OFDM Waveforms

Explains why the frequency channels in OFDM are orthogonal to each other from a Signals and Systems perspective.
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Related videos: (see: www.iaincolling...)
• OFDM and the DFT • OFDM and the DFT
• Why is Subcarrier Spacing Bigger in 5G Mobile Communications? • Why is Subcarrier Spac...
• What is a Cyclic Prefix in OFDM? • What is a Cyclic Prefi...
• Why is the OFDM Symbol Prefix Shorter in 5G Mobile and 802.11ac WiFi? • Why is the OFDM Symbol...
• 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...
For a full list of Videos and Summary Sheets, goto: www.iaincolling...
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[@JesperCheetah]

I love the way you just casually put an integral sign around the graph, then pointed out how/why the waves cancel out over time. Instant intuition achieved :) Thanks!

[@iain_explains]

That's great to hear. I'm so glad you like the presentation style and got the intuition I'm aiming to convey.

[@dmitrikazantsev3692]

I'd say this: If you explain complex things in plain language and slow pace using just pencil and paper to the people who know it all, you would be amazed how many of them didn't have a clue how it really works. What you are doing is great!

[@iain_explains]

Thanks. I'm really glad you see the value in my approach. One of the motivations I have for making these videos, is that I'm often frustrated by teachers who "brush over" topics that they know they don't understand fully themselves. There's no shame in not knowing something - but people often find it hard to admit it.

[@junaidjawedkhan5888]

That's the best explanation I've found on the internet. Your playlists are very helpful for revision, Thank you!

[@iain_explains]

Glad the videos are helpful!

[@mdominic7]

❤❤

[@jakubciborowski5400]

Best explanation of OFDM I have seen on the internet. Thank you very much!

[@iain_explains]

Thanks. Glad it was helpful!

[@herbieskids]

great videos. I am an orthopedic surgeon, but I happened to have dinner with a guy who brought up otfs and delay doppler as pertains to new cellular phone systems. I had no idea what he was talking about. Watching your videos, I now get it. thanks

[@iain_explains]

I'm so glad to hear that. It's always great to hear from people outside the engineering field who have found the videos helpful. I have the specific topic of OTFS on my "to do" list, as I haven't made a video on it yet. You've prompted me to move it up the priority order.

[@fifaham]

Nice explanation. To sum it up; to increase channel capacity we create w1 and all subsequent wn should be integer multiples of w1 (in frequency) - then we can bring those sinc lobes (data containers) close together without having any interference at the receiver. Very smart technique.

[@iain_explains]

Well, we're not actually increasing the "channel capacity", but we're finding a way to send data at a rate that is closer to the "capacity" without needing to do a difficult equalisation task at the receiver. For a video on the definition of "channel capacity" see: "What are Channel Capacity and Code Rate?" kzbin.info/www/bejne/hmG6imxsjKeIr6M and for an explanation of the relationship of OFDM and equalisation, see: "How are Different Equalization Methods Related? (DFE, ZF, MMSE, Viterbi, OFDM)" kzbin.info/www/bejne/noqxqIeKjNejapo

[@lifecalling9181]

Best channel for communicationa related stuff

[@iain_explains]

Thanks for your endorsement. I'm glad you like the channel.

[@lakshmikandula634]

Thank you so much professor ... i felt bad why i didn't find your videos before.. these are very helpful for understanding every concept clearly ...

[@iain_explains]

Glad you've found them now, and that you like them!

[@artubinha]

You have an excelent explanation over all topics! If I may suggest one thing: you may ordering the videos about the same topic, then we could easely follow the sequence to better undestand the topics

[@iain_explains]

Have you seen my Playlists on the channel? I've got 10 topics, and each one has the videos arranged in a way that builds on each other.

[@nimsbhide]

Another great video! This channel has been incredibly helpful this semester for me. Thank you, Iain!

[@iain_explains]

Great to hear!

[@jmckendry84]

Really excellent video. If you could go over "Hermitian symmetry" and how it is imposed on optical-OFDM signals that would be amazing - I'm trying to grasp it but it's melting my brain!

[@iain_explains]

Thanks for the suggestion. I've added it to my "to do" list. I'll have to give it some thought.

[@jmckendry84]

@@iain_explains That would be great. Thanks again for your videos, they're really helpful and I enjoy your clear, no-frills presentation.

[@mikkokanerva]

An excellent video. This one and the series. Many thanks, Ian! One comment about the math. At 3:30 you mention that the multiplied signals cancel out. This is, of course, true. However, your explanation has a small error. You said that because the signals are symmetric, the positive cancels out the negative. It's not the symmetry, or at least not in the way you explained. Please have a look at the start of the cycle on the time axis. Both f and 2f signals have positive values, and their product is positive. Then, at the end of the cycle both f and 2f signals have negative values, and also their product is positive. Two positive values, when added up, create a bigger positive value. The product, when summed up over the full cycle, is zero, but what cancels out what, is not what you explained.

[@iain_explains]

OK, thanks for pointing it out, but I think you're splitting hairs here. I just pointed to the wrong part of the signal, that's all. This is really just a small "visual typo". Everything I say is correct (I don't want others who read this comment thinking that there is anything wrong with what I say in this video.)

[@prof.dr.abdullahalnahid9914]

Very Nice. Easy to understand.

[@iain_explains]

Glad it was helpful!

[@trayennhuphan3892]

it's a great explanation. Thank you !

[@iain_explains]

I'm glad you liked it.

[@alexbogdanov3021]

Hello, could clarify this moment. Those orthogonal frequency has to be integer multiplication of each other. So if one is 2.4GHz, the other is 2.4x2=4.8GHz. And the third would be 7.2 GHz. so those carrier frequencies are far apart, usually you are given smaller bandwidth to operate in (like 500MHz)

[@iain_explains]

That's something that often confuses people. It's not the _actual_ _RF_ subcarrier frequencies that need to be integer multiples of each other. It's the "baseband subcarrier" frequencies that are integer multiples of each other (ie. before the "transmit waveform" gets multiplied by the RF carrier). This is essentially "by definition", since the IFFT in the transmitter implicitly assumes that the values in the input vector relate to equally spaced frequencies.

[@alexbogdanov3021]

@@iain_explains can you share a link that explains the difference between rf frequency and baseband for this case?

[@iain_explains]

Perhaps this video might help: "How are Complex Baseband Digital Signals Transmitted?" kzbin.info/www/bejne/Zp3Og32do96qock

[@rafaelaugusto2198]

Thank you very much for the excellent explanation!!! I'm subscribed now.

[@iain_explains]

You're welcome. Glad you like the channel.

[@mayurshankar3181]

Amazing sir ..!!

[@sapankushwaha4069]

Great explanation sir🛐🛐

[@iain_explains]

Thanks for liking

[@Salehinrafi]

Thank you very much for the videos! Those are really helpful. Could you please make an explanation video for the single-carrier ODFM waveform?

[@iain_explains]

I guess you haven't seen my webpage with a full listing of all my videos www.iaincollings.com/home which includes this video: "Why is SC-FDMA called "Single Carrier"?" kzbin.info/www/bejne/kJeUhH9sh55snLM

[@Salehinrafi]

@@iain_explains thanks! So, I wondered if OFDM is called a single carrier system with the lines I quoted from the video (kzbin.info/www/bejne/kJeUhH9sh55snLM). "That processing achieves the frequency orthogonality, and then you use a single carrier to upshift the entire digital waveform. So, this is called a single carrier system even though OFDMA uses multiple frequency channels (sub-channels)". I am a little confused. Can you tell me when OFDMA is called a multi-carrier system or if there is no such concept?

[@iain_explains]

People often use the term "carrier" in confusing ways (often without realising it). In principle, a "carrier" is any basis function that modulates a baseband waveform. This can be done digitally (using an IFFT as in ADSL), or using an analog miser (as in FDMA), or by using a combination of both digitally and using an analog mixer (as in OFDM and OFDMA). Perhaps this video might help: "How are OFDM and xDSL (DMT) Related?" kzbin.info/www/bejne/eXa3Y4irfMp4p9U

[@wwhyte1968]

I must be missing something, but I don't really understand how this works in practice. That is to say, if I send a signal on a 2.4 GHz carrier frequency, then this seems to say that it's orthogonal to a signal sent on 4.8 GHz. That makes sense, but I don't understand how we apply it within the 2.4 GHz channel, which is only 60 MHz wide and so doesn't allow for one frequency that's twice the other. How can we find two frequencies within the 2.4 GHz channel that are orthogonal? (Apologies if this is so far off base it isn't even wrong :-))

[@wwhyte1968]

Like, I can see that if you have two signals, one with frequency 100\omega_1 and one with frequency 101\omega_1, then they will be orthogonal over exactly 101 cycles of the first = 100 cycles of the second. But if you have any other numbers of cycles you lose the exact orthogonality. So I don't see how to use this trick on more than two signals at a time. If this is explained in a subsequent lecture just point me in that direction. Thanks!

[@iain_explains]

Good question. I think I should have pointed out that the frequency relationships between the subcarriers in the OFDM waveforms are all at baseband. You're right - no one ever seems to point this out - and it is confusing. I think you've just given me a topic for another video. In summary, the OFDM waveform that's generated from the IDFT operation still needs to be up-converted to whatever carrier frequency is being used.

[@wwhyte1968]

@@iain_explains Thanks Iain! I should note that in this video you specifically referenced the carrier rather than the baseband frequency -- maybe there was context that I was missing that made it clear the frequencies should be considered baseband? Watching some other videos on this elsewhere on KZbin I feel like I got a different explanation -- the exact length of the pulse results in a specific distribution in the frequency domain, given by the sinc function, and the zeroes of one frequency domain distribution are set to line up with the peaks of the adjacent frequency domains. That makes more sense to me but seems like a different definition of orthogonality than is given in your video. I love your presentation style so it'd be great to see a video from you addressing this. Thanks!

[@holgerschmidt9717]

Explanation why s_1 and s_2 are orthogonal is in fact - as already pointed out - wrong. You multiply and according to your explanation you would get the same values (i.e. also the same sign) and hence no cancellation. May should should just draw the multiplied version, otherwise its confusing.

[@iain_explains]

Yes, I think I made a "verbal typo" in my explanation. You're right about the signs. But the overall result is true. The integral equals zero. In fact, the first and last "quarters" are positive, and the "middle half" is negative - and they sum to zero.

[@pranavkumars.4070]

Thanks for the explanation Ian. Everywhere people use the word "OFDM waveform" left and right, but very rarely do they precisely explain or draw the shape of the waveform. One question though: this technique is called "Orthogonal Frequency" Division Multiplexing, but actually the waveforms are orthogonal in "time", not frequency. Right? Then why the name?

[@iain_explains]

That's a great question. The subcarrier waveforms are orthogonal, since if you were to match filter the received waveform with a particular subcarrier waveform, then the components from all the other subcarriers in the received waveform would not contribute anything to the output of that matched filter (as indicated by the equation/diagram on the top right hand side). Sure, you could view this as being "orthogonal in time", since the filtering process is done in the time domain, however it is the fact that the component waveforms are all sinusoids at different frequencies that means that they will be orthogonal. From an end-to-end perspective, the data (complex number) that goes into a particular element of the input vector into the IDFT at the transmitter, comes out in the same index of the output vector of the DFT at the receiver, and does not affect any of the other elements of the output vector. These indices correspond to the sub-carrier waveforms (which are each at a different frequency), and so in this sense it is orthogonal in frequency.

[@ranchordaschancad3410]

a really intuitive video professor moreover I would like to ask a question that if we are sending two-bit suppose [1 1] on two adjacent channels which are orthogonal to each other but how should we differentiate between the frequency component at the receiver because even after the demodulation by the subcarrier at the other end the two adjacent symbols of [11] must be having the same frequency component and ultimately we are collecting the energy of the frequencies to make our symbol.

[@iain_explains]

Sorry, but your question is not very clear. I don't know what you're asking.

[@ChelseaLaurenson]

what would be math prerequisite course/courses in order to gain a full, functional understanding of this?

[@zhaobryan4441]

god this is so clear!!!!

[@iain_explains]

I'm glad you found it helpful.

[@ankitsinha4124]

Nice work👍👍

[@iain_explains]

Thanks ✌️

[@zahraazaidan1152]

Sir I need a reference of BER derivative of ofdm QAM can you help please

[@nicolasperez4292]

I think there is an error in the video. At the end you label frequencies using 2*pi/T. At the beginning of the video you indirectly state that T is not a wave length or a frequency.

[@iain_explains]

Sorry, I don't know what you mean by "indirectly state". T is the length of the digital symbol, which means 2pi/T is the baseband bandwidth of that digital symbol. The video's correct. Perhaps this video might help: "Fourier Transform Duality Rect and Sinc Functions" kzbin.info/www/bejne/qIbKc5t7pcqkrtE

[@nicolasperez4292]

@@iain_explains on the x axis at 5:40 you label the frequency of the signal using 2pi/T.

[@nicolasperez4292]

@@iain_explains ​ by 'indirectly state' I mean that you didn't define it as a wave length or a frequency. sorry for my lack of clarity, I am new to this topic.

[@iain_explains]

Perhaps it's a good idea to think about the units. T is in seconds. 1/T is in (1/seconds) = Hertz

[@nicolasperez4292]

@@iain_explains I see, so T essentially serves two purposes: defining the length of time of the digital symbol, as well as the frequency.

[@nicolasperez4292]

I didn't quite get the part where you said "as we know, multiplication in the time domain is the same as convolution in the frequency domain". do you have a video explaining this? or even a reference I could read?

[@iain_explains]

Good question. I'll add it to my "to do" list. In any case, it is a standard property that is listed in all standard tables of Fourier Transform properties. You'll find it in any Signals and Systems textbook.

[@nicolasperez4292]

@@iain_explains great, thanks!

[@pitmaler4439]

I have a short comprehension question. For localization purposes, one need a high bandwidth due to the smaller symbol duration. That is clear. But, all modern comm. systems use OFDM and one build many channels with smaller bandwidth (number of channels = number of subcarriers). That is an advantage in a multipath environment, but, disadvantageous for localization. So, do we have the benefit of smaller symbol duration or not? It is a bit contradictory to me. Is the symbol duration for the localization purposes 1/B_full or 1/B_subcarrier? Thank you very much.

[@iain_explains]

If you've only got one antenna, then you're not talking about "localisation", just "ranging". And yes, for _ranging_ , the bandwidth is critical. But you don't only do it on a single sub-carrier, you would do it using the _full spectrum_ transmitted waveform (for an OFDM symbol, for example), by correlating what you receive back from the reflection, with the waveform (ie. the OFDM symbol) that you had sent out. See this for more details on radar: "Why is a Chirp Signal used in Radar?" kzbin.info/www/bejne/gKrRoGB4lsSfgdU

[@pitmaler4439]

@@iain_explains Thanks for your quick answer. Yes, I mean ranging. But, it is also a one way ranging. UE sends the signal to the base station. The BS measures the time. So there is no resonse. In that case, it must work without correlation. Ok, I take away that they use the full bandwidth, rather than just one subcarrier with a smaller B and its longer symbol duration.

[@iain_explains]

It sounds like we're talking about different things. I was referring to the recent research on the topic of "joint radar and communications", where the communications signal carries data, but the transmitter also listens for "bounce-back" versions of the transmitted signal, and performs radar processing on that. It sounds like you're talking about some sort of on-way timing delay estimation.

[@cahitskttaramal3152]

There is one thing I do not understand. To make frequencies orthogonal, I take they have to be proportions of each other like f / 2f / 3f. But 2G bandwidth is 2412 to 2484 MHz. So to use this wont we need 2412 / 4824 / 7236 MHz?

[@cahitskttaramal3152]

Sorry, I realized in a moment. They are proportional, just not f and 2f but 2000f and 2001f. Cheers.

[@iain_explains]

Yes, that's right. The "base band" frequencies are multiples of the fundamental frequency, but then they need to be up-converted to the carrier frequency.

[@nicolasperez4292]

when a frequency is expressed in the frequency domain, why does it have all those little 'side lobes'? If it is just a single frequency with no noise, wouldn't it just be a perfectly straight vertical line, where the base of the line is at the given frequency along the x axis?

[@iain_explains]

It's not just a pure sine wave when it's been modulated by a digital data sequence. You can think of it as a sine wave, multiplied by lots of square wave functions, each offset by an integer multiple of T. Therefore, in the frequency domain, it is the convolution of the sine wave transform (ie. two delta functions), with the square wave transform (which is a sinc function).

[@nicolasperez4292]

@@iain_explains great, thank you so much for these videos. Potentially another video you can cover haha XD

[@iain_explains]

Yes, I'm continually adding to my "to do" list.

[@yasserothman4023]

Thanks for sharing can you please add some 2 or more videos explaining the idea behind synchronization in ofdm both symbol time synchronization and frequency synchronization (handling both integer and fractional frequency offset ) The text books are full of mathematical expressions lacking the intuition and the insights unlike your videos

[@iain_explains]

Thanks for the suggestion. I'll see what I can do.

[@kingsman428]

Tut, didn't take you long to use the *F* word in this video. As soon as you said Fourier I came out in cold sweats and had flash backs to my college days causing a flurry of long forgotten thoughts such as Laplace, S domain transformation and the *feeling of fear* but apart from all of that, it was a great video dude

[@iain_explains]

I'm not sure if it will help with your cold sweats or make them worse, but if you're interested, I thought I'd point out that I do have videos on the Fourier and Laplace Transforms on the channel. Check them out, if you dare: iaincollings.com

[@kingsman428]

@@iain_explains Thanks I found my way there from another of your videos. Thanks for taking the time to put high quality videos like these together. Before the days of the internet you had to be very fortunate to find an instructor able to impart insights in the way you do. Very well done *A++* 😁

[@issaclee7114]

Hi, Professor Could you explain the difference between OFDM and OFDM-SPM?

[@iain_explains]

Thanks Issac, I've added those topics to my "to do" list.

[@nick1f]

I don't understand how the OFDM works. A mobile phone may operate on some a frequency band between 700 MHz and 710 MHz. There could be multiple carriers within this range. But the double frequency of 700 MHz is 1400 MHz and this cannot be used for OFDM, because it is outside the range. So what is a concrete example of these orthogonal frequencies? Are they carrier frequencies or modulation signals?

[@iain_explains]

The subcarriers are generated at baseband, and then the whole waveform is up-converted to the carrier frequency. So in your example, the subcarriers might be 10kHz apart, and if there are 1000 subcarriers, it would generate a complex baseband signal that is 10MHz wide. Then you up convert this to be centred at 705MHz, and the final transmitted signal will be in the range from 700MHz to 710MHz. Here's more details about up-conversion: "How are Complex Baseband Digital Signals Transmitted?" kzbin.info/www/bejne/Zp3Og32do96qock

[@nick1f]

@@iain_explains Thank you for explanations, now it is more clear.

[@ComputerScienceLessons]

I watched your video about the rect and sync functions and it was excellent. I am not a mathematician but am beginning to get a feel this. In this video, when you drew the sinc function, you drew all of the bumps above the x axis, rather than a wave form. Could you please tell me why? Thanks a million.

[@iain_explains]

Here I plotted the absolute value, or magnitude, of the function.

[@ComputerScienceLessons]

Thanks Iain I appreciate the response and I love your channel. In my mind I’m struggling to understand why it is that when an analogue signal is FM modulated, the information is carried (duplicated) in the side bands. Indeed, we can even discard one of the side bands. But when it comes to digital data and OFDM, it seems that the side bands (the little bumps of the sync functions) don’t matter, they can interfere with each other all they like as long as the big bumps are separated. Modulated digital data (E.G. QAM) might include a mixture of frequencies, so surely the little bumps are important. What am I missing? Is this picture of overlapping sync functions what it looks like before digital data are modulated onto the subcarriers? If so, what does the signal look like in the frequency domain after the data have been included? Can you point me to a resource (or one of your videos) that will clear up my understanding please? Again, thanks a million@@iain_explains

[@iain_explains]

In digital communications, a constant digital data value is sent over each period T, and the receiver is only really interested in those values. It adds up the energy in between the T-separated time values, and makes a digital decision every T seconds. For analog FM communications, you're interested in the signal at all values of time (not just integer multiples of T). And by the way, just because the sidelines in OFDM overlap, it doesn't mean we are not interested in them. They certainly are important. But, as this video points out, even though they overlap, it doesn't mean they interfere with each other - because at integer multiples of T, their values are orthogonal between subcarriers. Perhaps these videos will provide more insights: "What is a Matched Filter?" kzbin.info/www/bejne/eZqQdp2fgq-iaas and "Why is Doppler a Problem for OFDM?" kzbin.info/www/bejne/o3OTeHlvqrB2apo

[@ComputerScienceLessons]

Thanks a million for the reply Iain. As I work my way through all of your videos, things are becoming so much clearer. I have been focussing on the transmission side of things which, of course, is only half the picture. I’m not a mathematician so your largely intuitive approach is perfect for me. I hope you are enjoying your search for signals. I like to collect old postcards from places like Poldhu in Cornwall, St Johns in Newfoundland and Signal Point at Brant rock Massachusetts.@@iain_explains

[@iain_explains]

Your postcard collection sounds great. I haven't been to any of those sites. I think I was shown Maxwell's house when I was a kid, on a trip to Scotland, but I'm not 100% sure - it's just a vague memory. Did you see my recent lucky find, when I was visiting Darwin? "Australia's First Undersea Telecommunications Cable" kzbin.info/www/bejne/bILHqo19abZoock

[@DavidG2P]

Thanks! So all there is to OFDM over good old FDM is that you pick carrier frequencies that are multiples of each other!?

[@iain_explains]

No it's not just the relationship of the frequencies. Note that the Sinc functions (in the frequency domain) all have the same width. In other words, the digital symbol rate of the signals sent in each frequency channel must be the same, and it must also be an integer multiple of the wavelength of each carrier, otherwise they are not orthogonal. Also, for practical systems, the frequency synchronisation must be very accurate between each of the subcarriers (channels) - much more than for FDM.

[@DavidG2P]

@@iain_explains Ok thanks! So OFDM basically boils down to choosing and holding those very specific frequencies, and other than that, it's very similar to normal FDM?

[@iain_explains]

Yes that's right, although the acronym OFDM refers to a single user system, where the user divides up the data stream into multiple streams that are each sent on a different carrier (sub channel) (see my video: kzbin.info/www/bejne/kGWvepqEnLN0oqs ) In contrast, the acronym FDM refers to a multiuser system, where each user sends a single stream on it's own (separated) carrier. The multiuser version of OFDM is called OFDMA (for "multiple access").

[@issaclee7114]

Could you explain the relation of OFDM and PAPR?

[@iain_explains]

Excellent suggestion, thanks. Look out for it on the channel next week.

[@iain_explains]

Here's the link to the PAPR video: kzbin.info/www/bejne/fGWvco2KmdKSmJo

[@issaclee7114]

@@iain_explains Thanks.

[@aboodtayeh7705]

Thank you very much, greatly explained the concept, but have a question, from my understanding we are able to use a rect function in time domain only if the signals are well spaced in the freq domain, otherwise we resort to the raised cosine function? is there another reason on why we dont use raised cosine here?

[@iain_explains]

Yes, what you say is true for single carrier signalling. If you are sending multiple signals, each on its own seperate (non-synchronised, non-coordinated) carrier, then the carriers need to be well spaced in the frequency domain, and it's a good idea to use pulse shaping. This is to ensure that they are orthogonal (ie. that they can be seperated out at the receiver, eg. by using band pass filters). But, if the carriers are synchronised, and spaced according to the OFDM principles, then they are automatically orthogonal (by design), and you don't want to filter them in a way that destroys the orthogonality. If you haven't already seen my video on OFDM, then check out: kzbin.info/www/bejne/kGWvepqEnLN0oqs

[@aboodtayeh7705]

@@iain_explains Got it, your videos have helped me a lot through my digital communications course, thank you very much for the help

[@AliMarefat69]

Hi All, I am a CS grad student and would like to learn these stuff. I do not have ECE background so understanding the concepts its a bit difficult for me. what courses/topics you would recommend for me? (i.e. signal processing, digital communication, etc)

[@iain_explains]

I'd suggest watching the playlists on my channel. And check out my webpage, where I've categorised all the videos. Within each category, I've listed them in the order I'd suggest watching them in. iaincollings.com

[@abi_squee]

Sir could you please provide, hand written notes

[@iain_explains]

My webpage is linked in the description below the video. You’ll find all the summary sheets there. iaincollings.com

[@vishalgarg9512]

The OFDM chain I know is iFFT followed by DAC and then upconversion to carrier. Till iFFT we just have a vector of complex numbers. How do we get these multiple of tones just by DAC? What am I missing?

[@iain_explains]

Yes, that's right. Perhaps you might like to watch my other videos on OFDM to get more insights. For example: "OFDM and the DFT" kzbin.info/www/bejne/kGWvepqEnLN0oqs and others can be found listed at www.iaincollings.com/digital-communications under the OFDM tab.

[@vishalgarg9512]

@@iain_explains Your videos are just excellent. Many thanks for posting them. I have gone through them. Coming back to my question, how should the DAC work for OFDM? It should give rise to multiple tones. Could you please elaborate on that? If I understand correctly, sampling the continuous time expression in the "OFDM and the DFT" video gives rise to iFFT. So where does the sampling period and the frequency of tones comes into picture? How is the transition from discrete time to continuous time happens in OFDM is not very clear? Could you please explain that? Thanks.

[@iain_explains]

Have you seen: "How are OFDM Sub Carrier Spacing and Time Samples Related?" kzbin.info/www/bejne/oZ_NloulaLuNrMU ? That video explains how the frequency-domain vector gets converted into a time-domain vector (using the IFFT), and then how the elements of the time-domain vector get sent with a pulse shaping filter (this is what happens in the DAC). This video should also help: "How does the Discrete Fourier Transform DFT relate to Real Frequencies?" kzbin.info/www/bejne/pnqpq2tqpM9smaM

[@vishalgarg9512]

@@iain_explains Many thanks for your replies! It is clear now. Your videos are really awesome. Thanks again.

[@weakelement]

this topic needs further explaination

[@iain_explains]

Are there any points you think need more detail in particular?

[@rationalthinker9612]

This may sound like an ignorant question, but is it possible to combine OFDM, TDM and Phase DM all together to really maximize how many signals can be sent within a given bandwidth?

[@iain_explains]

It's certainly possible to combine time domain and frequency domain multiplexing techniques, but that doesn't necessarily "maximize how many signals can be sent within a given bandwidth". Channel capacity is determined by fundamental parameters of power and bandwidth - not the multiplexing technique.

[@zeynepyuksel6676]

I have studied my Phd proficiency exam with your videos and they help me so much that i can get the best result:) thanks for your clear and perfect explanations in which i could get the basics of the subject as well main ways of thinking the subject:) Thanks a lot for your guidance.

[@iain_explains]

I'm so glad to hear that. It's great to hear when people have found my videos helpful.

[@Hivatalo]

Dear Prof. Iain !!! Thank you for the efforts for letting people know how OFDM works. BUT I still dont understand that "ortogonal" means only that the sub freqs are 1x, 2x, 3x,...1000x..., so is that all? Thanks again!!!

[@iain_explains]

Have you seen this video on the channel? "Orthogonal Basis Functions in the Fourier Transform" kzbin.info/www/bejne/pGPOlqaCmLWMbdE

[@sotiriskopsinos]

Hello Professor. I am a telecommunications engineering student from Greece and I just wanted to tell you that I love your work on the platform and I have been watching your videos closely the last years with great interest! I have a question on this video: We are assuming that the signals we send through our channel are the result of the multiplication of our sin wave with the rectangular pulse in the time domain, which corresponds to a sinc wave in the frequency domain. However, in order to restrict ISI in telecommunications channels we are supposed to send sinc pulses in the time domain that result in rectangular like pulses in the frequency domain (so that the Nyquist theorem is satisfied). Aren't these two observations contradicting one another?

[@iain_explains]

Hi. I'm so glad you like the channel. It's great to hear from a long-term viewer. You've raised a good question, which often confuses people. It' s hard to explain in these comments, but these videos might help (if you haven't already seen them): "How are OFDM Sub Carrier Spacing and Time Samples Related?" kzbin.info/www/bejne/oZ_NloulaLuNrMU and "How does OFDM Overcome ISI?" kzbin.info/www/bejne/rpS0Z6Wqfr2pbK8

[@dominiqueg1477]

très bonne video ! merci beaucoup.

[@kristokinkela1815]

Please Ian tell me how many telecom signals do we have and how can we do their modeling and simulation. Do you have books about it? Thanks

[@iain_explains]

Hi, sorry, I'm not sure what you mean by "how many telecom signals do we have". Perhaps this video might help: "How is Data Sent? An Overview of Digital Communications" kzbin.info/www/bejne/g3LHlZV8m6imf9E

[@stellatauer761]

Thank you, I have one question. The higher the bandwidth, the smaller is the symbol duration (Tysm = 1/B). With OFDM one cuts it into chunks with a smaller bandwidth (carrierbandwidth -> Tsys = 1/Bcar). Does that smaller bandwidth counter the small symbol duration? It seems to be a bit contradictionary.

[@iain_explains]

Hopefully this video will help: "How are OFDM Sub Carrier Spacing and Time Samples Related?" kzbin.info/www/bejne/oZ_NloulaLuNrMU

[@wayofsalaf]

Sir, if a given communication system has 5MHz bandwidth and operated at 1.8 GHz of carrier frequency and using ofdm, how to estimate the minimum number of subcarrier in order to avoid selective fading? Thanks in advance

[@iain_explains]

Good question. This depends on the frequency coherence of the channel, which depends on the environment (number of reflected paths, etc.) Generally speaking, you want to have enough subchannels so that the width of each subchannel is less than the coherence bandwidth.

[@mauromelonicecconi5731]

Congratulations! Very very very very very very good JOB! :)

[@iain_explains]

Thank you so much 😀

[@austinbristow5716]

Thank you for this video Lain. Could you help guide my understanding for why n*s(t) is orthogonal to s(t) for any integer n? I have tried computing the orthogonality condition by integrating two signals (s(t)*ns(t)) from 0 to 2pi) and I cannot get it to compute to 0. Thank you!

[@iain_explains]

Sorry, I'm not sure what you're talking about. The term n*s(t) does not appear in this video. Also, I'm not sure what you are using the "*" symbol to represent. If it's supposed to be convolution, then it doesn't make sense to convolve an integer with a function. If it's supposed to be multiplication, then it also doesn't make sense to think that a simple integer scaling of a function would make it orthogonal to the original function.

[@austinbristow5716]

@@iain_explains Ok, I will be more clear here. You show at @3:35 that if you integrate s(\omega_1)s(2\omega_2) from 0 to T with respect to t, the integration goes to zero. I understand the pictorial representation of this, however, I was hoping to use specific functions to prove this orthogonality condition. I hope this is more clear. Thank you for your time.

[@iain_explains]

I'm not sure what you mean by "specific functions". I gave the equation for the exact functions that I'm talking about at 0:50 min. If you multiply sin(w_1 t) with sin(2w_1 t) and integrate them over a period T=2pi/w_1, then it equals zero. This is true for any value of the frequency w_1. These are the sinusoidal basis functions. You might like to watch: "Orthogonal Basis Functions in the Fourier Transform" kzbin.info/www/bejne/pGPOlqaCmLWMbdE

[@m.afsarali2520]

Thank you very much for nice explanation. How to apply these techniques in underwater wireless communication using acoustic signals? Please make a video on underwater acoustic wireless communication and what modulation techniques can be used to estimate the parameters data rate, channel impulse response, bit error rate etc. It will be very much helpful for those who are doing wireless communication for ocean or seawater or underwater.

[@iain_explains]

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

[@anoopkumarmishra7056]

Very nicely explained the othogonalities between the two waveforms.

[@iain_explains]

Thanks. I'm glad you liked it.

[@xiyoung3416]

that's great, thanks for your contribution prof

[@iain_explains]

Glad you liked it!

[@vishalgarg9512]

How is the orthogonality in the frequency domain defined? The peak of the sinc function in the frequency domain coincides with the nulls of all other waveforms is not really the definition of orthogonality. The orthogonality in the frequency domain follows from simply Parseval's theorem. It has nothing to do with peaks coinciding with nulls. Could you please say why peaks coinciding with nulls is important? Thanks.

[@iain_explains]

Hopefully this video will help: "Orthogonal Basis Functions in the Fourier Transform" kzbin.info/www/bejne/pGPOlqaCmLWMbdE

[@vishalgarg9512]

@@iain_explains Many thanks for your help. What is not clear is how peak of sinc waveform coinciding with nulls of other sinc waveform relate to orthogonality?

[@iain_explains]

It's a great question. Many people think that because the nulls of the neighbouring subchannels align with the peak of the subchannel of interest, that it therefore means they are orthogonal. But that's not the case. It's actually the opposite way around. They align _because_ the waveforms are orthogonal (that's the way the maths works out).

[@aki18able]

Well explained! Love your channel!

[@iain_explains]

Thanks. Glad you like it!

[@muhammedyusufsener1622]

Many thanks for the great explanation!

[@iain_explains]

Glad it was helpful!

[@alenqquin4509]

Great Work and thanks you !

[@iain_explains]

Glad you liked the video.

[@elijahsmith7552]

Thank you so much. Your videos have been super helpful in learning about different concepts useful in amateur radio.

[@iain_explains]

That’s great to hear!