1. Chapter 5
The Cellular Concept

2. Outline Cell Area Actual cell/Ideal cell Signal Strength
Handoff Region
Capacity of a Cell
Traffic theory
Erlang B and Erlang C
Frequency Reuse
How to form a cluster
Cochannel Interference
Cell Splitting
Cell Sectoring

3. Cell Shape (c) Different cell models (a) Ideal cell (b) Actual cell R

4. Impact of Cell Shape and Radius on Service Characteristics
Triangular cell (side=R)
2pR
p R2
Circular cell (radius=R) 6R
Hexagonal cell (side=R) 4R R2
Square cell (side =R)
Channels/Unit Area when Size of Cell Reduced by a Factor M
Channels/Unit Area when Number of Channels is Increased by a Factor K
Channels/ Unit Area with N Channels/ Cell
Boundary Length/ Unit Area
Boundary
Area
Shape of the Cell

5. Signal strength (in dB)
Select cell j on right of boundary
Cell j
-60
-70
-80
-90
-100
Cell i
-60
-70
-80
-90
-100
Select cell i on left of boundary
Ideal boundary

6. Actual Signal Strength
Signal strength (in dB)
Cell j
Cell i
-60
-70
-60
-80
-70
-90
-80
-90
-100
-100
Signal strength contours indicating actual cell tiling. This happens because of terrain, presence of obstacles and signal attenuation in the atmosphere.

7. Universal Cell Phone Coverage
Chittagong
Microwave Tower
Cell
Dhaka
Maintaining the telephone number across geographical areas in a wireless and mobile system

8. Variation of Received Power
Received power P(x)
Distance x of MS from BS

9. Handoff Region Signal strength due to BSj Signal strength due to BSi
Pi(x)
Pj(x) E E
Pmin
BSi MS
BSj
BSj X1 X3 X5
Xth
Xth
Xth X4 X4 X4 X2 X2 X2
By looking at the variation of signal strength from either base station it is possible to decide on the optimum area where handoff can take place

10. Cell Capacity
Average number of MSs requesting service (Average arrival rate): 
Average length of time MS requires service (Average holding time): T
Offered load: a = T where a is in Erlangs
e.g., in a cell with 100 MSs, on an average 30 requests are generated during an hour, with average holding time T=360 seconds
Then, arrival rate =30/3600 requests/sec
A completely occupied channel (1 call-hour per hour) is defined as a load of one Erlang, i.e.,

11. Cell Capacity
Average arrival rate  during a short interval t is given by  t
Average service (departure) rate is 
The system can be analyzed by a M/M/S/S queuing model, where S is the number of channels
The steady state probability P(i) for this system in the form (for i =0, 1, ……, S) -1
Where and

12. Capacity of a Cell
The probability P(S) of an arriving call being blocked is the probability that all S channels are busy
which is also defines the Grade of Service (GOS)
This is Erlang B formula B(S, a)
In the previous example, if S = 2 and a = 3, the blocking probability B(2, 3) is
So, the number of calls
blocked 30x0.529 = 15.87

13. Capacity of a cell The probability of a call being delayed:
This is Erlang C Formula
Blocked Calls Delayed  infinite sized buffer or queue, no calls dropped
For S=5, a=3, B(5,3)=0.11
Gives C(5,3)=0.2360

14. Erlang B and Erlang C (used to determine GOS)
Probability of an arriving call being blocked is
Erlang B formula
where S is the number of channels in a group
Erlang C formula
where C(S, a) is the probability of an arriving call being delayed with a load and S channels
Probability of an arriving call being delayed is

15. Cell Structure (a) Line Structure (b) Plan StructureF3 F2 F1
(b) Plan Structure F3 F2 F4 F1 F5 F6 F7 F2 F3 F1
(a) Line Structure
Note: Fx is a set of frequencies i.e., frequency group.

16. Frequency Reuse Fx: Set of frequencies 7 cell reuse cluster F1 F2 F3
Reuse distance D
Fx: Set of frequencies
7 cell reuse cluster

17. Reuse Distance Cluster RF1 F2 F3 F4 F5 F6 F7 R
Cluster
For hexagonal cells, the reuse distance is given by
where R is cell radius and N is the reuse pattern (the cluster size or the number of cells per cluster).
Reuse factor is
Reuse distance D

18. Reuse Distance (Cont’d)
The cluster size or the number of cells per cluster is given by
where i and j are non-negative integers
N = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, …, etc.
The popular value of N being 4 and 7
j direction
60°
… i
j direction
60°
… i
i direction

19. Cochannel Interference
First tier cochannel Base Station R D1 D2 D3 D4 D5 D6
Second tier cochannel Base Station
Mobile Station
(MS)
Serving Base Station (BS)

20. Worst Case of Cochannel InterferenceD6 R D5 D1
Mobile Station D4 D2 D3
Serving Base Station
Co-channel Base Station

21. Cochannel Interference
Cochannel interference ratio is given by
where I is co-channel interference and M is the maximum number of co-channel interfering cells
For M = 6, C/I is given by: å = ÷ ø ö ç è æ M k R D C I 1 -g
where  is the propagation path loss slope and  = 2 ~ 5

22. Cell Splitting Large cell (low density) Small cell (high density)
Smaller cell (higher density)
Depending on traffic patterns the smaller cells may be activated/deactivated in order to efficiently use cell resources.

23. Cell Sectoring by Antenna Design
(b). 120o sector a b c
120o
(c). 120o sector (alternate) a b c
(a). Omni
(d). 90o sector
90o a b c d
60o
(e). 60o sector a b c d e f

24. Cell Sectoring by Antenna Design
Placing directional transmitters at corners where three
adjacent cells meet A C B X