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Chapter 5

Chapter 5. The Cellular Concept. 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. Cell Shape. R. R. R. Cell.

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Chapter 5

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

  4. 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/ Cell Channels/Unit Area when Number of Channels is Increased by a Factor K Channels/Unit Area when Size of Cell Reduced by aFactor M Square cell (side =R) R2 4R Hexagonal cell (side=R) 6R Circular cell (radius=R) p R2 2pR Triangular cell (side=R) 3R

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

  9. Handoff Region Signal strength due to BSj Signal strength due to BSi Pj(x) Pi(x) E E Pmin MS BSj BSi 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 sizedbuffer 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 • Probability of an arriving call being delayed is Erlang C formula where C(S, a) is the probability of an arriving call being delayed with a load and S channels where S is the number of channels in a group

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

  16. Frequency Reuse F7 F2 F7 F2 F3 F6 F1 F1 F3 F6 F1 F1 F5 F4 F7 F2 F5 F4 F7 F2 F1 F3 F6 F1 F3 F6 F1 F1 F5 F4 F5 F4 Reuse distance D Fx: Set of frequencies 7 cell reuse cluster

  17. Reuse Distance • 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 Cluster R F7 F2 F3 F6 F1 F1 F5 F4 F7 F2 F3 F6 F1 F1 F5 F4 Reuse distance D

  18. Reuse Distance (Cont’d) 60° 60° j direction j direction 1 2 3 … i 1 2 3 … i • 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 i direction

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

  20. Worst Case of Cochannel Interference D6 R D5 D1 Mobile Station D4 D2 D3 Serving Base Station Co-channel Base Station

  21. Cochannel Interference C C where  is the propagation path loss slope and  = 2 ~ 5 = -g I æ ö M D å ç ÷ k R è ø = k 1 • 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:

  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 c 120o b a (c). 120o sector (alternate) f d e 60o a 90o a c d b b c (d). 90o sector (e). 60o sector c 120o a b (a). Omni (b). 120o sector

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

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