Welcome back, dear students. Today we are going to talk about the challenges of doing Wireless System Design, coming back to the challenges that we discussed last time and see how we can approach them. Let's first remember the challenges from last time, and I know that your memory is probably fairly perfect because you're young, enthusiastic students, my memory is not quite so good so I'm going to take them back here on the screen. These are the two challenges that we ended with last time, they're the ones that we identified. The first challenge is to accurately receive the weak signal from our own transmitter because we already identified in the previous lecture that because we're not using wires, the energy gets spread out from the transmitter in many directions and we receive only a small part, a small fraction of the transmitted energy. We also need to receive that accurately so that we can extract the information reliably. The second main challenge is that we should not receive any other transmitters. That, as you might remember, is the challenge that gives us eternal bliss and perfect job security. In this lecture we are going to look at the first one though, and actually, the first part of the first one, so just receiving the weak signal from our own transmitter. The accurate part we will do in the next lecture and also the lecture after that, we will go into not receiving the other transmitters and we're going to look at the weak signal. First, we are going to find out how weak that signal really is because we need to know that if you want to overcome that problem. How do you find out how weak the signal is at some distance from a transmitter? Which part of the signal actually arrives at the receiver? Well, a very straightforward way could be that you just measure it. In this case, I could take the [inaudible] from our lab and attach a good antenna and a good measure, for example, the signal strength from the Wi-Fi access points a little bit further in this building. Hence, that would work and I get an accurate number. However, that number is only applicable to this specific situation. It's probably similar to very similar situations but it doesn't give much insight in other situations. The other basic approach is to not do any measurements but to make a simple model that we can use to gain insights and the class of situations that are similar to that model, and that's what we're going to start with. We're going to start, just because it's start the of the course, with an extremely simple model. Not something like this studio, no lights, no cameras, no people, no floors, no walls, no doors, nothing. In fact, what would be the most simple model that you could think of? Well, how about nothing? I'll even take away the grid as background, just have a completely empty page. What if we have a completely empty universe, no stars, no planets, no gas clouds, no dark matter, no people, nothing? Nothing except a transmitter and a receiver. You might recognize this, this is the transmitter from last time, the original one from Ms. Marconi, and this is the original receiver from Ms. Marconi. Then add some distance in this further completely empty universe. Now if you want to calculate the power that arrives at the receiver in this situation, it's actually not all that difficult because there's nothing there except the transmitter and the receiver. There is also nothing to absorb the power that's being transmitted by the transmitter. We have no loss and that means that if we draw a sphere around the transmitter and we integrate the power that passes through every piece of the sphere surface, then it has to add up to the total transmitted power. That means that the total transmitted power has to be identical to the integral of the power density at the surface of the sphere, integrated over the area of the sphere. Since we also assume that the transmitter does not know in which direction the receiver is, the best thing that a transmitter can do is transmit equal signal strengths in all directions. The power density at the surface area of the sphere is constant independent of the direction. That means we can simplify this formula, we can say that the total transmitted power has to be equal to the area of that sphere, which is 4Pi times the square of the radius of the sphere times the power density that we find. What you see from this is that the power density decreases with the square of the distance. That means fairly quickly, we will get a very weak signal. To further complete this model, you have to make some assumptions about fellow parameters. Friis, and you will encounter him later in this course as well because of his work on calculating the total noise figure of cascaded signal processing stages. But yeah, he became famous for working out this model into an equation that we call the Friis transmission formula. Essentially what it says is received power, P_R, is equal to the transmitted power times this term, and in this term you will recognize the 4 Pi r squared path, the dependency of the received signal strength with the distance squared. What you also see in there is the wave length, Lambda squared in this case, and that's because the effective antenna area, the piece of the sphere from which the power density gets integrated into the energy that's received by the receiver antenna, that scales with Lambda squared, that explains this term. Then there are two terms left, and that's the gain of the transmit antenna and the gain of the receive antenna. Well, we started out saying that we assume that we don't know in which direction the transmit antenna is relative to the receive antenna or vice versa. That means that antennas are omnidirectional. That does not need to be the case, so if we know the direction, we could focus our energy a little bit more, and so we would concentrate energy a little bit more in one direction and a little bit less in a different direction. That's modeled with the parameter that's called antenna gain, and we have an antenna gain for the transmit antenna, that tells us how much signal strengths we improve by focusing our energy compared to an omnidirectional antenna on the same receive antenna. Okay, so this is the formula we understand, it's not all that's difficult but it's as an important lesson in there. If you want to become famous, you don't necessarily need to think of something very complex or invent a very complex formula, but you do need to be the first one. If you want to become famous, is probably more effective to choose an area where there's a lot of development and set a start of its development rather than something that's fairly old fashioned. Even though radio technology is more than a century old, it's still at the start, it's still growing at incredible pace. We will come back to that in other lectures, but you will see that there's really an enormous gold and so this is clearly an area where you also could become famous just by inventing simple things. Okay. We have this formula, we understand it, we think it's even simple and almost straightforward, and we could have thought about it if we only had been the first one, but what does it really mean? How weak is that now? Let's look at an example. Let's look at the WiFi access point that I mentioned earlier, and let's say we're about 10 meters away from it, how much would I receive here, if we has omnidirectional antennas? Well, if you have omnidirectional antennas, then we know that the gain of the transmit antenna has to be one, because it's omnidirectional. We also know that the gain of the receiver antenna is one because it's omnidirectional. We know the frequency because if it's WiFi and it's in the lower band, then the frequency is roughly 2.5 gigahertz, that means we also know the wavelength, that's 10, approximately 0.12 meters, right? C over f. We know the distance, which is 10 meters like I said before. If it's WiFi then the transmit power depends a little bit on the piece of equipment you have, but let's say, for simplicity sake, transmit power is a tender for what? If you put these numbers in this formula, then what you find, is that the receives power is roughly 0.1 micro-watt. That means that even at your 10 meters distance, you receive one-millionth spot of the power that has been transmitted. We know that scales with the square of the distance. If you would not be at 10 meters with antenna meters, you would have 100 times less receive power. This tells you what the main challenges and how better it is for wireless systems. If you look at this, what can you do about that? How can you improve the received power? Now, this equation tells you, if you want to receive more power, you can increase the transmit power. That's very simple. Of course, instead of 100 milliwatts, you can transmit tenth of watts or you can transmit hundredth kilowatts or 100 megawatts, and your received power will go up accordingly because in this simple model, there's nothing, right? The system has to be linear because there's nothing that makes it non-linear. That means that we have a perfect proportionality between the received power and the transmitted power and you can increase received power by just increasing transmitted power, of course, at a cost, and because the energy consumption of the transmitter will go up and we'll go up quite a lot. For every time that we make the distance 10 times larger, the transmit power has to go up by a factor of 100, and therefore the power consumption of the transmitter probably also goes up at a similar amount. What else can we do? Well, we can go to lower frequencies, Because if you go to lower frequencies the wavelength becomes larger and we receive more power. That's interesting, is it? It seems almost contradictory. We don't have any loss, the absorption of power not at any frequency. But still if you go to a lower frequency, it seems like the loss gets less, we get more power. Why is that? Well, that's essentially because an omnidirectional antenna at a lower wavelength takes energy from a larger area. It's effective area is larger, and you will learn more about this in the course, that's part of the series about antennas and propagation. That's why this is. It's not the power is really lost, but your antenna appears to be bigger. The other thing you can do is you can increase the gain of the transmit antenna and the gain of to receive antenna. You can do that by making them bigger, physically bigger, because of their results and directionality. It will result in focusing of the energy of the transmitter and focusing of the direction from which the receiver receives energy within corresponding increase and power that is being absorbed. From that point of view, it's probably better for the environment not to increase the transmit power, but to increase the gain of the transmit antenna and the gain of to receive antenna. It also has another advantage. If you do that, then the interference that you cause, the problems for other receivers to not receive our transmitter, become less because transmit power becomes less. Only FTL receivers are in the same direction as our receiver. Well, they'll suffer equally. But if they are in another direction because we focus the energy, they actually have less of a problem. That's something that we will come back to when we discuss this second main challenge of not receiving other transmitters. But I wanted to bring it up here already. Now, still, when you look at this, you think, well, looking at this formula, we should always go for the lowest frequency. But this is really true. Well, it depends what your boundary conditions are, what your assumptions are. Because if the assumption is that you antennas are always omnidirectional, then yes, low frequencies are better. However, you can also make other assumptions. If you make the assumption that your antennas are always the same physical size, then the gain of the antenna will actually increase, If you increase the frequency. The gain of the antenna will actually increase proportional to the square of the frequency. Same for this one. That will actually offset the square of the wavelength, and it will overrule that. If you have the same physical size antenna, in fact, your receive power will go up by increasing the frequency, and it will go up also with the square. Depending on your assumption, if you assume that you have omnidirectional antennas, it'll go to lower frequencies if you are size limited, For example, if you have a mobile phone and the size of your antenna is limited by the physical size of your phone, but not by anything else, then it makes sense to go to higher frequencies. You also see that in many applications. For example, in modern high data rate applications, people go to higher frequencies and they use directionality. They use high-gain antennas to actually get more signal at the receiver. This brings us to the end of this lecture. I think that you probably need some time to meditate about what this really means for you and for the systems that you're going to design. But this gives you the essential model for understanding what you can change in the system and how you can calculate a system that gets enough energy from the transmitter to the receiver. You can trade off antenna gains. You can trade off power, you can trade off frequency for distance using this formula. However, what you should remember during your meditations and also to your future career, is that this model is only valid in this completely empty universe. Maybe you don't mind so much that there are no suns and there's no stars and there's no planets, and there's no dark mass. Maybe you don't even mind that there's no people and no lectures. But also there will be no customer to pay you for the systems that you design and that might be a serious drawback. Always take into account that this model is extremely simple and does not have much in common with the real-world that most of us live in and so you always need to take that into account. You can use this to build insight, but you need more accurate models or measurements, to translate that into the boundary conditions and situations for which you are designing the system. With those last thoughts, I would like to thank you for your attention and conclude this lecture. Thanks.
