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Из курса от партнера Princeton University

Networks Illustrated: Principles without Calculus

40 оценки

Princeton University

Networks Illustrated: Principles without Calculus

40 оценки

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. Please note that per Princeton University policy, no certificates, credentials or reports are awarded in connection with this course.

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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

So the algorithm that tries to equalize receives signal quality, rather than

received signal power. It's called distributed power control, or

DPC. And DPC works as follows: we'll just

illustrate it very conceptually at first and soon we'll go through a computation.

The first thing that happens is that each of these transmitters here, in this case

we're just going to focus on three. Is going to start transmitting to the

cell tower. And they're all interfering with one

another as you can see here, we have our in direct gains as we've pointed out

before. And then the cell tower is going to

measure the signal to interference ratios, from each of these transmitters.

So it just takes that measurement has very strict ways of doing that by taking

the received power and dividing it by noise that is outside the signal and it

is going to send a message back to them telling each one of then what the

required SIR is and each of these transmitters is going to use a basic

formula similar to TPCL actually to adjust their power.

Then they'll readjust their power levels accordinginly.

And now, this is going to cause different types of interference in different types

of channel gains. And then, we're going to measure the SIRs

again, and send the SIRs back, and adjust their powers again, and so on.

So the next way is an iterative algorithm, and it will keep going on just

like this. Iterative means it's going to take

multiple steps, and eventually, we hope that the algorithm will converge which it

will converge, as we said, provided that the SIRs are feasible.

And again, by feasible we mean compatible, or that they can all be

satisfied simultaneously. So a good word for this would be

compatible [SOUND], for feasible. And, in fact, in addition to Converging

to a set of power levels that will work and that will achieve these desired

signal, interference ratios. They're also going to be optimal in the

sense that they're at the smallest power levels as possible.

So, the reason the higher power levels are bad, just to give you an idea is

that, the more power your cell phone uses to transmit, the more its batteries are

going to drain. So you want to always be setting it at

the lowest power you can while still achieving that SIR value.

And additionally, it's just not good to waste energy when you don't have to.

So that's another thing as well. So before we continue on to this example,

first let's point out a few of the values that we will be working with in the first

thing about each of the examples that you will see throughout this course is that

they're going to be much, much smaller than a real system.

So a real system in a real cellular are going to have many many many more devices

than you're going to see and we're going to be working with here, but we're

constrained by what we can write on a single piece of paper, and additionally,

it will illustrate the main ideas just by considering a smaller example.

So, now in this table over here, we're showing each of the three transmitters on

this side, A, B, and C and then the receivers as well.

And this, each of these values, is what we call a gain.

And the direct gains are from, for instance, from A to A, from B to B, and

from C to C. Those are the [SOUND] direct Channel gain

so we can write that here direct this is direct and this is direct.

And what this is really saying from A to A being point 9 is that whatever transmit

power we start with over here its multiplied by point 9.

And that is what it gets received at over here.

And we look at these as gain values, but since there less than one, we know that

is going to be less than what we transmitted at by the time we get to the

receiver because we're multiplying, so its really an attenuation but we look at

them as gain just strictly speaking for, in mathematical terms.

So then from B to B it's 0.8,so B has not as good of a direct channel gain as A

because you the direct channel gain to be as high as possible and C has 0.9 just

like as A does. Now we looking for the interfering gain,

for instance we can say from A strating with A to B, from A to B is 0.1, so this

value over here B 0.1. from A to C we have 0.2, so this couples

down here 0.2 of that. So wherever transmittive power we're at

we multiply it by 0.2 and we get how much power is going to come into the receiver

from as a result of A. So we want the indirect channel gains so

each of these dotted lines are indirect. And I'm not going to write all of the

indirect, I'm not going to write indirect six times.

And I don't need to write indirect six times, you get the idea.

So, we want the indirect gains to be as small as possible, whereas we want the

direct gains to be as high as possible. We can't always get all we want and then

from B we know B couples into A as 0.1 and B couples into C as 0.2 C couples to

A a 0.2 and C couples to B as 0.1 one thing we should know is that this table

is not symmetric And symetric would mean that going from B to A is the same thing

as going from A to B. So for many of the values here it

actually is symetric but for instance if you look at from C to B and B to C there

not the same cause we have point 1 and 0.2.

And the reason they're not the same is that different transmitters are going to

have different effects on different receivers.

Now, the next set of values that we need are based upon the links themselves.

So link A, link B, and link C have different parameters.

First is the target SIR, At the receiver. The target signal to interference ratio.

So A wants to get to 1.8, B wants to get to 2.0, and C wants to get to 2.2.

And now, in terms of noise, as we said, each noise is going to have a certain

amount of power. We're in a fraction of a milliwatt here.

A has 0.1 milliwatts noise, B has 0.2 milliwatts noise, and C has 0.3

milliwatts noise. So, you can see that they have different

necessities for different signal qualities, which'll depend upon the

specific phone and. Things along those lines, but

additionally, the receivers themselves are going to have different noises too,

and C is the worst in terms of noise, whereas A is the best.

So, in the next segment, we'll walk through the computations of a few

iterations of distributive power control which is the famous solution to the near

far problem.

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