The first example is on LTE air interface, okay? Let's actually go through the detail of calculating the speed. Well, first of all, let's just look at the connection between the end-user device over the air to the eNobe, okay? And let's only look at the physical layer first, okay? So, there's no application to speak of. Well, what is the formula of this speed here? Roughly speaking, it goes like this. We want to look at the number of bits transmitted, right? And then, divide by the time. So, the number of bits transmitted over time. And there is a standard unit of time called a sub frame of data, one unit of time, and that is one millisecond in the standardization. Let's just count how many bits can be sent over that one millisecond then, okay? Well, we need to know the number of symbols per frequency block. Then, we multiply that by the number of frequency blocks. Then, we multiply by the number of bits per symbol. Then, we multiply by any extra gains, such as the coding, or MIM, MIMO or multiple antenna gain, okay? So, the formula looks something like this. We look at the number of symbols per carrier, okay? Different how rich of descriptive power there is per carrier. Meaning, per small block of the frequency that you're using, okay? Minus the control overhead that you need for example for channel estimation, to know how good the channel is before deciding what kind of modulation you can use, okay? Then, you multiply that difference by the number of carriers per frequency block. As mentioned in advanced material part of last lecture and a quick summary here, is that the frequency block is divided into a few blocks, okay? a number of blocks. And each block is then further divided into different carriers, [SOUND] okay? So, signals are modulated onto different carriers and then we got many blocks of these carriers for LTE. So, you multiply this difference by the number of carriers you have for frequency block, then you subtract out other overhead, okay? Then, you multiply by the number of bits that you can transmit per symbol. If you got a good channel, you can carry more bits per symbol through a so called higher order modulation. Again, the detail doesn't concern us because this is not a signal processing for communication course. Then, we multiply the number of frequency blocks you have, all together. And then, you multiply by the additional gains such as coding gain and MIMO antenna gain. Now, in the ideal case, we get the following kind of numbers, okay? So, symbols per carrier is usually say, fourteen in the ideal case for LTE. And the control overhead per carrier is let's say one, [SOUND] okay? And then, we multiply by the number of carriers per frequency block. Usually, there are twelve carriers, okay? So, multiply by twelve, and each one has a frequency block of 180 kilohertz. And then, there's a channel estimation overhead, okay? And this amount of overhead is used to sense something called pilot symbols to estimate how good the channel is, and is ideally around, ten symbols, okay? For a four by four antenna system. And then, you look at the number of bits per symbol that you can run. Ideally, this would be say six. Meaning that you have two to the six which is 64, so-called 64 qam modulation, okay? That's when the channel is very good, you can afford a higher auto modulation as to be heard correctly at a receiver. So, you can carry six bits for every symbol. And then, you multiply the number of frequency blocks you have, which is altogether a 100 frequency blocks, okay? Together with some garband, you all together are consuming 20 megahertz then, which is the channel with typically an LTE system. Then, you multiply by the coding rate, [SOUND] okay? Which is basically a number between zero and one. Between zero and one. More efficient your error correction coding is meaning you'd only need to add a little bit of redundancy in order to prepare for the channel distortion of your bits then closer to one you are, for example 0.9, okay? Now, these days, we've got very advanced error correction coding methodologies developed in the past decade or so, that can get you very close to one but you still can get exactly to one. Say, for the kind of a good system that we are talking about, it get to a 0.9, okay? And then, there is the gain for using multiple antennas. Theoretically, if you use say, four by four MIMO system. Meaning, there are four antennas and the transmitter for other receiver. Then, you can have four spatially separate channels. So, you get a factor of four on the spacing. Alright. So, if you add these up, okay? Then, you get the following number, 315360 bits, okay? For every one millisecond. So that implies you divide it by one millisecond, you get basically 315 megabit per second. And that's the kind of number you hear in the physical layer speed for a 4G, okay? LTE. Which is a huge number, if you think about it, okay? Our home, broadband wireline access networks usually getting something like 25 to 50 megabit per second, okay? Wi-Fi, even if you use that 11N, a fancy version of Wi-Fi. So, we talked about last time, you are getting something like 100 megabit per second. So, this is talking about a wide area wireless network. And you can get 300, more than 300 megabit per second, okay? This is huge, okay? In fact, if you can truly get this, you can run ultra HD video, which requires 100 megabyte per second or so. You can run many, many channels of HD over the air on your cell phone, LTE cellphone, okay? If you can truly get applications layer useful through put at over 300 megabyte per second, okay? But in practice, what we get is the following. Still restricting ourselves only to the physical layer, and only to the link between the end-user device and eNobe, okay? Not talking about any other overhand, not talking about any other non-ideal network conditions yet. Just this very simple case where you should get very big number. Let's look at the practical number. Usually, we actually get something more like twelve symbols per carrier, and the overhead per carrier is like two symbols, okay? You multiply it by twelve carriers per frequency. The overhead in things like channel estimation tend to be bigger than ten. Say, 20 symbols and practice for a mime or four by four channel. And then, you multiply by the number bits per symbol which instead of two to the six is often two to the four. That is sixteen plan because the channel is not good enough or because too much interference, non-ideal interface condition that forces you to talk slower with a lower auto modulation. So, you multiply by four instead of six bits per symbol, okay? Then, you don't actually have 100 frequency blocks because you use so called two way communication based on half duplex, okay? Half of that goes to the one direction, the other half goes to the other direction. If you use time division multiplex, sometimes you get 60% of the frequency blocks for down-link, 40% for up-link. Let's say, we're talking about down-link from eNobe to you, okay? That would be 60, right? So, it's not 100. And then, you multiply by the coding gain. And for the channel that we're dealing with, we may only be able to get say 70% efficiency. Then, you multiply by the MIMO multiple antenna gain. You may have a four by four system, okay? Four transmit antenna, four receive antenna. But they may be placed so close to each other, and the air in between them may be such that you don't have four independent channels. You actually only have two independent channels. So, you got a factor of two instead of four. You carry out the calculation and you see a number that is [SOUND] 28,000 bits for each millisecond. So, you divide by one millisecond, that implies you get 28 megabit per second [SOUND] rather than 315 megabit per second. Now, 28 megabit per second is still very fast. If you can still actually get 28. in your application layer throughput, useful throughput, that is great, okay? That is faster than most Wi-Fi we are used to. So, can you get to 28 megabit per second for application layer useful throughput? Well, probably not. Okay? We have not add much beyond the physical and then lave the Mac layer. This is already 8% of ideal number. Let's add a few more. For example, more interference among users at peak hours. Upper layer, layers, layers three, four, five protocol over has headers, control signals protocol semantics, okay? You add back haul network congestion, okay? And that would reduce it further, okay? In fact, we haven't even added layer two fully, okay? Layer two for LTE, we mentioned there are three sub-layers, PDCP, RLE, MAC. They all have their own overhead just in the header, okay? So, you've got from 315 megabit per second, down to 28 or so just by physical layer. And then after layer two, all the header, you know, down to 25, okay? And after further overhead in terms of header and semantics and the control signal, and after further back on network non-ideal situations, you can easily get another factor of two to five reduction. That means, you know, finally are getting down to something like five to ten megabit per second that you can experience say, in downloading a bigger PowerPoint email attachment. Not 300 and fifteen, but five to ten. And you see that this is like 3% of the advertised speed, okay? Now actually, if you can get to ten megabyte per second, that's not bad at all. You can run a pretty good experience of video, okay? You can do many other applications on your phone. So, LTE compared to 3G is still great, okay? You just have to compare apple with apple, orange with orange, okay? You can either compare LTE's physical layer ideal condition just between device and eNobe with the same kind of number with 3G. Or you can compare the useful throughput application layer for LTE with that for 3G, okay? As long as you do a fair comparison, you can see that 4G LTE is indeed much faster than 3G. No doubt about that. What is tricky however, is that you can't just take these kind of numbers and say, oh, I'm going to get 300 megabit per second. it's going to be so fast in downloading everything and I can watch ultra HD movie on my iPhone 5 or something, okay? You have to say realistically by the time you experience in the application layer end to end in a normal time of the day, you're going to get down more like ten megabit per second. Which is still pretty good for like a normal video. But not HD, and way, way less than something like ultra HD. Well, that's just for the air interface detail example. Let's go through a couple of other examples in the back hall, just on the TCP side.