pt0000. 00/00/03 millimeter-wave path diversity improvement calculations using rain cell modeling...
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PT0000. 00/00/03
Millimeter-Wave Path Diversity Improvement Calculations Using Rain Cell Modeling
National Spectrum Managers Association
20th Annual Conference
May 21, 2003
Arlington, Virginia
Robert Ferguson, robert.ferguson@mci.com 972-729-5192
04/19/23
2
Outline
•The Problem
• Overview Of The Rain Cell Model
• Simulation Methodology And Assumptions
• Path Diversity Improvement Factor (PDIF)
• Definition
• Interpretations
• Simulation Results – Selected Examples
• Final Comments
04/19/23
3
Problem:
A Robust Millimeter-Wave System Extends A Fiber Network. Every Radio Node
Has One Or More Backup Links, Improving Reliability During Rain Fade Events.
How Effective Is This “Path Diversity”?
Fiber Network
= Fiber or Radio Node
Radio Link
99.995%
99.995%
99.999%
To Customer ?
There Will Be Some Correlation Of Rain Fading On Paths A & B – How Much ?
A
B
C 0.005% > to 0.001% ?
04/19/23
4
Fading Correlation: A Meteorology, Geometry, Radio Problem
The Shape, Size, Orientation, And Variation In Rain Rate Intensity Of Rain Cell Distributions
In A Region, In Relation To The Radio Path Distances, Angles And Operating Frequencies,
Must Be Considered
•If Critical Rain Cells Are Large Compared To Paths And Occur Frequently, Fading Will Be More Correlated (Cell 1)
•The Angle Between Paths To A Node Is Important, With More Correlation On Smaller Angles (Cell 2 & Cell 3)
A
B
C
3
1
2
To Estimate The Effectiveness Of Path Diversity, A Model Of Rain Cell Characteristics Is Needed
04/19/23
5
Rain Cell Modeling Overview
Based on Capsoni Model,
Radio Science Volume 22, Number 3, Pages 387-404, May-June 1987
• A “Rain Cell” is defined as connected region where the rain intensity (mm/hr) exceeds a given threshold
• Rain cells have intensity and spatial characteristics which have been statistically modeled based on experimental data collected using meteorological radar
• In the Capsoni Model, an elliptical rain cell is specified by:
•Peak rain rate (mm/hr) - Rm - at cell center
•Characteristic radius at which intensity falls by “1/e” of Rm
•Elliptical cell axial ratio = Minor Axis/Major Axis
•Orientation of ellipse (“tilt”) w.r.t. coordinate system
• The Capsoni Model specifies a cell “1/e radius” statistical distribution for an assumed cell peak rain rate; on average, higher peak rate rain cells have smaller “1/e radii”
04/19/23
6
Rain Cell Modeling Overview - continued
Based on Capsoni Model,
Radio Science Volume 22, Number 3, Pages 387-404, May-June 1987
• Intuitively, rain cell statistical characteristics are related to the point rain rate cumulative time distributions specified by the Crane and ITU rain zone classification systems
• Capsoni, et al, describe a methodology to convert the point rainfall rate rate time distribution data to the statistical factors necessary to complete a rain cell model which can reproduce the assumed point rainfall rate statistics
• This model can be used to evaluate the rain fade correlation effects on example desired/interfering path geometries, as well as the “path diversity” effects to be discussed
04/19/23
7
Elliptical Rain Cell Model Geometry
Cell Defined by Rm (Peak Rain Rate mm/hr) and rho_x, rho_y
Major Axis
Minor Axis
Cell Axial Ratio = Minor Axis/Major Axis
(on any rain rate isopleth)
= rho_y/rho_x < 1.0
R = Rm * exp (-sqrt( xf*xf + yf*yf))
where: xf = x/rho_x and yf = y/rho_y
By definition,
at (rho_x,0.0), R = 1/e * Rm
at (0.0,rho_y), R = 1/e * Rm
(rho_x, 0.0)
(0.0, rho_y) (1/e * Rm) Rain Rate Isopleth
Intensity falls off to infinity
9
04/19/23
8
Rain Cell Ellipse Major Axis “Split Geometry” Illustration
Proposed Modification To Model – To Account For Cell Asymmetry
For Interference Analysis And Path Diversity Problems
Model Ellipse Extends to Infinity on One Side of Major Axis
Assume only one portion of the split rain cell is “active”
If rain at origin, also at x1 and y1
If NO rain at origin, rain at x2 and y2
x1
x2
y1
y2
100 mm/hr Isopleth
As drawn, Minor/Major Axis Ratio = ~ 0.5
Major Axis
Origin
04/19/23
9
Rain Rate Vs rho(x,y)For Rain Cells With Selected Peak Rain Rates (Rm)
0
50
100
150
200
250
300
350
400
0 1 2 3 4Rho (km)
Ra
in R
ate
(m
m/h
r)
50 mm/hr - Peak Rate100 mm/hr150 mm/hr200 mm/hr250 mm/hr300 mm/hr350 mm/hr
Cell Peak Area 50 mm/hr0.0 km^2 1001.0 150 2.0 200 2.8 250 3.4 300 3.8 350 4.1
Exponential Fall-Off Of Rain Rate From Cell Center (For Circular Rain Cell, rho(x,y) = Distance from
Center)
Area Of >50 mm/hr
04/19/23
10
Example Of A Rain Cell – Peak Rate Rm=200 mm/hr
Typical (*) Size & Shape Cell Axial Ratio ~ 0.5
rho_x = 0.96 km rho_y = 0.48 km
x
y
0.96 km
121 mm/hr
Rm/e = 74 mm/hr
27 mm/hr
45 mm/hr
1.92 km
0.96 km
Rm = 200 mm/hr
0 mm/hr at infinity
(*) In Capsoni Rain Cell Model, Size And Shape Are Varied Statistically About Average / Median Values
04/19/23
11
Comments On Simulation Results • All Examples Are Based On The “Test Rain Zone” Point Rainfall Statistics
Approximation To ITU-R Zone N (Florida) – Highest Rates, Continental US (35 mm/hr @ 0.10%, 95 mm/hr @ 0.01%, 180 mm/hr @ 0.001%)
• All Examples Assume H-Polarization
• To Allow For Rain Cell Asymmetry, The Capsoni Model Has Been Modified By Adding “Cell Splitting”
• Only Rain Cells With Peak Rain Rates (Rm) > 50 mm/hr And Elliptical Axial Ratio Less Than The Median (0.56) May Be Split; Randomly, One-Half Of These Cells Are Split Along The Major Axis. Each Half Of The Cell Is Used Separately
• Results Will Change Somewhat With Differing “Split Criteria”
• For Fades Occurrences Of Small Times (e.g. 0.001%), Reliance Of Any Model To Predict Improvement Factors Is Questionable - And Difficult To Validate By Measurement
• The Simulation Evaluates A Single Rain Cell At A Time; The Model Is Likely More Valid For Shorter Paths That Would Be “Under The Influence” Of A Single Cell
04/19/23
12
Rain Rate Simulation - Random Factors Follow Model Statistics
Fade Correlation Statistics Are Accumulated As Simulation Runs
Simulation Radius
Path A
Generate random rain cells, following rain zone statistics, within Simulation Radius
Random Cells Factors:
Peak Rain Rate - Rm
Cell Radius - rho
Location of Cell Center
Axial Ratio
Major Axis Tilt Angle
Cell Split Criteria
Path B
Simulation should reproduce the point rain rate statistics assumed
11
Virtual Rain Gauges
04/19/23
13
Two-Path Fading Time Matrix
Describes Joint Fade Probability, Thus “Fade Correlation”
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
…
>40.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 … > 40.0
Path A Fade Increments - In dB
Path B
Fa de I nc re m
ents - I n dB
Entry Indicates Percentage of Time That:
Path A Is In Fade Between 5.0 dB and 6.0 dB
AND
Path B Is In Fade Between 9.0 dB and 10.0 dB
Note: The Sum of All Times In The Matrix Represents All Joint Fading Conditions
Note: One matrix would apply to two paths with specific geometry, frequency and rain zone statistics
04/19/23
14
Virtual Rain Gauge (VRG) Measured TimesVersus
Test Rain Zone (TRZ) Target TimesAt Selected Rain Rates
(Representative Simulation) Note: At 95 mm/hr TRZ=0.01%, All VRGs Time Within 1%VRG(0.0)=0.01008, VRG(2.0)=0.01009,VRG(4.0)=0.00996
-10
-5
0
5
10
0.001 0.01 0.1 1
TRZ Target Time (%) At Selected Rain Rates
Dif
fere
nce
(%
)
TR
Z a
nd
VR
G
0.0 km (At Center)
2.0 km From Center
4.0 km From Center
Why ?
04/19/23
15
Predicted Fade Depth Versus TimeComparison Of
ITU-R Method and Rain Cell Model 3 Path Lengths - 28 GHz - H-POL Test Rain Zone - Standard Split
0
10
20
30
40
50
60
70
80
0.001 0.01 0.1 1
Time - Percentage
Fad
e D
epth
Exc
eed
ed (
dB
)
2.25 km - ITU-R
2.25 km - Rain Cell Model
1.50 km - ITU-R
1.50 km - Rain Cell Model
0.75 km - ITU-R
0.75 km - Rain Cell Model
04/19/23
16
Predicted Fade Depth Versus TimeComparison Of
ITU-R Method and Rain Cell Model 3 Path Lengths - 60.5 GHz - H-POL
Test Rain Zone - Standard Split
0
10
20
30
40
50
60
70
80
0.001 0.01 0.1 1
Time - Percentage
Fad
e D
epth
Exc
eed
ed (
dB
)
2.25 km - ITU-R
2.25 km - Rain Cell Model
1.50 km - ITU-R
1.50 km - Rain Cell Model
0.75 km - ITU-R
0.75 km - Rain Cell Model
04/19/23
17
Fading Correlation
Using Two-Path Fading Time Matrix
Path A Fade Increments – In dB
Path B
Fad
e Increm
ent s – In
dB
F>35.0 dB
F>
29.0 dB
0 1 2 3 4 … 34
0 1 2 3 4 … 28
Sum Of Times Below Line
= 0.0354%
Sum Of Times Beyond Line
= 0.0033%
In This Area, Sum Of Times = 0.0023%
Fa > 35.0 & Fb > 29.0
04/19/23
18
Definition Of Path Diversity Improvement Factor – For This Presentation
• Other “Improvement Factors”: Space Diversity, Polarization Diversity, Frequency Diversity, …
• Path Diversity Improvement Factor - PDIF
• Assume Path A Has A Critical Fade Depth Fa, Path B Has A Critical Fade Depth Fb
• Based On Measured (Or Simulated) Fading Statistics
• On Path A, (Fade > Fa) Occurs For Time = TA(F>Fa)
• On Path B, (Fade > Fb) Occurs For Time = TB(F>Fb)
• Jointly, Path A (Fade >Fa) And Path B (Fade >Fb) For Time = TAB(Fa,Fb)
• Then, Assuming Either Path A Or Path B Can Provide “Service” If (Fade <= Critical), The Effectiveness Of Path Diversity Can Be Measured By Comparing Composite Performance To Either Path A or Path B Performance Alone:
• PDIF(A/B) = TA(F>Fa) / TAB(Fa,Fb) - “Path A Improved By Path B Diversity”
• PDIF(B/A) = TB(F>Fb) / TAB(Fa,Fb) - “Path B Improved By Path A Diversity”
04/19/23
19
An Example Of Path Diversity Improvement
• Two 28 GHz Paths Provide Redundant Traffic Paths To A Site;
• Path A – 1.5 km, Critical Fade Margin Of 35.0 dB
• 0.0033% = TA(F>35.0) – Time Of Predicted Rain Fade > 35.0 dB
• Path B - 3.0 km, Critical Fade Margin Of 29.0 dB
• 0.0354% = TB(F>29.0) – Time Of Predicted Rain Fade > 29.0 dB
• Angle Between The Paths Is 135 Degrees
• The Predicted Time When Both Paths Are Simultaneously Below Critical FM
• 0.0023% = TAB(35.0,29.0)
• Path Diversity Improvement Factors
• 1.4= PDIF(A/B) = TA(F>35.0)/TAB(35.0,29.0)–Path A “Improved” By B Diversity
•15.3= PDIF(B/A) = TB(F>29.0)/TAB(35.0,29.0)–Path B “ By A Diversity
B =3.0 km / 29 dB
A =1.5 km / 35 dB135 Deg
Customer
04/19/23
20
Interpretation Of PDIF
Using Two-Path Fading Time Matrix
Path A Fade Increments – In dB
Path B
Fad
e Increm
ent s – In
dB
F>35.0 dB
F>
29.0 dB
0 1 2 3 4 … 34
0 1 2 3 4 … 28
Sum Of Times Below Line
= 0.0354%
Sum Of Times Beyond Line
= 0.0033%
In This Area, Sum Of Times = 0.0023%
PDIF(B/A) = 0.0354/0.0023 = 15.3
PDIF(A/B) = 0.0033/0.0023 = 1.4
04/19/23
21
Path Diversity Improvement – Decibel Interpretation
• Path Diversity “Improves” The Reliability That Each Individual Path Can Provide, As Expressed By The PDIF
• The Diversity Improvement Can Also Be Expressed In The Equivalent Decibel Increase In Fade Margin Required To Give The
Same Improvement To A Single Path
• Path A (1.5 km, 28 GHz) Would Require An Increase In Fade Margin From 35 dB (0.0033%) To About 39 dB In Order To Achieve
The Improvement To 0.0023% (PDIF = 1.4).
• Thus, Path B “dB Improvement” Ref. To Path A Is ~4 dB
• Path B (3.0 km, 28 GHz) Would Require An Increase In Fade Margin From 29 dB (0.0354%) To About 69 dB In Order To Achieve
The Improvement To 0.0023% (PDIF = 15.3).
• Thus, Path A “dB Improvement” Ref. To Path B Is ~40 dB
• Note, Even Though Path B Is Very “Weak”, The Diversity Performance Is Still Equivalent To A Useful 4 dB Increase In FM of Path A
04/19/23
22
Geometric Interpretation Of PDIF
Using Simplified Assumptions, Diagram
A
•The Average Attenuation in dB/km To Reach 35.0 dB = 35/1.5 = 23.3 dB/km On Path A 29.0 dB = 29/3.0 = 9.7 dB/km On Path B
• Thus, Rain Cell Centers With A Given Peak Rain Rate May Be Significantly More Distant From Path B Than Path A And Still Cause The Critical Fade Values To Be Reached, And Area RC(B) >> Area RC(A)
• For A Low Peak Rain Rate Rm(1) Above, There Is No Overlap In The Areas RC1(A) & RC1(B) Where Rain Cell Centers Can Be Located And Provide The Critical Fade Or More; Thus Cells With Peak Rate Rm(1) Do Not Cause Simultaneous Outage And PDIF(Rm(1)) Contribution Is “Infinite” For Rm(1)
• For A Much Higher Peak Rain Rate Rm(2), There Is Overlap Which Indicates Simultaneous Outage,
• PDIF(Rm(2))(A/B) ~ RC2(A)/RC2(AB)~ 1.3 & PDIF(Rm(2))(B/A) ~ RC2(B)/RC2(AB) ~ 12.
• The Composite PDIF Of Cells Of All Rm() Values Weighted Likelihood Of Occurrence, Give The Composite PDIFs, PDIF(A/B) = 1.4 & PDIF(B/A) = 15.3
• This Example Is An Over-Simplification – Intended Only To Describe A Geometric Interpretation Of PDIF (In Reality, Cell Peak Rates/Shapes/ Locations Must Be Considered)
Area RC2(A)
Area RC2(B)
Overlap Area RC2(AB)
RC() Are Areas Of Rain Cell Centers
Area RC1(B)
B
Area RC1(A)
04/19/23
23
How Does The PDIF Vary With Included Angle, Path Length, Time ?
(Examples Follow)
Fixed Path
Included Angle
30 Degrees
45 Degrees
180 Degrees
135 Degrees
90 Degrees
Path Lengths Considered: 0.75 km, 1.5 km, 2.25 km
• PDIF Should Increase With Angle
• PDIF Should Increase With Path Length
04/19/23
24
How Does The PDIF Vary ?
All Paths Are 1.5 Km – 0.01% Single Path Fade Time
Fixed Path
30 Degrees
45 Degrees
180 Degrees
135 Degrees
90 Degrees
PDIF = 1.31
PDIF = 1.50
PDIF = 2.09
PDIF = 2.55
PDIF = 2.74
Pt Marked With On Next Page
1.5 km
04/19/23
25
PDIF Vs Single Path Fade Time Two Similar Paths - 3 Lengths - 90 Degree Included Angle
1
1.5
2
2.5
3
3.5
4
0.001 0.01 0.1
Fade Time - Percent
PD
IF
0.75 km1.50 km
2.25 km
Results Are Not Frequency Dependent – Why ?
0.0048%
0.071%
0.00035%
04/19/23
26
Frequency Independence Of The PDIF
Example
Path A Fade Increments – In dB
Path B
Fad
e Increm
ent s – In
dB
F>Fa dB
F >
Fb dB
0 1 2 3 4 …
0 1 2 3 4 …
Sum Of Times Below Line
= 0.010%
Sum Of Times Beyond Line
= 0.010%
In This Area, Sum Of Times = 0.0048%
For Differing Frequencies, The Same “Worst Case” Set Of Rain Cells For The Specified Times Determine The Fade Depth in dB. The Fade Depth Is Frequency Dependent, The PDIF Is Not.
Frequency Dependent
Frequency Dependent
Frequency Independent
Specified
Specified
04/19/23
27
PDIF Vs Single Path Fade Time Two 0.75 km Paths - Selected Included Angles
1
1.5
2
2.5
3
3.5
4
0.001 0.01 0.1
Single Path Fade Time - Percent
PD
IF
15 Degrees 30 Degrees 45 Degrees 90 Degrees135 Degrees180 Degrees
04/19/23
28
PDIF Vs Single Path Fade Time Two 1.50 km Paths - Selected Included Angles
1
2
3
4
5
6
7
0.001 0.01 0.1
Single Path Fade Time - Percent
PD
IF
15 Degrees 30 Degrees 45 Degrees 90 Degrees135 Degrees180 Degrees
04/19/23
29
PDIF Vs Single Path FadeTime Two 2.25 km Paths - Selected Included Angles
1
2
3
4
5
6
7
0.001 0.01 0.1
Single Path Fade Time - Percent
PD
IF
15 Degrees 30 Degrees 45 Degrees 90 Degrees135 Degrees180 Degrees
04/19/23
30
Other Examples
Selected Problems Defined By Specifying Decibel Values
• Note:
• The Decibel Improvement Values Shown Are Based On The Fading Statistics From The Simulation
• Unlike “Time-Based” Problems, The PDIF Is Frequency Dependent When Decibel-Related Variables Are Specified
04/19/23
31
PDIF Vs Single Path Fade Depth Two Identical 1.50 km Paths - Selected Included Angles
28 GHz & 60 GHz (Note: For Same Geometry, 28 GHz PDIF > 60 PDIF)
1
1.5
2
2.5
3
3.5
4
4.5
5
25 35 45
Single Path Fade Depth - dB
PD
IF
30 Degrees - 28 GHz
30 Degrees - 60 GHz
90 Degrees - 28 GHz
90 Degrees - 60 GHz
180 Degrees - 28 GHz
180 Degrees - 60 GHz
04/19/23
32
Equivalent dB Improvement Vs Single Path Fade Depth Two Identical 1.50 km Paths - Selected Included Angles
28 GHz & 60 GHz (Note For Same Geometry, 28 GHz Eq dB ~ 60 GHz Eq dB )Improvements From Simulation Fade Statistics
0
5
10
15
20
25 35 45
Single Path Fade Depth - dB
Eq
uiv
alen
t d
B I
mp
rove
men
t
30 Degrees - 28 GHz
30 Degrees - 60 GHz
90 Degrees - 28 GHz
90 Degrees - 60 GHz
180 Degrees - 28 GHz
180 Degrees - 60 GHz
04/19/23
33
PDIF Vs Path 1 ("Strong") Path Time Two 1.50 km Paths- 28 GHz - Selected Included Angles
(Path 2 Has 6 dB Less Fade Margin Than Path 1)
1
2
3
4
5
6
7
0.001 0.01 0.1
Path 1 (Strong) Fade Time - Percent
PD
IF
180 Degrees - Path 1180 Degrees - Path 2 90 Degrees - Path 1 90 Degrees - Path 2 45 Degrees - Path 1 45 Degrees - Path 2
Because The Paths Are Not Identical, The PDIF Differs For Each Path.
“Path 1” = “Path 1 Improved By Path 2” ”Path 2” = “Path 2 ‘ ‘ Path 1”
04/19/23
34
Final Comments
• Rain Cell Modeling Has Been Useful In Estimating The Advantage Of Having More Than One Millimeter-Wave Path Serving A Node
• The “Path Diversity Improvement Factor” Is A Convenient Way To Quantify Rain Fade Correlation Effects And Could Be Useful In The System Design Process
• The Simulation Method Is A General Purpose Tool That Has Been Used To Evaluate Correlation Effects; Less Complicated Analytic Approaches, Which Reflect The Path Geometry And Rain Cell Composite Statistics, Also Seem Plausible And Are Worth Investigating
• The PDIF Is Not Frequency Dependent For Time-Based Problems, Thus General Purpose Solutions For A Particular Rain Zone And Geometry May Be Practical
• The Single Rain Cell Model Is Conservative For Interference Analysis, But Optimistic For PDIF Estimates – More Of A “Upper Limit”
• The Results Shown In This Presentation Are Intended To Illustrate The Concepts Discussed And Are Believed To Be Accurate Subject To The Specific Rain Model And Statistics Employed; Independent Verification Would Be Useful
• This Presentation Has Summarized Initial Work On An Interesting Problem
/**/
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