Lecture 02

[Music] learn today is in this lecture one of the key 5G Technologies which is used to design 5G standard okay we will not talk about the standard for another few lectures to come but we'll start with something called this key technology and this technology is called adaptive modation and coding okay and the name tells something about the technology okay what is adaptive you can change right and the following words tell you what you can change okay modulation and coding okay this coding what is this coding is something called forward error correction coding which can basically detect and correct errors okay so why do you need to change it what are the objective what is the motivation of changing this adaptive modulation and coding that's what I'm going to briefly touch upon it okay so we saw this in the last lecture and there is a mobile phone there's a base station so the base Mobile phone is located close to the base station which essentially tells that like it will be able to it transmit some signal it will be received by the base station if it is Uplink the strength of the signal received by the base station from this user will be stronger when compared with the signal it receives from this user and the reason simple reason is that it is this mobile is located at a farther distance when compared with this mobile okay so depending upon the strength of the signal base station is a receiver mobile is a transmitter so this is which direction is this this is Uplink Direction okay so what base station can tell this user is to basically tell transmit at a high High rate when compared with this mobile okay because this signal strength is stronger how will it it can pass on the order but how will mobile do that and how do these Technologies do it okay whether it's 4G or 5G so these Technologies the standards Implement adaptive modulation and coding So based on the signal strength okay mobile can transmit at at a higher modulation order what do we mean by that that's what I'm going to show you okay so with which is basically instead of like if you're transmitting one bit per second okay you can transmit two bits per second in one unit of bandwidth okay per Hertz you can transmit two bits okay so basically you have double the data rate when compared with this user which will transmit at let's say 1 bits per second and one Hertz of bandwidth okay we'll talk about it in detail okay and this user this poor user was still further away transmit let's say .5 bits per second per Herz when Herz of bandwidth it can transmit only at5 bits per second so you see this at least this is clear that we are changing the adaptively changing the modulation basic communication like Engineers we know that if it is qpsk okay you can transmit 2 bits per second per Hertz if it is bpsk you can transmit one bits per second per Hertz okay right so this mobile will transmit at 2 bits per second per her this mobile will transmit at 1 bits per second per her so this mobile will use qpsk this mobile will use bpsk so modulation part is clear I'll show you why coding also needs to change okay and all of this the Genesis of all this comes from like one great man okay Shannon okay and what did Shannon give us Shannon told us that for a system like this so you see this I've started introducing a little bit of mathematics okay what is this is called additive white G noise Channel okay why it called additiv wide caution noise let's recapture it in 30 seconds this is X is a transmit signal which you want to transmit okay n is the noise it is called editor because it gets added white because it power spectral density is flat okay goian because it has a goian distribution okay it gets added to this where does this get added it gets added at the receiver front end and then then you receive the signal okay y x noise gets added you receive the signal y okay this is typical Communication channel one of the most common Communication channel which all our mobiles observe okay and if we Define this metric this is called SNR and what is it signal Power by noise power ratio of these Powers so p is signal power power of this Sigma Square power of noise variance of Noise Okay now if this is what you can calculate it's very easy to calculate okay so what Shannon gave us that how many bits per second per Hertz you can transmit over this channel okay the formula he gave us and what he said was you going to transmit at a rate more than this this is the SNR okay right if this is the ratio you can only transmit at this particular rate and what you can unit is bits per second per Herz in one Hertz of maget how many bits per second you can transmit and what do you need you only need this number okay and if you transmit at a rate more than this let's say this number comes at 2 bits per second per Hertz and you transmit at 3 bits per second per Hertz Shannon guaranteed that the receive signal the signal which you'll receive will not be error free you cannot decode that signal without making an and that's that's the that was the greatness of Shannon he gave us this simple formula okay and you plot this this is I vary this and I can plot it right it's a simple formula and that's what I'm going to do it for you okay so you see this x is if you see okay this is X is in is in DB okay SNR and DB and what is this SNR you take this SNR do this operation 10 log 10 you get this SNR and DB very simple okay right so you see this if SNR is 1 okay the SNR and DB will be 0 DB 10 log 10 of 1 is what log 10 of 1 is z so you get 0 DB and when is snr1 when signal power is equal to the noise power P by Sigma square is 1 right and this is there here right okay and what is happening here is so you look at this what we have done here is okay I've taken this SNR okay calculated this number log 1 plus SNR okay how do you plot this so you take the XS xais in DB okay right let's say this is z DB okay correct put write zero over here move it over here you get SNR in linear scale right so SN in linear scale will be one right and if you do that like you put that the 10 log 10 of 1 plus that formula you'll get this number right so what is it telling here is that if this is the SNR okay you can only transmit at this many bits per second per Herz let's read these numbers okay what is happening here and capacity of 4 bits per second per Hertz where can you achieve you can achieve at a SNR of approximately 12 DB this is you drop here right what am I doing here I'm taking this four and I'm dropping this here I'm seeing how much of SNR is required the 12 DB okay so what does this mean okay what this 4 bit for bits per second per her means okay 5G system just for example have a bandwidth of 100 MHz okay so for a bandwidth of 100 MHz how much B rate can you achieve 4 into this is per Herz okay so how many hers it will have 10 Power 8 Herz right okay so 4 into 10^ 8 that is 400 MVPs fine and so if you transmit at this 400 MVPs and as Shannon said that you will not make an error if you transmit at this rate if you transmit at any rate higher than this you'll make errors receiver will not be able to decode it without error but if you transmit at this you can decode it without error okay so you know that if the SNR is this much okay you can transmit at this particular rate okay capacity of 2 bits per second another example where is it coming five right 5 DB of SNR okay so for a 5 G bandwidth of 100 MHz so bit how much bit rate you can achieve 200 MVPs with zero error right now what is this telling that if You observe an SNR of 12 DB right you can transmit at a bit rate of 400 MVPs You observe an SNR of 5 DB you can only transmit at a bit rate of 200 MVPs okay bit rate can adaptively change based on the kind of SNR where what the user of the Mobile station is observing right and that was the motivation when will this a user observe higher SNR when it is located close to the receiver right that's the picture I showed you okay and when it is farther away it'll observe a lower SNR why higher SNR because SNR what is SNR ratio of signal by Noise Okay so the signal receive signal power is high SNR is high right it is as simple as that okay so how can this be achieved right okay Shannon has told us that this is guaranteed okay how do you achieve this in practice that's left to the implementation Eng genius okay people like us right who can not think of these formulas can at least try to implement this in practice okay so and that's where this comes this AMC short adaptive modulation and coding it helps us in achieving this capacity using these discrete constellations or the modulation format okay and what are this discrete formats we write it in terms of mqam okay it is basically quadrature amplitude modulations Okay so if it is 2 quam what is this other name is BPS 4 quam qpsk 16 quam 16 quam 64 is 256 okay right and what is happening if it is just to like recapture whatever we have learned in earlier classes if it is 2 cam how many bits per second per her we can transmit it's bpsk only one right if it is 4 quam how many bits per second per Hertz we can transmit 2 4 6 8 fine so what did we just see SNR is 5 DB right you have to transmit at 2 bits per second per Hertz which discrete constellation will help us in achieving that four qu correct so a user which is like observing this as scenar will use for quam qpsk if it is observing an SNR of 12 DB 4 bits per second per Hertz what modation scheme it will use 16 right okay so what is happening as the user is located is moving closer to the base station or to the receiver okay it will adaptively switch this modulation order but as far other away it'll use four quam if it is closer and it observes this SNR it will use 16 quam okay so this AMC adaptive modulation part is clear that user can switch these modation schemes adaptively based on the SNR it is observing okay so that's the idea very simple so then that's why I put this in red idea of switching this modulation according to SNR is called adaptive modulation okay right I just give you two example like 16 quam 4 quam and what points did we achieve using these two points 5 DB and 12 DB right but there are other points on this curve correct for example when SNR is 2.5 DB right okay the capacity is approximately 1.5 bits per second per Hertz you know that bpsk is going to give you 1 bit per second per Hertz qpsk is is going to give you 2 bits per second per Hertz right how do you achieve that that's where this coding part comes into picture okay that's a motivation another way of looking at it also okay that it helps in reducing the error that also we'll see okay so all the points on capacity curves are achieved using adap modulation and coding and what is this coding this is called error control coding and 5G systems do that so because it has to achieve all the points on this capacity curve okay see this is the best you can do you cannot operate at a rate higher than this or the capacity at a rate higher than this okay right if this is the SNR 15 DB you have to operate at 5 bits per second per Hertz you cannot operate at 5.1 bits per second per Herz right so all the systems these are the best system you need to design okay and you don't want to compromise on the the best part of it and what is the best here that the system you design should be able to achieve the capacity okay and this AMC helps you in achieving that and so as I said that in order to achieve all these points on the capacity curve you need this adaptive modation and coding okay so all the Cellular Systems inherently use coding okay there's no cellular system without error control coding okay that's one thing you have to always remember fine okay just to introduce you to this idea of using this FEC is implemented in these systems okay so uh this is the capacity achieving transceiver architecture transceiver is transmitter plus receiver okay and what is happening here is some of some part of this is already known to us right we just saw adaptive modulation modulator Channel demodulator okay a quam modulator you should have a quam demodulator also okay I have not taught you how to demodulate for quam that we'll see okay but this is a receiver part that it should be whatever modulation you are doing you should do the inverse operation of this so we saw this part just now correct okay and what I showing you here is this additional block this FC encoder okay this FC encoder and the opposite of that is this FC decoder okay so I'll spend 5 minutes talking about it now okay you can do a full one semester course on developing these and understanding this FC and codes and decoders okay there is not a course on FC encoding we'll use these Technologies to build a standard okay so we'll only pick up whatever is required for us to understand this 5G standard okay so today some basic ideas of this FC and what is this so what this FC encoder does is okay it takes in the data which you want to transmit okay these are the raw bits the output of that what it'll do is it'll basically append some okay so what it does it append some parity bits okay to this input message what is this this is like you call this as input message it calculates some parity bits based on this input message and the output of it will be this message bit plus this parity bits okay which are calculated based on this input bits understand okay and it calculates this input bits okay to basically one objective is to reduce the block error rate remember Shannon told that you can achieve this error of zero how is it achieved this fellow helps us in achieving that okay and what is this metric it's called block error rate let's say you transmit you always transmit data in blocks okay take one chunk of data encode it modulate it demodulate it and decode it if that data is received error free so the that block is error free let's say you transmitted 10 blocks of data you received nine blocks error free one block in error so the block error rate will be 1 out of 10 so that is a block error rate of 0.1 you want block error rate of depending on applications you want different block error rates we spoke about 5G being designed for different applications okay video applications work with the block error rate of 10 minus 1 okay URC applications work at blockr rate of 10us 3 okay so once out of th000 blocks can only be error okay so 5G should be designed for that you see the difference how is it coming okay now this is the notion of block error rate okay and how is this so This Is blr Now what is this encoder okay encodes at a particular rate okay and what is this rate number of input bits divided by the number of output bit okay let's say you just for an example you took three bits and FC encoder added one parity bit to that so output will be 4 bits so what will be the rate of this encoder will be 3x 4 three input bits and output is four so that right okay okay so rate is 3x4 what am I saying here rate is always less than one correct okay it can go very close to one let's say you took 999 bits and appended only one bit what will be the rate of that 999 by 1,000 okay right so that the rate is .99 okay so we understand this the rate is less than always less than one okay and another feature of this FC and cod is that it should use large code block length to guarantee a lock low block error rate okay so if you take only 10 bits and append some two par bits it cannot guarantee you a block error rate of 10 minus one that's what Shannon also said okay we not going to the details of this but it should be like large code block length if you take only few bits you are not guaranteed to have a this low block error rate okay so this is idea this is a capacity achieving architecture okay right now how is it used and how how will it enable us in achieving all the points on the capacity curve that was the motivation for us to understand this right okay to bring in this it helps us in achieving block error rate reduces the block error rate also okay so this is what we saw if the SNR is 2.5 DB right capacity is 1.5 bits per second per Hertz you cannot use bpsk you cannot use qpsk bpsk 1 bits per second per Herz qpsk 2 bits per second per Hertz okay so what how can you achieve this point okay one way to do here is what am I doing here you'll use four quam but how many bits you are transmitting 2 bits per second per her you know that you cannot transmit because you will not receive that is error free what are you doing what is happening here what I what will I do here is okay I will encode these two bits with a code rate of 3x 4 okay right what'll happen here the Cod rate of 3x 4 okay so for every three input bits I'm appending one parity bit right okay correct so now if I want to transmit two bits or like four bits okay correct so if I let's say I want to transl four bits if I use four quam correct how many symbols I'll transmit two symbols because each quam symbol can transmit two bits right okay correct is this clear okay now how is this happening okay so what will I do here is I'll not transmit four message bits okay I'll take three message bits fine okay then I'll add one parity bit to it what will the rate become rate will become 3x4 go back here 3 bits right you took this and then you encoded it using you got four bits now you are encoding it using you are modulating it using four qu so what is happening here this is your you have three bits you got four bits you're transmitting it using four qu you're transmitting this is two bits per second per Hertz correct but how many bits actual message bits are there three message bits okay so if what will happen here so 3x 4 this is 3x4 okay you're transmitting two bits in each symbol okay so the effective rate at which you are transmitting okay in those four bits how many message bits are there three so your effective rate will be 3x 4 because that's what is happening and you are transmitting using 2 bits per second per Hertz so what happens 3x 4 into two how many bits per second per her you are transmitting 1.5 okay so what is happening you like instead of if you did not have this FC encoder correct you'll take in two bits you right transmit using you'll take in four bits and transmit it using quam you are transmitting at two bits per second per Hertz you cannot do that so what have you done instead of transmitting four message bits you have taken only three message bits added one par bit to it okay right so effectively instead of what you have reduced the rate right from 2 bits per second per Hertz to 1.5 bits per second per Hertz 3x 4 into 2 right okay so now what happens so one example okay another example if the SNR is 15 DB it is the capacity is actually 5 bits per second per Hertz correct okay how will you do that you know that if you transmit at 64 quam what happen you'll transmit at 6 bits per second per Hertz you cannot do that what is the code rate you going to use you want to transmit at 5 bits per second per Hertz so what will what is this will transmit at six you'll use a Cod rate of 5x 6 what will this Cod rate do it'll take in five message bits and add one parity bit to it so the Cod rate is 5X 6 you're transmitting these six bits in one Hertz right correct so the code rate becomes capacity becomes 5 bits per second per Hertz right okay here what are you doing you're using 2 bits per second per Hertz but encoding it using 3x4 so the effective is 1.5 similarly here correct so I can achieve okay you can do this homework I can achieve any point on this capacity curve I took two examples okay 1.55 okay which was not possible using normal modulation scheme okay right so this is the idea of adaptive modation and coding okay I can achieve any point right you give me any number 7 bits per second per Hertz right what will I do I can similarly calculate this okay right I can modulation and coding scheme I can calculate I can transmit at 7 bits per second per Herz if it is 8 bits per per that's like 256 correct so you will what will you do okay you will right if you have to transmit at 7 you'll take 256 quam you will transmit at a rate of 7 by 8 right okay correct that's so any point on this curve you are able to achieve now how it is implemented in 5G that's what I want to show you okay I'll take up this example and then this is how I'll tell you this okay so the way this is calculated I'll have to write it here okay you look at this so what is this this modulation order you see this let's how do you read this table this is called MCS okay modulation and coding scheme as I said adaptive modulation and coding so what changes here is modulation and coding scheme so you read this what is happening here there is a table which is defined in the standard okay what is this row telling this is modulation order of this is the index okay look at this modulation order order is two which essentially means it is qpsk order means is how many bits per Herz you can per second per Herz you can transmit if it is two bits what modation scheme it is QPS similarly this look at this 16 64 okay another table Define it for 256 also okay now look at this index modulation order is two this is how is it defined what is this target code rate of 1024 into R okay what does that mean what is it telling you this is the way it is specified 1024 into R is this number 120 that's the number given here look at this right okay so what is this what is the rate this is basically the rate that's what 120 by okay right here it is called spectral efficiency you can call this as capacity okay what is the modulation order two 2 bits per second right okay this is the number which is given here okay and what is it telling this is .23 okay what is this you go back right it is this number is somewhere here it helps in achieving this point on the capacity curve okay right and at what SNR you know some SNR right okay similarly all these points look at this what is this modulation order is four okay and the rate is 340 by 1024 that's what that's how you have to read it 1024 into R is this number 340 that's correct okay so rate is this right what will the spectral efficiency or capacity in whatever we have understood okay into so the capacity will become R into 4 that's the number which is given here it achieves this MCS index helps in achieving this point on the capacity curve right so this table is defined in the standard okay and what happens is let's say if it is a down link okay right so UE will measure the SNR okay because we know that where is this number coming from log 1 plus SNR right it measures it its SNR and then what it does log 1 plus SNR it'll come up with one of these numbers any of these number depending on the SNR it is OB surve right and instead of reporting the SNR it will tell the base station that please transmit to me at this particular MCS right so this information has to be sent by the user to the base station and base station will accordingly transmit that this particular MCS this MCS MCS 17 basically what is it telling it is modulation order of six and coding scheme of coding rate of this right whatever this is the code 658 by 1024 right okay you see this how this how a capacity achieving system is being built on the simple principles of adap modation and coding right okay that def find this table both the this table is known to the mobile as well as to the base station what mobile senses only this index base station knows that this is a modation scheme and this is the coding rate at which this user data needs to be encoded so this is the basic idea of adaptive modulation and coding okay then I'll take five more minutes I'll uh so and what is the coding scheme what this the standard uses okay this is ldpc codes okay and they are called capacity achieving code why are they called capacity achieving code I'll just show you this okay you look at this okay that we see what are this I've given you this plots these are BL plot and this is the SNR okay right so what is happening here is let's read this plot carefully okay now this is the SNR of minus5 DP and look at this okay what what is this telling that this is the S mcs2 basically tells about a particular rate right that's what the particular capacity we just saw that okay right so this MCS okay can be supported at a minimum SNR of this okay right what am i showing here is what is this minimum SNR and what is the of this minimum snrs right if you look at the capacity curve okay this mcs2 which has a rate of let's go back mcs2 has this rate 3770 okay right we know that at what SNR this can be supported right that is what Shannon has told that's the capacity curve okay and this is the SNR let's say it is - 6 okay now what this ldpc code is able to achieve this BL is instead of minus 6 DB it pays a penalty of 1 DB okay it is able to achieve at a slightly higher SNR of minus 5 DP okay do you get this idea that instead of Channel told us that you can achieve this at Min - 6 DB this MCS but what ldpc is able to achieve it as- 5 DB a slightly higher but it is as close as it can be possible to the capacity curve okay so there's an offset of 1 DB there a degradation of 1 DB okay similarly you look at this another any okay right so this is let's say at around this is 16 okay DB of SNR MCS 26 particular rate can be achieved but ldpc is able to achieve it at a 17 DB of SNR 1 DB of penalty it is as close as it can get to be to the capacity curve given by Shannon okay are we able to digest this right that ldpc guarantees you that you can operate as close as possible to the capacity curve right and but with an offset of let's say few DBS okay right so this is BL curve for ldpc and the code the block rate of 6,000 okay so what is why am saying giving you this number n is equal to 6,000 is a practical number okay then you transmit blocks of 6,000 bits okay so why is the capacity achieving for reasons I just explained it to you that it gives you these points on the capacity curve with a margin of few DBS okay One DB I just showed it to you okay right so if you put everything together what is happening this is a capacity curve given to us by Shannon right okay and what is ldpc doing okay so you should be able to support this MCS 26 at this particular SNR right correct and let's say 15 DB okay but where is it supporting it is supporting at somewhere here this is the offset correct okay so what is happening here inside of this curve you able to achieve this curve right slight margins are there that's all correct okay instead of achieving this go you are able to achieve this so why it is called capacity achieving because it is getting very close to the capacity okay before this ldpc and the other code which was used in 4G the turbo code the curves were something like this huge margins 7 DV offset 8 DV offset from the capacity curve okay with the codes which were used in 2G 3G systems okay you could not operate close to the capacity and turbo and these ldpc codes change the game okay and they are inherently used in all the cellular standards as I said earlier the uncoded Cellular Systems do not exist okay and you can be as close as possible to the capacity okay [Music] [Music] [Music]