In this video we're finally going to use everything that we've learned in the
course. And we're going to learn how communication
systems actually work, and figure out the basic elements of communication system
design. First let's recall what the fundamental
model of communication is. There is a message that someone wants to
send to some destination, and the problem is that doing that is not easy because of
the channel. Nothing good happens in the channel.
Signals get attenuated, sometimes filtered.
There's noise, interference, all those kind of issues pop up.
So to best combat how the effects the channel has on transmissions, is that the
transmitter and receiver are, are there. They're systems which produce signals
related to the message, which makes it easier to get the message through the
channel and to bring back the original message as well as possible.
Like I said, we know all the tools already to figure out how transmitters and
receivers work. They involve modulation, and filtering,
and we already know how to do that. The thing we need to learn is so we've
figured out which tools to use, are the characteristics of the channel, that
governs everything. We need to understand the structure of the
message, and the channel. Well, in this video we're going to talk
about the wireless channel, electromagnetic radiation.
And we're going to see that it has several interesting characteristics, both good and
bad. Okay.
So everything in the world of antennas, wireless communication is governed by
Maxwell's equations. And here I show them.
We're not going to talk about how to solve them for any particular setup.
What I'm more interested in are the properties of Maxwell's equations, and
that's what I want to talk about. So interesting properties.
First of all, those equations are linear. That is very, very important.
So, the idea is that suppose there are two transmitters, one sending the signal S1
another sending signal S2, and they're coming out of these two antennas, and here
we have our cell phone sitting down here. What that antenna gets, on the cell phone,
is it's going to get both signals. And it looks like superposition.
So what' you're going to get are both signals.
You know, it could turn out that it's the transmitter sending signal 1, is what the
cell phone, person using this cell phone really cares about.
However S2 is going to come in also. So the idea is, how do you block this
signal you really don't want? Well the signal you don't want is called
interference. Interference is primarily produced by
humans. It's not necessarily a natural phenomenon.
Well it could be in some cases. So we have to figure out how you design a
communications system as a whole so that the receiver can figure out what's coming
in and pull out the signal it wants. Well, okay.
Here's another, side to the linearity thing.
And that is, suppose again, S1 is trying to send a signal to that cell phone.
Well, let's suppose the second antenna's trying to send a signal to that cell
phone. Well, they're going to pick up both, S1 is
going to be picked up by that cell phone and S2 is going to be picked up by that
cell phone. So the upshot of this is no privacy.
Once you send a signal over an antenna, a wireless signal, any, any other system
that has an antenna can pick it up. So this means you have to be a little bit
careful if privacy is a concerned, about how you send that message.
Okay. So another thing that's important, is that
waves electromagnetic waves propagate at a speed of c.
So, let me, illustrate what propagation is.
Suppose I draw a axis. And it's a little interesting.
Suppose this is space, and this is time. And in some particular location, I send
out a pulse that's of this width and time. What propagation means is that sometime
later, that same pulse appears at a different position x.
So, the distance here, let's call it delta x, and the difference in time, delta t,
the speed of propagation is delta x over delta t, whatever that may be.
Well, for wireless signals, that speed of propagation is the speed of light.
And, if you go back to Maxwell's equations, it's given by 1 over the square
root of epsilon mu, and we're not going to go into the details of how that's
calculated. But in free space the well-known result is
that the speed of propagation is 10 to the, 3 times 10 to the 8th meters per
second. That's the number we're going to use for
wireless systems. Now, there's another aspect of propagation
that applies for sinusoids. So, let's suppose I have a time axis, and
I have a sinusoid that's coming out of an antenna, so it's propagating.
So this time difference is the, that's the period, and we know that's 1 over f, from
all we've already learned. However, I can also plot this as a
function of space, same signal because it propagates.
And now, the period in space is called the wavelength lambda.
Lambda has units of distance, and it turns out for propagating waves, the wavelength
times the frequency is equal to the speed of propagation.
Very important result to keep in mind. So suppose we do a little example here.
Suppose we have a frequency of 1 gigahertz, and that's 10 to the 9th.
So that gives a wavelength of 0.3 meters, which is 30 centimeters.
So the wavelength is still pretty significant compared to the size of your
cell phone, if it's communicating at a frequency of 1 GHz, which is pretty close
to what is used these days. Now, another less understood result is
that because of Maxwell's equations and the properties of the atmosphere and other
things, and the properties of antennas, is that low frequency waves do not propagate
well at all. In fact, as we'll see a little bit later,
the United States government does not regulate the transmission of signals below
about 10 kHz. You can do anything you want.
So if you try to send an audio signal from one place to another directly using an
antenna it's not going to work very well, because it has no range.
Low frequency waves just don't propagate. So in wireless systems, somehow we have to
shift the frequencies of the message signal up to higher frequencies so they do
propagate. We'll see how that works a little bit
later. All right, more properties?
And there's the conservation of power issue, which means that the amplitude of a
signal transmitted by our wireless has to decay with distance from the transmitter.
So here's a little diagram. And here we have a antenna, that let's
assume, sends out a short pulse, just for fun.
If you look at a specific distance R, let's say that from the antenna, the
power, if you inverted the power over that sphere, right, we're in 3 dimensions here,
that has to be the total power radiated by the antenna.
If you go out a bit further, that power cannot be unchanged.
We're essentially assuming that the wireless meeting is lossless.
So there can't be a power change. However, this is a bigger surface area out
here than in here. Consequently, the power at a given
distance from the transmitter has to go down.
You must have the result that the power any given distance from the transmission,
transmitting tower times the surface area of the sphere has to be a constant.
So that leads to the fundamental result that the power that a receiver gets must
obey an inverse square law. So that the more distant the receiving
antenna is from the transmitter, the smaller the powers might be.
Or maybe said a little better, the amplitude has to go down like 1 over r.
It's the fact of life, fundamental physics.
Now the other thing is that materials both common and natural, can absorb and reflect
waves and this depends on their characteristics.
So let's suppose we're in a city environment now, where we have tall
buildings and there's a radio tower trying to send a radio signal to my little car
down here. Well, if there's a direct path, that's
fine, but it turns out these buildings can reflect, and in most cases do.
Buildings in the cities do reflect the electromagnetic energy.
And actually this antenna will see both the direct and reflected paths.
This turns out, causes a little bit of problem in communication systems.
More importantly, suppose there's another vehicle over here, which I'm going to draw
very badly, which is trying to receive the same signal.
Well, that signal is blocked by the buildings, and this antenna won't receive
anything. This is why driving in cities cell phone
signals and radio signals can go in and out, depending on the height of the
buildings and how many are, where their positioned and where their transmitter is.
It's a real problem. Well it also turns out natural entities
can also affect electromagnetic transmission.
I'm thinking here of a tree. And you may wonder, why would a tree block
a signal transmission? And the reason is because the leaves are
loaded with water. That's their primary constituent.
And water is a very good conductor of electricity, and essentially the tree
shorts out the electromagnetic transmission, and our poor little car
here, the only thing it can get is a signal by a reflected path.
So if you're going through even a, a rural area, where there are lots of trees, you
can have your transmission sorely affected by trees and other naturally growing
things. Now, more, let's talk about that direct
path a little bit more. And here we have what's called
Line-of-sight communication. And that means that the transmitting
receiver antenna, and the receiving antenna can quote on quote feed each
other. That's why it's called Line-of-sight.
There is a direct straight line path connecting the two.
Because of the curvature of the Earth, this is, doesn't go on forever.
If you're over here somewhere, there is no line of sight path to this receiving
antenna. And, in essence you cannot send a signal
from, directly from this transmitter over to the other one, because the Earth gets
in the way. So it's very interesting to know what is
the line of sight transmission distance. Well, simple geometry using the
Pythagorean theorem, it's pretty easy to derive, shows that the line of sight
distance is given by this formula. And this is the radius of the Earth.
So let's suppose we have a little example here.
Suppose we have a 100 meter tall antenna. That's a pretty tall antenna.
And you can plug it into the formula just as well as I can.
The line of sight distance is about 71 and a half kilometers.
Now that's the total distance here. If you were on the ground level, let's say
holding your cell phone, then that distance let's say from here over to the,
from the transmitter is going to be half of that.
So 35 or so, 37 kilometers is the total distance that a cell phone can be reached
by a 100 meter tall antenna. So it's pretty limited.
And certainly not small compared to the circumference of the Earth.
This was a big problem when they were trying to develop trans-oceanic,
communication. When Marconi was trying to figure out how
to send wireless telegraph signals across the Atlantic Ocean.
And it turns out he did this experimentally, and it turned out it
worked, because he discovered, and, and quickly was explained that there is an
ionosphere up there, which really helps. So here is my Earth.
And let me complete the circle as well as I can.
And suppose I'm over here and I'm trying to send over here.
Well, there is no line of sight path. It's too far away.
What[unknown] has discovered is that the ionosphere acts like an, a mirror.
Signals can come up and be reflected back down to Earth, enabling communication
between distant places. Now, I deliberately showed it over here as
being a little iffy, and that turns out to be true.
It turns out, at some frequencies, the ionosphere Is transparent, and radiation
goes straight through. At other frequencies, it acts like a
mirror. And so you have to understand the
frequency properties of the ionosphere. It's similar to a transfer function.
This is more of a reflectivity function that's a function of frequency.
Then there's another phenomenon, and that is that the transmission reflection
characteristics depend on the time of day. It turns out, solar radiation from our sun
interacts with the ionosphere, and during the daytime, it does not look much like a
mirror. Those same frequencies, where at night it
looks like a mirror. And I don't know if you've ever tried
this, but at night using classic AM radio, you can receive stations from a very long
distance away. However if you tune into that same station
during the daytime, it's impossible. You will not receive it at all, and that
is because the ionosphere changes its characteristics depending if it's the sun
is, is sending radiation to it, that affects it, or not.
Well, how about satellite communication? Now here, almost drawn to scale the idea
in satellite communication is that suppose there's a transmitter here, and here's our
little satellite, up here. And the way satellite communication works
is that a transmitter sends a signal up and that gets re-radiated back to Earth.
And, basically it's a coverage, basically about a third of the Earth's surface,
let's say. Well, now, as the Earth rotates, okay,
what you want for the geosynchronous orbit is that it rotates a greater distance, but
in the same time, so again, it appears that by the time the antenna gets over
here, our little satellite is directly overhead still.
So you don't have to change the transmitter at all.
That's called a geosynchronous orbit. And so, what happens in a geosynchronous
orbit is that the time it takes to go around once has to be exactly one day.
And when you do the physical calculations from Newton's equations, what you get, is
that means that the radius of that orbit from the center of the Earth has to be 42
million meters. That's a long, long way.
And in fact, it turns out there's a significant time delay.
If you take the speed of light, and try to figure out what the time delay is, the
time delay in sending a signal up to the satellite and back is at least about a
quarter of a second. And if you're, have to do this several
round trips, so to get around the earth let's say, that it's just going to add.
And so that's the big delay that you encounter in satellite communication
systems. I know in the old days we used to have a
telephone call from places like India from the States.
They used satellite communication ,and it greatly affected the quality of the
conversation, the delay was instantly noticeable.
Very interesting. So anyway, those are the characteristics
of wireless channels. It, there is a, just from fundamental
physics, an inverse square law governs the power that a receiver, an receiving
antenna can get from a transmitter. And the speed of light may be fast, but
it's not infinite. And you can get significant delays between
transmission and reception. It depends on distance, of course.
And this really affects the satellite communications scenario.
More importantly, Maxwell's equations are linear and superposition applies, which
has, as I pointed out, good and bad properties.
No privacy, but this enables broadcast. So one radio antenna can send to lots of
receiving radios. However radio is now faced with the fact
that all the other stations are sending at the same time, and you somehow have to get
rid of the ones you don't want. And if you think about it for a second
what this means is filtering. We'll talk about that a little bit later.
And the big down side in wireless channels is that lots of interference is possible,
and it's all because of the linearity and superposition principle.
We're next going to talk about wireline channels, and you'll see that the
characteristics are very, very different.