0:54

Optimization means management.

So management means we have to maximize the number of users in the wireless system

utilizing radio frequency spectrum resources very effectively.

So talking about the wireless resource and

management, I will try to answer six questions.

The first question is,

how does interference affect the capacity of wireless networks?

2:18

But as time goes, as the guest arrives in the cocktail room,

room becomes very noisy.

The so called interference is generating upon each communication pairs.

So your partner listener actually can't hear your voice,

or signal correctly due to increased interference that

is generated by your other surrounding communication pairs.

So in the cocktail party room, as time goes noise or

interference goes to high and then no one can communicate.

This is called cocktail party effect.

And such cocktail party effect is very well used in communication

3:15

Well, the question is if interference is actually going up what will be happening?

That was the first question.

Of course you may understand that when interference goes up no one can

communicate with each other.

It's very difficult to talk to each other so

there should be some coordinator such that some conversations may be possible.

Well, to see more precisely we may visualize

wireless network using a graph that's in your next slide.

4:04

In the previous graph, we have two things.

One is node, the other one is actually the edge.

In a wireless network nodes means transmitter.

In a cocktail party the speaker and another node is actually the receiver

Rx in a cocktail party who is your partner or listeners.

And the arrow, the direction arrow, means actually the wireless link.

Which is actually the wireless channel which

should be based on a radio frequency spectrum.

5:04

By definition the random network means that your

partner listener is actually the selected random name.

That means Each communication parties are randomly selected.

This is slightly different from cocktail party room.

In the cocktail party room, speaker and listeners are actually very close and

they are in a very closed proximity.

However, in the random network, mathematical formula,

mathematical form is actually transmitters and

receivers are actually located in a random position, that is slightly different.

But however, in many cases we can visualize cocktail

party room utilizing this random network.

Well, the question is if you increase the number of nodes or

the number of speakers, in other words number of communication pairs.

And this will generate lots of interferences

because they are using the same resources, same radio frequencies,

generating interferences and in certain level no one can communicate.

So this actually by intuition we could understand.

Well, question is, does node density increase?

We know that capacity equals zero.

Well, at this point let me define the meaning of capacity.

In a wireless network capacity means the number of communication

pairs that can successfully talk to each other.

If their communication is failed due to large interference or some other

reasons, then we count the capacity, I mean we do not count it as a capacity.

So if capacity goes to zero means there is no one successful to communicate.

6:51

So as interferences increases or

as node density increases like in cocktail party room capacity,

the number of successful communication pairs will be approaching to zero.

So due to the interferences, we think that capacity is going to be equal to 0.

7:08

Well, this is very intuitive and understandable.

Our next question is, is there any accurate mathematical formula so

that we can understand capacity and

interfacing relationships more concisely or more accurately?

That is related to answering the question more correctly.

So if I go to the next slide, there is some mathematical formula which was

actually originally published in a paper in the year 2000.

Published in the Journal of IEEE Transactions on Information Theory

by Gupta and Kumar.

7:46

And if you look at this formula, it looks complicated.

The formula itself is not that difficult to understand.

The lambda is a function of n.

Lambda means capacity.

As I said, capacity is the number of successful communication pairs.

So, Number of successful communication pairs is a function of n.

What is n?

n is node, number of nodes or node density.

How many nodes in a given area?

Or how many communication pairs?

8:19

Is a function of n and

the function is actually inversely proportional to n multiplied by log n.

So that means if you understand this formula,

as n goes to infinity, then lambda goes to zero.

And we understand that lambda is approaching to zero as n goes to infinity,

but however, we can more accurately understand the formula itself.

Well, there is another terminology here, c and w.

And c is actually the sum of constants.

it's very much related to the system.

So kind of the characteristics like antennas and

some other physical layered techniques or something which are given parameters.

9:03

Whereas w is a given frequency spectrum bandwidth.

In the beginning, I said actually the radio resource or

resource means frequency spectrum which is very much limited.

So w is a given bandwidth or bandwidth or one wireless link.

So as w becomes larger then capacity will be increasing.

But in this formula the authors, Gupta and Kumar, assume that c and

W are given and fixed.

So this formula gives more accurate answer to the first question,

as n goes to infinity, lambda goes to zero with such formula.

And in their original paper,

they defined the capacities slightly in a different way than the others.

That is called the transport capacity.

Transport capacity means, it is actually the multiplication.

If you look at this line in the middle, these are bits multiplied by meters.

So when Gupta and Kumar defines transport capacity,

they are interested in number of bits that can be transmitted per second.

However, they are also interested in the travel distance of bits.

If one bit travels twice meters than the others, then transport

capacity becomes twice of the others.

10:26

So transport capacity, understanding transport capacity is quite important

for answering the next questions in my other slides.

But at the moment just understand that the capacity is a function of n

which is inversely proportional to n.

And as n goes to infinity then lambda goes to zero.

Well this is actually the bad news for

us because in a wireless network n is number of communication pairs.

So people desire to communication more and

number of communicating people will be increasing.

However, if they are sharing the same radio channel, no one can communicate.

So this is actually the dilemma for us.

The question is how we handle such larger number of communication pairs

while keeping this capacity rosier.

11:20

Well, Radio Resource Management is, as I said in the beginning, is to maximize

capacity of the wireless network while utilizing frequency spectrum effectively.

How do we do that?

Well, Radio Resource Management is, to say, to control interferences.

We understand what is interference using this body effect.

11:43

Well, by contouring interference amount effectively, then we can maximize

the capacity or we can adjust it or we can increase the capacity wireless network.

That will be the topic in my next questions and following questions as well.

Well, of course you can think of a very simple

resource management technique even though it is not desirable on a solution.

For example, if you can't communicate with others

like in a cocktail party room due to huge interferences.

The best or very simple way of resource management is to make capacity zero.

That means, the best way is to shut off.

Of course this is very simple and

actually of extreme cases radio resource management technique.

12:31

Well, there might be some other cases, for

example there will be some coordinators in the room.

So the, for example, the imaginary situation, that the coordinator,

actually making some traffic controls like this car should communicate first and

the remaining will be staying there.

As there will be some kind of round robin way of communication.

For example, not in the cocktail party that mean the communication system,

this is possible for example.

So such a kind of radio resource management technique would be possible

to handler interferences such that maximizing or

in order to maximize the capacity of the wireless network.

So to know a little bit about that kind of techniques

let's take a look at the other questions following.

Thank you.