0:54

Optimization means management.

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

Â utilizing radio frequency spectrum resources very effectively.

Â So talking about the wireless resource and

Â management, I will try to answer six questions.

Â The first question is,

Â how does interference affect the capacity of wireless networks?

Â 2:18

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

Â room becomes very noisy.

Â So called interference is generating upon each communication pairs.

Â So your partner listener actually can hear your voice,

Â or signal correctly due to increased interference that

Â is generated by your other surrounding communication pairs.

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

Â interference goes to high and then no one can communicate.

Â This is so called cocktail party effect.

Â And such cocktail party effect is very well used in communication

Â 3:15

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

Â That was the first question.

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

Â communicate with each other.

Â So it's very difficult to talk to each other so

Â there should be some coordinator such that some conversations maybe possible.

Â Well, to see more precisely we may visualize

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

Â 4:04

The previous graph, we have two things.

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

Â In a wireless network nodes means transmitter.

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

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

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

Â Which is actually is the wireless channel which

Â should be based on a radio frequency spectrum.

Â 5:04

By definition the random network means that your

Â partner listener is actually the selected random name.

Â That means Each communication parties are randomly selected.

Â This is slightly different from cocktail party room.

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

Â they are in a very closed proximity.

Â However, in the random network, mathematical formula,

Â mathematical form is actually transmitter and

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

Â But however, in many cases we can visualize cocktail

Â party room utilizing this random network.

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

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

Â And this will generate lots of interferences

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

Â generating interferences and in certain level no one can communicate.

Â So this is actually by intuition we could understand.

Â Well, question is, is node density increases?

Â We know that capacity equals zero.

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

Â In a wireless network capacity means the number of communication

Â pair that can successfully talking to each other.

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

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

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

Â 6:51

So as interferences goes to increase or

Â as node density increases like in cocktail party room capacity,

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

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

Â 7:08

Well, this is very intuitive and understandable.

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

Â that we can understand capacity and

Â interfacing relationships more concisely or more accurately.

Â That is related to answering the question more correctly.

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

Â actually originally published in the paper in the year 2000.

Â Published in the Journal of IEEE Transactions on Information Theory

Â by Gupta and Kumar.

Â 7:46

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

Â The formula itself is not that difficult to understand.

Â The lambda is a function of n.

Â Lambda means capacity.

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

Â So Number of successful communication pair is a function of n.

Â What is n?

Â n is node, number of nodes or node density.

Â How many number of nodes in a given area?

Â Or how many number of communication pairs?

Â 8:19

Is a function of n and

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

Â So that means if you understand this formula,

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

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

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

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

Â And c is actually the sum of constants.

Â it's very much related to the system.

Â So kind of the characteristics like antennas and

Â some other physical layered techniques or something so which is given parameters.

Â 9:03

Whereas w is a given frequency spectrum bandwidth.

Â In the beginning, I said actually the radio resource or

Â resource means frequency spectrum which is very much limited.

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

Â So as w becomes larger then capacity will be increasing.

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

Â W is given and fixed.

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

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

Â And in their original paper,

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

Â That is so called the transport capacity.

Â Transport capacity is, it means it is actually the multiplication.

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

Â So when Gupta and Kumar defines transport capacity,

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

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

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

Â capacity becomes twice of the others.

Â 10:26

So transport capacity, understanding transport capacity is quite important

Â to answering the next questions in my other slides.

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

Â which is inversely proportional to n.

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

Â Well this is actually the bad news for

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

Â So people desire to communication more and

Â number of communicating people will be increasing.

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

Â So this is actually the dilemma for us.

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

Â while keeping this capacity rosier.

Â 11:20

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

Â capacity of the wireless network while utilizing frequency spectrum effectively.

Â How we do that?

Â Well, Radio Resource Management is, in order to say, is to control interferences.

Â We understand what is interference using this body effect.

Â 11:43

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

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

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

Â Well, of course you can think of very simple

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

Â For example, if you can't communicate with others

Â like in a cocktail party room due to huge interferences.

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

Â That means, the best way is to shut off.

Â Of course this is very simple and

Â very actually the extreme cases radio resource management technique.

Â 12:31

Well, there might be some other cases, for

Â example there will be some coordinators in the room.

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

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

Â the remaining will be staying there.

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

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

Â this is possible for example.

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

Â to handler interferences such that maximizing or

Â in order to maximize the capacity of the wireless network.

Â So to know a little bit about that kind of techniques

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

Â Thank you.

Â