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1 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 © by Leszek T. Lilien. Requests to use L. Lilien’s slides for non-profit purposes will be gladly granted upon a written request.

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 3 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

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Cell Area Cell R (a) Ideal cell (b) Actual cell R R R R (c) Different cell models [LTL] 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: Ideal cell shape (Fig. a) is circular Actual cell shapes (Fig. b) are caused by reflections & refractions 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 (Modified by LTL)

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 6 Impact of Cell Shape & Radius on Service Characteristics 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 Smaller cells in a city than in a countryside (Modified by LTL)

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Signal Strength and Cell Parameters [http://en.wikipedia.org/wiki/DBm] dBm (used in following slides) = an abbreviation for the power ratio in decibel (dB) of the measured power referenced to 1 mW (milliwatt) dBm is an absolute unit measuring absolute power Since it is referenced to 1 mW In contrast, dB is a dimensionless unit, which is used when measuring the ratio between two values (such as signal-to-noise ratio) Examples: 0 dBm = 1 mW 3 dBm ≈ 2 mW Since a 3 dB increase represents roughly doubling the power −3 dBm ≈ 0.5 mW Since a 3 dB decrease represents roughly cutting in half the power … more examples – next slide … © 2007 by Leszek T. Lilien

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Signal Strength and Cell Parameters – cont. [http://en.wikipedia.org/wiki/DBm] Examples – cont. 60 dBm = 1,000,000 mW = 1,000 W = 1 kW Typical RF power inside a microwave oven 27 dBm = 500 mW Typical cellphone transmission power (some claim that users’ brains are being fried) 20 dBm= 100 mW Bluetooth Class 1 radio, 100 m range = max. output power from unlicensed FM transmitter (4 dBm = 2.5 mW - BT Class 2 radio, 10 m range) −70 dBm = 100 pW (yes, “-”!!!) Average strength of wireless signal over a network See next slide!!! Average for the range: −60 to −80 dBm −60 dBm= 1 nW = 1,000 pW −80 dBm= 10 pW © 2007 by Leszek T. Lilien

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

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

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 12 Powers of Two Received Signals as Functions of Distances from Two BSs BS i Signal strength due to BS j X1X1 Signal strength due to BS i BS j X3X3 X4X4 X2X2 X5X5 MS P min P i (x) P j (x) Observe: P j (X 1 ) ≈ 0 P i (X 2 ) ≈ 0 P j (X 3 ) > P min (of course, P i (X 3 ) >> P j (X 3 ) > P min ) P i (X 4 ) > P min (of course, P j (X 4 ) >> P i (X 4 ) > P min ) P j (X 5 ) = P i (X 5 ) (Modified by LTL)

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 13 Received Signals and Handoff (=Handover) If MS moves away from BS i and towards BS j (as shown), hand over MS from BS i and to BS j between X 3 & X 4 MS (SUV in the Figure) can receive the following signals: At X < X 3 - can receive signal only from BS i (since P j (X) < P min ) At X 3 < X < X 4 - can receive signals from both BS i & BS j At X > X 4 - can receive signal only from BS j (since P i (X) < P min ) BS i Signal strength due to BS j X1X1 Signal strength due to BS i BS j X3X3 X4X4 X2X2 X5X5 MS P min P i (x) P j (x) X (Modified by LTL)

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 14 Handoff Area BS i Signal strength due to BS j X1X1 Signal strength due to BS i BS j X3X3 X4X4 X2X2 X5X5 E XkXk MS P min P i (x) P j (x) Between X 3 & X 4 MS can be served by either BS i or BS j Used technology & service provider decide who serves at any X k 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 (Modified by LTL)

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 15 Optimal Handoff Area & Ping-pong Effect BS i Signal strength due to BS j X1X1 Signal strength due to BS i BS j X3X3 X4X4 X2X2 X5X5 E XkXk MS P min P i (x) P j (x) Where is the optimum handoff area? Is it X 5 ? - both signals have equal strength there Ping-pong effect in handoff Imagine MS driving “across” X 5 towards BS j, then turning back and driving “across” X 5 towards BS i, then turning back and driving “across” X 5 towards BS j, then …. Solution for avoiding ping-pong effect Maintain link with BS i up to point X k where: P j ( X k ) > P j ( X k ) + E (E - a chosen threshold) © 2007 by Leszek T. Lilien

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 16 Handoff in a Rectangular Cell Handoff affected by: Cell area and shape MS mobility pattern 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 Derivation (next slides – skipped) Results: Intuitively handoff is minimized when: Rectangular cell is aligned [=its sides are aligned] with vertical & horizontal axes AND the ratio of the numbers N1 and N2 of MSs crossing cell sides R1 and R2 is inversely proportional to the ratio of the lengths of R1 and R2 © 2007 by Leszek T. Lilien

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 17 Rectangle with sides R1 and R2 and area A = R1 * R2 N1 - # of MSs having handoff per unit length in horizontal direction N2 - # of MSs having handoff per unit length in vertical direction © 2007 by Leszek T. Lilien Handoff can occur through side R1 or side R2 λ H = total handoff rate (# of MSs handed over to this rectangular cell) = = # of MSs handed over R1 side + # of MSs handed over R2 side = = R1 (N1 cos + N2 sin ) + R2 (N1 sin + N2 cos ) ** OPTIONAL ** Handoff in a Rectangular Cell – cont.1 Figure needs corrections Slant

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 18 How to minimize λ H for a given Assuming that A = R1 * R2 is constant, do: Set R2 = A/ R1 Differentiate λ H with respect to R1 Equate it to zero It gives (note: X1 = N1, X2 = X2): Now, total handoff rate is: H is minimized when =0, giving Intuitively: Handoff is minimized when: “Rectangular cell is aligned [its sides are aligned] with vertical and horizontal axes” AND the ratio of the number of MSs crossing cell sides R1 and R2 is inversely proportional to the ratio of their lengths [TEXTBOOK: “the number of MSs crossing boundary is inversely proportional to the value of the other side of the cell”] *** OPTIONAL *** Handoff in a Rectangular Cell – cont.2 R2/R1 = N1/N2 Slant Figure needs corrections

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Cell Capacity Offered load a = T where: - mean call arrival rate = avg. # of MSs requesting service per sec. 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. = … calls/sec.

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Cell Capacity – cont. 1 Erlang unit - a unit of telecommunications traffic (or other traffic) [http://en.wikipedia.org/wiki/Erlang_unit] 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: 1 channel being in continuous (100%) use OR 2 channels being at 50% use (2 * 1/2 Erlang = 1 Erlang ) OR 3 channels being at … % use (3 * 1/3 Erlang = 1 Erlang ) OR … Example 1: An office with 2 telephone operators, both busy 100% of the time => 2 * 100% = 2 * 1.0 = 2 Erlangs of traffic © 2007 by Leszek T. Lilien

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Cell Capacity – cont. 2 Example 2 (Erlang as "use multiplier" per unit time) [ibid] 1 channel being used: 100% use => 1 Erlang 150% use => 1.5 Erlang E.g. if total cell phone use in a given area per hour is 90 minutes => 90min./60min = 1.5 Erlangs 200% use => 2 Erlangs 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 Example: A cell with 30 requests generated per hour => λ = 30/3600 calls/sec. Avg. call holding time T = 6 min. /call = 360 sec./call a = (30 calls / 3600 sec) * (360 sec/call) = 3 Erlangs Modified by LTL

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 23 Erlang B and Erlang C 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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 24 Erlang B and Erlang C – cont. Examples a = # calls/sec can be handled S = # channels in a cell Erlang B examples (blocking prob.) B(S, a) = B (2, 3) = B(S, a) = B (5, 3) = 0.11 (p. 110) More channels => lower blocking prob. Erlang C example (delay prob.) C(S, a) = C (5, 3) = © 2007 by Leszek T. Lilien

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 25 System Efficiency (Utilization) Efficiency = (Traffic_nonblocked) / (Total capacity) More precisely: Efficiency = = (offerred traffic load [Erlangs] ) * (Pr. of call not being blocked) / / # of channels in the cell= = a [Erlangs] * [1 – B(S, a)] / S Example: Assume that: S= 2 channels in the cell, a = 3 calls/ sec => B (2, 3) = prob. of a call being blocked is 52.9 % Efficiency = 3 [Erlangs] * [1 – B(2, 3)] / 2 = 3 [Erlangs] * ( ) / 2 [channels] = = % Modified by LTL

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 26 Simplistic frequency use approach: Each cell uses unique frequencies (never used in any other cell) Impractical For any reasonable # of cells, runs out of available frequencies => must “reuse” frequencies Use same freq in > 1 cell Principle to reuse a frequency in different cells Just ensure that “reusing” cells are at a sufficient distance to avoid interference Frequency reuse is the strength of the cellular concept Reuse provides increased capacity in a cellular network, compared with a network with a single transmitter [http://en.wikipedia.org/wiki/Cellular_network] © 2007 by Leszek T. Lilien 5.5. Frequency Reuse

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 27 Cell Structure Frequency group = a set of frequencies used in a cell Alternative cell structures: F1, F2, … - frequency groups Simplistic frequency assignments in figures No reuse - unique frequency groups Modified by LTL

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 28 Reuse Cluster F1, F2, … F7 - frequency groups Cells form a cluster E.g. 7-cell cluster of hexagonal cells A reuse cluster Its structure & its frequency groups are repeated to cover a broader service are Modified by LTL

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 29 Reuse Distance Reuse distance Between centers of cells reusing frequency groups For hexagonal cells, the reuse distance is given by where:R - cell radius N - cluster size (# of cells per cluster) => need larger D for larger N or R Reuse factor is q ~ D & q ~ 1/R & q ~ N (“~” means “is proportional”) F1 F2 F3 F4F5 F6 F7 F1 F2 F3 F4F5 F6 F7 F1 Reuse distance D R Cluster Modified by LTL

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 30 Reuse Distance Again (a bigger picture) Modified by LTL

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

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

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 34 Neighboring Clusters for a Reference Cell © 2007 by Leszek T. Lilien For the yellow RC, the following NCs are shown: Right Right-top Left-top How to find name for NC? Draw a line from the center of RC to the center of each NC We see lines for 3 NCs in the fig. 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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 35 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 I.e., we travel exactly 2 steps to the right Fig. show i = 1, 2, 3, … but for N = 7 (and j = 1), we have i = 2 only Neighboring Clusters for a Reference Cell – cont. 1 © 2007 by Leszek T. Lilien

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 36 [Repeated] N = 7 (selected) & j = 1 (fixed) => i =2 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 60 degrees (j = 1) Neighboring Clusters for a Reference Cell – cont. 2 © 2007 by Leszek T. Lilien

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 37 Coordinate Plane & Labeling Cluster Cells 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 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) E.g., red cell identified as (4, -3) Modified by LTL

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 38 Clusters formed using formula N = i 2 + i + 1 Simplified from N = i 2 + ij + j 2 for j = 1 Cell label L 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) Cluster size N =7 => i = 2 (bec. N = i 2 + i + 1) & L = (3u + 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 Coordinate Plane & Labeling Cluster Cells – cont. 1 Find 1 error in Table 5.2

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 39 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! Modified by LTL

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 40 Cell Labels for 13-Cell Cluster OBSERVE: 1) For 7-cell clusters, cells within clusters had labels 0-6 2) Here, for 13-cell clusters, cells within clusters have labels ) 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 Modified by LTL

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Cochannel Interference 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) BSs of NCs are called 1st-tier cochannel BSs D i ≥ D - R (cf. next slide) BSs of “next ring” of neighbors are called 2nd-tier cochannel BSs At dist’s ≥ 2 * D (approx.) Assuring reuse distance only limits interference Does not eliminate it completely Observe that: (1) Di’s are not identical (D6 is the smallest) (2) Di’s differ from reuse distance ( ) Modified by LTL First-tier cochannel BS MS Serving BS Second-tier cochannel BS R D1D1 D2D2 D3D3 D4D4 D5D5 D6D6 D 2D

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 43 Worst Case of Cochannel Interference Worst case when D1 = D2 ≈ D – R and D3 ≈ D6 = D and D4 ≈ D5 = D + R Modified by LTL MS Serving BS Co-channel BS R D1D1 D2D2 D3D3 D4D4 D5D5 D6D6 R D D D D D D

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 44 Cochannel Interference Cochannel interference ratio (CCIR) whereI k is co-channel interference from BS k M is the max. # of co-channel interfering cells Example: N = 7 => M = 6 6 k k R D C I C 1 where - propagation path loss slope ( = from 2 to 5)

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved Cell Sectoring (by Antenna Design) So far we assumed omnidirectional antennas Propagate equal-strength signal in all directions (360 degrees) Actually, antennas are directional 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 For 120- / 90- / 60- degree antennas, respectively Cf. next slide © 2007 by Leszek T. Lilien

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 48 Cell Sectoring by Antenna Design –cont. A C B X Advantages of sectoring Smaller xmission power Each antenna covers smaller area Decreased cochannel interference Since lower power Enhanced overall system’s spectrum efficiency Placing directional antennas at corners Where three adjacent cells meet E.g., BS tower X serves 120-degree portions of cells A, B and C 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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 49 Worst Case for Forward Channel Interference in Three-sector Cells BS1 – BS in our cell (e.g., in the cluster center, N = 7) BS2 & BS3 – are first-tier cochannel BSs = closest cells reusing our Fx (BS 1 in center => BS2, BS3 in centers of NCs) BS4 – not reusing => does not interfere Distance from corresp. sector antennas of BS2/BS3 to MS D’ = D R (derivation - OPTIONAL - next slide & p. 118 ) © 2007 by Leszek T. Lilien CCIR (cochannel interf. ratio) : Recall: - propagation path loss slope ( = 2 - 5) R BS1 MS R D’ BS3 BS2 BS4 D D

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

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Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 51 Worst Case for Forward Channel Interference in Six-sector Cells D +0.7R MS BS R Modified by LTL CCIR (cochannel interf. ratio) for =4 : = 4 - propagation path loss slope = (q + 0.7) 4 1

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

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