2. Introduction
‘Cell’- the heart of Cellular Systems
A Cell is defined as-
the area where the radio communication resources is used by the MS & is
controlled by BS
Given -
the number of users
average frequency of calls being made
average duration of call time
Base on the given parameters the performance of the system is largely
depend on –
the size & shape of the cell
the amount of resources allocated to each cell
3. Cell Area
Most important factor of cell is
the size & shape
A cell is the radio area covered by
a transmitting station or BS
all MSs in that area are connected & serviced by BS
Ideally can be represented as circular cell with radius R from the center of the BS
The factors that cause reflections & refractions of the signals-
elevation of the terrain
presence of hill or valley or tall building
presence of particles in the air
The actual shape determined by the
received signal strength by the surrounding area
coverage area little distorted
4. Cell Area
Many possible models to represent cell boundary
hexagon
modeling & simulation
used because of shape closer to circle
no overlapping
no uncovered area in between
square
triangle
5. Signal Strength & Cell Parameters
Cellular systems depend on –
the radio signals received by a MS throughout the cell
the contours of signal strength emanating from the BSs of two adjacent cells i and j,
as illustrated in figure:
Actually the contours may not be concentric circles and could be distorted by –
atmospheric conditions &
topographical contours
6. The signal strength goes down as one moves away from the BS
A phenomenon known as ‘Handoff’ occurs as
the MS moves away from the BS of the cell
the signal strength weakens
implies radio connection to another adjacent cell
Signal Strength & Cell Parameters
7. Factors about ‘Where to perform handoff’
where two BSs have equal signal strength & critical consideration is ping-pong
effect
to avoid ping-pong effect MS is allowed to
continue maintaining a radio link with the
current BSi until the signal strength exceeds
a prespecified threshold value E
The area & the shape of the cell
How handoff is related to the mobility and
the cell area
Let assume,
A rectangular cell of area A with sides R1 and R2
The number of MSs having handoff per unit length in the horizontal direction is N1 &
similarly for vertical direction is N2
Handoff could occur along the side R1 of the cell
or through side R2
Signal Strength & Cell Parameters
8. The number of MSs crossing
along the R1 side of the cell can be R1(N1cosΘ+N2sinΘ)
along the R2 side of the cell can be R2(N1sinΘ+N2cosΘ)
The total handoff rate λH can be
λH = R1(N1cosΘ+N2sinΘ) + R2(N1sinΘ+N2cosΘ)
Area A = R1R2 is fixed. Minimization of λH for given Θ can be done by
substituting R2=A/R1
differentiating w.r.t. R1
equating to zero
Signal Strength & Cell Parameters
(2)
(3)
(4)
(1)
9. If we put the values of R1
2 & R2
2 in equation (1)
If we simplify the above equation we can get
Equation (6) is minimized when Θ = 0. Hence from equations (6), (3) & (4) we
get
Signal Strength & Cell Parameters
(5)
(6)
(7)
(8)
10. Capacity of a Cell
The offered traffic load is characterized by two important random parameters
1. Average number of MSs requesting the service (average call arrival rate λ)
2. Average length of time the MSs requiring the service (average holding time T)
The offered traffic load is defined as
a = λT
for example, in cell with 100 MSs, on an average , if 30 requests are generated
during an hour, with average holding time T=360 seconds, then the average request
rate (or average call arrival rate) is
λ = 30 requests/3600 seconds (1 hour=60min*60sec ) (9)
1 Erlang = A servicing channel that is kept busy for an hour
Then for the above example Erlang is, a = (30 calls/3600seconds)*360 seconds (10)
= 3 Earlangs (11)
The average arrival rate is λ, and the average service (departure) rate is μ
The steady state probabilities P(i)s for this system with S is the number of the
channel in a cell. we have
P(i) =
𝑎𝑖
𝑖!
𝑃(0) (12)
11. where a = λ/μ is the offered load and
(13)
the probability P(S) of an arriving call being blocked = the probability that all
channels are busy
(14) called the Erlang B formula &
denoted as B(S,a)
B(S,a) is also called blocking probability, probability of loss, or probability of
rejection
If S is given as 2 with a = 3, the blocking probability is,
(15)]
So, a fraction of 0.529 calls is blocked & need to reinitiate the call. Thus the total number
of blocked call is about 30*0.529=15.87
The efficiency of the system can be given by,
Capacity of a Cell
(16)
12. The probability of an arriving call being delayed is
This is called the Erlang C formula. If S=5 and a=3, we have B(5,3)=0.11. So
the probability of an arriving call being delayed is
Capacity of a Cell
(17)
13. Frequency Reuse
Earlier cellular systems employed
FDMA
range was limited to a radius from 2 to 20 km
‘Reuse’-
the same frequency band or channel used in a cell can be reused in another cell far
apart
the signal strengths do not interfere with each other
enhance the available bandwidth of each cell
‘reuse distance’
the distance between the two cells using the same
channel
represented by D
relation between D, R (the radius of each cell), and N (the number of cells in a cluster)
given by
the reuse factor q is
(19)
(18)
14. The number of cells N per cluster is given by N = i2+ij+j2
i represents the number of cells to be traversed along direction i, starting form the
center of a cell
j represents the number of cells in a direction 60₀ to the direction of i
Substituting different values of i and j leads to N= 1,3,4,7,9,12,13,16,19,21,28,…
the most popular values of N are 7 & 4
Frequency Reuse
15. How to Form a Cluster
The method to form a cluster is, N = i2+ij+j2 where i & j are integers and i>j
To form a cluster there are few more sequential steps:
1. select a cell
2. make the center of the cell as the origin
3. form the coordinate plane
1. the positive half of the u-axis and the positive half of the v-axis intersect at a 60-degree
angle
4. define the unit distance as the distance of centers of two adjacent cells
5. for each cell center it’ll generate an ordered pair (u,v) to mark the position
16. For a case j=1 with a given N & integer i is fixed then we get from the
equation
N = i2+ij+j2 = i2+i+1 (20)
Then using L = [(i+1)u+v]modN (21)
The cells with labels from 0 through N-1 form a cluster of N cells by using the
above equations
The cells with the same band can use same frequency
For example if given N=7 & by using equation (20) we get i=2 & from equation
(21) we can get L=(3u+v) mod 7
For center’s position (u,v) we can compute label L
How to Form a Cluster
17. For each cell L values use to label it
How to Form a Cluster
18. Co-channel Interference
The cells that are using same channels must be physically located at least
reuse distance
For avoiding the problem of ‘co-channels’ – the power level should controlled
carefully
Some degree of interference due to nonzero signal strength of cells
In a cluster of 7 cells there will be 6 cells using co-channels at the reuse
distance
Effect on the serving BS is negligible
if the second-tier co-channels are at two times reuse distance apart
19. The Co-channel Interference Ratio (CCIR) is given by
𝐶
𝐼
=
𝐶𝑎𝑟𝑟𝑖𝑒𝑟
𝐼𝑛𝑡𝑒𝑟𝑓𝑒𝑟𝑒𝑛𝑐𝑒
=
𝐶
𝑘=1
𝑀 𝐼 𝑘
(22)
where Ik is the co-channel interference from BSk
M is the maximum number of co-channel interfering cells
For cluster size of 7, M=6, CCIR is given by
𝐶
𝐼
=
1
𝐾=1
𝑀 𝐷 𝑘
𝑅
⁻γ
(23)
where γ is the propagation path loss slope and varies between 2 and 5
When D1=D2=D-r, D3=D6=D and D4=D5=D+R (from figure)
The co-channel interference ratio in the worst case for the forward channel
(downlink) is given as
𝐶
𝐼
=
1
2 𝑞−1 −γ
+2𝑞⁻γ
+2(𝑞+1)⁻γ where q(=
𝐷
𝑅
) is the frequency reuse factor
Two specific ways to reduce interference
1. Cell Splitting
2. Cell Sectoring
Co-channel Interference
20. Cell Splitting
Service providers would like to service users in a cost effective way
Resource demand may depend on the concentration of users in a given area
A way to cope up with increased traffic is
to ‘split’ a cell into several smaller cells
implies that additional BSs need – at the center of each new cell for handling higher
density calls effectively
new split cells –
coverage is smaller
transmitting power levels are lower
helps in reducing co-channel interference
21. Cell Sectoring
Omnidirectional Antennas
allow transmission of radio signals with equal power strength in all directions
difficult to design
can be achieved by employing several directional antennas to cover the whole 360
degrees
Directional Antennas
an antenna covers an area of 60 degrees or 120 degrees
cells served by these antennas are called sectored cells
sectored antennas are
mounted on a single microwave tower located at the center of the cell
adequate numbers of antennas placed to cover the whole 360 degrees of the cell
22. The worst case for the three sector directional antenna
From figure
Reuse distance, D=
9
2
𝑅 2 +
3
2
2
= 21 R ≈ 4.58R (25)
D΄= 5𝑅 2 + 3𝑅 2
= 28𝑅 ≈ 5.29R = D + 0.7R
CCIR,
𝐶
𝐼
=
1
𝑞−γ
+(𝑞+0.7)⁻γ (27)
In the worst case the CCIR for the six-sector directional antenna can be
𝐶
𝐼
=
1
(𝑞+0.7)⁻γ = (q+0.7)4 (28)
An alternative way of providing sectored or omni-cell coverage
placing directional transmitters at the corners where three adjacent cells meet
the number of transmitting towers are same
Cell Sectoring
23. Summary
A overview of various cell parameters including –
area
load
frequency reuse
cell splitting
cell sectoring
In Wireless Communications
limited bandwidth allocated
reuse technique useful for both FDMA & TDMA schemes