Lecture 12: Multiplexing

hello and welcome to lecture 12. this is our final lecture where we'll be looking at multiplexing so in our last two lectures we looked at digital modulation we looked at digital baseband modulation which was the same as pulse modulation we talked about digital band pass modulation which is carrier based wireless communication in our final lecture we want to say a few words about multiplexing so this is a really short lecture it shouldn't be more than around 20 minutes now all of these lectures starting from lecture 7 until this lecture 12 these are included in the class test on the 12th of may so quick recap in lecture 11 we spoke to we spoke about digital band pass modulation that's basically amplitude modulation frequency modulation and phase modulation we spoke about how to generate it how to detect it and a little bit about what the frequency domain representation looks like we spoke about different variants of these we said really in essence it's just the same as am fm and pm that we're familiar with the only difference is that the information instead of being an analog signal it's a line code generated from a digital signal now before we start today's lecture about multiplexing just a few words about the class test so a few things you need to know number one it's worth fifteen percent this is your second class test number two it's scheduled for 10 o'clock on wednesday the 12th that's the only time it'll be available so if you can't make it for that time you need to let me know um why that is and if you're entitled to a claim for extenuating circumstances then you need to make that um sooner rather than later lectures 7 to 12 are included in the test and the test comes in two parts a and b part a contains ten questions at seven and a half marks each and part b's five questions with five marks each there's roughly an hour allocated to each of these sections so section a starts at 10 o'clock and closes at 11 and part b is available from 10 o'clock until 12 o'clock okay so you've got two hours in total now part b involves handwritten solutions so rather than answering online you might need to provide a sketch write something out mathematically or provide some um explanation or an answer that's written so these are these are this is a different format to what you're familiar with so i do strongly suggest you spend a few minutes looking at the online demo so it isn't a practice test but it's a demo for part b so that's for the class test today's lecture we're going to introduce the idea of multiplexing multiplexing in the time domain multiplexing in the frequency domain and a combination of the two which we refer to as spread spectrum okay so you're going to see this symbol here mux representing a multiplexing or a multiplexer and d max representing a d multiplexer but before that before we get stuck into today's topic i want to say a few words about performance so when we're talking about a digital system where rather than talking about signal to noise ratio we're often interested in errors an error is a one that's transmitted that's received as a zero or a zero that's received sorry uh transmitted and received as a one both of these are considered errors so this is what we want to avoid in communications we want to avoid a situation where the transmitted signal and the received signal aren't the same so that's how we generally quantify the performance of a digital system so we use something called the bit error rate and by rate we mean what proportion of the total bits transmitted are received in error so the number of bits received in error divided by the total number of bits transmitted or received that's your bit error rate so ideally ideally we would want the bit error rate to be zero okay that means there'd be no bits received in error now that it's an ideal situation and that never really happens we have to accept that there's always going to be a bit error rate but to compare different communication systems it's useful to be able to compare their bit error rates and this isn't just a single number but rather it's a behavior or a bit error rate curve so if we were to plot the bit error rate against signal-to-noise ratio so here the horizontal axis is signal-to-noise ratio so here we have low snr and here we have high snr low snr means we have a lot of noise compared to the signal high snr means we have very little noise compared to the signal and again the vertical axis is decreasing bit error rate so that means that down here we have a low bit error rate and up here we have high bit error rate so what we want is something that has a low bit error rate so ideally we would want to be as low down here as possible and as far to the left as possible even though it says low snr we want to be able to get the best possible bit error rate with the lowest possible signal-to-noise ratio so if we compare these two curves so we've got two communication systems a and b now if we wanted to compare them solely on the basis of their bit error rate performance then it looks like for a given signal to noise ratio a will give you a lower bit error rate than b so we can say a gives a better bit error rate performance than b at a given snl why do we need to say it to give an snr because b can achieve the same bit error rate as a it just needs less noise or a higher snr so this is how we compare communication systems so for example remember quaam we looked at in lecture 10. so you can have different levels of quantum you can have um two-level calm 16-level camps 64-level crime and all of these are represented on the same plot and again what we have here is signal to noise ratio what we have here is bit error rate so here we have low bit error rate and here we have high bit error rate now if you look at that that's a one that means everything is received in error so that is the most undesirable situation and here you've got zero so this is the most desirable situation where you have no errors at all so you can see that as the signal-to-noise ratio increases as you get less and less noise you get lower bit error rate but at a given signal-to-noise ratio it looks like 64 calm has a much higher error rate than 2 prime why is that why do you think that as we increase the number of um the number of symbols encoded we're also increasing the bit error rate so if you just simplify this and think solely of the amplitudes if we only use two amplitudes compared to a situation where we have so if we have two amplitudes within our our range of say five volts compare that to a situation where you have multiple levels in the same the same voltage range so if we if that was 5 volts and that was 5 volts then clearly here if you were if you needed to detect between these different levels you would need a much more accurate sampling circuit so therefore the effect of noise on this will be much greater than the effect of noise on that so imagine if instead of having four levels we had 64 levels so that consists of phase and amplitude but also think about the phase if you have multiple phase shifts then the effect of noise will be more pronounced so you see that tube qualm is much better in terms of bit error rate but less good in terms of throughput i.e you can encode fewer symbols and therefore it's a slower communication and the opposite is also true so 64 cam is much faster than 2k1 but much more errors how do we get around that well you need to you need to go down this curve until you get to a level that you do accept so that means higher signal to noise ratio less noise so it is possible for these to have the same bit error rate performance or the same bit error rate but you would just need different signal-to-noise ratios okay here's a a question similar to a question i asked in an exam a few years ago so we we're given this plot that's comparing different digital modulation formats again it's the familiar bit error rate on the vertical axis where here we have everything in error and here we have low bit error rate so i'll just write that out to make it clear and the horizontal axis is signal-to-noise ratio in decibels so the question is how much more likely is a bit received via ask to be erroneous that means in error compared to dpsk so dpsk that's this one here ask that's this one here sorry no dpsk is the red line that's dpsk so it says at an snr of nine decibels if you look at nine decibels which is right here and you draw a vertical line upwards then you have these two points that you're interested so that corresponds to 10 to the minus 2 and 10 to the minus 4. so 10 to the minus 2 that means 1 in every 100 bits every 1 in 100 bits is an error and here that means every 1 in 10 000 bits is an error so clearly this is much better because you have fewer errors but the question is how much more how much better or how much more likely is that to give you an error so how much worse is ask remember ask is this blue line so how much worse so the answer is it's just the quotient of those two just divide those so you either divide 10 to the minus 2 divided by ten to the minus four or you divide ten thousand by a hundred the answer is the same it's a hundred times more likely so if you receive one bit you're a hundred times more likely for that bit to be an error if you use ask compared to dpsk how do we know that we know that from the graph we wouldn't have known it without the graph so back to today's lecture the topic is multiplexing multiplexing all it really means is having several communication channels share the same channel so several communication signals sharing the same channel demultiplexing is the opposite it's recovering the original signals from the multiplex signal it's because the channel is always in in high demand okay so think of something that's in high demand you've got lots of users all wanting to use it so multiplexing is just a way in which the channel can be shared so that multiple simultaneous data streams can use the same channel at the same time so we can do that in different ways but in general just think of it as you've got multiple sources multiple parties wanting to communicate so source one destination one source two destination two etc so you can have multiple parties wanting to communicate but there aren't multiple channels you don't have lots and lots of cables and this is particularly true in wireless communication but it's also true in baseband and wide communication so you have a multiplexer and you have a demultiplexer what what that allows it allows controlled access to the channel either by dividing up the frequency available or dividing up the time available so just to get a little bit of terminology out of the way when we talk about transmission protocol we either speak about a one-way communication system or a two-way communication system now the two-way communication system can either happen at the same time or it can happen asynchronously so not simultaneously so an example of a simplex system as we call it a simplex system it's a one-way communication system it's like um radio so you've got a transmitter and you've got a receiver you can't transmit from the receiver all you can do is receive so it's one-way communication two-way communication we call that duplex it can either be half duplex or full duplex half duplex is where one party is communicating at a time so you've got a transmitter and a receiver at one point in time and then when that stops then the other party can transmit and the original party will receive so that's what you're probably familiar with with a walkie-talkie system where one person is talking finishes over the next person can speak they finish they say over each of them will have to press the ptt button press to talk they'll press that button when they want to talk so it's called a half duplex system a full duplex system is where you have two-way communication you don't have to press a button you don't have to signal indicating that you've finished speaking by saying over you simply have a two-way communication system where both parties are talking at the same time so that's like a a telephone where you have a transmitter and a receiver and the transmitter can receive and the receiver can transmit so when we talk about multiplexing as i said we can either divide up the frequency and that's called fdm or we can talk about dividing up the time that's called tdm and generally time division multiplexing refers to digital multiplexing and frequency division multiplexing is analog or a better way of saying that is analog signals um benefit from frequency division multiplexing and digital signals benefit from time division multiplexing that's probably a better way of saying it so frequency division multiplexing we've spoken about that we didn't use the word multiplexing but when we spoke about radio radio stations sharing the frequency channel and adjacent radio stations and guard bands etc that's all examples of frequency division multiplexing where different channels can share the same um can transmit and receive at the same time because they don't overlap in the frequency domain something similar happens in the time domain and it's very common for fiber optic communications and telephone communications where time is subdivided into little slots because we have a sampling process and a digitization process so you can have multiple transmissions all happening um i want to say at the same time but it's not at the same time they happen simultaneously but the um the the bits and the packets they don't overlap in time now if we combine time and frequency division multiplexing we have something called spread spectrum and we see that in things like bluetooth and wi-fi we'll look at that in a second so if you imagine each of these colored bands is a different user so user one user two user 3 user 4 in frequency division multiplexing all four users are using the channel all of the time at the same time but they each allocated a different frequency band so the blue user has this frequency band the pink user has this frequency band and because they're different bands they don't overlap and therefore they can transmit at the same time so this could be a radio station so that's your blue and this could be pink could be radio station two i'll call it radio station 4. and they can be broadcasting all of the time at the same time but because they each have their own frequency range then they don't overlap and therefore they don't interfere so they've shared the wireless the wireless electromagnetic propagation channel that exists in the city they're all transmitting at the same time and different receivers can receive them at the same time now for time division multiplexing the opposite happens they all use all of the same frequency axis but they're all given individual slots individual periods of time where they can transmit and these are very short slots so what we're doing is we're exploiting the redundancy that exists within your signal so remember we spoke about redundancy before so when you sample an analog signal you are exploiting something called the redundancy so you're only sampling several times a second so between these samples nothing's happening so you have a a value here that's converted into digital you have a value here that's converted into digital you have a value here you have a value here but what's happening here what's happening in the period of time between samples well the answer is nothing's happening so that gives you time to sample another signal so there might be another signal that could be sampled at this time at the time when nothing else is happening and that could be converted to digital that could be converted to digital that could be converted to digital and if these streams are combined together that gives us these slots so each of these is a slot slot a slot b slot a slot b slot a slot b so that's time division multiplexing so another illustration of frequency division multiplexing again we're not talking about baseband these have to these have to be modulated it has to be band pass okay so why do they need to be modulated because without modulation they wouldn't have their own frequency band they'd all be at baseband but these have clearly been modulated so they all have their own frequency ranges so channel one channel two channel three when they're at baseband they're all low frequency right so they all start from zero and they end similar ranges so if these are all i don't know that one so if these are all audio then they'll all have some low kilohertz bandwidth so these are your baseband messages after modulation each of them will have a center frequency and will have an upper and a lower frequency and if they're placed on the frequency axis in such a way that they either don't overlap or very slightly overlap or they have guard bands in between them and i in all these cases we call this frequency division multiplexing so what they're doing is they're sharing the same channel at the same time so if you want to avoid overlap then the bandwidth of the medium must be at least n where n is the number of users times the bandwidth of the signal now if we want to introduce guard bands in between our users then we're going to have to add the guard bands here so so frequency division multiplexing is often used in telephone lines for radio stations we've already spoken about and for television so you've seen this illustration before where you have your frequency electromagnetic spectrum your frequency spectrum and you can see that different things are happening on the same spectrum at different regions but they're all happening at the same time so this is just looking at this this is an example of frequency division multiplexing where you have satellite communication and radio communication all happening at the same time but they're happening at different frequencies so again a little illustrated example so you've got these three users they're all using the same frequency band from zero to four kilohertz so they can't share the same channel at the same time because you'd have interference between the two between the three so what we do is we modulate so we increase the frequency so we've added 20 kilohertz here we add 24 kilohertz here and we add 28 kilohertz here that way they can sit next to each other on the channel on the frequency spectrum so obviously this is frequency so here once they arrive at the receiver you'll need some kind of a filter what kind of a filter well it's going to be a band pass filter you're going to need a band pass filter at the receiver and you'll need three of these one to filter out the first one for the second one for the third and each receiver will receive the corresponding message from the original transmitter so that that's how fdm works in practice now time division multiplexing as i said it's similar but you need to think about it or you you can visualize it as a rotating switch so you have a switch which rotates so when it's when it's in this position connecting conversation a or message a then the other corresponding switch with the synchronized d multiplexer because these have to be in sync we'll give you conversation a so this party will be communicating with this party and that is let's say your sample here so this slot here might correspond to what we just drew the next time slot this switch might move to position b at the multiplexer and position b at the d multiplexer so you would your sampler would then sample the second message and then you would be looking at the next slot and again that slot would through multiplexing and demultiplexing then manifest itself here as your second sample so effectively you have a interleaved multiplexed set of samples here which are these slots which are demultiplexed here and what you end up with after recovery is your original signals now if your original signals were digital then these will be digital if your original signals were analog then you'll need both a sampling circuit here and a recovery signal here or reconstruction signal here important to note that time division multiplexing doesn't involve a carrier so we're talking about the base band signal because we're sampling if it if it's analog we're sampling it if it's digital then it's baseband already but the bit rate of the medium is greater than the data rate of the signal so you can imagine that if we had one kilobit per second here each of these was one kilobits per second then what would the data rate here be it'll be four times one kilo bit per second because every second you have a thousand bits generated by this first user another thousand bits generated by this another thousand another thousand so basically you have four thousand bits being generated every second and all of these are sharing the same channel the same fiber optic cable the same ethernet cable the same medium so therefore you will have a bit rate which is a multiple of the um bit rates of the the users finally last thing we want to talk about is something called spread spectrum now spread spectrum is a combination of time domain multiplexing and frequency domain multiplexing now this is something that we see in bluetooth communications and wi-fi mobile communications and gsm and it's it's a more secure kind of communication where your transmitter and receiver agree on a particular dance a particular code where at any particular time each user has a different frequency so for example at this point in time one user has this frequency another user has this frequency and another user has this frequency a moment later the blue signal has hopped onto a higher frequency the orange signal has hopped down to a lower frequency and the green signal has hopped down to a much lower signal a frequency so with time you see each channel or each signal each user each link is hopping from frequency to frequency that's why we call it frequency hopping so basically we spread the spectrum over the entire frequency axis so if you were to look only at the blue only look at the blue and think about its spectrum its spectrum here looks like it's there but its spectrum here is the spectrum here is there so if you were to just look at the spectrum and think how that might look if that's your frequency axis then the spectrum for the blue would look something like this now the spectrum for the green would be similar spectrum for the green might look something like that and the spectrum for the orange might look something like that so it looks like all three users as are using the same frequency spectrum how is that possible how is it possible they're using the same frequency spectrum well it's because they're not using it at the same time so at any point in time they're not overlapping so that's why they call it a spread spectrum technique because we spread the spectrum over the entire frequency axis so it's almost impossible to intercept and to distort this signal it's impossible so you've got a transmitter and you've got a receiver and it's impossible for a man in the middle to actually recover the original message without knowing what the um what the code is between them that's why bluetooth is relatively secure so there are a few a couple of brief youtube clips i want to share with you just to show you a few of these things in practice it's less than a minute long here you can see in the top plot that's a spectral plot you can see the center frequency is changing with time okay anyone who wants to know what extreme hopping looks like for the ez uhf so center frequency is uh 440 megahertz so left to the grid is 430 right of the grid is 450 megahertz and there's your spread spectrum so that was spread spectrum sometimes abbreviated as ss so we use codes to be able to um to achieve this frequency hopping you might come across something called cdma code division multiple access and that just means that we use we use the codes so the the c in cdma is for codes it just means we use the codes to actually achieve this um this multiplexing so direct sequence these are abbreviations you might come across but where will you use this you have all used this before so you've used bluetooth wi-fi you've definitely used cellular communications all of these are forms of frequency hopping spread spectrum techniques so they are multiplexing so they're combinations of time division and frequency division multiplexing and you'll be pleased to hear that this is our final slide that's the end of the module we are right here okay so we've just finished our final lecture if you enjoyed that if you think communications um uh is something you want to look at further then look into elect 377 or elect 477. so that's all about digital communication so digital and wireless so when we speak about wireless communications therefore we are talking about band pass communications when we talk about digital well we're talking about digital so it's really the latter part of this module so lecture 11 and lecture 12 all of that will be um the topic of uh dr zeus elec 377 she looks at noise she looks at bit error rates she looked at multi-user communications all of these concepts in great mathematical depth in your third or fourth year if you're not interested in that you will be interested in the exam so the exam is on the 19th of may so that's not long from now you need to know a few things about the exam everyone will have a different set of questions okay so you won't all be sitting the same test you all have different questions you need to answer four questions but you don't get a choice of which questions to answer so which questions to answer will depend on your student id number instructions are given on the exam paper but what you need to do is follow the instructions so in this case here you're asked to look at the last two digits of your student id number and add those digits together that will give you something called an exam identifier and then from the exam identifier so for example if if that's your student id number and you add five and four together and you get nine then your exam identifier is nine you need to write that at the top of your paper so that is the column you're interested in because your exam identifier is nine so that means you answer question two you answer question five you answer question three and you answer question seven you don't answer question one you don't answer question four you don't answer question 6 you don't answer question 8. and when you do answer question 2 you get the parameters the numbers from here so if if question um two was about modulation and they asked for they asked you to use the modulation index you would use the parameter the number that you got from the table so this table is there to tell you which questions to answer and what parameters to use what values to use okay so there will be questions that ask you to design something to explain to compare to contrast to discuss there will be several questions asking you to sketch or to plot okay no questions will be straight from the lecture notes there won't be a single question where copying from the lecture notes will do you any good that doesn't mean it's a difficult exam it just means that the exam won't be asking you to copy things from the lecture notes because you'll all have the lecture notes in front of you so i will reward creativity and um there will be some scope to use your imagination and to um so i expect you many different responses all of which could be correct so there can be many different correct answers to the same question some questions are numeric in which case there won't be more than one correct answer but several questions will be open to interpretation okay it won't be a difficult exam it won't be as hard as the signals exam was last semester but the exam won't look like your problem sheets so i suggest you look closely at last year's exam paper because that was open book and you look at um the mock exam because there will be a mock exam uh released um on canvas and you're i i encourage you to look at the the style of the questions in the mock exam okay so that's it that that's the end of um of this module so well done for making it i hope you've enjoyed it if you haven't enjoyed it i hope you've at least found it useful i have really um enjoyed teaching you it's just been so frustrating that we haven't been able to meet so i hope at least i can meet you all next year so next year i'll be teaching elect 352 so i'll be um i'll be seeing you all next year so good luck in your revision good luck in your class test good luck for your exams and stay safe

hello and welcome to lecture 12. this is our final lecture where we&#39;ll be looking at multiplexing so in our last two lectures we looked at digital modulation we looked at digital baseband modulation which was the same as pulse modulation we talked about digital band pass modulation which is carrier based wireless communication in our final lecture we want to say a few words about multiplexing so this is a really short lecture it shouldn&#39;t be more than around 20 minutes now all of these lectures starting from lecture 7 until this lecture 12 these are included in the class test on the 12th of may so quick recap in lecture 11 we spoke to we spoke about digital band pass modulation that&#39;s basically amplitude modulation frequency modulation and phase modulation we spoke about how to generate it how to detect it and a little bit about what the frequency domain representation looks like we spoke about different variants of these we said really in essence it&#39;s just the same as am fm and pm that we&#39;re familiar with the only difference is that the information instead of being an analog signal it&#39;s a line code generated from a digital signal now before we start today&#39;s lecture about multiplexing just a few words about the class test so a few things you need to know number one it&#39;s worth fifteen percent this is your second class test number two it&#39;s scheduled for 10 o&#39;clock on wednesday the 12th that&#39;s the only time it&#39;ll be available so if you can&#39;t make it for that time you need to let me know um why that is and if you&#39;re entitled to a claim for extenuating circumstances then you need to make that um sooner rather than later lectures 7 to 12 are included in the test and the test comes in two parts a and b part a contains ten questions at seven and a half marks each and part b&#39;s five questions with five marks each there&#39;s roughly an hour allocated to each of these sections so section a starts at 10 o&#39;clock and closes at 11 and part b is available from 10 o&#39;clock until 12 o&#39;clock okay so you&#39;ve got two hours in total now part b involves handwritten solutions so rather than answering online you might need to provide a sketch write something out mathematically or provide some um explanation or an answer that&#39;s written so these are these are this is a different format to what you&#39;re familiar with so i do strongly suggest you spend a few minutes looking at the online demo so it isn&#39;t a practice test but it&#39;s a demo for part b so that&#39;s for the class test today&#39;s lecture we&#39;re going to introduce the idea of multiplexing multiplexing in the time domain multiplexing in the frequency domain and a combination of the two which we refer to as spread spectrum okay so you&#39;re going to see this symbol here mux representing a multiplexing or a multiplexer and d max representing a d multiplexer but before that before we get stuck into today&#39;s topic i want to say a few words about performance so when we&#39;re talking about a digital system where rather than talking about signal to noise ratio we&#39;re often interested in errors an error is a one that&#39;s transmitted that&#39;s received as a zero or a zero that&#39;s received sorry uh transmitted and received as a one both of these are considered errors so this is what we want to avoid in communications we want to avoid a situation where the transmitted signal and the received signal aren&#39;t the same so that&#39;s how we generally quantify the performance of a digital system so we use something called the bit error rate and by rate we mean what proportion of the total bits transmitted are received in error so the number of bits received in error divided by the total number of bits transmitted or received that&#39;s your bit error rate so ideally ideally we would want the bit error rate to be zero okay that means there&#39;d be no bits received in error now that it&#39;s an ideal situation and that never really happens we have to accept that there&#39;s always going to be a bit error rate but to compare different communication systems it&#39;s useful to be able to compare their bit error rates and this isn&#39;t just a single number but rather it&#39;s a behavior or a bit error rate curve so if we were to plot the bit error rate against signal-to-noise ratio so here the horizontal axis is signal-to-noise ratio so here we have low snr and here we have high snr low snr means we have a lot of noise compared to the signal high snr means we have very little noise compared to the signal and again the vertical axis is decreasing bit error rate so that means that down here we have a low bit error rate and up here we have high bit error rate so what we want is something that has a low bit error rate so ideally we would want to be as low down here as possible and as far to the left as possible even though it says low snr we want to be able to get the best possible bit error rate with the lowest possible signal-to-noise ratio so if we compare these two curves so we&#39;ve got two communication systems a and b now if we wanted to compare them solely on the basis of their bit error rate performance then it looks like for a given signal to noise ratio a will give you a lower bit error rate than b so we can say a gives a better bit error rate performance than b at a given snl why do we need to say it to give an snr because b can achieve the same bit error rate as a it just needs less noise or a higher snr so this is how we compare communication systems so for example remember quaam we looked at in lecture 10. so you can have different levels of quantum you can have um two-level calm 16-level camps 64-level crime and all of these are represented on the same plot and again what we have here is signal to noise ratio what we have here is bit error rate so here we have low bit error rate and here we have high bit error rate now if you look at that that&#39;s a one that means everything is received in error so that is the most undesirable situation and here you&#39;ve got zero so this is the most desirable situation where you have no errors at all so you can see that as the signal-to-noise ratio increases as you get less and less noise you get lower bit error rate but at a given signal-to-noise ratio it looks like 64 calm has a much higher error rate than 2 prime why is that why do you think that as we increase the number of um the number of symbols encoded we&#39;re also increasing the bit error rate so if you just simplify this and think solely of the amplitudes if we only use two amplitudes compared to a situation where we have so if we have two amplitudes within our our range of say five volts compare that to a situation where you have multiple levels in the same the same voltage range so if we if that was 5 volts and that was 5 volts then clearly here if you were if you needed to detect between these different levels you would need a much more accurate sampling circuit so therefore the effect of noise on this will be much greater than the effect of noise on that so imagine if instead of having four levels we had 64 levels so that consists of phase and amplitude but also think about the phase if you have multiple phase shifts then the effect of noise will be more pronounced so you see that tube qualm is much better in terms of bit error rate but less good in terms of throughput i.e you can encode fewer symbols and therefore it&#39;s a slower communication and the opposite is also true so 64 cam is much faster than 2k1 but much more errors how do we get around that well you need to you need to go down this curve until you get to a level that you do accept so that means higher signal to noise ratio less noise so it is possible for these to have the same bit error rate performance or the same bit error rate but you would just need different signal-to-noise ratios okay here&#39;s a a question similar to a question i asked in an exam a few years ago so we we&#39;re given this plot that&#39;s comparing different digital modulation formats again it&#39;s the familiar bit error rate on the vertical axis where here we have everything in error and here we have low bit error rate so i&#39;ll just write that out to make it clear and the horizontal axis is signal-to-noise ratio in decibels so the question is how much more likely is a bit received via ask to be erroneous that means in error compared to dpsk so dpsk that&#39;s this one here ask that&#39;s this one here sorry no dpsk is the red line that&#39;s dpsk so it says at an snr of nine decibels if you look at nine decibels which is right here and you draw a vertical line upwards then you have these two points that you&#39;re interested so that corresponds to 10 to the minus 2 and 10 to the minus 4. so 10 to the minus 2 that means 1 in every 100 bits every 1 in 100 bits is an error and here that means every 1 in 10 000 bits is an error so clearly this is much better because you have fewer errors but the question is how much more how much better or how much more likely is that to give you an error so how much worse is ask remember ask is this blue line so how much worse so the answer is it&#39;s just the quotient of those two just divide those so you either divide 10 to the minus 2 divided by ten to the minus four or you divide ten thousand by a hundred the answer is the same it&#39;s a hundred times more likely so if you receive one bit you&#39;re a hundred times more likely for that bit to be an error if you use ask compared to dpsk how do we know that we know that from the graph we wouldn&#39;t have known it without the graph so back to today&#39;s lecture the topic is multiplexing multiplexing all it really means is having several communication channels share the same channel so several communication signals sharing the same channel demultiplexing is the opposite it&#39;s recovering the original signals from the multiplex signal it&#39;s because the channel is always in in high demand okay so think of something that&#39;s in high demand you&#39;ve got lots of users all wanting to use it so multiplexing is just a way in which the channel can be shared so that multiple simultaneous data streams can use the same channel at the same time so we can do that in different ways but in general just think of it as you&#39;ve got multiple sources multiple parties wanting to communicate so source one destination one source two destination two etc so you can have multiple parties wanting to communicate but there aren&#39;t multiple channels you don&#39;t have lots and lots of cables and this is particularly true in wireless communication but it&#39;s also true in baseband and wide communication so you have a multiplexer and you have a demultiplexer what what that allows it allows controlled access to the channel either by dividing up the frequency available or dividing up the time available so just to get a little bit of terminology out of the way when we talk about transmission protocol we either speak about a one-way communication system or a two-way communication system now the two-way communication system can either happen at the same time or it can happen asynchronously so not simultaneously so an example of a simplex system as we call it a simplex system it&#39;s a one-way communication system it&#39;s like um radio so you&#39;ve got a transmitter and you&#39;ve got a receiver you can&#39;t transmit from the receiver all you can do is receive so it&#39;s one-way communication two-way communication we call that duplex it can either be half duplex or full duplex half duplex is where one party is communicating at a time so you&#39;ve got a transmitter and a receiver at one point in time and then when that stops then the other party can transmit and the original party will receive so that&#39;s what you&#39;re probably familiar with with a walkie-talkie system where one person is talking finishes over the next person can speak they finish they say over each of them will have to press the ptt button press to talk they&#39;ll press that button when they want to talk so it&#39;s called a half duplex system a full duplex system is where you have two-way communication you don&#39;t have to press a button you don&#39;t have to signal indicating that you&#39;ve finished speaking by saying over you simply have a two-way communication system where both parties are talking at the same time so that&#39;s like a a telephone where you have a transmitter and a receiver and the transmitter can receive and the receiver can transmit so when we talk about multiplexing as i said we can either divide up the frequency and that&#39;s called fdm or we can talk about dividing up the time that&#39;s called tdm and generally time division multiplexing refers to digital multiplexing and frequency division multiplexing is analog or a better way of saying that is analog signals um benefit from frequency division multiplexing and digital signals benefit from time division multiplexing that&#39;s probably a better way of saying it so frequency division multiplexing we&#39;ve spoken about that we didn&#39;t use the word multiplexing but when we spoke about radio radio stations sharing the frequency channel and adjacent radio stations and guard bands etc that&#39;s all examples of frequency division multiplexing where different channels can share the same um can transmit and receive at the same time because they don&#39;t overlap in the frequency domain something similar happens in the time domain and it&#39;s very common for fiber optic communications and telephone communications where time is subdivided into little slots because we have a sampling process and a digitization process so you can have multiple transmissions all happening um i want to say at the same time but it&#39;s not at the same time they happen simultaneously but the um the the bits and the packets they don&#39;t overlap in time now if we combine time and frequency division multiplexing we have something called spread spectrum and we see that in things like bluetooth and wi-fi we&#39;ll look at that in a second so if you imagine each of these colored bands is a different user so user one user two user 3 user 4 in frequency division multiplexing all four users are using the channel all of the time at the same time but they each allocated a different frequency band so the blue user has this frequency band the pink user has this frequency band and because they&#39;re different bands they don&#39;t overlap and therefore they can transmit at the same time so this could be a radio station so that&#39;s your blue and this could be pink could be radio station two i&#39;ll call it radio station 4. and they can be broadcasting all of the time at the same time but because they each have their own frequency range then they don&#39;t overlap and therefore they don&#39;t interfere so they&#39;ve shared the wireless the wireless electromagnetic propagation channel that exists in the city they&#39;re all transmitting at the same time and different receivers can receive them at the same time now for time division multiplexing the opposite happens they all use all of the same frequency axis but they&#39;re all given individual slots individual periods of time where they can transmit and these are very short slots so what we&#39;re doing is we&#39;re exploiting the redundancy that exists within your signal so remember we spoke about redundancy before so when you sample an analog signal you are exploiting something called the redundancy so you&#39;re only sampling several times a second so between these samples nothing&#39;s happening so you have a a value here that&#39;s converted into digital you have a value here that&#39;s converted into digital you have a value here you have a value here but what&#39;s happening here what&#39;s happening in the period of time between samples well the answer is nothing&#39;s happening so that gives you time to sample another signal so there might be another signal that could be sampled at this time at the time when nothing else is happening and that could be converted to digital that could be converted to digital that could be converted to digital and if these streams are combined together that gives us these slots so each of these is a slot slot a slot b slot a slot b slot a slot b so that&#39;s time division multiplexing so another illustration of frequency division multiplexing again we&#39;re not talking about baseband these have to these have to be modulated it has to be band pass okay so why do they need to be modulated because without modulation they wouldn&#39;t have their own frequency band they&#39;d all be at baseband but these have clearly been modulated so they all have their own frequency ranges so channel one channel two channel three when they&#39;re at baseband they&#39;re all low frequency right so they all start from zero and they end similar ranges so if these are all i don&#39;t know that one so if these are all audio then they&#39;ll all have some low kilohertz bandwidth so these are your baseband messages after modulation each of them will have a center frequency and will have an upper and a lower frequency and if they&#39;re placed on the frequency axis in such a way that they either don&#39;t overlap or very slightly overlap or they have guard bands in between them and i in all these cases we call this frequency division multiplexing so what they&#39;re doing is they&#39;re sharing the same channel at the same time so if you want to avoid overlap then the bandwidth of the medium must be at least n where n is the number of users times the bandwidth of the signal now if we want to introduce guard bands in between our users then we&#39;re going to have to add the guard bands here so so frequency division multiplexing is often used in telephone lines for radio stations we&#39;ve already spoken about and for television so you&#39;ve seen this illustration before where you have your frequency electromagnetic spectrum your frequency spectrum and you can see that different things are happening on the same spectrum at different regions but they&#39;re all happening at the same time so this is just looking at this this is an example of frequency division multiplexing where you have satellite communication and radio communication all happening at the same time but they&#39;re happening at different frequencies so again a little illustrated example so you&#39;ve got these three users they&#39;re all using the same frequency band from zero to four kilohertz so they can&#39;t share the same channel at the same time because you&#39;d have interference between the two between the three so what we do is we modulate so we increase the frequency so we&#39;ve added 20 kilohertz here we add 24 kilohertz here and we add 28 kilohertz here that way they can sit next to each other on the channel on the frequency spectrum so obviously this is frequency so here once they arrive at the receiver you&#39;ll need some kind of a filter what kind of a filter well it&#39;s going to be a band pass filter you&#39;re going to need a band pass filter at the receiver and you&#39;ll need three of these one to filter out the first one for the second one for the third and each receiver will receive the corresponding message from the original transmitter so that that&#39;s how fdm works in practice now time division multiplexing as i said it&#39;s similar but you need to think about it or you you can visualize it as a rotating switch so you have a switch which rotates so when it&#39;s when it&#39;s in this position connecting conversation a or message a then the other corresponding switch with the synchronized d multiplexer because these have to be in sync we&#39;ll give you conversation a so this party will be communicating with this party and that is let&#39;s say your sample here so this slot here might correspond to what we just drew the next time slot this switch might move to position b at the multiplexer and position b at the d multiplexer so you would your sampler would then sample the second message and then you would be looking at the next slot and again that slot would through multiplexing and demultiplexing then manifest itself here as your second sample so effectively you have a interleaved multiplexed set of samples here which are these slots which are demultiplexed here and what you end up with after recovery is your original signals now if your original signals were digital then these will be digital if your original signals were analog then you&#39;ll need both a sampling circuit here and a recovery signal here or reconstruction signal here important to note that time division multiplexing doesn&#39;t involve a carrier so we&#39;re talking about the base band signal because we&#39;re sampling if it if it&#39;s analog we&#39;re sampling it if it&#39;s digital then it&#39;s baseband already but the bit rate of the medium is greater than the data rate of the signal so you can imagine that if we had one kilobit per second here each of these was one kilobits per second then what would the data rate here be it&#39;ll be four times one kilo bit per second because every second you have a thousand bits generated by this first user another thousand bits generated by this another thousand another thousand so basically you have four thousand bits being generated every second and all of these are sharing the same channel the same fiber optic cable the same ethernet cable the same medium so therefore you will have a bit rate which is a multiple of the um bit rates of the the users finally last thing we want to talk about is something called spread spectrum now spread spectrum is a combination of time domain multiplexing and frequency domain multiplexing now this is something that we see in bluetooth communications and wi-fi mobile communications and gsm and it&#39;s it&#39;s a more secure kind of communication where your transmitter and receiver agree on a particular dance a particular code where at any particular time each user has a different frequency so for example at this point in time one user has this frequency another user has this frequency and another user has this frequency a moment later the blue signal has hopped onto a higher frequency the orange signal has hopped down to a lower frequency and the green signal has hopped down to a much lower signal a frequency so with time you see each channel or each signal each user each link is hopping from frequency to frequency that&#39;s why we call it frequency hopping so basically we spread the spectrum over the entire frequency axis so if you were to look only at the blue only look at the blue and think about its spectrum its spectrum here looks like it&#39;s there but its spectrum here is the spectrum here is there so if you were to just look at the spectrum and think how that might look if that&#39;s your frequency axis then the spectrum for the blue would look something like this now the spectrum for the green would be similar spectrum for the green might look something like that and the spectrum for the orange might look something like that so it looks like all three users as are using the same frequency spectrum how is that possible how is it possible they&#39;re using the same frequency spectrum well it&#39;s because they&#39;re not using it at the same time so at any point in time they&#39;re not overlapping so that&#39;s why they call it a spread spectrum technique because we spread the spectrum over the entire frequency axis so it&#39;s almost impossible to intercept and to distort this signal it&#39;s impossible so you&#39;ve got a transmitter and you&#39;ve got a receiver and it&#39;s impossible for a man in the middle to actually recover the original message without knowing what the um what the code is between them that&#39;s why bluetooth is relatively secure so there are a few a couple of brief youtube clips i want to share with you just to show you a few of these things in practice it&#39;s less than a minute long here you can see in the top plot that&#39;s a spectral plot you can see the center frequency is changing with time okay anyone who wants to know what extreme hopping looks like for the ez uhf so center frequency is uh 440 megahertz so left to the grid is 430 right of the grid is 450 megahertz and there&#39;s your spread spectrum so that was spread spectrum sometimes abbreviated as ss so we use codes to be able to um to achieve this frequency hopping you might come across something called cdma code division multiple access and that just means that we use we use the codes so the the c in cdma is for codes it just means we use the codes to actually achieve this um this multiplexing so direct sequence these are abbreviations you might come across but where will you use this you have all used this before so you&#39;ve used bluetooth wi-fi you&#39;ve definitely used cellular communications all of these are forms of frequency hopping spread spectrum techniques so they are multiplexing so they&#39;re combinations of time division and frequency division multiplexing and you&#39;ll be pleased to hear that this is our final slide that&#39;s the end of the module we are right here okay so we&#39;ve just finished our final lecture if you enjoyed that if you think communications um uh is something you want to look at further then look into elect 377 or elect 477. so that&#39;s all about digital communication so digital and wireless so when we speak about wireless communications therefore we are talking about band pass communications when we talk about digital well we&#39;re talking about digital so it&#39;s really the latter part of this module so lecture 11 and lecture 12 all of that will be um the topic of uh dr zeus elec 377 she looks at noise she looks at bit error rates she looked at multi-user communications all of these concepts in great mathematical depth in your third or fourth year if you&#39;re not interested in that you will be interested in the exam so the exam is on the 19th of may so that&#39;s not long from now you need to know a few things about the exam everyone will have a different set of questions okay so you won&#39;t all be sitting the same test you all have different questions you need to answer four questions but you don&#39;t get a choice of which questions to answer so which questions to answer will depend on your student id number instructions are given on the exam paper but what you need to do is follow the instructions so in this case here you&#39;re asked to look at the last two digits of your student id number and add those digits together that will give you something called an exam identifier and then from the exam identifier so for example if if that&#39;s your student id number and you add five and four together and you get nine then your exam identifier is nine you need to write that at the top of your paper so that is the column you&#39;re interested in because your exam identifier is nine so that means you answer question two you answer question five you answer question three and you answer question seven you don&#39;t answer question one you don&#39;t answer question four you don&#39;t answer question 6 you don&#39;t answer question 8. and when you do answer question 2 you get the parameters the numbers from here so if if question um two was about modulation and they asked for they asked you to use the modulation index you would use the parameter the number that you got from the table so this table is there to tell you which questions to answer and what parameters to use what values to use okay so there will be questions that ask you to design something to explain to compare to contrast to discuss there will be several questions asking you to sketch or to plot okay no questions will be straight from the lecture notes there won&#39;t be a single question where copying from the lecture notes will do you any good that doesn&#39;t mean it&#39;s a difficult exam it just means that the exam won&#39;t be asking you to copy things from the lecture notes because you&#39;ll all have the lecture notes in front of you so i will reward creativity and um there will be some scope to use your imagination and to um so i expect you many different responses all of which could be correct so there can be many different correct answers to the same question some questions are numeric in which case there won&#39;t be more than one correct answer but several questions will be open to interpretation okay it won&#39;t be a difficult exam it won&#39;t be as hard as the signals exam was last semester but the exam won&#39;t look like your problem sheets so i suggest you look closely at last year&#39;s exam paper because that was open book and you look at um the mock exam because there will be a mock exam uh released um on canvas and you&#39;re i i encourage you to look at the the style of the questions in the mock exam okay so that&#39;s it that that&#39;s the end of um of this module so well done for making it i hope you&#39;ve enjoyed it if you haven&#39;t enjoyed it i hope you&#39;ve at least found it useful i have really um enjoyed teaching you it&#39;s just been so frustrating that we haven&#39;t been able to meet so i hope at least i can meet you all next year so next year i&#39;ll be teaching elect 352 so i&#39;ll be um i&#39;ll be seeing you all next year so good luck in your revision good luck in your class test good luck for your exams and stay safe

Transcript for:Lecture 12: Multiplexing

Transcript for:
Lecture 12: Multiplexing