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

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

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.

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!

Good old QAM, I love their song Qareless Qisper.

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

"QAM!!" is my new favorite exclamation!

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.

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.

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

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

This better be about quadrature amplitude modulation

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.

. Yup I checked.

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!

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.

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.

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.

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.

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.

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!

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.

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°.

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 😊

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.

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

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.

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.

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.

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 😮

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

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

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

So how many reuploads did it take?

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

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

Matt is using 5g to infect my brain with maths

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

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?

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.

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

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

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!

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

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

It says the UK release is "6/20"?? That isn't a date??!

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

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 😺💜🎉💖🎉😺😻

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

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

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

You, sir, just blew my mind. I subscribed. Please. More.

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

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!

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.

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

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 KZfaq about it are pretty dry lectures.

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.

The more finely we manipulate physical phenomenon to transfer data, the more I think, "Thank goodness for error correction". Every part of this technology is amazing!

Huge fan of this video, had a class on this in uni just on the last year and i love seeing my studies explained by youtubers i love :^)

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

Congratulations and good luck with your next book. I've just finished my first book. I'm so inspired now, I think I'll read another one (-:

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!

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.

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.

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.

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

Hi Matt! Love your videos.

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

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!

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.

The funny thing is that i literally just took an exam on Data Communications yesterday...

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.

You absolute madman xD Thanks for actually going through the effort with the video ID xD

4 years of Electronics and Communication Engineering

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!

as an audio engineer, this is super fascinating and much more comprehensive than i initially thought it would be

Brilliantly explained, thank you!

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

The real magic using math is in encoding and decoding COFDM. Thousands of orthogonal carriers each with QAM generated with an IFFT! Just fantastic. See the BBC paper "The how and why of COFDM" by J.H. Stott

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

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.

Thanks for this video!

Yay new book! Your first two were a great read. Humble Pi was amazing, I even referenced it yesterday😊 (the Boeing programming mistake)

1:07 I came here to watch some maths and all I can think of is: stubble! I much prefer the previous look!

Great length of video. Tight and clear

Brilliant! Thank you!

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

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

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.

8:14 surprise Fourier! (ok, not really a surprise considering the math up to that point)

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

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

"Which shot should we use to show Matt next to the dynamic graph?" "Been a while since we used the drone huh?" At least, that's how I imagine it went.

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).

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.

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.

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.

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!

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!