1. Chapter 5 Cellular Concept
Prof. Chih-Cheng Tseng
EE of NIU
Chih-Cheng Tseng

2. Cell Shape
A cell is the radio coverage by a transmitting station or a BS.
Why hexagon?
closer to a circle
can be arranged next to each other without having any overlap and uncovered space in between R
(c) Different cell models R
Cell R
(a) Ideal cell
(b) Actual cell
EE of NIU
Chih-Cheng Tseng

3. Impact of Cell Shape and Radius on Service Characteristics
Shape of the Cell
Area
Boundary
Boundary Length/ Unit Area
Channels/Unit Area with N Channels/Cells
Channels/Unit Area when Number of Channels Increased by a Factor K
Channels/Unit Area when Size of Cell Reduced by a Factor M
Square cell (side =R) R2 4R
Hexagonal cell (side=R) 6R
Circular cell (radius=R)
pR2
2pR
Triangular cell (side=R) 3R
EE of NIU
Chih-Cheng Tseng

4. Signal Strength Signal strength (in dBm) Cell i Cell j -60 -70 -80 -90
Select cell i on left of boundary
Ideal boundary
Signal strength (in dBm)
Select cell j on right of boundary
Cell j
-60
-70
-80
-90
-100
Cell i
EE of NIU
Chih-Cheng Tseng

5. Actual Signal Strength
Signal strength contours indicating actual cell tiling. This happens because of terrain, presence of obstacles and signal attenuation in the atmosphere.
-100
-90
-80
-70
-60
Signal strength (in dBm)
Cell i
Cell j
EE of NIU
Chih-Cheng Tseng

6. Variation of Received Power
Received power P(x)
Distance x of MS from BS
EE of NIU
Chih-Cheng Tseng

7. Handoff Region BSi MS BSj X1 X3 X5 Xth X4 X2 E
Pi(x)
Pj(x)
Signal strength due to BSi
Signal strength due to BSj E
Pmin
BSi MS
BSj X1 X3 X5
Xth X4 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.
EE of NIU
Chih-Cheng Tseng

8. Handoff Rate in a Rectangular Area
N1 is the number of MSs having handoff per unit length in horizontal direction
N2 is the number of MSs having handoff per unit length in vertical direction
Since handoff can occur at sides R1 and R2 of a cell R2 R1 N2 N1 
Assuming area A=R1R2 is fixed, substitute R2= A/R1, differentiating lH with respect to R1 and equating to 0 gives
N1cosq + N2sinq-A/R12 (N1sinq +N2cosq)=0
EE of NIU
Chih-Cheng Tseng

9. Handoff Rate in a Rectangular
Thus, we have:
Simplifying through few steps gives
H is minimized when  = 0, giving
EE of NIU
Chih-Cheng Tseng

10. The Offered Traffic Load of A Cell
Average number of MSs requesting service (Average arrival rate): 
Average length of time MS requires service (Average holding time): T
Offered load: a = T
Example:
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 channel kept busy for an hour is defined as one Erlang
EE of NIU
Chih-Cheng Tseng

11. Analyses of The Call Blocking Probability (1)
Average arrival rate is 
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)
where and
EE of NIU
Chih-Cheng Tseng

12. Analyses of The Call Blocking Probability (2)
The probability P(S) of an arriving call being blocked is the probability that all S channels are busy
This is Erlang B formula B(S, a)
Example: If S=2 and a=3, the blocking probability B(2, 3) is
So, the number of blocked calls is about 300.529=15.87
EE of NIU
Chih-Cheng Tseng

13. The Probability of A Call Being Delayed
The efficiency of a system can be given by
The probability of a call being delayed
This is Erlang C Formula
For S=5, a=3, B(5,3)=0.11, we have C(5,3)=0.2360
EE of NIU
Chih-Cheng Tseng

14. Erlang B and Erlang C Probability of an arriving call being blocked is
where S is the number of channels in a group.
Probability of an arriving call being delayed is
where a is the traffic load in Erlang and S is the number of channels.
Erlang B formula
Erlang C formula
EE of NIU
Chih-Cheng Tseng

15. Frequency Reuse: 7 Cell Reuse Cluster
Fx: A set of frequency bands
EE of NIU
Chih-Cheng Tseng

16. Reuse Distance (1) Cluster RF2 F3 F4 F5 F6 F7 F1 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
EE of NIU
Chih-Cheng Tseng

17. Reuse Distance (2)
The cluster size or the number of cells per cluster is given by where i and j are integers and N = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, …, etc.
The popular values of N are 4 and 7.
Finding the center of an adjacent cluster using integers i and j
j direction
60°
… i
i direction
EE of NIU
Chih-Cheng Tseng

18. How to Form a Cluster?
Select a cell and make the center of the cell as the origin.
u-axis and v-axis intersects at 60-degree angle.
Define the unit distance as the distance of centers of two adjacent cells.
Each cell can then get an ordered pair (u,v) to mark the position.
(4, -3)
(-3, 3)
u (v =0) 1 2 -1 -2 3 4 -3 -4
v (u =0)
EE of NIU
Chih-Cheng Tseng

19. Labeling Cells with L Values for N=7 (i.e. i=2, j=1)
For j=1, the cluster size is given by N=i2+i+1.
Define L=[(i+1)u+v)] mod N, we can obtain cell labels L for the cell whose center is at (u,v).
For N=7, i=2 and j=1
An alternative choice for 7-cell cluster u v 3 6 5 4 1 2 u 1 -1 v L 3 4 6 5
EE of NIU
Chih-Cheng Tseng

20. Labeling Cells with L Values for N=13 (i.e. i=3, j=1)4 8 12 11 9 5 1 2 10 3 7 6
EE of NIU
Chih-Cheng Tseng

21. Common Reuse Pattern of Hex Cell Clusters
EE of NIU
Chih-Cheng Tseng

22. Worst Case of Cochannel Interference (Omnidirectional Antenna)
Mobile Station D4 D2 D3
Serving Base Station
Co-channel Base Station
EE of NIU
Chih-Cheng Tseng

23. Cochannel Interference Ratio (CCIR)
Cochannel interference ratio is given by
Ik is co-channel interference from the kth co-channel interfering cell.
M is the maximum number of co-channel interfering cells
Techniques to reduce CCIR
Cell splitting
Cell sectoring
EE of NIU
Chih-Cheng Tseng

24. Cell Splitting
Large cell (low traffic density)
Small cell (high traffic density)
Smaller cell (higher traffic density)
Depending on traffic patterns, the smaller cells may be activated/deactivated in order to efficiently use cell resources.
Smaller cell size, smaller transmitting power, and reduces cochannel interference
EE of NIU
Chih-Cheng Tseng

25. 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
EE of NIU
Chih-Cheng Tseng

26. Worst Case for Forward Channel Interference in Three-sectors
The CCIR in the worst case for 3-sectors
 is the propagation path loss slope and  = 2 ~ 5 BS MS R D’ D
EE of NIU
Chih-Cheng Tseng

27. Worst Case for Forward Channel Interference in Six-sectors
The CCIR in the worst case for 6-sectors
 is the propagation path loss slope and  = 2 ~ 5
D+0.7R MS BS R
EE of NIU
Chih-Cheng Tseng

28. Cell Sectoring by Placing Directional Antennas at Three Common CornersX
EE of NIU
Chih-Cheng Tseng

29. Homework
P5.5
P5.7
P5.11
P5.14
P5.15
EE of NIU
Chih-Cheng Tseng