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Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 1 Chapter 5 The Cellular Concept.

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Presentation on theme: "Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 1 Chapter 5 The Cellular Concept."— Presentation transcript:

1 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 1 Chapter 5 The Cellular Concept

2 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 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 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 3 Cell Shape Cell R (a) Ideal cell R R R R (c) Different cell models (b) Actual cell

4 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 4 Impact of Cell Shape and Radius on Service Characteristics 3R Triangular cell (side=R) 2R2R  R 2 Circular cell (radius=R) 6R Hexagonal cell (side=R) 4R R2R2 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 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 5 Signal Strength Select cell i on left of boundary Ideal boundary 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

6 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 6 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 -70 -80 -90 -100 Signal strength (in dB) Cell i Cell j

7 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 7 Universal Cell Phone Coverage Maintaining the telephone number across geographical areas in a wireless and mobile system Microwave Tower Cell Dhaka Chittagong

8 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 8 Received power P(x) Distance x of MS from BS Variation of Received Power

9 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 9 Handoff Region BS i Signal strength due to BS j E X1X1 Signal strength due to BS i BS j X3X3 X4X4 X2X2 X5X5 X th MS P min P i (x) P j (x) BS j X4X4 X2X2 X th E X4X4 X2X2 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 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 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 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 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) Where and

12 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 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 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 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 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 14 Erlang B and Erlang C (used to determine GOS) Probability of an arriving call being blocked is where S is the number of channels in a group Erlang B formula 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 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 15 Cell Structure F2 F3 F1 (a) Line Structure F3 F2F1 F3 F2F1 Note: Fx is a set of frequencies i.e., frequency group.

16 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 16 Frequency Reuse Fx: Set of frequencies 7 cell reuse cluster Reuse distance D

17 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 17 Reuse Distance Reuse distance D 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 F1 F2 F3 F4F5 F6 F7 F1 F2 F3 F4F5 F6 F7 F1 R Cluster

18 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 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 ° 1 2 3 … i j direction 60 ° 1 2 3 … i i direction

19 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 19 Cochannel Interference Mobile Station (MS) Serving Base Station (BS) Second tier cochannel Base Station First tier cochannel Base Station R D1D1 D2D2 D3D3 D4D4 D5D5 D6D6

20 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 20 Worst Case of Cochannel Interference Mobile Station Serving Base Station Co-channel Base Station R D1D1 D2D2 D3D3 D4D4 D5D5 D6D6

21 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 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:          M k k R D C I C 1  where  is the propagation path loss slope and  = 2 ~ 5

22 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 22 Cell Splitting Large cell (low density) Small cell (high density) Depending on traffic patterns the smaller cells may be activated/deactivated in order to efficiently use cell resources. Smaller cell (higher density)

23 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 23 Cell Sectoring by Antenna Design (a). Omni 120 o (b). 120 o sector a b c 120 o (c). 120 o sector (alternate) ab c (d). 90 o sector 90 o a b c d 60 o (e). 60 o sector a b c d e f

24 Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 24 Cell Sectoring by Antenna Design  Placing directional transmitters at corners where three adjacent cells meet A C B X


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