What are Coherence Bandwidth and Coherence Time?

Explains the concepts of coherence bandwidth and coherence time in digital communications, and shows why these two terms are only approximate, and can sometimes be misunderstood.
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Full categorised list of videos with pdf Summary Sheets: iaincollings.com

[@emanueleziglioli499]

Really clear explanation, thank you!

[@iain_explains]

Glad it was helpful!

[@emanueleziglioli499]

@@iain_explains just one basic thing always confuses me: why are time delay and phase shift not the same thing, how can a signal rotate in phase without changing the delay? isn't carrier phase an actual (precise) measurement of a delay? (sorry too many questions)

[@luuhinz]

Thank you for the great overview! I would propose a small correction though: The Doppler Power Spectrum usually looks more like a "U" (Jakes Spectrum) instead of what you drew. At least that's what I learned, if you consider doppler shifts to be fd = f0 * v/c0 * cos(alpha) and assume the angle alpha to be uniformly distributed. Keep up the good work, your videos have helped me immensely throughout my studies!

[@iain_explains]

I'm not sure that an idealised model based on a uniform distribution of scatterers really qualifies as a justification for saying that my curve needs "correction". The Jakes spectrum is only a model. In reality the curve will look more like a response curve of a low pass filter.

[@luuhinz]

@@iain_explains Thanks for your answer! I've only learned this last year or so, and therefore have not much experience with "reality" yet. One more example of how theory and practice are two pairs of shoes.. :D

[@user-ex2iw4hi3f]

Dear Professor, thanks for sharing. When using the expected value for self-correlation for channel gain for the multi-path intensity profile, it seems that the expected value is a constant number without the variable of time. Do you mean to use multiple channel gains and get the expected value? Or h(t) is a 1*n dimension matrix. multi-path intensity profile should be E(h*(t)(trans(h(t))))?

[@khalifi2100]

Thanks for the amaizing explination. I guess If you choose the coherence bandwidth to be the inverse of twice the standard deviation of the multipath intensity profile that will be more appropriate to reflect the spread of the power impact from time domain to the frequency domain.

[@iain_explains]

Perhaps. It really depends on the shape of the delay power profile.

[@ImranMoezKhan]

When I started studying rf a couple of years ago, the coherence time/bandwidth and power delay profile concepts confused me to no end. Thanks for this really good explanation and for pointing out where common misconceptions occur. Aside from being concepts, are the CB and PDP often used as important paramaters in design?

[@iain_explains]

They're generally used as "rule of thumb" type parameters, but in any real design people/companies take lots of field measurements of typical channel parameters to get more accurate statistics.

[@furqanhaider6839]

Hi Ian, can you please tell what is precoding? OR What are precoding vectors ? in terms of Satellite Comm. Thanks

[@iain_explains]

You might like to watch: "How are Beamforming and Precoding Related?" kzbin.info/www/bejne/n36sonimr92Bb7s

[@pitmaler4439]

We assume the channel to be roughly satic over Bc. That is clear to me. But it could also be that the deep fading notch is exactly within that bandwidth when Bc is shifted a bit. We don't define the exact start of Bc. Is that thought right?

[@iain_explains]

As I mentioned in the video, the "deep fading notch" is not real. There is no "notch". It only looks like there is because it is plotted on a log scale. In truth, the channel gain goes up and down smoothly as a function of frequency. There is just as much chance that it is roughly constant through the "low gain frequency regions" as it is through the "high gain frequency regions".

[@tuongnguyen9391]

When they said quasi static fading, does the word "quasi" have some relationship with the "coherence time" ?

[@iain_explains]

Yes, generally it means it's not static, but they're going to model it as "block static". In other words, constant for a time period, and then changes to another value for another time period, and so on. Generally they choose the time period to be related to the coherence time.

[@user-zk7in2ri3c]

Thank you sir. I have one question. In LEO satellite system, if there is only one LOS path, then I think the doppler spread is very small. So I think coherence time is big... On the other side, because the moving speed is very fast, the channel state changes quickly. Could you some explain about LEO channel coherence time? Thank you.

[@iain_explains]

Thanks for the topic suggestion. I've added it to my "to do" list.

[@stringstoparadise2392]

overall nice and informative video sir, but I want to know that since this concept of coherence time and coherence bandwidth is kind of vague and not really accurate thus how in real-time communication our channel is estimated in terms of coherence bandwidth and coherence time means are there any exact approximation or anything like that , practically how it's done?

[@iain_explains]

As I said, people might define these terms, and use them as a guide in their system designs, but the terms don't refer to anything that is precise, and they are only ever used as a general guide.

[@faust-cr3jk]

Hello Iain, Quick question, not related directly to the video. Why PDP is often modelled using a some sort of expontential decay. My best guess is that when channel gains are modelled using Rayleigh distribution (to be more specific, their amplitude is Rayleigh distributed), then this means that their power must be exponentially distributed. Kind regards

[@iain_explains]

No, that's not it. It's because the paths with the longer delays will have resulted from having bounced off reflectors that are further away, which means the energy will have dissipated more by the time it gets to the receiver (due to the 1/r circular radiation pattern).

[@faust-cr3jk]

@@iain_explains Thanks a lot for your explanation!

[@rudrasingh9501]

great video sir but i have few doubts 1> is the graph fourier transform of delay spread periodic in frequency domain and graph of inverse fourier transform of doppler spread periodic in time domain because it seems like the way you have plotted 2> if they are not periodic than any specific reasons for that because when we take fourier transform of discreat samples (which is time samples corresponding to delay spread ) is periodic in nature (analogy says discrete in time is periodic in frequency)

[@iain_explains]

Those graphs are not "discrete". They are continuous. Delta functions with arrows on the top are continuous functions. These videos give more details: "How to Understand the Delta Impulse Function" kzbin.info/www/bejne/rqmqlHxvjLuiebs and "Delta Function Explained" kzbin.info/www/bejne/oqrVkqSqgrynfc0

[@khaledramdan6188]

as-salaam-alaikum professor lian I have a question we observe a frequent call drop at high speed when traveling through train this I guess is due to Doppler effect , so my question is that is there any solution available for this problem according to you as now also travelling at such high speed leads to low data rate and frequent call drops thanks in advance 😊

[@iain_explains]

The important thing is the _fading rate_ . If the fading rate is high, then it is hard to track, and requires more training data to be sent (per unit time), at the expense of actual data. But the _fading rate_ doesn't only depend on the vehicle speed. It also depends on the data symbol rate. See this video for more details: "What are Fast Fading and Slow Fading?" kzbin.info/www/bejne/ip6QhqyXn8iop9U

[@khaledramdan6188]

@@iain_explains thanks for considering my question moreover I have a doubt for a particular coherence time Tc of a channel how many training sequences we are sending ? and for a particular coherence time we are sending only training sequence for estimating channel or we are sending combination of data+training

[@iain_explains]

You might like to watch: "Channel Estimation for Mobile Communications" kzbin.info/www/bejne/kKSvmWNno9GFsLs

[@aarzoosingh8316]

hello sir, hope you are doing fine the formulae which you have written for coherence time is 1/fm but i have learnt this formulae as written in books as 1/(4*Fd) where Fd is the doppler frequency can you please explain the difference in the formulae ? and what is the difference between doppler frequency and doppler spread are both the same thing ?

[@iain_explains]

I guess you didn't watch up until the end of my video. The Doppler shift and spread are explained at 10:50 min, and the different definitions are mentioned at 11:34 min. Basically your question highlights one of the main reasons I don't like these terms - because they are not actually related to anything precise, and different people define them differently (as I explained in the video). Perhaps you might also like to watch the following video too: "What are Doppler Shift, Doppler Spread, and Doppler Spectrum?" kzbin.info/www/bejne/gn3VZGChpNmVsJY ... and you can find lots of other videos that might help you at iaincollings.com

[@tuongnguyen9391]

@@iain_explains Wow this is something that I haven't notice

[@aarzoosingh8316]

@@iain_explains got it thankyou sir

[@badalsoren2947]

hello sir, I have a doubt running on my mind that even if in the absences of dopplers effect i.e for the stationary user why our channel is said to be time varient as the gain of the channel Is not changing with respect to time , since the coherence time is infinite as Doppler shift is zero according to formulae(Tc=1/Fd) and my 2nd question does the channel becomes non linear in nature in case of Doppler as we are receiving the signal with shifted frequency due to CFO, according to this concept the channel is a non linear one but I have read few articles where they are considering the channel to be linear in case of dopplers ? sir if you could please spread some light on these concepts it would be very helpful thanks

[@iain_explains]

Even when the user and the base station are both stationary, the channel can still be time varying if the scatterers are moving (eg. cars, people, trees blowing in the breeze, etc.). This causes the path length to change - which is what leads to Doppler shift/spread. And we call the channels Linear Time Variant, because at any instant all the paths add up in a linear way (and if you doubled the input, you would double the output, etc.), but the frequency offset means they vary with time. They are not "instantaneously" nonlinear.

[@badalsoren2947]

@@iain_explains sir first of all thanks for the wonderful answer, I have drawn some conclusions, that doppler is present always just it becomes significant when the transmitter or receiver is moving with higher velocity, and that's when the concept of coherence time is coming in to picture. after all sir can we say that when the mobile and base station is stationary the channel is under slow fading and when the mobile and base station is moving with high velocity the channel is under fast fading please correct me sir if I have understood it wrong thanks

[@iain_explains]

Sort of. Perhaps this video will give more insights into fast and slow fading: "What are Fast Fading and Slow Fading?" kzbin.info/www/bejne/ip6QhqyXn8iop9U

[@user-eb3dc3oz9e]

Hello，sir! Thanks for your excellent explanation! Really helpful for me! But here's a question: recently I'm studying the book 'Wireless Communications:Principles and Practice' written by Rappaport,and he says "coherence bandwidth is a defined relation derived from the rms delay spread" instead of using tor max, he defines Bc based on sigema tor(rms delay spread). I'm wondering is there any differences between the two definitions or they are the same thing? Looking forward to your reply, Thank you!

[@iain_explains]

Well, yes, the question you're asking is an example of exactly what I was saying in the video: namely that Coherence Bandwidth is an ill-defined concept that I don't like, because it is so vaguely defined, and different people use different definitions. In Rappaport's book, you'll notice that he provides two different definitions (5.38) and (5.39) (in the Second Edition of the book), which are a factor of 10 different, indicating that he also seems to agree that there is no "one single canonical" definition.

[@user-eb3dc3oz9e]

@@iain_explains Thank you,sir! Your explanation is really enlightening! The definition of bandwidth is quite confussing. I have another question:If a channal featuring in several delay (equal amplitude)，Is there any differences between it and a comb filter? We always emphasize that if the frequency band of a signal is smaller than coherence bandwidth,then channel creates flat fading on the received signal.But if a signal whose carrier frequency is where comb filter exactly decreases(It is assumed that the channel can be equivalent to a comb filter.) ,and the filer is high quality(the edge is steep),will it be a flat fading? Looking forward to your reply!

[@iain_explains]

Don't forget, these are only models. And the channels are random. Perhaps in very specific locations, with very specific surrounding buildings, there might be situations where a "usually flat fading channel" might display "frequency selective" characteristics. It's not out of the question. But overall, on typically, if the bandwidth of the signal is narrow, and the coherence bandwidth is wide, then it will be a flat fading channel. ... and once again, the imprecise nature of that statement is another example of why I don't like the term "Coherence Bandwidth"!

[@ranchordaschancad3410]

hello, sir hope you are doing fine, greetings from India want to ask a question about the vague concept of coherence time in your terms 😊hope you will address it why this definition of coherence time is like time uptill which the gain of the channel remains constant. in actuality if we observe the phase which is changing abruptly not the gain as given by equation (exp-(j*pi*fd*t------(1)), fd = dopplers shift in frequency) so accordingly at t=1/4fd,(where t=is the coherence time) the equation ----(1) becomes -j and when we take mod of it becomes 1 so the gain is constant it's actually the phase which is changing abruptly, so why we measure coherence time in terms of gain of channel why the definition it's not like the phase of the channel is remaining constant? and secondly, even if the phase change is pi/2 which is abrupt according to the coherence time definition why can't we measure that phase after all its the phase shift only? thank you !

[@iain_explains]

Sorry, I'm not really understanding your question. The only situation in which the phase changes abruptly, is when the gain goes down to zero, and then back up again. The gain and phase are related to each other, they don't change independently.