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Near-far Problem
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Из курса от партнера Princeton University
Networks Illustrated: Principles without Calculus
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Power Control in Cellular Networks
How is it possible that we can all communicate effectively without disrupting each other's calls, messages, or Internet usage? In this lesson, we will take a look at some of the methods that have been developed for letting us "share" the air over which our phones communicate.
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Christopher BrintonLecturer
Electrical Engineering
Mung ChiangProfessor
Electrical Engineering
As we said, CDMA did have its fair share of problems before it became a cellular
standard. We'll look at two of those in this
lecture, but specifically we'll focus on the first one that we point out.
And we'll start that off by looking at what's called the near-far problem.
The first, suppose we have a bunch of transmitters, like a bunch of cell
phones, and we're all transmitting close proximity.
So, as we said, under a CDMA scheme, they're all going to be transmitting on
the same frequency and at the same time. So with CDMA, they have different codes,
but still this will cause some interference, so there will be inevitable
interference if everyone's transmitting at the same time.
And we have to overcome some of that interference here.
So, now, in this picture, in this diagram, we have all these transmitters
in very close proximity to one another. But, this problem gets exacerbated when
we have transmitters that are different lengths and distances away from the
recipient tower. So we could have one transmitter in your
car, maybe, and another transmitter that's behind a few trees and much
farther away from the cell tower. And so, we say that this guy Is going to
have much better channel quality than this guy over here because there is
trees, and there's a lot more distance in between.
And the distance as well objects in the path that obstruct the channel lead to
different levels of channel quality, and this guy's going to have a degraded
channel quality relative to this guy. And so, this is known as the near-far
problem, is that we have different levels of channel quality depending upon how far
we are from the base station. So before we look at the solution to the
near-far problem, we first have to define how we go about measuring power.
So how do we measure transmit power? We need a way so that if you put it on a
ruler, rather than having inches we'd have some other quantity.
And the quantity that we use is called the watt, and that is the standard unit
for power. So a watt is actually much larger than
anything your phone will ever transmit. Your phone transmits is on the order of
milliwatts instead of on watts, and a milli is times 10 to the negative 3.
So it's one-thousandth, rather than kilos we saw before which time, which was
thousands. Milli is thousandths.
So the well, the levels on your phone transmissions are on the orders of
milliwatts. So, let's suppose that the first car over
here is transmitting at 20 milliwatts, and he's transmitting to the base
station, and as we said before, we have attenuation, and by the time it gets
there, it's down to ten milliwatts. So it's cut in half by the time it gets
to the base station. But now is the near far problem would
tell us this car who may be also transmitting at 20 miliwatts by the time
he gets to the station his power is all the way down at 2 miliwatts because not
only does he have more attenuation because he's a farther distance but
there's also trees and objects obstructing the signal's path so its
weaker by the time it gets there. So we want a way to be able to equalize
the power levels at the recipient, so at the base station, at the base station
over here, we want to be able to make these two levels the same.
We want these two to be the same, and so we need to boost.
The transmit powers and that's the way that we do that.
And so there's an algorithm that does this and we'll its a very simple
algorithm and we'll look at that right now so basically by the time this signal
gets over here as we said its cut in half because if we take 20 divided by 10 we
get 2 which indicates that this is twice the power at the recipient.
And now, suppose that the receiver wants to see 5 milliwatts.
So it doesn't even want to see 20 milliwatts or 10 milliwatts or anything.
It wants to see 5 milliwatts. So this transmitter, even by the time the
power gets there, is still too high. And this transmitter is, on the other
hand, too low. So this 20 over 10 gives us a factor of
two which tells us how much this guy has decreased by the time it got to its
recipient. So, basically, the tower is going tell
this car, right here, this transmitter is going to tell him to transmit.
Rather than at 20 milliwatts, it's going to say okay well I know that your signal
gets cut in half by the time it gets to the receiver then I want to receive at 5
milliwatts. So I want to see you transmit twice 5
milliwatts, so 2 times 5 milliwatts, which is equal to 10 milliwatts.
So the tower is going to send a signal back that says send at 10 milliwatts.
And so the idea is then, if this guy changes to 10 milliwatts, hopefully this
signal will the cut down to 5 milliwatts by the time it gets to the receiver.
It may not be exactly so, and you may have to iterate it a few times before it
gets exactly to the desired, but you get the basic idea.
Now, on the other hand, with this transmitter over here, he starts at
twenty milliwatts, and by the time he gets there he's down to two milliwatts.
So 20 divided by 2 is 10. So it's a factor of 10 reduction rather
than just having it's dividing it by 10 by the time it gets over there.
And as we can see, the receives power in this case is less than this desire
perceived power, so they take this ten, this factor reduction and well, say,
transmit at ten times. Whatever I want to receive, or five
milliwatts. So he's going to say, okay, transmit at
50 milliwatts. So, while this guy's transmit power goes
down, this guy's transmit power goes up to 50 milliwatts.
And the hope is that if he sends at 50 milliwatts, then by the time it gets down
here, this will be at 5 milliwatts, as desired.
So we can rearrange this equation just a little bit to make it a little more
convenient if we just take this, this example right here.
Let's say we have this 20 divided by 10 times 5, which is going to give us our
result. So this, as we said, is the transmit
power. This is the receive power, and this is
the desired power. So, if we take this, and let's rearrange
this and put the transmit power out front.
So we can say that this is equal to 5 divided by 10.
We're multiplying, so I can just move over I can move any of the terms.
So, 5 divided by 10, and then we'll multiply that by 20, which is the transit
power. So we can take this as a constant term,
because the 5mW is constant and whatever it's received at is constant for this
time, and that gives us how much we want to multiply the current transit power by
to get the next transmit power. And that gives us the basics of the
transmit power control algorithm, where we basically take, say, for the next
power, is equal to this thing called the ratio times the current power, and the
ratio is this guy down here, this 5 over 10, that defines the ratio.
So if we look at that again, for this example, very quickly, and see What that
tells us is over here, we can take this and rearrange, so we have 20 divided by 2
times 5 instead. And we said, well we want to take the,
the desired power of 5 and divide that by the received power of 2 and multiply that
by the transitive power of 20. So now this ratio is 5 halves rather than
5 tenths. Notice that the ratio tells us whether
the transit power in the next iteration is going to be higher or lower.
If the ratio is less than one, as it is in this case over here, then it means
that it's going to be lower next time. And if it's greater than one, it means
it's going to be greater, as it is over here.
And in the case that it was the same as one, which is where we want to get to
eventually, it would stay the same.
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