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

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

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

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.

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

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

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

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.,

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

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

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

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

Cell Structure (a) Line Structure (b) Plan Structure F3 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.

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

Reuse Distance Cluster R F1 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

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

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)

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

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

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.

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

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