So the concept of atenuation led engineers to start dividing reasons

geographically into what we call cell. Now we're not speaking of a biological

cell clearly so don't get confused there speaking of the cell in terms of a

cellular network or a cellular system. And the way that we represent a cell is

geometrically, as a hexagon. So we divide our region into a bunch of

hexagons, and the reason that we divide them into hexagons is be, perhaps beyond

our scope here. We can point out one important idea.

And one of the reasons is that at the intersection each of these cells we have

what we will be called cell towers or base stations.

And rather than having a base station at the middle of each cell serving to the

ends of each cells, we have a base station serving a portion of 3 different

cells. So, if there a bit serve this portion,

[UNKNOWN] serve this portion, they're going to serve this portion that's on.

So that's one of the reasons, and the other ones are perhaps beyond our scope

here. So now, within each of these cells, we

have our phones and each of our phones, or our mobile subscriptions, lie within

one of these cells. And we call cell phones, or any device

that can transmit and receive according to a cellular standard, a Mobile Station,

or an MS. And the MS's are going to connect to base

stations depending upon where they are. And another term you may have heard for

base station could be node B or evolvable node B meaning E node B that's a 4G term.

And we're not going to use that term here, even though you could call it node

B or enode B, depending upon what you're speaking in.

For our purposes here they're really synonymous, so we'll just stick with the

term, Base Station. So now, with FDMA, we have to determine

which frequency bands allocate to which cell.

And with the cellular network there's certain rules that this imposes upon that

from having a detrimental impact on conversations.

So what we say with the cellular network is that each cell is going to get a band

of frequencies. So naturally within each cell they are

all going to use one band of frequencies. But each mobile station has to be on a

different channel. So if this is the channel allocation for

this cell each mobile station on this channel is going to be on different one

of these channels. Each of the adjacent cells to this one

,so this cell right here is adjacent because it is touching, this cell is

adjacent this one also is adjacent. Each of them has to use a block of

frequencies that's different than the one that this cell is using.

So this cell up here would have to use a different set of frequencies, than this

cell over here. But, as long as the cells are not

adjacent, we can reuse the existing frequencies.

So up here for instance, in this cell, we can use the same frequency bands that

this cell down here is using. Because they're far enough away, that the

attenuation would cut down the signal level so far when we travel from here up

to here. That you won't even be able to hear the

conversations anymore, even if these people are using the same frequency bands

as the ones in this cell. So we have to determine how to allocate

the bands of frequencies in order to use the minimum number of channels.

Because that will clearly be the most specially efficient as we would say.

Or its making best use of our available capacity so that's a pretty difficult

problem mathematically if you have a really large saw region.

To determine what each cell would get, what frequency banny cell would get.

So that we conform to these ideas of only reusing if the cell blocks are not

adjacent, as we said. And using the minimum number, because

that's the most special efficient is to use the minimum, number of frequency

bands. So, we can look at this simple example

of, is it small enough, and we can just eyeball it would be in order to use the

minimum number. The way that we can go about doing that

is by assigning each one a different color, and a color here will be a band of

frequencies. So we can start by coloring this first

cell, blue over here. And now, as we said, these are each

adjacent to this blue cell. So, we have to color them a different

color than this blue. So, we'll choose red, green and orange

maybe. Now, let's try to color this cell over

here. Now, this cell, is adjacent to green and

red. But it is not adjacent to either blue or

orange. So we can color this either blue or

orange, and so rather than adding a fifth color, or a fifth set of frequencies.

We can reuse, as we choose, this orange over here, to make it more spectrally

efficient. Which means we're making better use of

our available frequency, capacity. We could have also taken this orange over

here and made this one green. Because these are not adjacent, but we

just chose three different colors off the bat over here.

Because on this one, without it being able to be green it would have had to

have been orange. So it's still using four, and so we just

want to make sure we're using the minimum number of colors possible.

Now, we can continue to allocate colors to each of these cell blocks.

And we might get something like this, and there's not only one answer.

There's different allocations clearly that would work.

But the idea is that we just want to make sure we're using them minimum number of

colors possible. Because that's going to give us the

maximum use of our available capacity. And so, you can verify on this diagram

that no two adjacent cells have the same color, and that's the idea.

That's what we want to get across here. And so, if we look at a frequency chart

down here, just to draw this out. We may say that the blue is on channels

one, two, and three if there were only three channels within each frequency

band. That's clearly not anywhere near enough.

But just for illustration purposes, we would say that these three would be one,

two, and three. So now anyone in the red bands would use

4, 5, and 6 to allocate to their cell blocks, which is separate from 1, 2, and

3. Separate color, separate bands, and 7, 8,

and 9, for green, and ten, 11, and 12, for Orange.

So now, as we have more and more channels within each frequency block, we would

need to add more spectrums. So we would have to increase the size of

this accordingly. But right here we're just showing three

for each for a total of 12 channels, divided accordingly.

So rather than needing, so now, we're using 12 channels to allocate to this

entire spectrum in here. So we need 12 channels to do this

allocation if we want each, if we want each cell to have three channels.

So now, if we count up the number of cells, we have 1, 2, 3, 4, 5, 6, 7, 8, 9,

10, 11, 12, 13. So if we wanted to give Each cell a

different band of frequencies you would need 13 times 3, 3 per cell which is 39

channels. And we're doing this in only 12, so we

have that factor of improvement. Instead of 39 we've now reduced it now to

only the number 12 to do this same allocation.

So clearly, using cells give us a lot of capacity advantage over not using cells.