Near-far Problem

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Networks Illustrated: Principles without Calculus

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Princeton University

Networks Illustrated: Principles without Calculus

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What makes WiFi faster at home than at a coffee shop? How does Google order its search results from the trillions of webpages on the Internet? Why does Verizon charge $15 for every GB of data we use? Is it really true that we are connected in six social steps or less? These are just a few of the many intriguing questions we can ask about the social and technical networks that form integral parts of our daily lives. This course is about exploring the answers, using a language that anyone can understand. We will focus on fundamental principles like “sharing is hard”, “crowds are wise”, and “network of networks” that have guided the design and sustainability of today’s networks, and summarize the theories behind everything from the social connections we make on platforms like Facebook to the technology upon which these websites run. Unlike other networking courses, the mathematics included here are no more complicated than adding and multiplying numbers. While mathematical details are necessary to fully specify the algorithms and systems we investigate, they are not required to understand the main ideas. We use illustrations, analogies, and anecdotes about networks as pedagogical tools in lieu of detailed equations. All the features of this course are available for free. It does not offer a certificate upon completion.

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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 Brinton
Lecturer
Electrical Engineering
Mung Chiang
Professor
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.

[SOUND]

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