Post on 14-Dec-2015
1
CS 6910 – Pervasive ComputingSpring 2007
Section 5 (Ch.5):
Cellular ConceptProf. Leszek Lilien
Department of Computer ScienceWestern Michigan University
Slides based on publisher’s slides for 1st and 2nd 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.
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 2
Chapter 5
Cellular Concept
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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 4
5.1. 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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 5
5.2. 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 popularSquare cell model second most popular
(Modified by LTL)
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)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 7
5.3. 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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 8
5.3. 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
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 boundary Select cell j on right of boundary
Cell i Cell j
-60
-70-80
-90
-100
-60-70
-80-90
-100
Signal strength (in dBm)
Recall:−70 dBm = 100 pW- average strength of wireless signal over a network
Ideal boundary
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.
-100
-90-80
-70
-60
-60-70
-80
-90
-100
Signal strength (in dB)
Cell i Cell j
Recall:−70 dBm = 100 pW- average strength of wireless signal over a network
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
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
BSi
Sig
nal s
tren
gth
due
to B
Sj
X1
Sig
nal s
tren
gth
due
to B
Si
BSjX3 X4 X2X5
MS
Pmin
Pi(x) Pj(x)
Observe: Pj(X1) ≈ 0 Pi(X2) ≈ 0 Pj(X3) > Pmin (of course, Pi(X3) >> Pj(X3) > Pmin)
Pi(X4) > Pmin (of course, Pj(X4) >> Pi(X4) > Pmin)
Pj(X5) = Pi(X5)(Modified by
LTL)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 13
Received Signals and Handoff (=Handover)
If MS moves away from BSi and towards BSj (as
shown), hand over MS from BSi and to BSj between X3 & X4
MS (SUV in the Figure) can receive the following signals: At X < X3 - can receive signal only from BSi (since Pj(X) < Pmin) At X3 < X < X4 - can receive signals from both BSi & BSj
At X > X4 - can receive signal only from BSj (since Pi(X) < Pmin)
BSi
Sig
nal s
tren
gth
due
to B
Sj
X1
Sig
nal s
tren
gth
due
to B
Si
BSjX3 X4 X2X5
MS
Pmin
Pi(x) Pj(x)
X
(Modified by LTL)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 14
Handoff Area
BSi
Signal strength due to BSj
X1
Signal strength due to BSi
BSjX3 X4 X2X5
E
Xk
MS
Pmin
Pi(x) Pj(x)
Between X3 & X4 MS can be served by either BSi or BSj Used technology & service provider decide who serves at any Xk
between X3 & X4
As MS moves, handoff must be done in the handoff area, i.e., between X3 & X4
Must find optimal handoff area within the handoff area (Modified by
LTL)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 15
Optimal Handoff Area &
Ping-pong Effect
BSi
Signal strength due to BSj
X1
Signal strength due to BSi
BSjX3 X4 X2X5
E
XkMS
Pmin
Pi(x) Pj(x)
Where is the optimum handoff area? Is it X5? - both signals have equal strength there
Ping-pong effect in handoff Imagine MS driving “across” X5 towards BSj, then turning
back and driving “across” X5 towards BSi, then turning back and driving “across” X5 towards BSj, then ….
Solution for avoiding ping-pong effect Maintain link with BSi up to point Xk where:
Pj(Xk) > Pj(Xk) + E (E - a chosen threshold)© 2007 by Leszek T. Lilien
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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 17
Rectangle withsides 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 λH = 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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 18
How to minimize λH for a given
Assuming that A = R1 * R2 is constant, do:
Set R2 = A/ R1 Differentiate λH 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
sincos
cossin
21
212
1 XX
XXAR
cossin
sincos
21
2122 XX
XXAR
cossinsincos22121
XXXXAH
2
1
2
1212
X
X
R
RandXAXH
R2/R1 = N1/N2
Slant
Figure needs corrections
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 19
5.4. Cell Capacity Offered load
a = Twhere: - mean call arrival rate = avg. # of MSs requesting service per sec. T – mean call holding time = avg. length of call
ExampleOn 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 20
5.4. Cell Capacity – cont. 1
Erlang unit - a unit of telecommunications traffic (or
other traffic) [http://en.wikipedia.org/wiki/Erlang_unit]
http://en.wikipedia.org/wiki/Erlang: 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%) useOR 2 channels being at 50% use (2 * 1/2 Erlang = 1 Erlang )
OR 3 channels being at 33.333… % 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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 21
5.4. 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 Erlangsa [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
Erlangscall
Sec
Sec
Callsa 3
360
3600
30
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 requestsThen Probability P(n, t) that n calls arrive in an interval of length t: t
n
en
ttnP
!),(
tetS 1)(
- 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
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
,
!
1
!,
0
S
k
k
S
kaS
aaSB
,
!!1
!1,
1
0
S
i
iS
S
ia
aSSa
aSSa
aSC
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 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) = 0.529B(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) = 0.2360
© 2007 by Leszek T. Lilien
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) = 0.529 - prob. of a call being blocked is 52.9
%
Efficiency = 3 [Erlangs] * [1 – B(2, 3)] / 2 = 3 [Erlangs] * (1 - 0.529) / 2 [channels] = 0.7065
= 70.65 %Modified by
LTL
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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 27
Cell Structure
F2 F3F1F3
F2F1
F3
F2
F4
F1F1
F2
F3
F4F5
F6
F7
(a) Line Structure (b) Plan Structures
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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 28
Reuse Cluster
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F1
F1
F1
7-cell 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
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
RND 3
where: R - cell radiusN - 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”)
NR
Dq 3
F1
F2
F3
F4F5
F6
F7
F1
F2
F3
F4F5
F6
F7
F1
F1
Reuse distance D
R Cluster
Modified by LTL
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 30
Reuse Distance Again (a bigger picture)
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F1
F1
F1
7-cell reuse cluster
Reuse distance D
Modified by LTL
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 31
5.6. How to Form a Cluster The cluster size (# of cells per cluster):
N = i2 + ij + j2
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
Modified by LTL
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 32
Hex Clusters of Different SizesClusters designed for freq reuse
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 33
Finding Centers of All ClustersAround 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-toprightright-bottomleft-bottomleftleft-top
By finding centers of neighboring clusters (NCs), we simultaneously determine cells belonging to the current cluster
© 2007 by Leszek T. Lilien
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 followingNCs are shown:
Right Right-top Left-top
How to find namefor NC?
Draw a line fromthe center of RC tothe center of eachNC
We see lines for 3 NCsin the fig.
Thick red lines E.g., the cluster with green center cell is the “right”
neighborfor the cluster with the yellow center bec. Red line cuts the right edge of the yellow hexagon
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F1
F1
F1
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 35
For j = 1, the formula: N = i2 + ij + j2simplifies to: N = i2 + 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
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
ExampleTo get from the yellow cellto the green cell, we travel2 steps to the right(i = 2) & 1 step at60 degrees (j = 1)
Neighboring Clusters for a Reference Cell – cont. 2
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F2
F3
F4F5
F6
F7 F1
F2
F3
F4F5
F6
F7
F1
F1
F1
F1
© 2007 by Leszek T. Lilien
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 centersof 2 adjacentcells
E.g., green cellidentifiedas (-3, 3)(-3 along u,3 along v)
E.g., red cellidentifiedas (4, -3)
Modified by LTL
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 38
Clusters formed using formula N = i2 + i + 1 Simplified from N = i2 + ij + j2 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 = i2 + 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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 39
Cell Labels for 7-Cell ClusterNote: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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 40
Cell Labels for 13-Cell ClusterOBSERVE:
1) For 7-cell clusters, cells within clusters had labels 0-6
2) Here, for13-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 3steps right, then 1 step at 60 degreesNote: “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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 42
5.7. 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 called1st-tier cochannel BSs
Di ≥ D - R (cf. next slide)
BSs of “next ring” of neighbors are called2nd-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 (< or >) Modified by
LTL
First-tiercochannel BS
MS
Serving BS
Second-tiercochannel BS
R
D1
D2
D3
D4
D5
D6
D
2D
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 43
Worst Case of Cochannel Interference
Worst case whenD1 = D2 ≈ D – RandD3 ≈ D6 = DandD4 ≈ D5 = D + R
Modified by LTL
MS
Serving BSCo-channel BS
R
D1
D2
D3
D4
D5
D6
R
D
D
D
D
D
D
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 44
Cochannel Interference
Cochannel interference ratio (CCIR)
M
kkI
C
ceInterferen
Carrier
I
C
1
where Ik is co-channel interference from BSk
M is the max. # of co-channel interfering cells
Example: N = 7 => M = 6
6
k
k
RD
C
I
C
1
where - propagation path loss slope( = from 2 to 5)
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 45
5.8. Cell Splitting
Medium cell(medium density)
Large cell (low density)
Small cell(high density)
Use largecell normally
When trafficload 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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 46
5.9. 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 antennasCells 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
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 47
5.9. Cell Sectoring (by Antenna Design) – cont.
60o
120o
(a). Omni (b). 120o sector
(e). 60o sector
120o
(c). 120o sector (alternate)
ab
c
ab
c
(d). 90o sector
90o
a
b
c
da
bc
d
ef
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
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-degreeportions of cells A, B and C
Might seem that placement in corners requires 3 times more towers than placement with towers in centersActually, 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 49
Worst Case for Forward Channel Interference in Three-sector Cells
7.0qq
C
I
C
RDq /
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 MSD’ = D + 0.7 R (derivation - OPTIONAL - next slide & p. 118 )
© 2007 by Leszek T. Lilien CCIR (cochannel interf.
ratio):
Recall: - propagation path loss slope ( = 2 - 5)
RBS1
MS
R
D’
BS3
BS2
BS4
D
D
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
BS
BS
BS
D
Copyright © 2003, Dharma P. Agrawal and Qing-An Zeng. All rights reserved 51
Worst Case for Forward Channel Interferencein Six-sector Cells
D +0.7R
MS
BS
BSR
Modified by LTL
RDq
q
C
I
C
/
7.0
CCIR (cochannel interf. ratio) for =4:
= 4 - propagation path loss slope
= (q + 0.7)41