The beautiful maths which makes 5G faster than 4G, faster than 3G, faster than...

[@D4M14N1989]

QAM now goes up to 4096QAM in WiFi 7, also called 4K-QAM since 4K is now such a buzzword. The physics required in signal processing to reliably distinguish 4096 code words is mindboggling.

[@Scraxxer]

Only Marketing could take some really clever invention like this and make it sound like a samsung TV

[@qboy2terafirma]

It has for quite some time. I’ve had backhaul radios operating for years that run 4096 QAM. But given the time to implement standards and costs of parts WiFi is only adopting it now while 5GNR adopts 1024. Today no phone could sustain this level as the signal degradation would be too high

[@rogerphelps9939]

Higher error rates too.

[@friedpicklezzz]

I wonder how this translates to error rates. At this point the differences (the wave) becomes so small, it may be read wrong, and now it relies more on the actual TCP/IP protocol (or whatever protocol is relevant) to resend the packages, from my limited understanding. I guess there’s a threshold where it’s better to have a lower QAM number, to keep the read error rates lower?

[@qboy2terafirma]

@@friedpicklezzz yes you can have higher QAM and slower speed due to lost packets and rely on retransmit. That’s why radios tend to have an option for max QAM to keep it locked on the best reliable level as moving up and down also causes losses and latency.

[@brenni01]

10:19 I am afraid your explanation of why the constellation points are grey-coded in QAM is not quite right. The cell tower needs to be able to switch from one codeword to any other in order to maximise throughput. The grey-coding of the codewords actually minimizes the number of bit-errors that occur because of added white gaussian noise (AWGN) during the radio-transmission. But kudos for explaining QAM encoding in ca. 10 minutes, that took me at least one semester at uni to understand properly!

[@scienteer3562]

Agree. So if there is an error, it is highly likely to only be a single bit error which can easily be corrected by the error correction scheme.

[@peregarauburguera]

You're correct

[@DrewNorthup]

TY Fabian, my brain was screaming "that's not what the V.92 spec said!" (Not too forget V.32bis, V.34bis, etc…)

[@MrCrayztrain]

Is the higher density of QAM encoded words the reason we need more 5G towers closer together? As in signal attenuation and noise lead to less effective error correction?

[@scienteer3562]

@@MrCrayztrain yes. You need more power to enable faster data.

[@scottmacs]

The left side of the 16-QAM chart @4:25 has duplicate values. "45º, 1.000" is at the top ("0000") and near the middle ("1010"); "18.4º, 0.745" lines up with both "0001" and "1011"; "315º, 1.000" lines up with "0010"and "1000"; et c.

[@ltcolthorin8661]

Okay, I wasn't the only one who noticed that. I paused the video to check, and each one is on there twice. I suspect some of those numbers should be negative

[@Henrix1998]

Parkers qam

[@DatShepTho]

Parker QAM Square

[@mimasweets]

Thank you. I was very confused.

[@briandarroch]

I'm glad i wasn't the only one!

[@yt2979a]

As far as I know Gray code is used to minimize bit errors. Since the most common error is to detect a constellation point near the one that was transmitted, when converting the point to its bit label Gray code will ensure only one bit out of four is in error.

[@maxaafbackname5562]

Grey codes are indeed to optimize the hamming distance to detect errors.

[@tirsek]

Came here to comment the same thing. If the only point of the Gray code was to avoid a transition through the origin, you could still only transmit one bit per symbol, so that makes no sense. It does make a lot of sense when it comes to error detection though.

[@mikefochtman7164]

Also see Gray code used in position encoders and such where the exact transition 'clocking' isn't controlled. Having two or more bits transition when moving one 'step' is problematic if you 'read' each bit individually.

[@khaloscar]

This is how I have learned it too

[@peregarauburguera]

Yes

[@jimclark5982]

Good old QAM, I love their song Qareless Qisper.

[@boRegah]

It's the sound a Swiss cheese wheel makes when it falls on its side

[@playgroundchooser]

This is an underrated comment 😂

[@Andrew-Kerr]

Qub Tropiquana is my fav

[@dycedargselderbrother5353]

Qilty Feet Qot No Rhythm

[@drenz1523]

Qast Qristmas Qi Qave Qou Qy Qeart

[@Staymare]

I would be about 63.0315 times more impressed if the the ID contained "5G" instead of just "G".

[@AeroCraftAviation]

Hahaaaaaaa

[@tolik75x]

It says 5AG, is that close enough?

[@DanielGirardBolduc]

I'm surprised too, Mat only had 1296 Video Upload Reset to Do 🤣

[@Peter-bg1ku]

At least it says Lisa which is kinda cool

[@igornet4211]

You should actually be 65.2072 (or exactly 11736367906285382977 / 179985715540787584) times more impressed. If you're assuming that youtube video ids are uniformly random base64 strings of length 11 of course.

[@A2ne]

"Every triangle's a love triangle when you love triangles" - Pythagoras, probably

[@jovetj]

He sure was acute little chaser.

[@matthewdion6092]

Dammit, Springleaf, get in my office now

[@makkusaiko]

Glad i wasnt the only one to think of this

[@SupremeInvigilator]

You took a really dry angle with that joke.

[@sayantanguha707]

QAM has been used since 3G, and to some extent, 2G. In fact, QAM is the most common modulation scheme in 4G.

[@gcolombelli]

Good old QAM... QAM is also used in ADSL and analog QAM is used in NTSC and PAL.

[@oasntet]

Yeah, QAM goes back a long ways. It was also used in several modem standards, like V.34, which is how we got beyond the theoretical limit of 28.8k using just frequency/phase shift keying.

[@ayuminor]

Yea have to admit, I'm left a bit unsatisfied with regards to the answer to the title of the video.

[@mmmmmratner]

@@ayuminor ditto. I think 4G uses the same modulation and bandwidth as 3G, but allows a single handset to use multiple channels when the cell is uncrowded. And 5G introduced beamforming so different signals can be sent to different handsets. 6G will support adhoc mesh networks a la IoT.

[@AbsoluteTVYT]

@@mmmmmratner No, 4G doesn't use the same modulation and bandwidth as 3G. 3G supported up to 5 MHz paired bandwidth per carrier, while 4G bumps that to 20 MHz. 5G bumps that again to 100 MHz (or something lower if the band isn't wide enough for 100 MHz) or up to 400 MHz for mmWave spectrum. Also, both 4G and 5G support 1024QAM, but that's not used very widely due to it needing extremely clean signals to "snap" to the right codeword.

[@peregarauburguera]

First of all, great video! A few insights on the last part of the video (Gray coding), hope it is useful to some people: Gray coding is not because of transitions from different symbols. It is to separate symbols cleverly. With additive white Gaussian noise (AWGN) at the receiver, the received signal will be noisy. To minimize bit errors, we place the symbols with less distance between them closer than those with more distance between them (distance meaning how many 0s and 1s change from one symbol to the other). Due to noise statistics, it is more likely that the errors occur between close symbols. If we have Gray coding, these close symbols have only 1 bit of distance, and we can reduce the bit error rate. Then 2 bit errors are less likely than 1 bit errors, for example. In addition to that, forward error correcting (FEC) codes are able to correct bit errors up to a certain number. It is always better to have less than more errors in the detected bits, but it is even better if we allow FEC to correct the errors. With Gray coding, not only we reduce bit errors, but we also increase the probability that FEC is able to correct those errors. About the transitions, we want them to be "fast", we don't want the signal to linger around 0 amplitude for most of the symbol period. This is seen in the eye diagram. There is nothing wrong with transitions through 0, we don't want to restrict any transition between two symbols. In an ideal world with infinite bandwidth we would want infinitely fast transitions. The eye diagram would be as open as possible. In the real world we want an open eye, we don't avoid certain transitions but their quality affects performance.

[@dacharyzoo]

God I love it in the weeds, thank you.

[@digitig]

I learned about Gray coding when I was working on radar systems. The radar heads had optical sensors to detect which way the head was pointing, and Gray codes were used so the detector only changed one bit at a time and the head didn't seem to jump via a wildly different angle if multiple bits didn't *quite* change over at the same instant.

[@ChrisKChandler]

Top comment! The only part of Matt's explanation that confused me was this bit about Gray coding, and your clarification really helped, thank you!

[@allanjmcpherson]

Thanks! I couldn't see how that arrangement prevented transitions through zero or why that would be a problem. That makes far more sense.

[@shadiester]

What do you mean by 'eye diagram'?

[@scienteer3562]

3G HSPA supported up to 64 QAM. The biggest step in 4G was OFDM.

[@smunaut]

Yup and LTE (4G) already did 256 QAM, same as NR (5G). ( AFAICT in the spec it's still limited to that although there has been experiments with 1024 QAM ).

[@TheIronPI]

DOCSIS 3.1 requires support of QAM 4096, but designed to support 16,384 QAM

[@RevJR]

OFDM is a method of using PSK or QAM though, in discrete channels. It is a massive leap for sure, but I think it kinda falls outside the scope of this video since he's really just discussing the discrete steps involved in QAM/PSK, not the overall implementation. It's a neat way to visualize it for sure.

[@jeremyloveslinux]

@@TheIronPIperks of being a completely isolated rf environment, eh?

[@gcolombelli]

@@TheIronPI That's pretty wild, but I guess it's just "raw" QAM instead of being modulated on top of CDMA / OFDM, right? There are tons of books about all the nitty gritty details on 2G/GPRS/EDGE, 3G/HSDPA/HSUPA/HSPA+, 4G and 5G (didn't care to read about the "enhanced" steps in-between those), but I never found something as in-depth as those for DOCSIS.

[@rickguerrero2282]

Nice job on explaining QAM. I am an 30+ year veteran of the cable TV industry and your explanations of the constellations of various QAM modulation schemes (16, 64, 256, etc) was spot on!

[@clairecelestin8437]

QAM is also part of the DOCSIS standard that we use for Cable Internet here in the US. You left out my favorite little detail, which emerges from the combination of Gray Code, decision boundaries, and error correction. As a signal gets distorted, the received codeword will wander farther from the intended point on the constellation, and that means that the first errors as signal degrades are likely to be the adjacent codewords, which as you pointed out, differ by exactly 1 bit from the intended transmission. Many types of error correction code can not only detect if an error has taken place, but if a single bit was flipped, they can figure out which bit it was and flip it back. By having orthogonally adjacent codewords arranged under a Gray code, that means that the most likely errors (from just barely bad signal distortions) will most likely be correctable, single bit errors instead of multi-bit errors that are more bandwidth-intensive to correct. Still, a great intro-level video into QAM, and quite a shiny thing. Well done!

[@letterAZornumber09]

That's not really how error correction works in cellular. We use interleavers (in NR this is just part of the rate matcher) to mix the bits so that an errors in a single subcarrier (one QAM constellation symbol) won't tend to fall "next" to each other in when they arrive at the decoder. This is important because frequency selective fading will tend to impair entire subcarriers. All of this was a lot more important back in the 3G error when the state-of-the art forward error correction was convolutional coding, which was very susceptible to burst errors. Today though, we have shannon-approaching block codes (turbo/ldpc/polar) and they are much less susceptible to burst errors by their nature

[@clairecelestin8437]

@@letterAZornumber09 I don't really know the specifics of interleavers; I'm not sure that we use that. I'm speaking in a more implementation agnostic way that doesn't make deep assumptions about the specific error correction or encoding that's being used beyond Gray Code on a QAM constellation. I maintain my assertion that the value of arranging codewords on the constellation according to Gray Code, as opposed to some other scheme, is that as the MER transitions from ideal to degraded, the resulting errors will have a statistically lower number of bit flips per errored codeword which are more likely to be correctable with lower error correction overhead. We're more likely to see correctable codeword errors than uncorrectable codeword errors.

[@letterAZornumber09]

Yes gray codes are used so that all of the decision boundaries (-2, 0, and 2 for unnormalized 16-QAM) are only associated with a single bit flip. In fact for SISO you can even use a super simplified approximate LLR algorithm (softbit_0 = x; softbit_1 = abs(x) - 1) that gets very near MAP performance.

[@Cyberguy42]

Thank you for this clear explanation

[@StephanLuik1]

The guys who had to add the analogue colour TV signal while remaining backward compatible with B&W broadcasts already knew this back in the 1950s. Phase angle can be split in X and Y (red and green) values. Subtract from the original black and white signal and you have blue.

[@shaunhw]

Actually it was red(-Y) and blue(-Y) which was transmitted via QAM on a subcarrier, and the green ( not blue ) was derived from the this and the black and white (Y luminance signal) in both NTSC and PAL colour TV signals. NTSC had the two axis slightly rotated. Blue could have been derived instead of course, but it was decided to derive green, possibly because our eyes are more sensitive to it.

[@thedroningbore]

Yess! "Phasenquadratur-Amplitudenmodulation!": the monster word comes right back to me! And the very famous "Farbhilfsträger" at 4.33. MHz, plus a 64 microsec. sort of electro-mechanical delay line. Jeeze, it's been decades…

[@LordBrozart]

No matter how many times this is explained to me, it still feels like magic. How the data of this video is sent through the air into the phone I’m watching it on is still amazing to me.

[@JohnCena-te9mi]

I've been explained this for the first time and I am like WHOOAA, it's that simple!?

[@yeroca]

@@JohnCena-te9mi It actually isn't quite that simple, because he didn't discuss the amount of "side splatter" this kind modulation produces, SNR, needed filtering, error prevention and correction, etc. etc.

[@JohnCena-te9mi]

@@yeroca Sure, but I went from "it's magic" to "I can breadboard something with this".

[@MrSkinkarde]

@@JohnCena-te9mino you can’t

[@JohnCena-te9mi]

​@@MrSkinkardeI can, ask your mom

[@matstjader]

Great video - it summarizes the basics quite nicely. WIFI 6 uses 1024-QAM, so it's probably coming with the 6G networks. The high-number QAM modulation techniques itself has been known for a very long time, but the spacing between the constellations has been too small and any interference in the radio signal (of which there is a lot) could easily shift a bit to be the wrong value. What is allowing the newer networks to start using these larger constellations is the use and advancement of Forward Error Correction (FEC) codes. These codes basically allows the receivers to receive wrong signals, but by sending a number of extra bits (and encoding them in smart ways) which allows a receiver to work out which bits are wrong, and correct them. The more extra bits you send, the more noise and interference you can counter.

[@WhatDennisDoes]

I wish you explained how it's impossible to transmit more information without taking up more bandwidth. Changing phase and amplitude introduce harmonics and so you really aren't transmitting a single frequency but a spread of frequencies in the spectrum. 5G of course has a much wider frequency spread than 4G.

[@maxaafbackname5562]

Very long ago, it took me a long time to understand while AM requires a frequency range.

[@mikefochtman7164]

At one time when CB radio was a big fad, I learned about SSB, the idea you can eliminate the main carrier and just transmit that 'side band' frequences that contained the modulated information. Warps the mind to think about 'not transmitting' the carrier and still transmitting the signal. lol

[@G1ZQCArtwork]

Harmonics get filtered out (but not 100% eliminated) by filtering.

[@johnopalko5223]

@chtman7164 It's not just suppressing the carrier. It's also suppressing one of the two sidebands. Hence, "single sideband." The carrier is reintroduced in the receiver to allow demodulation. Get the frequency a little off and your interlocutor sounds like Donald Duck. That's what the "Clarifier" control adjusts. SSB has been around for a while. The first US patent for SSB modulation was filed in 1915. Ham radio operators have been using it since the late 1940s.

[@KingJellyfishII]

​@@maxaafbackname5562this still confuses me, until I think of AM as literally multiplying the AF (I imagine just a sine wave) with the carrier, which makes it intuitive that it both only changes the amplitude _and_ of course there are other frequencies there because they were multiplied in!

[@MrRoboticBrain]

Wait.. how did you know there would be a "G" in the id?! Did you seriously re-upload until you got a G?

[@deefdragon]

it's a far from the dumbest thing he's done over and over to get a specific result. it's also actually not that bad. Just starting the upload gives you the ID, so it's a pretty quick process.

[@squelchedotter]

It's not that statistically unlikely and the video ID already gets created when you start your upload, so you can just cancel when it's wrong. It''s pretty easy to do.

[@LaughingOrange]

It is possible to upload really slow, and editing a video while it is still uploading. And some channels have the ability to change a video after the fact, but I'm not sure that feature is available to everyone.

[@pikapomelo]

And he welcomes us back, just as I'm done checking the ID. Amazing!

[@janhetjoch]

@@LaughingOrange but the joke only makes sense with a G. I don't think this is what happend

[@rowanjones3476]

Great to see some content making signal processing more accessible. And well done describing this without once using the term ‘complex number’, whilst still using the complex description of the waveform. Its really not that, well, complex, but the mere mention of the term is sometimes enough to put people off. This is a great example of how its so often simply a useful tool in engineering to characterise the behaviour of a system. It would be great to see a follow video on Forward Error Correction e.g. turbo codes, LDPC, Reed-Solomon, BCH etc given they’re just as important in dealing with error-prone real world conditions.

[@vleliv11]

>And well done describing this without once using the term ‘complex number’ It's also confusing for anyone who doesn't already know a lot of DSP

[@dziban303]

This better be about quadrature amplitude modulation

[@standupmaths]

QAM!

[@ericpeterson6520]

ive been asking for a quadrature amplitude modulation video for years

[@youdontknowme5969]

OFDM next 😉

[@marks2c]

COFDM even

[@boRegah]

​@@ericpeterson6520I only asked for it since January. Seems like I was more efficient

[@DarkZeros]

I worked in the design of NU-QAM in TV and later ported to 5G, so I am glad to see you showing this in the "proper way" it should be explained. However, you should have said as well: * Grey code is used because it help reducing errors. When you have noise and a codeword is distorted, only 1 bit is lost. Then the Error correction can probably fix it at a later stage. Without it, noise would have a catastrophic effect of messing all bits in transmission. * Also it is interesting to mention that the Power of the transmission is important, more amplitude more power. That is why codewords with many 0000 are in the corners, becaus emost transmissions should have more zeros than 1 in general. * If you want to enter NUQAM area, the reason the points in the corners become round, is to reduce power of those points.

[@jumpingman6612]

Interesting!

[@sacielo]

"QAM!!" is my new favorite exclamation!

[@LordHonkInc]

Reminds me of the old Batman comics :D POW! SOK! QAM!

[@MOSMASTERING]

Qam Qam Qam Quammity Qam... Qam Qam Qam I'm a telephone network engineer and I'm okay...

[@wacomtexas]

Can we use it in Scrabble though? :)

[@ZeroKage69]

not only is there a capital G in the video ID but you timed it perfectly that I was just scrolling back up from the comments when you welcomed me back from checking the ID and of course, the comments.

[@scragar]

4:25 I think your table is wrong. There's duplicates for all values and some are missing. That clearly shouldn't happen. I think whatever you used to generate the table wasn't working correctly for negative X coordinates on your graphed version. That'd also explain missing values like 135° and 161.6°.

[@hallohoegaathet7182]

I was wondering why some values were duplicated.

[@Janduin45]

Thank you for making this post so that I didn't have to.

[@nathanrcoe1132]

so what he showed is... a parker table? :)

[@altrag]

Almost certainly. If you're into computer programming at all, look up the atan2() function (and compare it to the simpler atan() function).

[@nbboxhead3866]

@@altrag I've made that mistake myself a few times, because atan(y/x) for a point almost works for getting the angle right but inverts when you cross an axis. Sorta annoying to work around when you don't have atan2 available, in limited settings like with block coding websites. Good thing I didn't publish anything before getting it to work properly!

[@jamesyoungquist6923]

Information theory, encoding schemes and error correction are some of the most interesting and useful maths that people have invented. Thank you Shannon and so many others

[@zuban222]

Actually, this video is about math of 4G and explains why 4G is faster then 3G. I wish this video explains why 5G is faster than 4G, because the reason is mindblowing! On the first sight, it is so fast that it defies the laws of nature (Shannon-Hartley theorem). 5G is about MMIMO technology. EDIT: Well, QAM was adopted even earlier, it is used even in 3G. 4G added (simple) MIMO and OFDM. Never mind, point is: 5G is MMIMO and it blows my head.

[@peregarauburguera]

Underrated comment

[@dacjames]

Seriously! I came here hoping for an explanation of MMIMO.

[@paulsengupta971]

Not all 5G is Massive MIMO though.

[@janhetjoch]

at ~ 7:18 you show the "64 qam", but it doesn't have 64 unique values. it's 8 x 8 so 64 values, yes. but on the bottom row there is 000000 as the 1st and 5th column. There might also be other duplications. the grid appears to use greycodes; only needing one bitflip for going up down left or right (presumably so when an error occurs its minimal and will be caught by the checksum) so I think the value in the 5th column should be 110000 which I also can't find anywhere else in the grid Edit: so watching the whole video, it does use grey codes but for a reason I hadn't considered. Though I'm sure what I said plays a role as well

[@0xstuff625]

Matt if you haven’t already you HAVE to try this hobby project, I obsessed over it for months: write one script that takes data of any type (text, binary, image etc) and encodes it as an audio file using any method you like (QAM, PSK, FSK etc). Then write a separate script that takes an audio recording and decodes the original data. Bonus points if you play the original audio out of a speaker and into a microphone, double bonus points if you use Trellis Coded Modulation for error correction 😊

[@QuibizOwl]

Non negotiable.

[@peregarauburguera]

The Parker link simulator!

[@Squant]

Bangai-O Spirits on the Nintendo DS allowed you to save and share custom levels as audio files, which you'd then play into the microphone to load. It sounded like a direct line to the underworld, but a great workaround given the file-sharing limitations of the device. I'd be interested to see it done using more ear-friendly audio.

[@analog_guy]

Assignments are more fun to give than to receive. 🙂

[@nbboxhead3866]

I might have to try this whole thing myself! I've wanted to get into understanding how radio works and how to transmit data wirelessly with radio parts, and I think this would be a great place to start.

[@feelincrispy7053]

I really like the new ‘corrections’ section in the description. Never seen it before but it’s a long over due feature

[@pawepawlik6987]

4g has a lot in common with 5g if consider only air interface. 5g introduced much bigger flexibility of defining logical channels. It was necessary for better use new (wider) bandwiths in 5g standard.

[@AlokMeshram]

I took Digital communications in my 4th year for my Electrical Engineering Degree and this video did a much better job of explaining than the entire course.

[@LSS94]

Oh my god, some good old fashioned action packed 10 min video about an interesting topic. Almost forgot how the good old days felt. Thank you so much for this!

[@aspzx]

Great explanation. I'd also love an explanation on how 5G uses multiplexing which is the technique needed to get high speed data to multiple users at once. Most videos on KZbin about it are pretty dry lectures.

[@peregarauburguera]

I totally agree!

[@haxi52]

Really cool visualizations. Thanks. It's also good to see you get out more.

[@YamiOni]

You have a gift for presenting information in an easily understandable and digestible way. Love the work you do, Matt, thanks.

[@Keithustus]

. Yup I checked.

[@miallo]

Obviously I checked, and obviously I KNEW that it would be in there. There was no other possibility of any of the two things right from the start

[@anto8722]

What even is the video id😭

[@lunarna]

​@@anto8722It's in the video link

[@Jonago.]

@@anto8722 To7Ll5AGboI, so it does indeed have a capital G

[@circuitgamer7759]

I want to know how that ID is generated now :) Guess I'm doing some research later...

[@tom05011996]

All of this is the same for fiberoptics FYI. 400G traffic is commenly sent using a Dual Pole 16-QAM modulation for example. Duel Pole by the way refers to two diffrent polorisations of light both of witch have a seperate 16QAM 200G signal totaling 400G

[@Umski]

I started in telecoms on the cusp of 3G launching - EDGE on 2G introduced 8PSK which worked on a good day at point blank range (16 and 32-QAM was in the spec but not used as far as I know). Similarly 64-QAM was introduced on 3G but again only really worked at point blank range from the cell 😑 Then 4G introduced 256- QAM but hardly anyone bothered with it. Current 5G just piggybacks on to the existing 4G network but the underlying radio is very similar just with more efficiency and overall bandwidth i.e. bigger pipes. Carrier Aggregation and MIMO are more significant in the radio interface now and going up to 1024 QAM like wifi isn’t going to happen just yet due to signals not being clean enough. The more interesting aspect is how the modem is running FFTs to decode all of this stuff - pretty amazing how the specs are conjured up even before the chipsets can physically achieve the expectations 😮

[@ohp98]

Hey mate, great explanation of IQ modulation as per usual. I'm currently using finishing up my masters thesis on the topic of communication (specifically wireless security) and using this to procrastinate. Just wanted to mention that the purpose of greycodes is actually not to avoid crossing the (0,0) coordinate, though there do exist methods to avoid this. Instead the purpose is to reduce the bit error rate. For simplicity let call the coordinates that the symbols take in both x and y (-3, -1, 1, 3). Now if I want to send a bit that is at coordinate (-1,-1), this would be 0101 in your diagram. Then the received signal is going to be (-1,-1) + noise. As the noise is additive for the position, it means that if the bit is erroneously received, it is the likeliest that it lands at one of the directly neighbouring codewords. Thanks to Gray coding, the difference between the codewords only has a hamming distance of 1, means that of the 4 transmitted bits, 3 of them were correctly received, and there was only one error despite decoding the wrong codeword. Hope this was clear enough, if not then I'm more than happy to elaborate further. Keep up the good work, and I'd love to see more communication theory in the future. The mathematics is fascinating but it's so rarely taught in a manner approachable outside of academia.

[@MitchBurns]

Electrical Engineer here. Here is what you missed in your video. 1. QAM has been used in 4G forever 2. QAM has a cool property that lets you send more data in exchange for using more power. 3. 5G Towers use new antenna technology that uses an array of patch antenna with different delays to each antenna in order to make the net signal go largely in a single direction. 4. These antenna require less power for the same signal. 5. The power savings from more efficient antenna are used to increase the amount of data with QAM, while keeping actual power the same. 6. 5G uses higher frequencies, which in a way have more bandwidth. (There are more numbers at higher orders of magnitude.) So yeah, you missed a lot in the video. You weren’t exactly wrong, but you only told the simplest and least interesting part of what 5G is. Also, you really should have mentioned how QAM only uses odd magnitudes of its base waves in order to keep spacing even.

[@peregarauburguera]

We've been SISO'd

[@andresmartinezramos7513]

5G antenas are phased array?

[@rogerphelps9939]

Electronically steerable directional antennae are not a lot of use if the mast is in the centre of its cell. In some cases 5G will reuse 3G bandwidth and not always higher frequencies so bandwidth increase is not always possible. Out in the sticks 5G would be very expensive and would be overkill.

[@mubangansofu7469]

correct... the video does not do justice at all apart from an attempt to explain Modulation (in this case higher order modulation), I thought he would discuss the math behind Shannon's channel capacity equation to explain why NR has a higher throughput than Option 1(LTE). We truly have been SISO'd as peregarauburguera remaked 🤣

[@RickJaeger]

Wow, I've been reading these comments, and it seems like you guys have a lot of experience and knowledge about various interesting subjects. You might consider trying to translate that expertise into your own video where you discuss it to your heart's content, instead of commenting.

[@aresorum]

4:17 There are duplicated sets of angles and amplitudes: 45 and 315, two sets at each angle are listed twice; angles 225 and 135 are missing, two of sets of each.

[@PlagueDoctor-87]

As an extra: 5G in cellular telecommunications is not the same as 5G in WiFi. In the context of WiFi, it's often used to refer to the frequency band used for transmission: 5GHz

[@phasor50]

Yes! I was just thinking about this, it's really misleading that they call 5GHz wifi 5G - I wonder if this is to jump on the marketing bandwagon

[@fooniepoo]

The geometry of QAM constellations is fantastically complex. How neatly your received data fits into each box determines whether you can increase or decrease the QAM order in use, dynamically trading noise immunity for bandwidth. You can also tell a lot about the different types of noise on the channel by the way the constellation gets distorted. Beautiful radio math!

[@hedgehog3180]

That sounds fascinating, I'd love to learn more about the maths involved in this. I'm guessing it's just a simple threshold distance with some statistics involved since some errors are acceptable due to error correction.

[@TrimutiusToo]

So how many reuploads did it take?

[@ELYESSS]

Now we need a video doing the math of how many expected reupload to get a capital G.

[@tapio_m6861]

Probably didn't need too many attempts.

[@Sam_on_YouTube]

Didn't do the math, but I did spot check. About 15% or so of the videos I checked had a G. Probably didn't take too many tries.

[@wincentywilk7511]

My maths think about 6

[@joostvhts]

@@wincentywilk7511I was about to do them. Care to share your maths?

[@darioinfini]

I remember working on I think it was a 9QPR telemetry radio 30 years ago. Quardrature Phase radio. I remember watching the constellation spinning like random noise as the radio software worked to "lock on" to the signal. It took something like a minute or so until the radio hardware finally identified the state of the constellation and then you'd see the constellation LOCK solid. I was the hardware guy working on the board and programmable hardware, the radio and software guys did the constellation thing. It was fascinating to watch. This was before cellphones, back in the beeper days. One of the software guys said something about the code he was writing after an incident. He finally got it working and we had made significant progress. Then someone asked him to change the name of a variable and the whole thing broke. He decided it was time to go to lunch. As we walked out he goes with full software guy exasperation: "NOTHING IS EASY!" I still say that to this day, 30 years later LOL.

[@davidisonyt]

Matt is using 5g to infect my brain with maths

[@magnushultgrenhtc]

His signal wasn't strong enough, though. I may have understood parts of it, but it seems I have to infer the rest. Oh no.

[@hedgehog3180]

Bill Gates are using 5G to turn the kids into mathematicians!

[@RyanJ_]

I have looked at the constellation diagrams so many times before and never really understood the theory. This is the first time it has clicked, thanks!

[@TheOoblick]

Why is the date for the UK edition of your new book in US format?

[@db_2112]

I wondered if it was purposeful and actually a fraction, but 6/20 is 0.3, 0.3 of the year is the 19th of April. I then wondered if any dates in US format, when taken as a fraction equate to that fraction of the year through the calendar. Turns out 3 (for a leap year) 16 Feb = 2/16 or 0.125 which is 46 days into the year, so 16 Feb 14 Apr = 4/14 or 0.2857 which is 104 days into the year, so 14 Apr 13 Aug = 8/13 or 0.6154 which is 225 days into the year, so 13 Aug

[@richardramos5124]

The reason they’re spaced that way is to optimize for noise resilience. If two code words were too “close” together in magnitude and phase it would increase the rate of error at the receiver. Environmental noise injects phase & magnitude to the transmission which causes the signals to shift, as long as the receiver picks something up within that box it attributes the value of what it is receiving to that codeword. This is one of the downsides of higher order QAM, noise resilience goes down.

[@LeeSmith-cf1vo]

Matt, why is the British release date in American date format? 🤦

[@aes0p895]

he's just trying to ease you into correctness

[@EthanReesor]

I'd love to see a video on synchronous CMDA and/or ODFM. Using orthogonality to multiplex and isolate communications is fascinating to me. Side note, in engineering school we had constellation diagrams where symbol (code) was a Gaussian representing the effect of noise on inter-symbol interference. There's a direct correlation between symbol spacing, signal to noise ratio, and bit error rate, assuming the noise is Gaussian. In a zero noise system, when a given symbol is transmitted, the receiver will receive exactly that phase and amplitude. However in a real system with noise, the phase and amplitude received by the receiver will have some drift due to noise, so the symbols effectively spread out. Assuming the noise has a Gaussian distribution, you can calculate the probability that a given symbol will deviate to the point where it is received as a different symbol, based on the symbol spacing in the constellation diagram, and thus you can calculate the expected bit error rate. And vice versa, given a target BER and spacing or SNR you can calculate what the other parameter must be to achieve that target.

[@Chip_in]

I got free 5G with my covid vaccination...apparently 🤣⛳

[@rustycherkas8229]

Yeah, me too... When I'm really quiet I can actually feel those nanobots skittering around inside... 🤣 This is why spending hours watching YT videos is so good at this time. Those nascent AI overlords devote less-and-less of their attention to "my" transmissions... 🤣

[@hedgehog3180]

I can never get over how absolutely revolutionary it would be if we could have something the size of mRNA transmit and receive radio signals yet people think that technology actually exists

[@CCarlquist]

Just amazing! I'm a Telecom Engineer, preparing myself for a presentation and this video really helped me getting prepared for the task. Cheers!!!

[@zefiro19587]

what the cork is that release date? what is the month 20? does 2024 have 8 leap months?

[@Aesculathehyena]

Matt lives in England and their dates are day, month, year, like makes sense.

[@catcoder7812]

Did anyone else get 'Pello!' when decoding the message at the beginning (2:08) using ASCII? I'm guessing he meant 'Hello!' because he paused on the l and 1010000 (P) is similar to 1001000 (H). For reference here's the binary I read: 1010000 1100101 1101100 (1101100) 1101111 0100001

[@maxaafbackname5562]

Is that also a off-by-one error? ;)

[@Bob94390]

@@maxaafbackname5562 An off-by-one error is when one value is one unit larger than it should be when they are regarded as integer numbers, e.g. 0100 instead of 0011. A single-bit error is when one bit is wrong, e.g. 0111 instead of 0011. Since P and H are 1010000 and 1001000, the error is neither off-by-on nor single-bit.

[@maxaafbackname5562]

@@Bob94390 I know. The joke was that the 1 was shifted in the bit string.

[@AlexForencich]

Parker encoding, perhaps?

[@momomunsta8887]

This explains why when the 5G horse visited me it said “QAM!”

[@sumansaha295]

this is the first time I have understood QAM, constellation diagram, and inphase and quadrature phase components. all within 11 mins! you are an excellent teacher.

[@boswell255]

Why don't they just do the maths for 7G now and skip 6G?

[@kasiphia]

But then it'd still be the 6th "G" 😢

[@rudilambert1065]

Because that's one less model phone they can sell you... Not to mention network upgrades.

[@scivids1999]

Godalming Westbrook Road, near the train station? If so I do not believe any 5G live at that mobile site yet - a lot of the equipment at the location is almost prehistoric - however neighbouring sites have 5G so device may well show 5G indicator.

[@scivids1999]

The technical detail of the phenomenon of device showing 5G when connected to a cell site without 5G usually boils down to the 4G cell site (without 5G) being configured to send Upper Layer Indication on 4G cells. Depending on network configuration and various factors, device will be able to use 5G carrier from a separate cell site that has 5G at the same time as 4G from the site without 5G. However, even in the absence of any accessible 5G connectivity, the presence of Upper Layer Indication alone is enough for many devices to happily display 5G.

[@andljoy]

Oh my god , you are next to a 5g tower , you are going to get super corona :D

[@moktatafatforyou-2378]

Sir, your channel has been usefull for me since 3 years ago, from the time i was studying for a math competition in high school to now as an under graduate IEEE student. you have amazing content, fun and beneficial. Great work.

[@harris9624]

Of course I discover this video AFTER I took my Communication Systems final! Excellent video and great, succinct explanations!

[@VapidVulpes]

The cut at the end! Oh my gosh! Oh it's so perfect! Amazing video as always! And that last little bit at the end is just the cherry on top 😺💜🎉💖🎉😺😻

[@elishmuel1976]

One of your best videos! Hats off, Mr. Parker! 💯

[@Stelios.Posantzis]

I always wondered about these and wanted to know their meaning but was never interested enough to decide to expend any effort. That was relatively painless and quick so thanks!

[@martinh2783]

I think it's super cool how this stuff works. I was radio operator in the army for a while and I just loved how all the physics and technology worked. You should do a video on antennas. From basic monopole and dipole antenna to things like phased array antennas.

[@vitorschwaab]

Kudos for the great video. Cool presentation format using the drone shots from above and the chair :D

[@mikewillis1592]

Nice to see electromagnetic fields being discussed, in a field. This must have been shot a while back or you would have been frozen. How about doing one on Shannon, balls in a jar, forwarded error correction and decoding Reed Solomon, Turbo Codes, LDPC? Inter-symbol interference, filtering, Multipath, OFDM perhaps?

[@garyquinn8014]

Yes, it's true that by using more and more amplitude/phase combinations (16QAM, 64QAM, 256QAM, etc) to encode longer and longer strings of bits, you can increase the speed of data transmission. But you should also mention the downside is that each higher level is much more likely to create errors from noise than the previous one. (The reason is clear from the constellation diagram: It's harder to know which amplitude/phase point is the correct one when a particular amplitude/phase bit is received, because the points are closer together and it's easier to make a mistake.)

[@alexrox321]

Great explanation. I love when maths gets visualised really well and that grid is one of my favourites.

[@funtechu]

Oh, it goes way further than just 256-QAM. The newest WiFi standard uses 4096-QAM. I'd recommend checking out the constellation diagram for that because it's crazy.

[@whitcwa]

QAM is how NTSC and PAL encoded color. We used vectorscopes to display the phase and amplitude variations. It was all analog. The digital modulation analyzers use constellation displays to show the grid of dots representing the possible states. Now explain COFDM.

[@SparkDragon42]

4:35 Yeah, it looks like a mess because there's multiple code word assigned to the same amplitude and phase shift

[@smolboi9659]

8:15: They are also called orthogonal cause when viewed as elements of the Inner product Space L2, the inner product of cos and sin is 0: Integral of sin(x)cos(x)dx from -pi to pi is 0.

[@Leonardqh5kp]

Wonderful explanation, wish I'd had this lecture back when I was at Uni - so much easier to understand!

[@edforthought]

Makes me miss my old job. With the right scope you can visualize the constallation plot from the tower and see how discrete the values are. Super helpful troubleshooting slow data rates.

[@markusklyver6277]

sin(x) and sin(x+pi/2) are called orthogonal because they are orthogonal in C[0, 2pi], not because their relative phase is 90 degrees.

[@MyLifeOfficial]

Just an amazing video! Thanks so much for making it, and making such complex concepts so accessible and easier to understand for a Layman like me! (Also thanks to MrRobiticBrain for the correction comment)

[@mikepembo8297]

As a network engineer who lives and breathes this, well done. Very well explained!

[@KarldorisLambley]

this video was ruddy awesome. i kinda like maths, but i LOVE radios and electronics. cheers matt

[@pastek957]

Electrical/Electronics engineering has a ton of cool math tricks and details like these to make everything work, in particular telecom Glad to see a video on that!

[@hedgehog3180]

I fell down a rabbit hole of trying to figure out how cellular networks work a while ago so this is super cool to see, I'd love more of it.

[@HomeofLawboy]

Cell communication feels to me to like black magic. I kinda get it how the transmitters and reveivers works, but how do they receive from our tiny transmitters in the cell phones, and how do they keep the connection between hundreds of devices with no overlapping, is the connection staggered, do they have a separate transmitter for each receiver Everything feels like a impossible logistics challenge

[@shrimpzilla1969]

It is absolutely black magic, but to partially answer your question there are several schemes that a communications system can use to allow multiple devices to access a wireless network at once. A simple example is called TDMA (time division multiple access) where, as the name suggests, the messages from different devices are separated in time i.e. they take turns talking. FDMA seperates devices by the frequency that they use, CDMA uses clever scrambling codes to achieve a similar effect. Googling any of these terms will give you much more detailed overviews of how they work and the maths involved. Communications engineering is an extremely deep topic but there are some great online resources.

[@vleliv11]

> I kinda get it how the transmitters and reveivers works, but how do they receive from our tiny transmitters in the cell phones, Amps and a bunch of towers > and how do they keep the connection between hundreds of devices with no overlapping, is the connection staggered, do they have a separate transmitter for each receiver short answer: Resource Blocks long answer: they split the signal into small blocks of frequency and time and dedicate them to cell-phones. > Everything feels like a impossible logistics challenge This is really a huge DSP challenge.

[@HomeofLawboy]

@@vleliv11Thanks for the breakdown, this is actually helpful

[@aes0p895]

@@HomeofLawboy you could think of it (roughly) like a whole bunch of ppl trying to communicate complex messages to a bunch of other ppl downstream river by dropping 'notes-in-a-bottle', knowing that some of them won't get recovered. intuitively, you'd want to have each bottle and message piece include some kind of header to let the recipient know who the sender and intended recipient was, as well as which bottle 'series' it belongs to, and you'd want to send enough that you know at least one of each bottle will get opened and looked at successfully. from there it's just picking up the bottles, looking at the header, and organizing them. you get rid of redundant bottles and then you're done. obviously this is a rough analogy as it doesn't really address why you'd break the packets up, but it just has to do with efficiency.

[@teelo12000]

6:53 "and if it receives one over here, it just goes to the closest one" If it drifts so far that it sends the wrong data, TCP/IP kicks in to catch the mistake and resend the packet

[@peregarauburguera]

Or maybe HARQ kicks in :)

[@DrPowerElectronics]

Brilliant explanation! Thanks. BTW I watched at 1.75x because the last video I was was watching - not one of yours- was tedious and you were so fun. So brilliant to the power 1.75! And the point about visualising maths and your demo were both wonderful and straight forward!

[@EebstertheGreat]

QAM can also be used for sending analog data. The color signal in NTSC TVs had two components, which were represented simultaneously on a single carrier wave using QAM. The main monochrome signal was unchanged from B&W TVs (called the luminance signal), while the color signal carried hue and saturation information (though not in that format). TV is now all digital of course, but cable channels (not broadcast channels) still use QAM in an unrelated way to increase throughput.

[@KnowArt]

Working on a video very much related to this! love it

[@Mikey_AK_12]

Not a filler episode! This one was quality, very interesting, nice work!

[@vsikifi]

I guess this explains why cellular phones are so efficient interference generators. For example the speakers of my computer go crazy one second before my phone rings. Those incontinuities that happen when the phase shifts contain theoretically every possible frequency, so there is always some part of the signal that matches perfectly the resonant frequency of any electronic device.

[@hedgehog3180]

I thought that stopped happening after 3G?

[@paulsengupta971]

@@hedgehog3180 Yeah, that tends to only happen on 2G.

[@jonathandawson3091]

Very amazing video. Loved it. Thank you!

[@russellking747]

Hi Matt - this is great! I actually teach this as part of a wifi course, maybe you could cover OFDM and multipath in a separate video? There is some amazing math in there, and talking about wifi 5/6/7 would give a lot of people insight! But seriously, this is the best explanation of transmission theory I've seen and you spin on it just makes it perfect!

[@duck-in-space-engineers]

I have consistently wished for captions on your videos. Not only do they permit me to understand what you're saying better, but it also allows me to listen in suboptimal environments. (This is well known with the "green needle/brainstorm" phenomenon, where if you are visually primed, you have a much better chance of understanding the audio). Captions also allow for a wider range of audiences (which I believe can include language learners). Thank you for reading this rant, I hope it does not discomfort you.

[@LotsOfS]

I believe Matt has been trying for years to get captions on his channel but KZbin, for some reason, doesn't allow it

[@JustWasted3HoursHere]

The clever ways engineers keep finding to squeeze ever more data into the signal reminds me of the extremely clever ways that engineers have been able to add data storage to mp4 streams. H266 is so much more advanced than the original MPEG stream protocol it's not even funny.

[@xriskava2151]

Oh man! I loved the digital communications coarse in uni when I took it 2 years back! Would love to see a follow-up video on the math of OFDM. A trick to have multiple frequencies very close to each other without the need for the space between them (the guard).

[@yak27_0]

Yikes, I just had a lecture on this today. We covered BPSK and only started on constellations. Yes, I did check the 'G' on cue.

[@JuulCPH]

All the way up to 256 eh? You know, WiFi 6 which was launched around 2019 already had 1024 QAM with some consumer WiFi routers supporting up to 4096 QAM (which is officially part of the WiFi 7 standard from this year). There are consumer WiFi routers supporting 4k QAM that have already been discontinued as they've since been replaced by newer models.

[@jdos2]

Oh, wow - the examples... So much bandwidth to change direction so quickly!

[@andrewsteer1562]

Yes - in the real world you normally only change the phase (or QAM state) on a timescale of many thousands of radiowave cycles :-) And often smooth the transition so there isn't too much of an abrupt jump.

[@patlawler5532]

'Constellation Diagram' is a great way to explain that mess. Including Gray code makes it a perfect way to wake up. I hope the rest of my day is as good! 👍

[@BrothersCoffee]

Great video. This is the first video I've watched on 5G and you explained it very clearly

[@paulsengupta971]

Yes and no. It was a video on QAM and we've had that since 3G.

[@aeriose]

I learned this during university and I have to say, you explained it so much better than my professor.

[@kibels894]

The math of communications is beautiful, made me consider an applied math minor when studying electronics.