s Fourier transform is proportional to sinc(w / 2πa), so R(a t)'s bandwidth is Inversely proportional to 1 / a, i.e., the short duration of the pulse width, the larger of its frequency bandwidth.

though pulse of IR-UWB is a more complicated pulse signal rather than the simple rect signal R(a t), but still has similar result.

could see more in the following lecture:
Fourier transform of Rect Signal

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@chxt seems to have already covered it better than I could have based on my poorly remembered communications theory class from 20 years ago.
To clarify one detail, it’s not true that higher bandwidths require shorter pulses, you could create a high bandwidth modulation system for any duration signal. It is however true that short pulses do require high bandwidths.

Hey thanks for all your support here.
@chxt I also read about the solution coming from the Fourier transform. Unfortunately as I stated I don’t have much knowledge in radio communication field so I wasn’t aware of the Fourier Tranformation solution.

Would you and @AndyA agree though that with Gabor’s principle it can be explained why UWB in general can create much shorter pulses than narrowband technologies? For educational purposes it would be pretty helpful for me to have something like a formula that expresses this relationship easily without having to go into too much detail of radio communication and frequency demodulation with Fourier. Even though I know for a more sophisticated analysis I would have to go into more detail.

Cheers, Max

Yes. But only because it’s not possible to generate a short pulse with a narrow bandwidth.
This comes out of maths and methods that are 100 years older and far simpler than the explanations you are trying to use.

To give you an analogy, if I want to work out how fast something will accelerate when I push it technically I should use general relativity. However for virtually all applications F=ma is good enough and a lot simpler.
Don’t look for overly complex explanations when far simpler ones are good enough to explain what you need to know.

Yeah you’re right, overly complex explanationas aren’t very good. It’s just the first one I came across and it explained my question perfectly since I wanted to have an answer to the question:
Why can’t you create short pulses in narrowband systems or why are their pulses not sufficient for positioning purposes? That’s why I like it and prefer it over Fourier transform solutions because of my lack of knowledge.

Anyway, thanks for clarifying that. I may look further into the Fourier transformation solution.

Cheers, Max