PT0000. 00/00/03 Millimeter-Wave Path Diversity Improvement Calculations Using Rain Cell Modeling National Spectrum Managers Association 20 th Annual Conference

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, [email protected] 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


0.75 km - ITU-R


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


1.50 km - ITU-R


0.75 km - ITU-R


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 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


= 0.0354%


= 0.0033%


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 B

Fad

e Increm

ent s – In

dB

F>Fa dB

F >

Fb dB

0 1 2 3 4 …

0 1 2 3 4 …


= 0.010%


= 0.010%


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


PD

IF


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


PD

IF


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


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



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

/**/

Documents

PT0000. 00/00/03 Millimeter-Wave Path Diversity Improvement Calculations Using Rain Cell Modeling National Spectrum Managers Association 20 th Annual Conference