Chapter 5: Chapter 5 The Cellular Concept


Outline: Outline Cell Shape Actual cell/Ideal cell Signal Strength Handoff Region Cell Capacity Traffic theory Erlang B and Erlang C Cell Structure Frequency Reuse Reuse Distance Cochannel Interference Cell Splitting Cell Sectoring


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


Impact of Cell Shape and Radius on Service Characteristics: Impact of Cell Shape and Radius on Service Characteristics


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


Signal Strength: 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 -60 -70 -80 -90 -100 Signal strength (in dB) Cell i Cell j


Handoff Region: Handoff Region BSi Signal strength due to BSj E X1 Signal strength due to BSi BSj X3 X4 X2 X5 Xth MS Pmin Pi(x) Pj(x) 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.


Handoff Rate in a Rectangular: Handoff Rate in a Rectangular  R2 R1 X2 X1 Since handoff can occur at sides R 1 and R 2 of a cell where A=R 1 R 2 is the area and assuming it constant, differentiate with respect to R1 (or R 2) gives Total handoff rate is H is minimized when =0, giving 


Cell Capacity: 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 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 channel kept busy for one hour is defined as one Erlang (a), i.e.,


Cell Capacity: Cell Capacity Average arrival rate during a short interval t is given by  t Assuming Poisson distribution of service requests, the probability P(n, t) for n calls to arrive in an interval of length t is given by Assuming  to be the service rate, probability of each call to terminate during interval t is given by  t. Thus, probability of a given call requires service for time t or less is given by


Erlang B and Erlang C: Erlang B and Erlang C 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


Efficiency (Utilization): Efficiency (Utilization) Example: for previous example, if S=2, then B(S, a) = 0.6, ------ Blocking probability, i.e., 60% calls are blocked. Total number of rerouted calls = 30 x 0.6 = 18 Efficiency = 3(1-0.6)/2 = 0.6


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


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


Reuse Distance: Reuse Distance F1 F2 F3 F4 F5 F6 F7 F1 F2 F3 F4 F5 F6 F7 F1 F1 Reuse distance D For hexagonal cells, the reuse distance is given by R 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


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


Reuse Distance (Cont’d): Reuse Distance (Cont’d) (b) Formation of a cluster for N = 7 with i=2 and j=1 60° 1 2 3 … i j direction i direction (a) Finding the center of an adjacent cluster using integers i and j (direction of i and j can be interchanged). i=2 i=2 j=1 j=1 j=1 j=1 j=1 j=1 i=2 i=2 i=2 i=2


Reuse Distance (Cont’d): Reuse Distance (Cont’d) (c) A cluster with N =12 with i=2 and j=2 (d) A Cluster with N = 19 cells with i=3 and j=2 j=2 j=2 j=2 j=2 j=2 j=2 i=2 i=2 i=2 i=2 i=2 i=2


Cochannel Interference: Cochannel Interference Mobile Station Serving Base Station First tier cochannel Base Station Second tier cochannel Base Station R D1 D2 D3 D4 D5 D6


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


Cochannel Interference: 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 where  is the propagation path loss slope and  = 2~5.


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


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


Worst Case for Forward Channel Interference in Three-sectors : Worst Case for Forward Channel Interference in Three-sectors BS MS R D + 0.7R D BS BS BS


Worst Case for Forward Channel Interference in Three-sectors (Cont’d): Worst Case for Forward Channel Interference in Three-sectors (Cont’d) BS MS R D’ D BS BS BS D


Worst Case for Forward Channel Interference in Six-sectors: Worst Case for Forward Channel Interference in Six-sectors