What is a Cyclic Prefix in OFDM?
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- čas přidán 11. 09. 2024
- Explains the Cyclic Prefix in OFDM and DMT from a signals perspective.
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• Why is the OFDM Symbol Prefix Shorter in 5G Mobile and 802.11ac WiFi? • Why is the OFDM Symbol...
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• OFDM and the DFT • OFDM and the DFT
• How are OFDM Sub Carrier Spacing and Time Samples Related? • How are OFDM Sub Carri...
• How does OFDM Overcome ISI? • How does OFDM Overcome...
• How are Complex Baseband Digital Signals Transmitted? • How are Complex Baseba...
• How are Throughput, Bandwidth, and Data Rate Related? • How are Throughput, Ba...
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What separates your videos from other NPTEL videos of IIT prof.s is that they only explain the maths part of the concepts, whereas you additionally explain them using waveforms and that's fantastic.
PS: In the CZcams 'About' section mention that you are an IEEE fellow!
Thanks for your comment. Glad you like the videos. And I've just updated my 'about' section - good suggestion.
Believe me guys this is best explaination of cyclic prefix on CZcams. Thanks Iain, you are doing a marvellous job.
Thanks for the endorsement! Glad you like the videos.
Iain was my postdoc supervisor, I learnt a lot from him. All the best
Hi Tom, great to hear from you. Thanks for your nice comment.
I like the way you explained the reason for adding the cycle pad between 2 serial symbols, to prevent interference of symbols, and to cut the end portion of sum of time domain signals and pad it into the start of the second signals sum. 30 years ago they told us to do so but they never explained to us why they did that, now 30 years later I know - thank you. This method of coding is very smart indeed.
Glad the video was helpful.
Sir, i am a big fan of your videos. Your way of teaching is incredible! To the point and simple. Thankyou sooo much!
Thanks for your nice comment. I'm glad you have found the videos helpful.
Finally it makes sense!
Thank you for a very nice explanation! I'd like to emphasize that this line of reasoning works the same way even when we only have a single OFDM block surrounded by zeros. The second path would shift some of the zeros inside our listening interval, which will make the beginning of the received message "special". If we do prepend a sufficiently long cyclic prefix, however, this will not happen (we'll have a sum of two sinusoids for all carriers and all time instances within our listening interval), and we'll be able to use the length-N DFT at the receiver as explained in the video.
An alternative way to interpret the purpose of the cyclic prefix is that it makes sure the output of the channel looks like the output of circular convolution (convolution with a periodic input), even though the actual channel performs linear convolution. Only for circular convolution the length-N output (and hence the length-N DFT) straightforwardly contains all information (because the output of a convolution with a periodic input with period N is itself periodic with the same period). How do we emulate circular convolution with linear convolution? Well, we need to include the end of the previous period in our transmission. That in turn is equivalent to copying the end of the message and prepending it to the beginning, which is exactly what we do when we add the cyclic prefix.
Turns out the same point was raised and answered along the same lines several times in the comments earlier.
what if we zero-padding in CP? looks like it also have some advantages such as power saving and PAPR reduction in transmission.
this channel is very good. It is difficult to find explanation for these kind of material. Thank you for your dedication !
Also about the basics things, could you do a video demonstrate the difference between SNR and Eb/No :)
Great suggestion. I've added it to my to-do list. Thanks.
Here's the link to the SNR and Eb/No video: czcams.com/video/bNYvXr6tzXQ/video.html
Your series of ofdm are vivid and interesting , which help me a lot. Thank you , my professor.
Glad you like them!
This professor is a legend, thanks!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
This is incredable! Thank you so much for not only the valuable information you share but the organization and thought that goes into it.
You are so welcome! You're right, it does take considerable thought and effort (much more than I expected when I started the channel), but it's definitely worth it when I hear that people really find the videos helpful.
I love this explanation of cyclic prefix in OFDM.
Great. I'm glad you like it.
Amazing, clear and easy to understand. Appreciated for your effects.
Glad it was helpful!
Your videos are amazing. The best on youtube about this topic! Would be really nice if you could explain how these concepts apply to modern DVB standards or WiFi.
Thanks for the suggestion, I've added them to my "to do" list.
SIr, I fall in love with the amazing explanation
I'm so glad you liked it.
Thanks for the clear and excellent explanation.
Glad it was helpful!
This is a request from india. Please make series of videos for digital and wireless communications. From basics to advanced. We like your way of teaching. We hope you will definitely consider our request.
Thanks for the suggestion. As you night have seen, I've already started doing this. On my channel page I've created a couple of playlists which are (mostly) on digital communications: Communication System Fundamentals (czcams.com/play/PLx7-Q20A1VYKTk9LLRNdViuWeYUe1o207.html), and Orthogonal Frequency Division Multiplexing (OFDM) (czcams.com/play/PLx7-Q20A1VYIvtMUWX3yd_sQGbQx1qPGP.html). I'm planning to add more. Please let me know if there are specific topics you would like me to cover, or specific things you can't seem to find good explanations for.
@@iain_explains yes sir. I have seen all your videos. They are short and good. What i am asking is... Please provide an overview of communication systems. Start with say, time division multiple access. Next, why we moved to CDMA, then why we reach OFDMA. An overview of how the things are evolving.. thank you.
Thanks. Good suggestion. I've added it to my to-do list.
Love it so much. I finally understood what is C.P. Thanks a lot!
Glad it helped!
Amazing, unique and one of a kind explanation which exactly hits nail on its head. Thank You so much, I request you to continue spreading your deep acquired knowledge.
Thanks. I'm glad you like the video.
Undoubtedly the best video
Very nice explanation. Your explanation motivate to read more.
Glad to hear that
Amazing series. Look forward to more such great content.
Thanks. Glad you like the videos! And yes, I've got a long "to do" list, so I'm planning to keep making new videos. I'm always happy to hear suggestions for specific new topics.
one of the best explanations thanks
Glad it was helpful!
Great video, incredibly helpful!
Understood it at a first glance, thanks Iain :D
Glad you liked it!
Super clear!! very nice explanation
Glad it was helpful!
Hi Ian, this answers a lot of questions that a friend and I had about this topic a couple of days ago, thanks! I have a couple more 😊
Are the terms 'cyclic prefix' and 'guard interval' interchangeable?
Is the effect, from a transmitter perspective, identical to lowering the symbol rate? Does this therefore mean that the bandwidth per carrier is narrower? Does that affect orthogonal carrier relationships, or does it help with carrier IM as well as ISI?
Does the duration of the cyclic prefix need to be an integer number of cycles of the base carrier frequency, so that it is also an integer number on all orthogonal carriers?
Thanks again for a great explanation!
Wonderful videos thank you very much Lain, these videos are exactly what I needed. Can you please make another video on OFDM based on Index Modulation (IM)?
Thanks for the suggestion, I'll add it to my "to do" list.
Thank you so much Mr. Iain for this excelent explanation. I believe it is the best playlist in communicatio I've seen on YT so far!
I just have a question, if I may. When I convert the constelation set into the time domain using IDFT, I do have a complex signal with both real and imaginary components, in some cases.
Does that mean that I need to transmit two time domain signals (Re and Imag) over the antenna in separate intervals? Or should I just transmit the absolute value of the sequence?
Thank you so much for this excelent content!
Yes, you need to send the "complex signal". Here's a video that explains how: "How are Complex Baseband Digital Signals Transmitted?" czcams.com/video/0lkRJgnywkg/video.html
@@iain_explains Thank you!
Made my day! Thank you very much!
My pleasure!
Sir, Thank you so much for your explanation. I under stand what you teach clearly. However I have a question.
Before adding the cyclic prefix, each symbol occupies the whole symbol period. Now, to add cyclic prefix, we need an extra time. How can we get that.
The symbols don't "occupy the whole symbol period" until they have the prefix added to them. Or in other words, the "symbol period" needs to take into account the prefix time.
@@iain_explains Thank you so much.
What a fantastic video!! There are lots of animated videos on this but what you explained with Pen and paper is irreplaceable.
Sir, May I ask you a question
What I understood is, for the digital detector(I have gone through your video) the total energy within that symbol period is constant after adding the cyclic prefix to make out the transmitted symbol. In this case, since it was BPSK the symbol rate is equal to the bit rate.
But how the detector will make out the bits practically for higher bit modulation?
Suppose for QPSK or QAM, how it is going to know the bits?
I hope I'm clear in writing down my doubts.
Thanks for your nice comments. And thanks for your question. I think I might need to make a video on the superheterodyne radio receiver (keep an eye out for it). In summary though, the (time domain) baseband (down converted) samples are complex valued, and when they are put through the Fourier Transform, the output vector also contains complex values (one for each sub channel), and those are then compared to the respective constellation (for that sub channel), and the nearest point is chosen. It is general for any constellation.
@@iain_explains Thanks for helping me out, Sir. Though I didn't get it very clear but maybe once I'll work out more on this, I'll be able to get it. I'll eagerly look out for your video as suggested by you.
Basically, I want to know for a higher order of modulation in OFDM, how bits are extracted from symbols after demodulation after appending CP.
that little smiley face in the right down corner. BIG FAN
:-) Thanks.
Thanks for sharing but some questions 1-what is the harmful impact of the discontinuity ?
2-Is the cyclic prefix a solution to intersymbol intrfence or signal discontinuity ?
3-why not only transmitting zeros instead of the cyclic prefix and the lot energy problem ?
Discontinuities happen at the boundary (ie. transition time) between symbols (when the digital sequence changes from one constellation point to another). Reflected signal paths arrive later than the direct path, and cause ISI. This means that within a defined symbol period there will be discontinuities in the received signal (as shown in the video). These will result in the received complex value not aligning exactly with the intended constellation point, and lead to errors in detection. The cyclic prefix is added so that it can be removed at the receiver, leaving only the time period when the discontinuities do not occur. Transmitting zeros instead of the cyclic prefix would add a second discontinuity boundary (at the end of the prefix). It would solve the first discontinuity problem, but generate a new one.
@@iain_explains Thanks Iain. CP seems to me confusing because different people (even very well known people) have very different ideas. For instance, In Lathi's book, he says adding zero padding is same. Also some people argue that CP is because DFT has a periodic nature or because of CP we have circular convolution which is needed for DFT (since we use DFT and H(f)X(f) is only true for DFT when the circular convolution is achieved) However, I like your discontinuity approach. If we have discontinuity problem, we cannot have a simple equalization because sum of two sins cannot be another sin as I see.
Please upload CP-OFDM with WOLA also
I don't understand why there is a gap on the left, in the IDFT, at 8:45 that "has to be filled" with the prefix. Since all subcarriers fill the whole time slot, their sum should also fill the same time slot and there should be no need for filling that gap with a copy. Since we're discarding the prefix at the receiver end, we already have a longer transmitted signal duration on the transmitter side (you can't extend the transmission time of one symbol on the emitter side; the only thing you can do is reduce the symbol sampling duration on the receiver side - and we do this already). Therefore the symbol is already "extended" from the perspective of the receiver. It's actually conspicuous on the pictures at the start of the video (5:00): what is in the prefix is exactly the same as what is at the end of the time slot.
Said otherwise: when do we transmit the prefix, since we're already using the whole transmitting time slot with the combined OFDM symbol?
Or are we _deliberately_ generating the symbol on transmitter side with a delay, during a reduced duration, equal to the receiver sampling duration. And why would we need to do that if the suffix and prefix are equal? Are they not?
Seems we started with the idea of a guard and then realised we needed to fill it with some thing that turned out to be the same things as if we did not have a guard in the first place. I'm lost.
I explained that in the "single carrier" case at the 3:27 point of the video. You want to extend the symbol, in order to avoid having a discontinuity within the received symbol. The output of the IDFT at the OFDM transmitter does _not_ include the cyclic prefix. It's just the symbol that you would like to send (ie. the 4-cycle symbol in the single-carrier example at the top of the page). It needs to be extended, so that the ISI affected portion can be removed at the receiver.
@@iain_explains Thanks for trying to help, but I'm afraid I'm a hard case, :( . I'm sorry Iain I still don't get it. The single carrier example you took is precisely why I'm asking the question. In your example, there is no copy of the tail.
You even explicitly show that transmitting a 5 cycle symbol is sufficient if we decide to only sample symbols on the 4 last cycles 3:34.
On transmitter side, you add a "prefix" first cycle (which indeed looks like a copy of the 6th cycle) but we did not need to do that copy, we just generated that cycle in our longer transmitter-side symbol duration, unaware of whether the receiver was going to take it into account or not.
Just as your single carrier example shows, copying cycle # 5 on top of cycle # 1 would be achieving nothing. Cycle #1 is _already_ the same as cycle # 5.
Assuming orthogonality, and assuming that the prefix length is a multiple of the period of the lowest subcarrier, the same would apply in multi-carrier added signal.
So, IDFT could do the same and just generate on the whole duration instead of copying a tail on top of an identical prefix.
In short, in your single carrier introduction, the solution is to have a longer symbol generation duration, but in the multi-carrier situation, the solution is to have the same symbol generation duration and then patch the resulting prefix gap with a copy of the tail. I realize I must be missing something since, everyone is on the same page, except me.
So, what did I miss?
In my single carrier example: The "actual symbol" that you ideally want to transmit, is only 4 cycles long. The #1 cycle (according to your definition) does not exist in the "actual symbol". The #1 cycle is added, in order to avoid inter-symbol-interference affecting the "actual symbol". The added #1 cycle is a copy of the last cycle of the "actual symbol" ... ie. it is a copy of the #5 cycle, in your definition of the cycle numbering. This is why it is called a cyclic prefix. I agree that it looks like just an "extension at the start" of the sinusoidal waveform, but that's only because the start and the end of a sinusoidal waveform are the same (ie. it's only an "extension at the start" since the waveform in this case is a sinusoid). Once you start adding sinusoids together (as in the multi-carrier OFDM case), the start and the end of the "actual symbol" are not the same any more.
@@iain_explains Thanks for reverting. Regarding "Once you start adding sinusoids together (as in the multi-carrier OFDM case), the start and the end of the "actual symbol" are not the same any more."
Is the generated IDFT signal not periodic anymore? We can picture that it would be periodical if all phases of all subcarriers were identical. But even with different phases, I think it should be. I guess I need to go back to studying OFDM. Thanks again.
The lowest frequency subcarrier has a period that is the length of the IDFT vector. So the start and the end are not the same. Here's some code you can try in Matlab:
X=zeros(1,100);
X(2)=1;
X(100)=1;
plot(ifft(X))
Hi professor, IEEE channel model D(typical office) has max delay of 390ns, and 802.11ac short guard interval(should be the length of cyclic prefix?) is 0.4us which is 400ns and is longer than max delay. Does it mean model D won't create any inter-symbol-interference? But why are we still seeing WiFi throughput drop when testing when testing with channel emulator and applying model D?
Yes, there won't be any ISI between the OFDM symbols in that case, however that doesn't mean that the channel is flat across the spectrum. There will still be an effect from the multipath, causing some sub channels to have low gain. I'm planning to make a video about this in the next week or so. Keep a lookout.
Hi,professor,I like this video,but I'm looking for some rigorous mathematical derivation of CP in OFDM,could you recommend some valuable paper?
Nicely done.
Thanks.
Can we summarise and say that due to the delay in the ofdm symbols, the symbols are shifted such that we lose some of the right most part of it but due to the CP at the fron we get that exact part back in the waveform? Kepping full symbol data intact although out of order. How would we know how much of the cp needs adding back to recover the full symbol?
Not really. We're not "adding it back" at the receiver. We're adding the cyclic prefix at the transmitter. It means that when there are multiple paths in the channel, the paths that come into the receiver with a delay don't disrupt the next symbols, and don't cause components of the previous symbols to disrupt the current symbol.
감사합니다
You're welcome!
Thank you Sir!
You are welcome!
at 2:48 if the problem of rotation of the constillation has been soved by the process of equilization than what is the need of cyclic prefix ultimately what we want is our constillation at the right posiotion at the receiver in order to be detected that has been aceived by the process of equilization . so where there is need of CP sir please spread some light i have watched the whole video many times but everytime my mind is stuck on the same question
It’s not possible to do the equalisation until after the inter-OFDM-interference has been removed. That’s what the prefix is for. It ensures that there is no interference from one OFDM symbol to the next.
Great sir!!!!! Thankyou very much
Glad you liked it.
Great video, thank you!
Glad you liked it!
Sir, to prevent ISI we go for OFDM. Now, while we implement OFDM, the symbol period is made much greater than the delay spread. So, ISI will not occur, right? Then why should we still use cyclic prefix? Sir, I have had this doubt for a long time. Please explain this sir
Making the symbol period longer doesn't "remove" ISI. It just makes the ISI have less effect, since the delay spread becomes a smaller percentage of the symbol period.
@@iain_explains Thank you sir
Thank you for the video. I have one question: why not just make the multipath delay time as "silent"?
You could do that, but then there would still be a discontinuity when the delayed paths start appearing in each symbol period.
In your example we have e.g. in the single carrier case we have multiple periods of the same symbol. My assumption was that one symbol takes exactly one T (periode). In the picture the "Transmit Symbol" has 5*T. Is that normal?
Thanks.
The exact frequencies depend on the system and bandwidth being used. This video might give more insights into what I mean: "How are OFDM and xDSL (DMT) Related?" czcams.com/video/CET2UuGeEqs/video.html
Hi,
Thanks a lot for your videos. These are very interesting videos that you explain the concept very well.
I was wondering if you could tell me why we use CP and don't use something else for example all zeros. In the concept of circular convolution or linear convolution and taking FFT it doesn't matter and both ended up with multiplication of FFT's i.e., FFT (X * Y)=FFT(X).FFT(Y). I am not sure why we have to use cyclic extension by considering the this cyclic extension probably damaged with the delayed one.
Thanks again for your great explanation.
If you go to the 3min40sec point of the video, it explains that a cyclic prefix means that the delayed (second path, ISI) signal results in a smooth transition within the "received symbol period". This is another way of showing the circular convolution you mentioned. If the prefix was full of zeros, instead of the (cyclic) extension of the symbol, then there would be a discontinuity coming into the "receiving symbol period" (it would be a flat "zero" signal coming in from the left, instead of the sinusoidal signal that I highlighted in red pen). This discontinuity would cause the spectrum of the subcarrier to broaden out, since it is no longer a simple sinusoid. And then the subcarriers would not be orthogonal any more. It is possible to use a zero prefix, but you have to understand that there will be cross carrier interference. It turns out that this may be a positive thing, if the channel is highly frequency selective and unknown at the transmitter, since the symbols transmitted in the deeply faded sub channels will be spread into the other sub channels, and then potentially recovered through the error correction decoding process.
And another thing to note is that the FFT operates on a (finite length) signal sampled over a finite time period. It implicitly assumes that the signal is periodic. In other words, it assumes that the finite time period signal repeats for ever, before and after the finite part that it knows about. Therefore there is _no_ "linear convolution" when it comes to FFTs. There is only circular convolution.
@@iain_explains Dear Iain, thanks a lot for your response. It is very helpful and I understand its reason now. I searched it a lot but couldn't find the reason, but here, you explained it very well and I really appreciate that.
@@iain_explains Yes, as you said FFT comes to cyclic signals, that is a great point, thank you.
One more thing, may I ask you please introduce me a good (theoretical or practical) book for wireless systems?
Thank you very much
These are a couple of good books on fundamental aspects of wireless communications (although they were published some time ago, so don't include specifics of the current standards): T.S. Rappaport, “Wireless Communications Principles and Practice”, and D. Tse and P. Viswanath, “Fundamentals of Wireless Communication”
thanks alot
Happy to help
Hello, can you explain why it is necessary that we use the cyclic prefix in the second example? Because there is no delay or ISI like in the first example. So there would be no discontinuity in the received signal.
Sorry, you'll have to give me a time-stamp of which exact part of the video you're referring to.
Professor, this is a great video, I read lots of articles recently regarding ZF-OFDM vs CP-OFDM in the transmission path, looks like there will be a linearity benefit when using ZF-OFDM in the TX path, if we use this in TX path, the RX has to pair it as well, how ZF-OFDM system deal with the discontinuity ?
Do you mean zero padded (ZP) OFDM? It's not clear what you mean by ZF-OFDM. Zero forced? In what way?
can you tell advantages and disadvantage of ofdm also
Great question. I'll add that suggestion as a topic on my "to do" list. In the meantime, you might like to watch this video, where I explain some of the pros and cons of OFDM: "What is SC-FDMA? And why is it used for the Uplink of 4G/5G Mobile?" czcams.com/video/ODx7mDCjDwQ/video.html
professor earlier you were clearing the doubts but now idont know the reason why you are not doing so , please sir have a look at my question which i have aked its 9 days still waiting for reply .
thanks
Sorry, I’m a busy person. It would be great if this channel provided enough income to support me, but currently it doesn’t. I respond to as many questions as I can. If you’d like to support the channel, you could consider becoming a member of the channel (the link is under the video) - it all helps, and I give preference in my answers to channel members.
Great video
Thanks!
how to calculate the value of the portion taken (from the symbol)of the cyclic prefix in ofdm?
i watched a lot of videos and they all say that we take the last portion! but how can i calculate it?
and for your explanation, we are making the cyclic prefix before the parallel to serial conversion because it's adding a cp to every subcarrier right?
The length of the cyclic prefix is a design choice. There is no absolute rule for how long it has to be. The longer it is, the more resilience there will be to the effects of ISI from the channel, but it will also mean that there will be a smaller percentage of transmission time for the actual received signal (since the prefix is discarded at the receiver). Standards define the prefix length (eg. the 3GPP standard for 4G and 5G, and the IEEE802.11x standards for WiFi).
great great video..
Thanks. Glad you liked it.
We took last few samples as cyclic prefix.
Can we relate it to some thing like forming a circulant matrix which can be unitarily diagonalized by DFT matrix ?
Yes, that's exactly right. Nice connection!
Hi sir, I have doubt here, can we send zeros instead of sending last portion of symbol? In cyclic prefix.
Yes, but it's not a "cyclic" prefix then. It's a zero padded prefix. There are advantages and disadvantages to each.
@ 2:40 sir can you please elaborate what will be the problem due to discontinuty
If there is a discontinuity then the waveform on each subcarrier frequency won't be a pure sinusoid. It will be a sinusoid with a "phase glitch" at the time of the discontinuity. Then the fourier transform of that waveform will not be a delta function. It will spread out in frequency. This will then overlap with the neighbouring subcarriers, causing them to not longer be orthogonal.
thanks sir now everything is cleared . sir you are gem replying even small doubts and revealing the mysteries of wireless communication to us 👍
How is the discontinuity dealt with during signal acquisition ?
Not exactly sure what you're asking. The CP is actually used to help the signal timing acquisition since the start of the received OFDM symbol and the end are correlated (they would be identical if it wasn't for the ISI from the channel), therefore the receiver can search for correlation peaks, and then work out where the boundaries are between the OFDM symbols. The actual CP is discarded in the symbol detection process. Losing that energy (and transmission time) is the price you pay for obtaining a symbol format for which channel equalisation is easy.
Amazing
Thanks. Glad it was helpful.
The phase portion we just rotate and get the constellation , now cyclic prefix will only take care of discontinuity , what do we do for the phase rotation of the sine component in case of multiple OFDM carrier, do we simply rotate or is there any solution to that as well?
Sorry, I'm not sure what you are asking. Perhaps you can explain a little more?
@@iain_explains Sorry , I am just learning so may be I a wrong, in the video u said the equalization can be done at the receiver just by rotating the constellation, so i was wondering do we any fix for that .. like the discontinuity is taken care by the cyclic prefix do we have any such mechanism for the phase shift due to the multipath environment.
The phase shift is corrected in the digital domain (ie. after sampling). It is done simply by multiplying the sampled complex number in each sub-carrier by e^(-j theta), where "theta" is the phase shift that the channel applied to the signal in that particular sub-carrier.
hello, does anyone know how to count the size of CP? is it based on the subcarrier or the symbol in the subcarrier?
The length of the CP for 4G and 5G mobile is defined in the 3GPP standard. In general, it needs to be longer than the maximum delay of the significant reflected channel paths.
@@iain_explains
for example, I have a program at matlab
with 256 subcarrier, and there are 100 symbols per subcarrier
so the CP is count based on the symbola per subcarrier or the total number of subcarrier?
if I use 25%, then the CP is 25% of the symbols per subcarrier (25%x100=25 symbols), is it right?
so, it is like a guardband?
Well, yes, in a way. Guardbands are in the frequency domain, and the CP is in the time domain. So it's more like a Guard-period.
@@iain_explains instead of a guard period for each user in the TDM, here the period is for all of them. Right?
The CP is between OFDM symbols in the time domain (from a single user). It is not separating different users from one another - that's what a guard period does in TDM, or a guard band does in FDM.