2Outline Cell Area Actual cell/Ideal cell Signal Strength Handoff RegionCapacity of a CellTraffic theoryErlang B and Erlang CFrequency ReuseHow to form a clusterCochannel InterferenceCell SplittingCell Sectoring
3Cell Shape (c) Different cell models (a) Ideal cell (b) Actual cell R
4Impact of Cell Shape and Radius on Service Characteristics Triangular cell (side=R)2pRp R2Circular cell (radius=R)6RHexagonal cell (side=R)4RR2Square cell (side =R)Channels/Unit Area when Size of Cell Reduced by a Factor MChannels/Unit Area when Number of Channels is Increased by a Factor KChannels/ Unit Area with N Channels/ CellBoundary Length/ Unit AreaBoundaryAreaShape of the Cell
5Signal strength (in dB) Select cell j on right of boundaryCell j-60-70-80-90-100Cell i-60-70-80-90-100Select cell i on left of boundaryIdeal boundary
6Actual Signal Strength Signal strength (in dB)Cell jCell i-60-70-60-80-70-90-80-90-100-100Signal strength contours indicating actual cell tiling. This happens because of terrain, presence of obstacles and signal attenuation in the atmosphere.
7Universal Cell Phone Coverage ChittagongMicrowave TowerCellDhakaMaintaining the telephone number across geographical areas in a wireless and mobile system
8Variation of Received Power Received power P(x)Distance x of MS from BS
9Handoff Region Signal strength due to BSj Signal strength due to BSi Pi(x)Pj(x)EEPminBSiMSBSjBSjX1X3X5XthXthXthX4X4X4X2X2X2By 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
10Cell CapacityAverage number of MSs requesting service (Average arrival rate): Average length of time MS requires service (Average holding time): TOffered load: a = T where a is in Erlangse.g., in a cell with 100 MSs, on an average 30 requests are generated during an hour, with average holding time T=360 secondsThen, arrival rate =30/3600 requests/secA completely occupied channel (1 call-hour per hour) is defined as a load of one Erlang, i.e.,
11Cell CapacityAverage arrival rate during a short interval t is given by tAverage service (departure) rate is The system can be analyzed by a M/M/S/S queuing model, where S is the number of channelsThe steady state probability P(i) for this system in the form (for i =0, 1, ……, S)-1Where and
12Capacity of a CellThe probability P(S) of an arriving call being blocked is the probability that all S channels are busywhich 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) isSo, the number of callsblocked 30x0.529 = 15.87
13Capacity of a cell The probability of a call being delayed: This is Erlang C FormulaBlocked Calls Delayed infinite sized buffer or queue, no calls droppedFor S=5, a=3, B(5,3)=0.11Gives C(5,3)=0.2360
14Erlang B and Erlang C (used to determine GOS) Probability of an arriving call being blocked isErlang B formulawhere S is the number of channels in a groupErlang C formulawhere C(S, a) is the probability of an arriving call being delayed with a load and S channelsProbability of an arriving call being delayed is
15Cell Structure (a) Line Structure (b) Plan Structure F3F2F1(b) Plan StructureF3F2F4F1F5F6F7F2F3F1(a) Line StructureNote: Fx is a set of frequencies i.e., frequency group.
16Frequency Reuse Fx: Set of frequencies 7 cell reuse cluster F1 F2 F3 Reuse distance DFx: Set of frequencies7 cell reuse cluster
17Reuse Distance Cluster R F1F2F3F4F5F6F7RClusterFor hexagonal cells, the reuse distance is given bywhere R is cell radius and N is the reuse pattern (the cluster size or the number of cells per cluster).Reuse factor isReuse distance D
18Reuse Distance (Cont’d) The cluster size or the number of cells per cluster is given bywhere i and j are non-negative integersN = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, …, etc.The popular value of N being 4 and 7j direction60°… ij direction60°… ii direction
19Cochannel Interference First tier cochannel Base StationRD1D2D3D4D5D6Second tier cochannel Base StationMobile Station(MS)Serving Base Station (BS)
20Worst Case of Cochannel Interference D6RD5D1Mobile StationD4D2D3Serving Base StationCo-channel Base Station
21Cochannel Interference Cochannel interference ratio is given bywhere I is co-channel interference and M is the maximum number of co-channel interfering cellsFor M = 6, C/I is given by:å=÷øöçèæMkRDCI1-gwhere is the propagation path loss slope and = 2 ~ 5
22Cell 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.