Practice English Speaking&Listening with: Lecture 4 - The cellular concept - System Design issues

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We shall now talk about the system design issues involved in cellular systems. First the basic

concepts involved in a cellular system design.The basic requirement is of high capacity.High

capacity is achieved by limiting the coverage of each base station to a small geographic

region called a cell. This is different from the traditional radio transmitters which would

cover the entire city and the whole city was one cell. This is a paradigm shift.In order

to achieve higher capacity that is to support a larger number of users the city first must

be divided into smaller cells and each cell must have a transmitting tower called the

base station. The same frequencies or timeslots or codes are reused by spatially separating

the base stations. So this factor of being able to reuse the frequencies actually allows

you this high capacity.That means, a larger number of customers, more revenue and sustainability

of the system.

However the movement we put more number of cells and at the same time promise the customers

that they can move around because it is a mobile situation, we should have a mechanism

to handoff the calls from one cell to another. So this is the price we have to pay in order

to give enough mobility. This approach resolves the problem of limited radio spectrum.If we

had the luxury of using infinite bandwidth, we donít need to reuse.Otherwise we will

have to resolve to the techniques of frequency reuse.

Letís look at some more basic concepts.Theneighboring base stations are assigned a different group

of channels so as to minimize the interference. What do we mean by channels?As we saw earlier,

we have certain frequencies or timeslots or codes and they form the channels. Since we

have differentiated the entire regions and dividedit into sub cells, the neighboring

cells must not use the same resources. But then we have to reuse it after sometime.So

we have to come up with this notion of ëreuse distanceí and ëfrequency reuse planningí.If

we do not plan well, at the end of the day, we will increase the overall interference.Interference

will be an issue.We will also see certain mobile systems are interference limited. By

systematically spacing base stations and the channel groups, we may reuse the recourses

as mentioned before.

As the demand increases, the number of base stations may be increased thereby providing

additional capacity. So there are ways and means today to expand your services.If your

number of customers increases you can scale up your system. So this reuse factor and certain

other advanced techniques will allow you to continue providing service to more and more

number of stations even though you are not asking for extra bandwidth.This is the basic

concept all. A very intuitive understanding is as follows.Just like the whole city has

been divided into cells, each cell can be divided into sub cellsand further and further.So

use smaller and smaller sub cells within the cell but keep in mind that the cell size can

be reduced only if you reduce the power.Actually what determines the cell size and cell shape?

We will discuss all these things. But clearly the transmitted power is a factor which will

decide how big your cell is. So I can reuse and include more number of users provided

I keep my emitted power under control. Nowletís gradually buildup and understand how cellular

network is laid out.

Suppose I have a base station here shown by a tower. There are transmitting antennas at

the top and a transmitting unit may be at the bottom or at the top. It has a region

of coverage. Here I have shown it as a hexagon.We will discuss why hexagons are traditionally

used though in reality the real cell shapes have nothing to do with the hexagon.Itís

a concept which we will discuss. So every cell has a base station.Suppose we would like

to provide coverage to an area, may be city ëxí using this cells, now I would like to

put more number of cells to cover the region of coverage. So I have several cells. Here

for the sake of simplicity, I have shown all cell sizes to be equal.Within the same geographical

location most likely, all cells will not be of the same size.In fact, the terrain, the

blockage, the density of people, traffic etc. Will determine how big or small the cells

would be.

For example in Delhi, the cells near the Carnot place area which has high urban density will

be much smaller.Hence we shall provide higher capacity. so cell size can be made smaller

to do higher degree of reuse and hence provide much higher outskirts of Delhi

where the density of mobile phonesare not so high, we will have larger cells. So the

entire city has been subdivided into cells with each base station put at the center of

the cell. Now somehow, these base stations need to communicate with each other and also

to the external world because the mobile system doesnít stand alone.It has to talk to the

public switch telephone networks because I should be able to make a call from my mobile

phone to a landline phone and vice versa. So the brain behind the cellular system lies

in this MSC or the mobile switching center.

Clearly if I have to coordinate the activities of various cells, I need to put a line to

all the base stations and connect them to the mobile switching center. So letís do every base station is actually connected to the mobile switching center. Now letís

put a customer, a mobile station, a car with a mobile phone in one of the cells and if

this person wishes to establish a call from the mobile phone up to a public switched telephone

network, I would like to have connectivity between the mobile switching center and PSTN

or the public switched telephone network. We will talk about how the calls happen, what

is the anatomy of a phone call, how to initiate a call from a mobile station to a landline

phone or from a landline phone to a mobile phonelater.

The other thing that I mentioned is, suppose my user is truly mobile he loves to talk while

driving.We should be able to provide some kind of a handoff as the mobile station moves

from one cell to the other. We have to discuss these strategies.This slide gives you an overall

picture of the cellular telephone systems. Remember this is a very simplistic model.In

reality, cells are neither hexagonal nor equal in shape nor are they non-overlapping.In reality

all the cells have a fair amount of overlap. Now talking about establishing a call from

the mobile to the base station and from the base station to the mobile, we make use of


Most likely these channels are frequency bands or timeslots or codes.So the forward voice

channel is used for voice transmission from the base station to the mobile station. The

reverse voice channel is used for voice transmission from the mobile station to the base station.

However, as we know voice channel can be only activated once the hand shaking has been done.So

we required some kind of control channel. A forward control channel is used for initiating

a call from the base station to the mobile station. A reverse control channel is used

to initiate a call from the mobile station to the base station.Please remember the FCC

and the RCC, the control channels are also called setup channels because of the nature

of work they do. Needless to say the control channels are not used for sending voice but

are used as overheads.They will take a percentage of the bandwidth, typically 5%.

In this slide, letís look at the anatomy of a cellular call.A cell phone when turned

on but not engaged in a call scans the group of forward control channels to determine the

one with the strongest signal. Please note even though you are not making a call, you

are using a battery power.Therefore when you buy a phone, you have two kinds of time available;

the talk time and the standby time. So your phone can get discharged over several days

even though you donít make a single call because it has to monitor and keep itself

updated as to which cell it is talking to.

Therefore even though you donít touch the phone, the display may change depending on

which base station it is connected to. It is continuously monitoring the signal strength

and knows at any time, at least one if not more, base stations with which it can communicate.

So the mobile phone monitors the channel and keeps on monitoring because if the strength

drops below a certain threshold, it scans for the next strongest. Control channels are

defined and standardized throughout the service area.Typically the control channels use up

to 5 % of the total number of channels.So5 % of your resources go into controlling setting

up your calls.

Let us now look at the case when you make a call to a mobile user.So imagine a scenario

where a mobile station is somewhere in the geographical area.We have no clue and we try

to make a call to a mobile user. So we dial this number 98182xyzpq and see what happens.

so the moment you make this call, that is would dial this number which is pertaining

to a mobile, the mobile switching center which is actually connected to the PSTN- public

switched telephone network provided your making a call from the landline otherwise from one

mobile to another mobile, the mobile switching center must come into the picture.It dispatches

the request to all the base stations. Remember we are connected the mobile switching center

to all base stations.Typically how do we have this connectivity? We can have a fiber we

can have a point to point micro wavelength or any other way to connect the mobile switching

center to the base stations. So once the mobile switching center dispatches the request to

all the base stations, all the base stations send out a paging message. Now what is this


The mobile identification number which is a characteristic of that mobile station is

being broadcast.It is unique to that mobile.This number may not be the same as the phone number.

Itís another code. So mobile station receives the paging message from the base station it

is monitoring because it was already in touch with one base station at least. So when that

particular base station pages it that is, broadcast this mobile identification number,

the mobile station must respond. it responds by identifying it but over the reverse control

channel. The base station conveys the handshake to the mobile switching center.The mobile

switching center instructs the base station to move to an unused voice channel. So it

gives an instruction for the base station to look for an unused voice channel.It may

be possible that that particular base station has run out of all the available voice channels.

At that time they will not be the initiation of a call.

Student: Sir, you mentioned that mobile identification number and the mobile number are different.

So where actually is the mobile identification number stored? Is it on the mobile itself

or on the base station? Professor: No. this is actually setup in a

lookup table inside the mobile switching center.So there is a lookup table which has the phone

numbers and these identification numbers. There is a host of other identification numbers

also which can be used to ensure that legal calls are made. So for example, in GSM there

is a provision that you can deactivate or label a phone as a stolen phone. So no phone

call can be made from that phone which is labeled as a stolen phone because that number

isblacklisted. Now what number will be blacklisted? Most likely the MIN will be blacklisted. So

it stays with the mobile switching center.

Then there is something called as a location register.When we talk about GSM phones and

basic protocols, we look at the home location register and the visitor location register

where we will keep a lot of information about the mobile phones including the prepaid card

details of whether the prepaid money is there, whether it has not defaulted and what are

the call charges.In fact, before a call is established a lot of things are checked.The

validity, the legality and other thingsand only then you initiate a call.

Student: sir, about what activities takes place in the handshake phenomenon?Professor:

so if we are talking about only the conceptual level we only verify whether a response comes

from the mobile phone and that mobile phone is a valid phone with a valid SIM card. We

are not talking about the physical activity about the voltage levels or the received single

strength.So there are several numbers. The SIM card has a number.The hardware has a number

and then there is a logical phone number. So it is possible to have a combination of

valid numbers. SoMIN is the hardware number.Letís look at a call to a mobile user now.

Actually we are continuing with the call to the mobile user having being paged and responded

and being allocated an open frequency band. The base station signals the mobile station

to change over towards unused forward voice channel and reverse voice channel. Please

remember both these voice channels have to be available for the call to be initiated.The

call has not yet been initiated.We are working on it. Next, a data message called the alert

is transmitted over the forward voice channel to instruct the mobile to ring. Mobile so

far has not run.

All these sequences of events have occurred just in a couple of seconds and are usually

not noticeable to the user. You may here a series of beeps or a silence period of three

seconds till you hear the ring.During this process this figuring out where the mobile

is, checking out the identification numbers, allocating of frequency bands etc. takes place

and then you hear the first ring. While the call is in progress, the mobile switching

center adjusts the transmitted power in order to maintain the call quality. So lot of intelligence

is built into the mobile switching center.However, things have gradually changed and in the modern

base station, a lot of this activity takes place right at the base station.

The mobile switching center cannot really handle so much of traffic and the power control

issues are taken care at the base station itself. As the handsets are becoming more

and more microprocessor friendly and powerful microprocessor being built into handsets a

lot of these power calculations are also done by the handset itself. So the idea is to distribute

the computing so that the mobile switching center is not over loaded.The series of steps

I have shown to you belong to the original GSM standard. Letís now look at the other

scenario where a call from a mobile user is being made.

Remember at any time the mobile user is already in touch with at least one base station. So

first, a call initiation request is sent to the reverse control channel.Remember the reverse

channels are from the mobile to the base station.Along with this, the mobile station transmits its

MIN. so it is in the hardware but it is also in the table of the mobile switching center.Along

with this, another number called the electronic serial number and the phone number of the

called party is also set. These different numbers have different utilities in terms

of verification at different levels. The mobile station also transmits something called as

a station class mark-SCM which indicates the maximum transmitted power level to the particular

user. Basically this is a way to control the transmit power.

This request is sent to the base station which forwards the data to the mobile switching

centerwhich in turn validates the data because it has the register locators.It has the data

base.So it validates the data, makes the connection to the called party through the public switched

telephone networkif it is to a landline number or to another mobile.But how to make a call

to a mobile is already known to you. We will follow that procedure. Again you may hear

a series of beeps or a silence period while all these activities are taking place until

you hear the first ring.

Next we come to a very fundamental concept of frequency reuse.i have already mentioned

about it that the spectrum is limited.The only way out is to reuse the spectrum.What

is the best way to do it? What is the most efficient way to do it?Before that let us

look at an example to see the true need for frequency reuse. Suppose we had fixed telephone

networks and they were running wires to every householdbut we are not talking about wire

line truly.We have compared it to a wireless situation because we are looking at wireless

cellular systems. Suppose we would like to give every household in Delhi a voice bandwidth.They

can talk.So we need to give about 4 KHz of spectrumbut the number of households in Delhi

is about 12.5 million.Suppose we get into a stage where we can actually give them 4KHz

of bandwidth, we are talking about 50GHz of bandwidth. Clearly we cannot allow this kind

of outrage on a mobile phone network.We do not have the luxury to touch fifty GHz of

bandwidth.We have to reuse our frequency. So clearly in practical, no other service

is possible using radio transmission.Most of the spectrum unfortunately will remain

unused most of the time. If I give a phone line connection, I cannot do adaptive reallocation.So

clearly there is a need to do frequency reuse. This calculation has been done only for voice.If

you have to provide additional data, allow them to check their emails over the phone,

downloads stock codes and cricket commentary, we are out of business.

Cellular radio systems rely on intelligent allocation and reuse of channels throughout

the coverage area.We need to emphasize this point because this forms the crux of the matter.

Each base station is allocated a group of radio channels to be used within the small

geographic area which we have already defined as a cell.Soit is not just a frequency but

a frequency band. Neighboring base stations are given different channel allocation from

each other because we would like to avoid interference. The biggest problem with frequency

reuse is manmade noise or interference. If I am going to reuse the same frequency for

transmitting data at a distance, I will definitely get some stray interfering signals. Theyare

exactly in the same band.You cannot use a filter to filter it out because your data

is also in the same band. That also makes a point that I cannot improve my performance

by simply increasing the signal to noise ratio. If I increase my signal strength to beat the

noise, Iíll also create more interference for my friend because the frequency is being

reused. Cellular networks must have an efficient power control mechanism. Itís very important.In

fact your GSM phone monitors the transmit power level 800 times/ sec.

Now by the design of antennas and regulating the transmit power, the coverage area within

the cell is limited. The same group of frequencies are reused to cover another cell separated

by quote-unquoteìa large enough distanceî. Why a large enough distance because you want

to keep this co-channel interference which is generated by cells using the same frequency

band under control. Clearly I would like this co-channel interfering cell to be as far as

possible because of the inverse square law that will take place. However the farther

we put the co-channel cell, the less frequently I reuse the frequency, the less capacity I

can have. so that is the tradeoff between how much capacity I can pack in in terms of

closely putting the reuse factors and then we can go ahead and reuse the frequency as

and when it is desired.

The design procedure for allocating cells for the cellular base station within a system

is called the frequency reuse or frequency planning. Frequency planning should not be

very complicated because at the end, we have to ensure that certain base stations are using

certain bandsand the other base stations are using another band. So we cannot really come

up with a very complicated scheme also frequency reuse is done in terms of a cluster. So you

have a cluster of cells where you reuse the frequency bands and then you replicate that

cluster over the entire geographical area. Letís look at an example of a frequency reuse

over a certain geographical area say, Delhi.So here we have an approximate outline of the

city of Delhi.

We have the neighboring states.We can see the river flowing by.Our job is to setup a

frequency reuse pattern in this city of Delhi. So we first start with a cell.Typically, a

cell will be of a radius of 3km -5 km in a city which is urban.

I have put in a hexagonal shape just for the sake of is put in blue indicating

a certain frequency band being used. I have another cell which is using another frequency

band denoted by light blue in the slide. Itís another hexagonal cell.i am not showing an reality, there will be overlap.Iím going to fill up the space by adding more

hexagonal cells. So I have put up a cluster of 7 cells here, each one represented by a

different color and each color represents a different frequency band. Clearly, the user

of adjacent cells are not interfering because they are using different frequency bands and

are not going to interfere. I like this cluster and I would like to replicate this cluster

all over the geographical area. So I put exactly this cluster of 7 cells nearby. note that

the deep blue one which I started off with is being repeated herebut the distance between

this blue and this blue is the same as light green with this light green.So the reuse distance

is the same. It is interesting to note that you cannot have any random number of cells

in your cluster. I cannot have for example, a cluster of 5 cells which can have this uniform

repeat pattern. We will look at what are the possible cluster sizes.

Letís take this example forward by putting another cluster. Again note that the distance

between the green cells here are the co-channel cells. It is the same between this cluster

and this cluster this cluster and this cluster. No frequency band is being discriminate.All

frequency bands are going to suffer through the same co-channel interference levels. We

are excited about this plan.So we keep adding clusters and we are happy that we have been

able to cover most of the region by these cells. This pictorial figure gives where we

use what frequency.

Conversation between student and professor: The question being asked is: whyshould the

distance be same? The answer is the following.Suppose you take this cell, rotate it and keep it,

then certain cells will have more distance and certain cells will have less distance.Certain

group of cells will have poor quality of service because of interference because distance will

attenuate the radiations coming from a co-channel cell. If the distance is fixed and pre-calculated,

then we know how much interference we are dealing with. Therefore I am saying the distance

should be same to guarantee a certain level of affordable co-channel interference. If

we have this cluster size smaller, say a cluster of 4, then the reuse distance will go down

and the capacity will go up. Therefore you will have to tradeoff between the co channel

interference and the reuse distance. So cells with the same color in this diagram reflect

same frequencies.In this example we have used a reuse factor of 1/7.

Conversation between student and professor: The question being asked is: when we switch

on a mobile phone and we want to initiate a call which frequency do we choose? Suppose

my mobile phone is in this light green cell and it is switched on, it has only a set of

frequencies with which it can communicate to this base station. The mobile has a possibility

to use any of the frequencies in all the cells.But which particular reverse channel will it use

will be dictated by the base station and eventually through the mobile switching center. But the

base station in this region would communicate using a frequency band represented by green

and tomorrow if the base station wishes to move to the purple cell or to the orange cell;

it will choose the frequency sub-band accordingly. Student: Sir, patterns depending on the channel

available or frequencies allocatedto the mobile center?

Professor: Thatís right. depending upon the channels available, the frequencies available

and allocated and suppose a base station can only support these green frequencies while

the mobile station moves from green to the purple cell, a handover will take place not

only to the base station but a new channel will be given which is nothing but a new frequency.

So explicitly I have put arrows to all the light green cells which form the co-channel

cells.Similarly all the purple cells are co-channel cells and will interfere.

In the next couple of slides, letís look at the shape of the cells.what determines

the shape of the cells and how can we regulated if at all. Consider cell i and cell j which

are co channel cells.Assuming the base station is located at the center of the cell and itís

an omnidirectional base radiates circularly in all directions. As we move away,

the received strength just for the sake of this example, letís assume the received

power is in dBm with respect to 1 mW. So itís at -60 dbm,-70 dBm and so and so forth as

you move away from this cell. same is the case with cell j.

The question is: how much you would like to separate the cell so that the received power

by cell i coming from cell j is below a certain level.if your handset can handle interferences

below 80 but not more than that, I need to decide a certain reuse who decides

the reuse distance because the reuse distance can be changed it can be as low as 1, I donít

reuse at the sense that, every neighboring cell uses the same frequency 2,3 or change

to 4 or 7 or 12.These are the certain possible reuse numbers. We will talk about which one

to choose for your application depends upon, how much interference you can tolerate. sometimes

you can have interference mitigation techniques by signal processing which will allow you

to handle larger interference. Then your reuse distance can actually go by signal

processing you can make the capacity of the system higher. In reality, the cell shapes

would look like this.

Why is there a dent here? Possibly there is a building here.Why is there a big dip here?

Possibly there is a forest area or foliage which is attenuating the signals. Remember

these contours represent the received signal strength.note2 things.not only the cells and

the received contours are irregular; they are also not equally spaced any more. In this

region this the radiations are going through a medium which is attenuating it differently.most

likely is going through a concrete jungle here so that it is falling much faster. So

the cell shapes in reality look like this and these pictures should be taken into consideration

to actually decide the reuse distance. Signal strength contours are indicating actual cell

coverage. This depends on the terrain whether its rocky, foliage, water bodies, presences

of obstacles, buildings, towers and the attenuation in the atmosphere like rain, fog, dust, smog

and other factors. All these factors will determine the received signal strength and

hence the shape of the cell. As a system planner you must considered all these factors before

you say ìi would like to have a reuse factor of 7î.

So let us now see the applicability of the hexagonal cell shapes. Why are we using this

hexagonal shape? Why is it of importance even academically? So we have a base station which

will if it is in omnidirectional radiation, we would have a circular cell.itís reality we would not like to have it for several reasons. Suppose the ideal

cell is of radius 2 ñ 10 km. who decides this 2 ñ 10 km radius? It starts with the

radiated power and then the obstacles that may be encountered in the cell. Let us put

up one mobile station here and another mobile phone in a car so that they are very much

contained in this circular cell. I would like to do system planning and cover my entire

area of interest using circular cells. I can do so but the problem with putting circular

cells for coverage is that you are left with these empty spaces where I cannot predict

any coverage. Itís clearly a bad modeling as a mobile system service provided I must

be able to give 99.99 % coverage if not 100 % because my competitor will. I cannot have

frequency planning done based on cell shapes which leave out by design some of the

what do I do?

I have to try and come up with other cell models which can approximate the circular

shape but not leave out sections. So one of the simplest shapes that allow me to cover

the entire space by placing cells next to each other is the triangular cell. I can cover

the entire area with triangular cells without leaving any place.

Clearly, triangle is a poor approximation of a circle. So in order to maintain close

contact with reality I come up with another cell shape called the square also

has a property to cover the entire geographical region without leaving open spaces. It also

approximates the circle but in a poor reality we do not actually use the cell except

in certain cases for example, the LMDSñìlocal to multi point distribution serviceî which

is based on the IEEE 802.16 which by designed uses square cells. But we are not going to

discuss that at this moment in time. So in a quest to come up with a cell shape which

approximates the circular ideal shape but is not completely counter intuitive, we go

to the next possible shape which is the hexagonal cell.

Clearly it is closer to the circular ideal shapeand it also covers the entire space without

leaving blank spaces.hence hexagonal cell is used as an approximation to the circular

pattern and thus what we will use and will look at the hexagonal geometry and see how

we determine the reuse distance, how much co-channel interference we will get in terms

of hexagonal cell please remember hexagonal cells are conceptual.

For most theoretical treatment, hexagonal model of cells is adopted because they are

shapes that approximates a circle. Using a hexagonal geometry, fewest numbers of cells

can cover the entire geographical region as opposedto square cell or a triangle cell.

So letís stick with hexagonal cells and you will find it in most textbooks and research

papers that they are using hexagonal cells.

Next a few slides on the geometry of hexagons.the regular Cartesian coordinates of x and y which

are orthogonal are not completely appropriate. So consider the x axis and the y axis and

I have placed a lot of hexagons which are closely spaced and here if you look carefully

with a slightly darker shade I have outlined a cluster.a cluster of seven cells we had

seen earlier. we have also repeated the cluster so that there is a reuse distance. but we

are not comfortable with this hexagonal cells because the moment I go along this x axis,

I sometimes start with a complete cell, then go through it, cut in the middle and I donít

like this geometry. what if I look at this axis which is at a diagonal but touches the

centers of each of the hexagons kept in this way and we put another axis which touches

the centers of all the hexagons along this axis.

In that case, we donít have to count fractional amounts of hexagons as we go along any axis.

So let us define this funny U-V axis which are actually separated by 60 degrees.isthe

logic clear? We would like to count hexagons after what is a reuse distance. we would like

to quantify that number in terms of the cell radius. So the cell radius R is the same as

the length of a side of a hexagon. I would like to count the distance in terms of the

cell radius. How many units are there? How many radii do I move from one cell to other?

So it will be a normalized unit. If I would like to measure the distance between two co-channel

cells D, I want to quote it in terms of this number R which is the cell radius and the

length of the side of a cell.

So the axes U and V intersect at 60 degrees as you have seen because hexagons have great

affinity to this 60 degree angle.unit scale is distance between cell centers. If a cell

radius of a point in the hexagon from the distance on the center to one of the corners

is R, then 2R cos30 is 1 or R can be written as 1 over root 3 normalized. If you do the

basic mathematics, you will come to the equation that r = square root of v squared + u squared+uv,

coming from simple geometry if you go back. So what it means is we can represent our distance

ërí in terms of units on the uv axes. The u-v axes are special because they are separated

by 60 degrees.

S o that equation written here as a distance is nothing but I units that you move along

the u axis, j units that you move along the v i squared + v squared +uv. Square

root of that is the distance. And what happens after this distance? After this distance you

reuse the D is the frequency reuse distance. N is a number which is found

by substituting only integer values for i and jand that tells us after how many cells

I reuse the frequency. That is, how many cells are in my clusterbecause after we run out

of the cells in the cluster, we reuse it.from the hexagonal geometry alone we have that

not all integer values of capital N are possible. In fact, if you use integers for i and j,

the possible values are 1, 3, 4, 7, 12, Ö

In fact if you look at a table for integer values of i and j, we come up with 1, 3, 7,

12, Ö and if you calculate the distance which is the reuse distance in terms of the normalized

radius, you get a certain figure. This will tell you how far must your co channel cells

would be and whether you can tolerate the interference.

Let us look at a few quick examples. How to look at a co-channel cell, because co-channel

is clearly going to limit the performance of the system.This is your typical 7 cell

reuse pattern. You can see 7 cells here and we have seen this structure before. So I would

like to find out after what distance will this cell repeat. Now for N = 7, using that

formula i squared + j squared +ij, i =2, and j =1 gives you N =7.2 squared is4 + 1 squared

is 5 +1 into 2 is 2.That gives us 7. So all it means is that if I move 2 units along the

i axis and 1 unit along the j axis, I should be able to get a co-channel cell that uses

the same frequency.

So letís translate this cell 2 units along the i axis which is at favorite U axis and

1 unit along the j axis which is the V axis and see where we go.So if we go along the

y axis, we move 1 unit and we will use another unit. So the original cell as now we moved

2 units along the i axis. Weare only half way through because we have to move it 1 unit

along the V axis which is at60 degrees. So letís do that along this j axis.So this original

cell has not translated here and the co-channel cells are actually shown in red. So if we

complete the picture, letís put in the cluster and you see that these 2 cells which are the

co-channel cells indeed have the own clusters and repeat. This logic is true for every cell

in the cluster. So I have several cells. So take the total band, suppose it is 700 MHz,

you divide it into 100 MHz each, put each 100 MHz sub band into the cells and repeat


Letís look at two quick examples.This is a cluster size with 12 cells and this number

N =12 comes from the same formula i squared + j squared +ij with i =2 & j =2. So in this

case, these are the two co channel cells. If you move 1 unit & 2 units along the i axis

and then move 1 unit & 2 units along the V axis, you get the co-channel cells.

Student: Is N =12the number of cells? Professor: N =12 is the number of cells inside

the cluster and N = 12 has been found by using integer value i = 2 and j = 2 in the formula.

Student: Is the whole thing a cluster? Professor: Yes.

Student: Are there 13 in it? Professor: Yes because the 13th cell is a

reuse cellbecause in the cluster I cannot repeat.

Letís look at the next larger cluster size of N =19. Suppose I have to provide service

where my system is extremely sensitive to interference I cannot reuse frequencies very

frequently.i must increase the reuse distance. Iíll go to larger cluster size.Again for

i =3 & j =2, you can have these two cluster co channel cells. If you move along the i

axis, you have 1, 2 & 3 units.Along i 1 unit,2 along the j again at 60 degrees and you are

with the co-channel cell. Please note distance here is less than the distance here. This

scenario has less interference whereas clearly, this scenario has more interference, much

more than the N =7. In GSM we use N = 7 and sometimes N =4 and if I am very ambitious,

you can also use N = 3.

Here we summarize in the sense that I have drawn two clusters for N =7.You have F 1 to

F7 in the first cluster. I am not using color coding here and similarly for the second segment.

F 1 and F 1 are co-channel cellsseparated by something called is a reuse distance from

the formula that we have done earlier and if you substitute in terms of NR and D, you

get the reuse distance. This is D as under root 3 N times Rwhere R is the side of a cell

also the cell radius.Clearly, the distance increases as you increase the cluster size.

the reuse factor is defined as D over R. itís a normalized distance with respect to the

radius and it is nothing but under root 3 N. We will conclude at this point and will

take cell capacity and reuse distances in the next class.

The Description of Lecture 4 - The cellular concept - System Design issues