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來自 Princeton University 的課程

Networks Illustrated: Principles without Calculus

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Princeton University

Networks Illustrated: Principles without Calculus

40 個評分

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.

從本節課中

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, we just looked at what was initially proposed solution to the near-far problem

and we said it was called the TPC or transmit power control algorithm.

The TPC algorithm tries to do is to equalize the received signal power, but,

it turns out that signal power isn't really what we need the calls to be

equalizing. We need to equalize something else, which

is called the signal quality. Now, quality is different than power,

because quality takes interference into account.

So when we looked at the TPC algorithm, we were only concerned with what issue

the transmitters were sending, so this one was sending may be 2 milliwatts and

this guy closer to the station was send 1 milliwatt if the station was over here or

something. And, while we, we were looking at this

person's link to the transmitter and this person's link to the transmitter.

And we said, while this person needs to then increase his power to 4 milliwatts

and this person cuts it down to 0.5 milliwatts I'm just making these numbers

up, then everything might be okay. The problem is that when this person

increases up to 4 millawatts that he's causing extra interference to this

transmitter right over here. So we kind of have a vicious cycle, where

as this person increases his power and this person would have higher

interference, then he might have to increase his power, which would cause

this person more interference. Then he might have to increase his power

and so on and it'd be a vicious repetitive cycle or an arms race if you

will to the maximum transfer of power. So we need a way to do that, and we'll

look at now, exactly what signal quality really is and we'll define this.

So suppose we have three transmitters, A, B, and C, and they're all looking to

transmit to a base station. Now we can consider the receivers on the

single base station as co-located. So this is receiver A, receiver B, and

receiver C. Even though they're all going to a point

on the base station, just look at them as three separate places on the base

station. So if we look at receiver, if we look at

transmitter B for a second, let's focus on him first.

We have a few parameters here. The first one is the direct channel.

So B has a direct channel right to his receiver B.

This is transmitter B, this is receiver B.

And that's where he wants to get his signal, so he wants to get it to receiver

B. But now, if you look at these receiver,

what we also have to take into consideration is the fact that A and C

are going to cause interference. So, this is the direct channel, and this

is the indirect or interference channel. And direct here really means desire to

indirect this undesired, and this is also an indirect as well.

And, we have the same exact thing for each of the other transmitters and

receiver pairs. So for A, he has a direct channel and his

interference comes from interfering channels with channels B and C.

And then in addition, each of these receivers themselves are going to have

some amount of internal noise. It's just basically random fluctuations

of electrical signal. We won't go into it in much detail, but

each receiver has a certain amount of a noise that is within it as well.

So, this leads us to define what's is known as the signal to interference

ratio. And we'll look at exactly how that is

computed when we look at the next algorithm, but basically, we want to take

all this good stuff and divide it by all this bad stuff.

So the good stuff is the direct signal. Now, the bad is the interfering signal.

We can call that the interference. In this diagram right here, we can see

for B, the interference would be this arrow coming through, as well as this

arrow coming through. Plus, we have some noise in the receiver

that we have to get over. So, every transmitter needs a certain

signal to interference ratio or SIR, and SIR is how we quantify signal quality.

So, when we try to equalize signal quality rather than signal power, we're

trying to equalize the desired signal to interference ratios.

So now, suppose we have three phones that are standing close to one another and

each of them has some desired signal to interference ratio that they all want to

pick. So, this phone first sees some it, that

he's lower than his desired signal to interference ratio, so we increase this

power. Now, that causes interference for this

phone, and this phone. So now, each of them increase their

powers, which then causes this phone to increase his power, again.

Causing this phone to increase his power, causing this phone to increase his power,

and it becomes a really vicious cycle again, as we said.

So the question we have to ask is, is there a way to avoid this arms race?

Is there a way that we can follow some sort of a courtesy procedure on each of

these phones so that no one will ever come up and transmit too loud?

And the answer is, yes. That is possible to do provided that the

signal to interference ratios are feasible.

So we want the desired SIRs, the SIRs that each of these guys choose and that

they want to get to, to be feasible. And as long as they're feasible, then we

can have a solution and we can find a set of transmit powers for each of these

phones to send that. Such that all of these signal

interference ratios will be satisfied at the same time.

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