Chapter 5 Cellular Concept Prof. Chih-Cheng Tseng tsengcc@niu.edu.tw http://wcnlab.niu.edu.tw EE of NIU Chih-Cheng Tseng

Cell Shape A cell is the radio coverage by a transmitting station or a BS. Why hexagon? closer to a circle can be arranged next to each other without having any overlap and uncovered space in between R (c) Different cell models R Cell R (a) Ideal cell (b) Actual cell EE of NIU Chih-Cheng Tseng

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/Cells Channels/Unit Area when Number of Channels Increased by a Factor K Channels/Unit Area when Size of Cell Reduced by a Factor M Square cell (side =R) R2 4R Hexagonal cell (side=R) 6R Circular cell (radius=R) pR2 2pR Triangular cell (side=R) 3R EE of NIU Chih-Cheng Tseng

Signal Strength Signal strength (in dBm) Cell i Cell j -60 -70 -80 -90 Select cell i on left of boundary Ideal boundary Signal strength (in dBm) Select cell j on right of boundary Cell j -60 -70 -80 -90 -100 Cell i EE of NIU Chih-Cheng Tseng

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 Signal strength (in dBm) Cell i Cell j EE of NIU Chih-Cheng Tseng

Variation of Received Power Received power P(x) Distance x of MS from BS EE of NIU Chih-Cheng Tseng

Handoff Region BSi MS BSj X1 X3 X5 Xth X4 X2 E Pi(x) Pj(x) Signal strength due to BSi Signal strength due to BSj E Pmin BSi MS BSj X1 X3 X5 Xth X4 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. EE of NIU Chih-Cheng Tseng

Handoff Rate in a Rectangular Area N1 is the number of MSs having handoff per unit length in horizontal direction N2 is the number of MSs having handoff per unit length in vertical direction Since handoff can occur at sides R1 and R2 of a cell R2 R1 N2 N1  Assuming area A=R1R2 is fixed, substitute R2= A/R1, differentiating lH with respect to R1 and equating to 0 gives N1cosq + N2sinq-A/R12 (N1sinq +N2cosq)=0 EE of NIU Chih-Cheng Tseng

Handoff Rate in a Rectangular Thus, we have: Simplifying through few steps gives H is minimized when  = 0, giving EE of NIU Chih-Cheng Tseng

The Offered Traffic Load of A Cell Average number of MSs requesting service (Average arrival rate):  Average length of time MS requires service (Average holding time): T Offered load: a = T Example: 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 an hour is defined as one Erlang EE of NIU Chih-Cheng Tseng

Analyses of The Call Blocking Probability (1) Average arrival rate is  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 EE of NIU Chih-Cheng Tseng

Analyses of The Call Blocking Probability (2) The probability P(S) of an arriving call being blocked is the probability that all S channels are busy This is Erlang B formula B(S, a) Example: If S=2 and a=3, the blocking probability B(2, 3) is So, the number of blocked calls is about 300.529=15.87 EE of NIU Chih-Cheng Tseng

The Probability of A Call Being Delayed The efficiency of a system can be given by The probability of a call being delayed This is Erlang C Formula For S=5, a=3, B(5,3)=0.11, we have C(5,3)=0.2360 EE of NIU Chih-Cheng Tseng

Erlang B and Erlang C Probability of an arriving call being blocked is where S is the number of channels in a group. Probability of an arriving call being delayed is where a is the traffic load in Erlang and S is the number of channels. Erlang B formula Erlang C formula EE of NIU Chih-Cheng Tseng

Frequency Reuse: 7 Cell Reuse Cluster Fx: A set of frequency bands EE of NIU Chih-Cheng Tseng

Reuse Distance (1) Cluster R F2 F3 F4 F5 F6 F7 F1 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 EE of NIU Chih-Cheng Tseng

Reuse Distance (2) The cluster size or the number of cells per cluster is given by where i and j are integers and N = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, …, etc. The popular values of N are 4 and 7. Finding the center of an adjacent cluster using integers i and j j direction 60° 1 2 3 … i i direction EE of NIU Chih-Cheng Tseng

How to Form a Cluster? Select a cell and make the center of the cell as the origin. u-axis and v-axis intersects at 60-degree angle. Define the unit distance as the distance of centers of two adjacent cells. Each cell can then get an ordered pair (u,v) to mark the position. (4, -3) (-3, 3) u (v =0) 1 2 -1 -2 3 4 -3 -4 v (u =0) EE of NIU Chih-Cheng Tseng

Labeling Cells with L Values for N=7 (i.e. i=2, j=1) For j=1, the cluster size is given by N=i2+i+1. Define L=[(i+1)u+v)] mod N, we can obtain cell labels L for the cell whose center is at (u,v). For N=7, i=2 and j=1 An alternative choice for 7-cell cluster u v 3 6 5 4 1 2 u 1 -1 v L 3 4 6 5 EE of NIU Chih-Cheng Tseng

Labeling Cells with L Values for N=13 (i.e. i=3, j=1) 4 8 12 11 9 5 1 2 10 3 7 6 EE of NIU Chih-Cheng Tseng

Common Reuse Pattern of Hex Cell Clusters EE of NIU Chih-Cheng Tseng

Worst Case of Cochannel Interference (Omnidirectional Antenna) Mobile Station D4 D2 D3 Serving Base Station Co-channel Base Station EE of NIU Chih-Cheng Tseng

Cochannel Interference Ratio (CCIR) Cochannel interference ratio is given by Ik is co-channel interference from the kth co-channel interfering cell. M is the maximum number of co-channel interfering cells Techniques to reduce CCIR Cell splitting Cell sectoring EE of NIU Chih-Cheng Tseng

Cell Splitting Large cell (low traffic density) Small cell (high traffic density) Smaller cell (higher traffic density) Depending on traffic patterns, the smaller cells may be activated/deactivated in order to efficiently use cell resources. Smaller cell size, smaller transmitting power, and reduces cochannel interference EE of NIU Chih-Cheng Tseng

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 EE of NIU Chih-Cheng Tseng

Worst Case for Forward Channel Interference in Three-sectors The CCIR in the worst case for 3-sectors  is the propagation path loss slope and  = 2 ~ 5 BS MS R D’ D EE of NIU Chih-Cheng Tseng

Worst Case for Forward Channel Interference in Six-sectors The CCIR in the worst case for 6-sectors  is the propagation path loss slope and  = 2 ~ 5 D+0.7R MS BS R EE of NIU Chih-Cheng Tseng

Cell Sectoring by Placing Directional Antennas at Three Common Corners X EE of NIU Chih-Cheng Tseng

Homework P5.5 P5.7 P5.11 P5.14 P5.15 EE of NIU Chih-Cheng Tseng