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

Summary

The video script delves into the intricacies of 5G technology, explaining how 5G data is incredibly fast. It begins by clarifying that '5G' stands for 'fifth generation,' emphasizing that the 'G' is a generational marker. The presenter then explores how radio waves, or photons, are used to encode data at high rates, focusing on phase manipulation to encode binary data. The concept of phase shift keying (PSK) is introduced, where data is encoded by shifting the phase of the wave. The video progresses to discuss quadrature phase shift keying (QPSK), which allows for more data to be sent by using four different phase shifts. The presenter also touches on higher-order modulation schemes like 16-QAM and 64-QAM, which increase the number of code words and thus the data transmission rate. The script highlights the use of constellation plots to visualize these complex phase and amplitude combinations, making the encoding process more understandable. The video concludes by explaining the importance of orthogonal amplitude modulation (OFDM) and the use of Gray codes to transition between code words without signal loss, underlining the clever geometric and trigonometric principles that enable 5G's high-speed data transmission.

Takeaways

• 📱 The 'G' in 5G stands for 'generation', indicating it's the fifth generation of mobile networks.
• 🌐 5G data is incredibly fast due to advanced encoding techniques that pack more information into radio waves.
• 📶 5G uses radio waves, which are sine waves, to transmit data by manipulating their phase and amplitude.
• 🔀 Phase Shift Keying (PSK) is a method where the phase of the wave is changed to represent binary data (1s and 0s).
• 📈 Quadrature Phase Shift Keying (QPSK) allows for more phase shifts, thereby increasing the amount of data that can be sent.
• 🔢 Higher order QAM (Quadrature Amplitude Modulation) increases the number of code words and thus the data transmission rate.
• 📊 A constellation plot is a graphical representation used to visualize the phase and amplitude of the signal, making it easier to understand the encoding process.
• 🔄 Orthogonality in signal waves allows for the creation of various combinations of phase and amplitude by combining two waves that are 90° out of phase.
• 🔗 Gray code is a binary numbering system where two successive values differ in only one bit, which is used to avoid signal loss during transitions between code words.
• 📚 The video's creator is writing a book about geometry, trigonometry, and data, which will delve deeper into these topics.
• 🔗 The video provides a link for pre-orders of the upcoming book in the description for those interested in learning more about these subjects.

Q & A

What does '5G' stand for in the context of mobile networks?

5G stands for 'fifth generation', which refers to the latest generation of mobile networks, succeeding 4G and earlier generations.

How is data encoded into radio waves for transmission in 5G networks?

Data is encoded into radio waves using techniques like phase shift keying (PSK) and quadrature amplitude modulation (QAM), which involve varying the phase and amplitude of the waves to represent binary data.

What is the significance of the phase in encoding binary data in 5G technology?

The phase is significant as it allows for the encoding of binary data (ones and zeros) by shifting the wave pattern. A change in phase, such as a half-wavelength shift, can represent a bit flip from a one to a zero.

How does the concept of QAM contribute to the high speed of 5G data?

QAM contributes to the high speed of 5G by allowing for the transmission of more bits of data per wave cycle. It does this by varying both the amplitude and phase of the signal, enabling multiple combinations that represent more complex data patterns.

What is a 'constellation plot' in the context of QAM?

A constellation plot is a graphical representation used in digital communications that illustrates the mapping of signal points to the amplitude and phase of a modulated wave. It helps visualize the arrangement of signal points in a QAM system.

Why is the term 'orthogonal' used to describe certain waves in QAM?

The term 'orthogonal' is used because certain waves that are 90 degrees out of phase with each other are perpendicular in the context of their phase relationship. This property allows them to be combined to create any desired phase and amplitude for signal transmission.

What is the purpose of using a Gray code in the arrangement of QAM signal points?

Gray code is used to ensure that adjacent signal points in a QAM system differ by only one bit. This minimizes the potential for error when transitioning between signal points and prevents the signal from passing through a state of zero amplitude.

How does the author suggest the use of trigonometry in understanding the encoding of data in 5G technology?

The author suggests that trigonometry plays a crucial role in understanding how data is encoded onto sine waves through phase and amplitude adjustments, and how these adjustments are visualized and calculated in the context of QAM.

What is the role of amplitude in encoding data with QAM?

Amplitude plays a role in encoding data by allowing different levels of signal strength to represent different bits of information. By combining changes in amplitude with phase shifts, QAM can represent multiple bits per signal cycle.

How does the author describe the evolution from binary phase shift keying (BPSK) to higher levels of QAM?

The author describes the evolution as an increase in the number of phase and amplitude combinations, allowing for the encoding of more bits of information per signal cycle. This progression from BPSK to higher QAM levels is what enables 5G to achieve higher data transmission speeds.

What is the significance of the author's upcoming book in relation to the content of the video?

The author's upcoming book is significant as it is focused on the same themes of geometry, trigonometry, and data transmission that are central to the video's explanation of 5G technology. The book promises to delve deeper into these concepts.

How does the video script help in visualizing complex concepts like QAM?

The video script uses the concept of constellation plots and the geometric arrangement of signal points to visualize the complex encoding schemes used in QAM. This visualization helps make the abstract mathematical concepts more tangible and understandable.

Outlines

00:00

📱 Understanding 5G Technology

The first paragraph introduces the concept of 5G as the fifth generation of cellular technology. The speaker explains that the 'G' stands for generation and emphasizes the importance of radio waves in transmitting data. The explanation delves into the encoding of data through phase shifts in these waves, which is a fundamental principle behind the high-speed data transfer in 5G networks. The paragraph also hints at the speaker's next book, which will presumably explore these topics in more depth.

05:03

🌀 Phase Shift Keying and Quadrature Amplitude Modulation

This paragraph delves into the technicalities of how data is encoded onto sine waves for transmission. The focus is on phase shift keying (PSK) and quadrature amplitude modulation (QAM). The speaker explains binary phase shift keying (BPSK) and how it evolves into quadrature phase shift keying (QPSK) and then into higher-order QAM, which allows for more efficient data transmission by varying both the phase and amplitude of the waves. The use of constellation plots is introduced as a way to visualize the different combinations of phase and amplitude, which are crucial for the high-speed capabilities of 5G.

10:07

🔍 The Geometry of 5G Signaling

The final paragraph discusses the geometric aspects of 5G signaling, particularly the use of orthogonal amplitudes and the gray code. The speaker explains how two sine waves that are 90° out of phase can be combined to create any conceivable wave, forming the basis of QAM. The paragraph also touches on the practical implementation of these principles in 5G technology, including the use of gray codes to transition between signal states without a loss of signal. The speaker concludes by teasing their upcoming book, which will cover these topics in greater detail.

Keywords

💡5G

5G stands for the fifth generation of mobile networks. It is characterized by its high speed and the ability to handle more data and more devices at once compared to previous generations. In the video, the presenter explains that 5G's fast data speeds are achieved through advanced encoding techniques, which is the main theme of the video.

💡Radio Waves

Radio waves are a type of electromagnetic radiation with longer wavelengths than visible light. They are used in telecommunications to transmit data. In the context of the video, radio waves are the medium through which 5G data is sent, with the presenter discussing how data is encoded onto these waves to achieve high data transfer rates.

💡Phase Shift Keying (PSK)

Phase Shift Keying is a method of encoding digital signal by changing, or modulating, the phase of the carrier wave. In the video, the presenter uses Binary Phase Shift Keying (BPSK) as an example to illustrate how flipping the phase of a wave can represent binary data (1s and 0s).

💡Quadrature Amplitude Modulation (QAM)

QAM is a modulation method that conveys digital data as changes to the amplitude and/or the phase of the carrier wave. The video explains that higher order QAM, such as 16-QAM or 64-QAM, allows for more bits to be sent per symbol, thus increasing the data rate. This is a key technology behind the high speeds of 5G.

💡Constellation Diagram

A constellation diagram is a graphical representation used in digital communications to illustrate the mapping of digital data to the amplitude and phase of a carrier wave. In the video, the presenter uses constellation diagrams to visualize and explain how different combinations of amplitude and phase represent different bits of data in QAM.

💡Orthogonality

Orthogonality in the context of the video refers to the property of two waves being 90 degrees out of phase with each other, allowing them to be combined to create a variety of different phase and amplitude combinations. This concept is fundamental to Quadrature Amplitude Modulation (QAM), where orthogonal waves are used to transmit data efficiently.

💡Gray Code

Gray code is a binary numbering system where two successive values differ in only one bit. The video discusses how Gray codes are used in QAM to ensure that when switching between code words, the transition is smooth and does not go through a state that represents no signal (zero amplitude), which would cause a loss of data.

💡Trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. In the video, the presenter mentions that trigonometry is used to calculate the phase shifts and amplitudes of the waves, which is essential for encoding data in 5G transmissions.

💡Sine Wave

A sine wave is a continuous wave that oscillates about a central value, typically representing a smooth, periodic oscillation. The video explains that data in 5G is encoded onto sine waves by altering their phase and amplitude, and these sine waves are then transmitted via radio waves.

💡Backwards Compatibility

Backwards compatibility refers to a design feature that allows a system to work with older versions or technologies. The video mentions that 5G is designed to be backwards compatible, meaning it can still use older encoding methods like Phase Shift Keying while also supporting newer, faster methods like QAM.

💡Data Encoding

Data encoding is the process of converting data into a specific format for efficient transmission or storage. In the context of the video, the presenter discusses various methods of data encoding used in 5G, such as PSK and QAM, which allow for the fast and efficient transmission of data over radio waves.

Highlights

5G is the fifth generation of mobile networks, offering incredibly fast data speeds.

The speed of 5G data is achieved through advanced encoding of radio waves using trigonometry.

The video explains the concept of phase shift keying, where data is encoded by altering the phase of a sine wave.

Binary phase shift keying (BPSK) is used to send binary data (ones and zeros) by flipping the wave.

Quadrature phase shift keying (QPSK) allows for four different phase shifts, doubling the data transmission rate.

16-QAM (Quadrature Amplitude Modulation) increases the data rate by using a combination of phase and amplitude changes.

64-QAM and 256-QAM are higher levels of modulation that further increase the amount of data that can be transmitted.

Constellation plots are used to visualize the phase and amplitude combinations used in QAM, making the encoding logic clear.

Orthogonal amplitudes are key to QAM, using two sine waves that are 90° out of phase to create any combination of phase and amplitude.

Gray code is used in QAM to transition between code words by changing only one bit at a time, avoiding signal loss.

The video also serves as an announcement for the creator's upcoming book on geometry, trigonometry, and data.

The creator emphasizes the importance of the right visualization in understanding complex mathematical concepts like QAM.

5G technology is backwards compatible, retaining the ability to use older phase shift keying methods.

The video provides a detailed explanation of how 5G uses sine and cosine waves to transmit data efficiently.

The use of positive and negative amplitudes in orthogonal waves allows for a wide range of phase and amplitude combinations.

The arrangement of code words in QAM is optimized to ensure smooth transitions between different signals without loss.

The video concludes by encouraging viewers to subscribe and pre-order the upcoming book for more insights into geometry and data.

Transcripts

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