CS 6910 Pervasive Computing Spring 2007 Section 5

CS 6910 – Pervasive Computing Spring 2007 Section 5 (Ch. 5): Cellular Concept Prof. Leszek Lilien Department of Computer Science Western Michigan University Slides based on publisher’s slides for 1 st and 2 nd edition of: Introduction to Wireless and Mobile Systems by Agrawal & Zeng © 2003, 2006, Dharma P. Agrawal and Qing-An Zeng. All rights reserved. Some original slides were modified by L. Lilien, who strived to make such modifications clearly visible. Some slides were added by L. Lilien, and are © 2006 -2007 by Leszek T. Lilien. Requests to use L. Lilien’s slides for non-profit purposes will be gladly granted upon a written request. 1

Chapter 5 Cellular Concept Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 2

Outline n n n n n Cell Shape n Actual cell/Ideal cell Signal Strength Handoff Region Cell Capacity n Traffic theory n Erlang B and Erlang C Cell Structure Frequency Reuse Distance Cochannel Interference Cell Splitting Cell Sectoring Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 3

5. 1. Introduction n Cell (formal def. ) = an area wherein the use of radio communication resources by the MS is controlled by a BS n Cell design is critical for cellular systems n Size and shape dictate performance to a large extent n n For given resource allocation and usage patterns This section studies cell parameters and their impact Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 4

5. 2. Cell Area [LTL] n n n Cell size & shape are most important parameters in cellular systems Informally, a cell is an area covered by a transmitting station (BS) (with all MSs connected to and serviced by the BS) Recall: n Ideal cell shape (Fig. a) is circular n Actual cell shapes (Fig. b) are caused by reflections & refractions n n n Also reflections & refractions from air particles Many cell models (Fig. c) approximate actual cell shape Hexagonal cell model most popular Square cell model second most popular R R R Cell R (a) Ideal cell (b) Actual cell R (c) Different cell models Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved (Modified by LTL) 5

Impact of Cell Shape & Radius on Service Characteristics n n Note: Only selected parameters from Table will be discussed (later) For given BS parameters, the simplest way of increase # of channels available in an area, reduce cell size n Smaller cells in a city than in a countryside Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved (Modified by LTL) 6

5. 3. Signal Strength and Cell Parameters [http: //en. wikipedia. org/wiki/DBm] n d. Bm (used in following slides) = an abbreviation for the power ratio in decibel (d. B) of the measured power referenced to 1 m. W (milliwatt) n d. Bm is an absolute unit measuring absolute power n n n Since it is referenced to 1 m. W In contrast, d. B is a dimensionless unit, which is used when measuring the ratio between two values (such as signal-to-noise ratio) Examples: n n 0 d. Bm = 1 m. W 3 d. Bm ≈ 2 m. W n n Since a 3 d. B increase represents roughly doubling the power − 3 d. Bm n ≈ 0. 5 m. W Since a 3 d. B decrease represents roughly cutting in half the power … more examples – next slide … Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 7

5. 3. Signal Strength and Cell Parameters – cont. [http: //en. wikipedia. org/wiki/DBm] n Examples – cont. n 60 d. Bm = 1, 000 m. W = 1, 000 W = 1 k. W n n n Typical RF power inside a microwave oven n Typical cellphone transmission power 27 d. Bm = 500 m. W 20 d. Bm= 100 m. W n n Bluetooth Class 1 radio, 100 m range = max. output power from unlicensed FM transmitter (4 d. Bm = 2. 5 m. W - BT Class 2 radio, 10 m range) − 70 d. Bm = 100 p. W n n n (some claim that users’ brains are being fried) (yes, “-”!!!) Average strength of wireless signal over a network See next slide!!! Average for the range: − 60 to − 80 d. Bm n − 60 d. Bm= 1 n. W = 1, 000 p. W n − 80 d. Bm= 10 p. W Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 8

Signal Strength for Two Adjacent Cells with Recall: − 70 d. Bm = 100 p. W - average strength of wireless signal over a network Ideal Cell Boundaries Signal strength (in d. Bm) Cell i -60 -70 -80 -90 Cell j -60 -70 -80 -90 -100 Select cell i on left of boundary Select cell j on right of boundary Ideal boundary Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 9

Signal Strength for Two Adjacent Cells with Actual Cell Boundaries Recall: − 70 d. B m= 100 p. W average strength of wireless signal over a network Signal strength (in d. B) Cell i Cell j -60 -90 -100 -70 -80 -90 -100 Signal strength contours indicating actual cell tiling. This happens because of terrain, presence of obstacles and signal attenuation in the atmosphere. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 10

Power of Single Received Signal as Function of Distance from Single BS n Next slide: Situation for signal power received from 2 BSs Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 11

Pmin BSi n Pj(x) Pi(x) X 1 X 3 Signal strength due to BSj Signal strength due to BSi Powers of Two Received Signals as Functions of Distances from Two BSs MS X 5 X 4 BSj X 2 Observe: n Pj(X 1) ≈ 0 Pi(X 2) ≈ 0 n Pj(X 3) > Pmin (of course, Pi(X 3) >> Pj(X 3) > Pmin) Pi(X 4) > Pmin (of course, Pj(X 4) >> Pi(X 4) > Pmin) n Pj(X 5) = Pi(X 5) Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved (Modified by LTL) 12

Received Signals and Handoff (=Handover) n n n can receive the following signals: At X < X 3 - can receive signal only from BSi (since Pj(X) < Pmin) At X 3 < X 4 - can receive signals from both BSi & BSj At X > X 4 - can receive signal only from BSj (since Pi(X) < Pmin) (SUV in the Figure) Pmin BSi Pj(x) Pi(x) X 1 X 3 MS X 5 X 4 Signal strength due to BSj MS Signal strength due to BSi n BS X 2 j X § If MS moves away from BSi and towards BSj (as shown), hand over MS from BSi and to BSj between X 3 & X 4 Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved (Modified by LTL) 13

Handoff Area Signal strength due to BSi Signal strength due to BSj Pj(x) Pi(x) E Pmin BSi n n X 3 X 5 Xk X 4 BSj X 2 Between X 3 & X 4 MS can be served by either BSi or BSj n n X 1 MS Used technology & service provider decide who serves at any Xk between X 3 & X 4 As MS moves, handoff must be done in the handoff area, i. e. , between X 3 & X 4 Must find optimal handoff area within the handoff area Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved (Modified by LTL) 14

Optimal Handoff Area & Ping -pong Effect Signal strength due to BSi Signal streng due to BS Pj(x) Pi(x) E Pmin BSi n MS X 5 Xk X 4 X 2 BSj Is it X 5? - both signals have equal strength there Ping-pong effect in handoff n n X 3 Where is the optimum handoff area? n n X 1 Imagine MS driving “across” X 5 towards BSj, then turning back and driving “across” X 5 towards BSi, then turning back and driving “across” X 5 towards BSj, then …. Solution for avoiding ping-pong effect n Maintain link with BSi up to point Xk where: n Pj(Xk) > Pj(Xk) + E (E - a chosen threshold) Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 15

Handoff in a Rectangular Cell n n Handoff affected by: n Cell area and shape n MS mobility pattern n Different for each user & impossible to predict => Can’t optimize handoff by matching cell shape to MS mobility Illustration: How handoff related to mobility & rectangular cell area n Derivation (next slides – skipped) n Results: Intuitively handoff is minimized when: Rectangular cell is aligned [=its sides are aligned] with vertical & horizontal axes AND n the ratio of the numbers N 1 and N 2 of MSs crossing cell sides R 1 and R 2 is inversely proportional to the ratio of the lengths of R 1 and R 2 n Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 16

** OPTIONAL ** Handoff in a Rectangular Cell – cont. 1 n n Rectangle with sides R 1 and R 2 and area A = R 1 * R 2 N 1 - # of MSs having handoff per unit length in horizontal direction N 2 - # of MSs having handoff per unit length in vertical direction Figure needs corrections Slant Handoff can occur through side R 1 or side R 2 n λH = total handoff rate (# of MSs handed over to this rectangular cell) = = # of MSs handed over R 1 side + # of MSs handed over R 2 side = = R 1 (N 1 cos + N 2 sin ) + R 2 (N 1 sin + N 2 cos ) Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 17

*** OPTIONAL *** Handoff in a Rectangular Cell – cont. 2 n How to minimize λH for a given n Assuming that A = R 1 * R 2 is constant, do: n n Figure needs corrections Set R 2 = A/ R 1 Differentiate λH with respect to R 1 Equate it to zero Slant It gives (note: X 1 = N 1, X 2 = X 2): n Now, total handoff rate is: n H is minimized when =0, giving R 2/R 1 = N 1/N 2 n Intuitively: Handoff is minimized when: “Rectangular cell is aligned [its sides are aligned] with vertical and horizontal axes” AND n the ratio of the number of MSs crossing cell sides R 1 and R 2 is inversely proportional to the ratio of their lengths n n [TEXTBOOK: “the number of MSs crossing boundary is inversely proportional to the value of the other side of the cell”] Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 18

5. 4. Cell Capacity n n Offered load a = T where: n - mean call arrival rate = avg. # of MSs requesting service per sec. n T – mean call holding time = avg. length of call Example On average 30 calls generated per hour (3. 600 sec. ) in a cell => Arrival rate = 30/3600 calls/sec. = 0. 0083333… calls/sec. Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 19

5. 4. Cell Capacity – cont. 1 n Erlang unit - a unit of telecommunications traffic (or other traffic) [http: //en. wikipedia. org/wiki/Erlang_unit] n http: //en. wikipedia. org/wiki/Erlang: n n n Agner Krarup Erlang (1878– 1929) the Danish mathematician, statistician, and engineer after whom the Erlang unit was named Erlang Shen is a famous Chinese deity 1 Erlang: n 1 channel being in continuous (100%) use OR n 2 channels being at 50% use (2 * 1/2 Erlang = 1 Erlang ) OR n 3 channels being at 33. 333… % use (3 * 1/3 Erlang = 1 Erlang ) OR n … n Example 1: An office with 2 telephone operators, both busy 100% of the time => 2 * 100% = 2 * 1. 0 = 2 Erlangs of traffic Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 20

5. 4. Cell Capacity – cont. 2 n Example 2 (Erlang as "use multiplier" per unit time) n 1 channel being used: n 100% use => 1 Erlang n 150% use => 1. 5 Erlang n n E. g. if total cell phone use in a given area per hour is 90 minutes => 90 min. /60 min = 1. 5 Erlangs 200% use => 2 Erlangs n n [ibid] E. g. if total cell phone use in a given area per hour is 120 minutes Traffic a in Erlangs a [Erlang] = λ [calls/sec. ] * T [sec. /call] Recall: λ - mean arrival rate, T -mean call holding time n Example: n A cell with 30 requests generated per hour => λ = 30/3600 calls/sec. n Avg. call holding time T = 6 min. /call = 360 sec. /call a = (30 calls / 3600 sec) * (360 sec/call) = 3 Erlangs Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 21

** OPTIONAL ** Cell Capacity – cont. 3 Avg. # of call arrivals during a time interval of length t: t Assume Poisson distribution of service requests Then n Probability P(n, t) that n calls arrive in an interval of length t: n n - the service rate (a. k. a. departure rate) - how many calls completed per unit time [calls/sec] Then: n Avg. # of call terminations during a time interval of length t: t n Probability that a given call requires service for time ≤ t: Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 22

Erlang B and Erlang C n n n a – offerred traffic load S - # of channels in a cell Erlang B formula = (mnemonics: “B” as “Blocking”) Probability B(S, a) of an arriving call being blocked Erlang C formula = (mnemonics: “C” closer to “d” in “delayed”) Probability C(S, a) of an arriving call being delayed Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 23

Erlang B and Erlang C – cont. n Examples n a = # calls/sec can be handled S = # channels in a cell n Erlang B examples (blocking prob. ) B(S, a) = B (2, 3) = 0. 529 B(S, a) = B (5, 3) = 0. 11 (p. 110) More channels => lower blocking prob. n Erlang C example (delay prob. ) C(S, a) = C (5, 3) = 0. 2360 Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 24

System Efficiency (Utilization) n n Efficiency = (Traffic_nonblocked) / (Total capacity) More precisely: Efficiency = = (offerred traffic load =a n [Erlangs]) * (Pr. of call not being blocked) / / # of channels in the cell= * [1 – B(S, a)] / S Example: n n Assume that: S= 2 channels in the cell, a = 3 calls/ sec => B (2, 3) = 0. 529 - prob. of a call being blocked is 52. 9 % Efficiency = 3 =3 [Erlangs] * [1 – B(2, 3)] / 2 * (1 - 0. 529) / 2 [channels] = 0. 7065 = 70. 65 % Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 25

5. 5. Frequency Reuse n Simplistic frequency use approach: Each cell uses unique frequencies (never used in any other cell) n Impractical n n For any reasonable # of cells, runs out of available frequencies => must “reuse” frequencies n n n Use same freq in > 1 cell Principle to reuse a frequency in different cells n Just ensure that “reusing” cells are at a sufficient distance to avoid interference Frequency reuse is the strength of the cellular concept n Reuse provides increased capacity in a cellular network, compared with a network with a single transmitter [http: //en. wikipedia. org/wiki/Cellular_network] Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 26

Cell Structure n Frequency group = a set of frequencies used in a cell n Alternative cell structures: n n F 1, F 2, … - frequency groups Simplistic frequency assignments in figures n No reuse - unique frequency groups F 7 F 1 F 2 F 6 F 3 (a) Line Structure F 3 F 2 F 3 F 1 F 4 F 5 F 4 (b) Plan Structures Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 27

Reuse Cluster n n F 1, F 2, … F 7 frequency groups Cells form a cluster n n F 7 E. g. 7 -cell cluster of hexagonal cells A reuse cluster n Its structure & its frequency groups are repeated to cover a broader service are F 6 F 2 F 3 F 1 F 5 F 6 F 4 F 2 F 5 F 7 F 6 F 4 F 2 F 7 F 2 F 1 F 6 F 3 F 1 F 1 F 5 F 3 F 4 7 -cell reuse cluster Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 28

Reuse Distance • Reuse distance • Between centers of cells reusing frequency groups Cluster R F 7 F 6 • For hexagonal cells, the reuse distance is given by F 2 F 3 F 1 F 5 F 4 F 7 F 6 F 2 F 3 F 1 e us Re => need larger D for larger N or R • Reuse factor is F 4 e. D nc sta di F 5 where: R - cell radius N - cluster size (# of cells per cluster) Þ q ~ D & q ~ 1/R & q ~ N (“~” means “is proportional”) Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 29

Reuse Distance Again (a bigger picture) F 7 F 6 F 2 F 3 F 1 F 5 F 6 F 4 F 2 F 5 F 7 F 6 F 3 F 1 F 4 F 2 F 1 F 6 F 3 F 1 F 7 F 5 F 3 F 4 e us Re F 4 e. D nc sta di F 5 7 -cell reuse cluster Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 30

5. 6. How to Form a Cluster § The cluster size (# of cells per cluster): N = i 2 + ij + j 2 where i and j are integers § Substituting different values of i and j gives N = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, … § Most popular cluster sizes: N = 4 and N = 7 § See next slide for hex clusters of different sizes § IMPORTANT (p. 111/-1) Unless otherwise specified, cluster size N = 7 assumed Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modifiedbyby LTL 31

Hex Clusters of Different Sizes Clusters designed for freq reuse Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 32

Finding Centers of All Clusters Around a Reference Cell n Finding centers of neighboring clusters (NCs) for hex cells n Procedure repeated 6 times n For each reference cell (RC), the six immediate NCs are: (once for each side of a hex reference cell) right-top right-bottom left-top n By finding centers of neighboring clusters (NCs), we simultaneously determine cells belonging to the current cluster Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 33

Neighboring Clusters for a Reference Cell n For the yellow RC, the following NCs are shown: n n Right-top Left-top How to find name for NC? n n Draw a line from the center of RC to the center of each NC We see lines for 3 NCs in the fig. n n F 7 F 2 F 1 F 6 F 5 F 7 F 1 F 6 F 3 F 4 F 2 F 5 F 7 F 6 F 4 F 2 F 7 F 2 F 1 F 6 F 3 F 1 F 5 F 3 F 4 Thick red lines E. g. , the cluster with green center cell is the “right” neighbor for the cluster with the yellow center bec. Red line cuts the right edge of the yellow hexagon Copyright © Leszek 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved © 2007 by T. Lilien 34

Neighboring Clusters for a Reference Cell – cont. 1 n n n For j = 1, the formula: N = i 2 + ij + j 2 simplifies to: N = i 2 + i + 1 j = 1 means that we travel only 1 step in the “ 60 degrees” direction (cf. Fig. ) N = 7 (selected) & j = 1 (fixed) => i =2 n n I. e. , we travel exactly 2 steps to the right Fig. show i = 1, 2, 3, … but for N = 7 (and j = 1), © 2007 by Leszek T. Lilien we have i = 2 only Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 35

Neighboring Clusters for a Reference Cell – cont. 2 n n [Repeated] N = 7 (selected) & j = 1 (fixed) => i =2 n I. e. , we travel only 2 steps to the right Example To get from the yellow cell to the green cell, we travel 2 steps to the right (i = 2) & 1 step at F 7 60 degrees (j = 1) © 2007 by Leszek T. Lilien F 7 F 2 F 1 F 6 F 5 F 1 F 6 F 3 F 4 F 2 F 5 F 7 F 6 F 4 F 2 F 7 F 2 F 1 F 6 F 3 F 1 F 5 F 3 F 4 Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 36

Coordinate Plane & Labeling Cluster Cells n n Step 1: Select a cell, its center becomes origin, form coordinate plane: u axis pointing to the right from the origin, and v axis at 60 degrees to u Notice that “right” (= direction of u axis) is slanted to LHS n n n All other directions are slanted analogously Unit distance = dist. between centers of 2 adjacent cells E. g. , green cell identified as (-3, 3) (-3 along u, 3 along v) n E. g. , red cell identified as (4, -3) Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 37

Coordinate Plane & Labeling Cluster Cells – cont. 1 n Clusters formed using formula N = i 2 + i + 1 n n n Simplified from N = i 2 + ij + j 2 for j = 1 Cell label L n For cluster size N and cell coordinates (u, v), cell label L is: L = [(i+1) u + v] mod N Examples (more in Table below) n n Cluster size N =7 => i = 2 (bec. N = i 2 + i + 1) & L = (3 u + v) mod N (u, v) = (0, 0) => L = 0 mod 7 = 0 (u, v) = (-3, 3) => L = [(-9) + 3] mod 7 = (-6) mod 7 = 1 (u, v) = (4, -3) => L = [3 * 4 + (-3)] mod 7 = 9 mod 7 = 2 © 2007 by Leszek T. Lilien Find 1 error in Table 5. 2 Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 38

Cell Labels for 7 -Cell Cluster Note: Circles drawn to help finding clusters Green and red dots indicate cells at (-3, 3) and (4, -3) OBSERVE: Cells within each cluster are labeled in the same way! Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 39

OBSERVE: 1) For 7 -cell clusters, cells within clusters had labels 0 -6 Cell Labels for 13 -Cell Cluster 2) Here, for 13 -cell clusters, cells within clusters have labels 0 -12 3) N = 13 & j = 1 => i=3 => to get from (0, 0) to the center of blue NC, go 3 steps right, then 1 step at 60 degrees Note: “right” is slanted (bec. axis v is slanted)! E. g. , to get from (0, 0) to its blue dot NC go 3 steps along u, then 1 step at 60 degrees Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 40

Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 41

5. 7. Cochannel Interference n Second-tier cochannel BS Slide 39: N = 7 => 6 NCs (neighboring clusters) with cells reusing each Fx of “our” cluster (Slide 40: N = 13 => 6 NCs w/ cells reusing each Fx) n BSs of NCs are called 1 st-tier cochannel BSs n n D 6 D 1 D 5 (cf. next slide) At dist’s ≥ 2 * D D 4 D 2 MS D 3 (approx. ) Assuring reuse distance only limits interference n R BSs of “next ring” of neighbors are called 2 nd-tier cochannel BSs n n Di ≥ D - R First-tier cochannel BS D 2 D Serving BS Does not eliminate it completely Observe that: (1) Di’s are not identical (D 6 is the smallest) (2) Di’s differ from reuse distance (< or >) Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 42

Worst Case of Cochannel Interference n Worst case when D 1 = D 2 ≈ D – R and D 3 ≈ D 6 = D and D 4 ≈ D 5 = D + R R D 5 D 6 D D 2 D D 4 Serving BS D 1 D R D MS D 3 Co-channel BS Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 43

Cochannel Interference § Cochannel interference ratio (CCIR) where Ik is co-channel interference from BSk M is the max. # of co-channel interfering cells Example: N = 7 => M = 6 C = I C æ Dk ö å= çè R ÷ø k 1 6 -g where - propagation path loss slope ( = from 2 to 5) Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 44

5. 8. Cell Splitting n n Use large cell normally When traffic load increases (e. g. , increased # of users in a cell), Large cell (low density) Medium cell (medium density) Small cell (high density) switch to mediumsized cells n n If increased again, switch to small cells n n Requires more BSs Requires even more BSs Smaller xmitting power for smaller cells => reduced cochannel interference Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 45

5. 9. Cell Sectoring (by Antenna Design) n So far we assumed omnidirectional antennas n n Actually, antennas are directional n n Propagate equal-strength signal in all directions (360 degrees) Cover less than 360 degrees Most common: 120 / 90 / 60 degrees Directional antennas are a. k. a. sectored antennas Cells served by them known as sectored cells To cover 360 degrees with directional antennas, need 3, 4 or 6 antennas n n For 120 - / 90 - / 60 - degree antennas, respectively Cf. next slide 2003, T. Dharma ©Copyright 2007 by © Leszek Lilien P. Agrawal and Qing-An Zeng. All rights reserved 46

5. 9. Cell Sectoring (by Antenna Design) – cont. c c 120 o a b b (a). Omni (b). 120 o sector (c). 120 o sector (alternate) f d 90 o a c b (d). 90 o sector n e d 60 o c a b (e). 60 o sector Above - sectoring of cells with directional antennas n Together cover 360 degrees n n a Same effcect as a single omnidirectional antenna Many antennas mounted on a single microwave tower n E. g. , for a BS in cell center: 3, 4, or 6 sectoral antennas on BS tower Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 47

Cell Sectoring by Antenna Design –cont. n Advantages of sectoring n Smaller xmission power n n Decreased cochannel interference n n n Since lower power Enhanced overall system’s spectrum efficiency Placing directional antennas at corners n n Each antenna covers smaller area B C Where three adjacent cells meet n E. g. , BS tower X serves 120 -degree portions of cells A, B and C X A Might seem that placement in corners requires 3 times more towers than placement with towers in centers Actually, for a larger area, # of towers approx. the same (convince yourself) © 2007 by Leszek T. Lilien Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 48

Worst Case for Forward Channel Interference in Three-sector Cells n BS 1 – BS in our cell (e. g. , in the cluster center, N = 7) BS 2 & BS 3 – are first-tier cochannel BSs = closest cells reusing our Fx (BS 1 in center => BS 2, BS 3 in centers of NCs) BS 4 – not reusing => does not interfere n Distance from corresp. sector antennas of BS 2/BS 3 to MS D’ = D + 0. 7 R (derivation - OPTIONAL - next slide & p. 118 ) n D BS 2 BS 1 D’ R CCIR ratio): © 2007 by Leszek T. Lilien (cochannel interf. MS BS 4 BS 3 R D n Recall: - propagation path loss slope ( = 2 - 5) Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 49

** OPTIONAL ** Derivation of D’ for Worst Case for Forward Channel Interference in Three-sector Cells – cont. BS D D’ BS MS BS R D BS Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 50

Worst Case for Forward Channel Interference in Six-sector Cells R MS BS D +0. 7 R n CCIR (cochannel interf. ratio) for =4: 1 BS = (q + 0. 7)4 = 4 - propagation path loss slope Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Modified by LTL 51

The End of Section 5 Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 52