Thanks for your comment. Glad you like the videos. And I've just updated my 'about' section - good suggestion.

Thanks for the endorsement! Glad you like the videos.

Glad the video was helpful.

Hi Tom, great to hear from you. Thanks for your nice comment.

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.

Thanks for your nice comment. I'm glad you have found the videos helpful.

Glad it was helpful!

Glad you liked it!

Thanks for the suggestion, I've added them to my "to do" list.

Glad you like them!

Glad it helped!

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.

Thanks. I'm glad you like the video.

Great suggestion. I've added it to my to-do list. Thanks.

Here's the link to the SNR and Eb/No video: kzfaq.info/get/bejne/mLSJqbujm9reiIU.html

Great. I'm glad you like it.

My pleasure!

Glad it was helpful!

Thanks for the suggestion, I'll add it to my "to do" list.

I'm so glad you liked it.

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.

Glad it was helpful!

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Thanks.

Thanks!

Glad to hear that

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Thanks. Glad you liked it.

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You are welcome!

Happy to help

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You're welcome!

:-) Thanks.

Yes, you need to send the "complex signal". Here's a video that explains how: "How are Complex Baseband Digital Signals Transmitted?" kzfaq.info/get/bejne/ZtKbha2Y09_bm5s.html

@@iain_explains Thank you!

Do you mean zero padded (ZP) OFDM? It's not clear what you mean by ZF-OFDM. Zero forced? In what way?

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 (kzfaq.info/sun/PLx7-Q20A1VYKTk9LLRNdViuWeYUe1o207), and Orthogonal Frequency Division Multiplexing (OFDM) (kzfaq.info/sun/PLx7-Q20A1VYIvtMUWX3yd_sQGbQx1qPGP). 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.

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.

You could do that, but then there would still be a discontinuity when the delayed paths start appearing in each symbol period.

Yes, that's exactly right. Nice connection!

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).

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.

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.

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”

Sorry, you'll have to give me a time-stamp of which exact part of the video you're referring to.

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?" kzfaq.info/get/bejne/eauEZbimrMupoac.html

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.

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.

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.

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 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?" kzfaq.info/get/bejne/haqoatB1qNCop4U.html

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?

Yes, but it's not a "cyclic" prefix then. It's a zero padded prefix. There are advantages and disadvantages to each.

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.

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 👍

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.

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))

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.

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