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. Now, one other term we should point out is that of the Frequency Reuse Factor, which is exactly what we were just discussing here. The Frequency Reuse Factor is the number of colors that you need in this diagram. It's really the number of bands that you need to use. So, in here, we have a frequency reuse factor of four, because we're using four different colors or four different bands of frequencies. So cells were first used in the first generation, and that's when we started to use the name cell, as we said. So we evolved from zero G then so what we call 1G, which is when we started to use this style concept. And it was first used in the AMPS system, which was pushed out by Bell in 1986. AMPS is called the Advanced Mobile Phone System, which operated around in the 800 MHz band. The cellular concept marked a transitions from 0G to 1G technology and the first such 1G or First Generation Technology was called AMPS. Or the Advanced Mobile Phone System which was introduced in the United States in 1978 and in other countries a little later. Now the first field trial of AMPS was in Chicago, and it consisted of 10 cells and 90 people. And AMPS operated in the 800 MHz band. And this really demonstrated the feasibility of the cell concept and the cell concept is employed to the present day. Under AMPS, the number of mobile phone users skyrocketed. In the United States, by the mid 1990s, there were already around 25 million mobile subscribers.
