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

this is a 5G phone tower and I'm going to explain  why 5G data is so incredibly fast and I'm going   to explain what 5G actually [Music] means I mean  that bit's easy uh the five means fifth generation   that's what the capital g means generation so all  these things 4G 3G Etc it's just the generation   we're up to the capital G is meaningless it's  about as important as the capital G in the   video ID on this video what I care about is the  fact that this Tower behind me is putting out   well photons it's putting out radio waves and  that's just a standard kind of sine wave but   somehow we're able to encode data at incredible  rates into just waves well how is that done okay   spoiler it's Mass it's always Mass it's actually  trigonometry in this case and bonus spoiler I'm   currently writing my next book and I think this  is technically the official announcement of that   it's why I've got writing a book face uh I'll  have a link to pre-orders in the description   more details about that at the end of the video  Welcome Back everyone who went to check the video   ID to make sure it did have a capital G of course  it does so we're now going to have a closer look   at these waves because if you've got a sine wave  there's three things you can vary you can mess   around with the frequency you can mess around with  the amplitude that's kind of how big it is and you   can mess around with the phase that's where it  starts and we're going to ignore frequency and   amplitude and we're going to focus in on messing  with the phase because we can use that to encode   binary data all right give me a wave there it is  right so this is our signal wave that's what's   being sent by the phone tower and we're going  to split it up into individual wavelengths and   we're going to send one bit of information per  wavelength and by bit I mean a one or a zero   they're currently all set to one but what we can  do is decide if we're going to send a zero so we   switch that one to a zero it flips the wave the  other way up and so what you do now is you take   your message of ones and zeros you have the ones  and zeros across the top and you flip the wave   each way depending if it's a one or it's a zero  I say flip it's a sine wave what you're actually   doing is moving it across half a wavelength so  we've actually got some bits of the wave are   unchanged those are the ones and some are offset  by a phase of half a wavelength and those are the   zeros we call this key of information by Shifting  the phase phas shift keying in this case binary   phase shift keying because we're only sending ones  or zeros but what if we had different amounts of   shift what if we wanted to send up to four options  quadrature phase shift key we're going to switch   each of these now to be either z01 1 011 but now  we need four different phase shifts so what we're   going to do is have them each a quarter of a  wavelength apart and this works this is how   phones way back in the day when there were so few  G's used to send data but now we've got more G's   we want to send more data so we need to be able  to have more different phase offsets and you're   right we could just split each wavelength up into  more and more different offsets but what if we did   bring back our friendly amplitude but what if  we bring in some more options so yeah I'm just   I'm inside a giant Georgia profile by the way and  now for each of our code words that's what we call   just each string of ones and zeros we want to send  for each code word we can assign different amounts   of phase change and amplitude change and if we  mess around with these you can see the things   we're sending change and yeah well hang on surely  there's a really clever way to adjust the phase   and amplitude for each code word to make them more  efficient to send and maybe if we pick just the   right values we can have more than four we can go  up to 16 wouldn't that be amazing but there would   have to be some very clever values and probably  that form of encoding would have a whole different   name quam of course someone's worked out how to do  more it's quam quadrature amplitude modulation and   you can do this with different numbers of code  words here's the case for 16 code words this is   called 16 quam so we got four bit code words now  and these are the various amplitudes and phases   you need to send those and people very carefully  worked out exact what combinations of amplitude   and phase work the most efficiently but if you  look at it it looks like a mess and this is where   we need a better way to kind of think about and  visualize these phases and amplitudes here I am   with the geile I've got a single wavelength that's  what we were using to encode each code word and we   were shifting at different amounts for each code  word and as you can see it's a sine wave so it   goes from 0 to 360° that's when it's it starts  repeating so in fact we can measure the amount   of shift the change in Phase as an angle and you  know what else you can measure with angles angles   so on the side over here I've got a that I can  move around as I change the angle a is making   to the positive x axis it changes the phase so  whatever angle goes up to a is how far we've moved   the sine wave and so before we were encoding uh  one we were doing one bit there and then at 180°   over here we were doing the other bit in fact I  can turn uh that on so we can see it so there's   we encode a one there we encode a zero there but  you can also see that now amplitude is built in   if I move this closer to the origin the wave gets  smaller further away it gets bigger we can encode   more data points which is why when we were doing  for code words we had them like weirdly spaced out   with 45° well actually 90° between each pair cuz  what we had here is uh code with 0 Z's up there   and then 0 1's down there and then 1 Zer and 1 one  now these are technically all on a circle they've   all got exactly the same magnitude and what  we started to discuss was could we have other   points where we're changing the both the phases  an angle and the magnitude is the distance from   the origin to encode different words and you can  the 16 I showed you before here is 16 quam and   look at them they form a grid how incredibly  cool is that so if you want to send 11 one0   that's the phase and amplitude you send there's  0111 and so on so you can pick all of these out   because they're spaced out if there's any you  know wavering in the signal when it's received   by a device like if it receives one over here it  just goes to the closest one it's like that the   code word and so by plotting these on a phase  amplitude diagram it makes the arrangement so   obvious suddenly we can see all the logic behind  why we have those phases and amplitudes and we   call this a constellation plot check it out 64  quam isn't that amazing it actually goes all the   way up to 256 quam which I'm not going to draw  here you know what it looks like it's a lot of   dots on a grid and this is why 5G is so fast  it's using quam it can still use the old face   shift keying it's backwards compatible in that  regard although it doesn't in quite a clever way   different video but quam is the secret to being  able to send so much data so fast just using sine   waves although I may have mildly distracted  us with the constellation diagrams I mean I   love them because it's one of those fantastic  examples in mathematics where just having the   right way to visualize or to kind of think about  something suddenly makes it make sense and the   constellation diagrams are so incredibly useful  but we started by looking at adjusting phasee   and I had said we're going to ignore amplitude  and we gradually brought amplitude back in again   however it turns out phase almost a distraction  it's actually all about the amplitude it's all   about orthogonal amplitudes here I have two sine  waves which are 90° out of phase and that's why   we call them orthogonal waves if you just look at  the waves you're like how is that orthogonal well   what do we call things that are 90° apart they're  perpendicular so which is why this level of phase   difference is called orthogonal waves and you can  see on the phase diagram over here why that's the   case cuz a the phase is zero and then B is up  here and of course we can move them around as   always but if we plant them on zero and 90 and  we only change the amplitude we can actually   get every conceivable other combination of phase  and amplitude by adding those two together so if   I turn on the sum of those those two waves in  green and now all I do is adjust the amplitude   of a and b so if I bring amplitude of a down and  up if I just mess with these I can actually get   that Green Wave to become any wave I want and we  have to use negative amplitude is like phase the   other way around totally counts so by using  positive and combinations of these two waves   which are orthogonal to each other 90° apart we  can generate any wave and this is how quam is   actually encoded you're actually just using the  X and Y coordinates of each of the points you put   one of those into each of these waves which is  a sine wave and a COS wave you add them together   and that's what gets transmitted from the tower  and now for the final bit of plot it's this plot   so this is our 16 quam arrangement of the code  words when I first saw this I was like why are   they arranged like that so I looked into it and  and they're using something called a gray code   and a gray code is a way you can go from any  code word to any other code word and you only   ever change one bit at a time and they're arrange  such that all of those gray code Transformations   never go through the origin because if you're  sending one signal you got to move continuously   to another one and if it goes through the origin  that's zero amplitude that's no signal you don't   want no you don't want a sudden loss of signal  just cuz you're switching code words and so by   using this Arrangement or other equivalent ones  and only using gray code Transformations one   bit at a time you can change the code word you're  sending without going through the origin another   very clever bit of geometry which reminds me I  think I'm writing I am I'm writing a book all   about geometry trigonometry data Foria it's  incredible you should absolutely check it out   and thank you so much for watching this video uh  you can also watch that video uh that that's what   Google thinks you should watch that's not on me  whatever that is that's up to you uh up there you   can subscribe I don't know uh we'll put a link  in the description down there somewhere you can   pre-order the book uh they're hugely appreciated  yeah there you go uh I guess we got a bit more

Channel: Stand-up Maths

Views: 578,814

Keywords: maths, math, mathematics, comedy, stand-up

Id: To7Ll5AGboI

Length: 11min 17sec (677 seconds)

Published: Thu Feb 29 2024