Rain Cell Ellipse Major Axis

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NSMA Annual Meeting May 22-23, 2001 - Arlington,
VA Propagation Panel Rain Cell Modeling and
Correlation of Radio Path Fading Application To
Prediction Of Interference Degradation A Review
Robert Ferguson WorldCom [phone] Robert.Fe
rguson_at_wcom.com
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Overview of This Presentation The
Problem Summary of the Rain Cell Model Computer
Simulation Technique Fade Correlation Results -
Format and Usage Discussion and
Conclusion Addendum This report is a condensed
version of three previous presentations given at
NSMA (WG-23) meetings. Contact Robert Ferguson
at Robert.Ferguson_at_wcom.com or [phone] for
more details.
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The Problem In the mm-wave bands, rain fade is
the dominant outage mechanism on the typical
path. During significant rain events, when the
full fade margin of the desired path is needed,
interfering paths are also often faded due to
rain -- at least to some extent.
Traditional methods of setting interference
criteria, which assume a constant level of
interference, are conservative. (Simultaneous
fading on the desired and interfering paths is
not considered.) Can the correlation of fading
on desired/interfering paths be quantified and
more appropriate interference criteria be
developed ?
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Example Interference Path Geometries - Rain Fade
Correlation(Correlation Depends on Angles and
Distances)
Q
Site B
R
P
Receive Site A
A deep rain fade at Site A (from B) will coincide
with A deep fade on Path Q, less likely a
fade on Path R, still less likely a fade on Path
P But, a complete analysis depends on path
lengths and rain cell geometry (shape /
/extent), intensity and likelihood
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Example Interference Path Geometry - Rain Fade
CorrelationDoes Fade Correlation Reduce Apparent
Harmful Interference ? (Angles and distances,
rain cell characteristics must be considered)
Q
R
Cell 2
P
Cell 1
Receive Site A

• Degree of correlation depends on path and
  critical rain cell dimensions
• If Cell 1 is typical, high correlation of fading
  at A with paths P, Q, R
• If Cell 2 is typical, correlation of fading at A
  with paths P, R will be less

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The Need to Integrate System Geometry and Rain
Cell Modeling
Without consideration of the long term patterns
of rain cell shape, intensity, and likelihood in
a locale, interference effects may be evaluated
inaccurately. If details of the primary fading
mechanism (rain attenuation) of millimeter wave
systems are ignored, the tendency is to over
estimate the degradation of intrasystem/intersyste
m interference. Integration of rain cell
modeling (for a given locale) with proposed
system layouts may provide a worthwhile
improvement in traditional design evaluation
techniques. How is rain cell modeling
implemented ? First you need a model ...
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Rain Cell Modeling OverviewBased 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
• Elliptical cell axial ratio Minor Axis/Major
  Axis
• Orientation of ellipse (tilt) w.r.t. coordinate
  system
• Characteristic radius at which intensity falls by
  1/e of Rm
• 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

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Rain Cell Modeling Overview - continuedBased 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

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Elliptical Rain Cell Model Geometry Cell Defined
by Rm (Peak Rain Rate mm/hr) and rho_x, rho_y
Minor Axis
(0.0, rho_y)
(1/e Rm) Rain Rate Isopleth
(rho_x, 0.0)
Major Axis
Intensity falls off to infinity
R Rm exp (-sqrt( xfxf yfyf)) 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
Cell Axial Ratio Minor Axis/Major Axis
(on any rain rate
isopleth)
rho_y/rho_x lt 1.0
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Rain Cell Ellipse Major Axis Split Geometry
Illustration (Proposed Modification To Model For
Interference Analysis)Model Ellipse Extends to
Infinity on One Side of Major Axis (1/e Radius
Shown)
y2
100 mm/hr Isopleth
y1
x2
Major Axis
x1
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
As drawn, Minor/Major Axis Ratio 0.5
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Rain Rate Simulation - Random Factors Follow
Model StatisticsFade Correlation Statistics Are
Accumulated As Simulation Runs
Simulation Radius
Generate random rain cells, following rain zone
statistics, within Simulation Radius
Desired Path
Random Cells Factors Peak Rain Rate - Rm
Cell Radius - rho Location of cell center
Axial Ratio Major Axis Tilt Angle Cell
Split Criteria
Interfering Path
Simulation should reproduce the point rain rate
statistics assumed
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Desired / Interfering Path Fading Time
MatrixDescribes Joint Fade Probability, Thus
Fade Correlation
Interfering Path Fade Increments - In dB
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 14.0 15.0 gt15.0
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 gt40.0
Note The Sum of All Times In The Matrix
Represents All Joint Fading Conditions
Desired Path Fade Increments - In dB
Note One matrix would apply to a specific
desired and interfering path geometry and rain
zone
Entry Indicates Percentage of Time That
D-Path Is In Fade Between 9.0 dB and 10.0 dB AND
I-Path Is In Fade Between 5.0 dB and 6.0 dB
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Example Desired / Interfering Path Fading Time
MatrixEntire Matrix Describes Likelihood of All
Joint Fade Conditions (Incremental Buckets Are
1 dB)
Desired Path _
Incremental D-Path Fade Time Fade
Below ______ __________ 0 dB 3.34911
1 0.24961 2 0.11048 3
0.06484 4 0.04625 5
0.03404 6 0.02737 7
0.02241 8 0.01839 9
0.01581 10 0.01302 11
0.01109 12 0.00943 13
0.00850 14 0.00752 15
0.00646 20 0.00349 ...
Cumulative Fade Time Below ___________ 4.05049
0.70138 0.45177 0.34129 0.27644 0.23020 0.
19616 0.16879 0.14638 0.12799 0.11219 0.09916
0.08807 0.07864 0.07014 0.06262 0.03670
Interfering Path Fade - 1 dB Increment
_
0 dB 1 dB 2 dB 3 dB 4 dB
5 dB 6 dB 7 dB 8 dB 9 dB
Time D-Path Fade gt 6 dB
0.0044 0.0113 0.0072 0.0025 0.0009 0.0003
Time Contribution () D-Path Fade 6 to 7 dB,
I-Path Fade 3 to 4 dB
0.0025
Sum of All I-Path Fade Times With D-Path Fade of
6 to 7 dB 0.02737
Robert Ferguson - WorldCom Robert.Ferguson_at_wcom.co
m [phone]
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Desired / Interfering Path Fading Time Matrix-
UsageIllustration of Interference Adjusted
Outage Calculation
Interfering Path Fade Increments - In dB
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 14.0 15.0 gt15.0
0.0 1.0 2.0 3.0 4.0 5.0 ... 21.0
22.0 23.0 24.0 25.0 26.0 gt40.0
Solid Line Represents (Schematically) Altered
Fade Margin Threshold Due To Interference With
No Fade On I-Path, Degradation is 26.0 - 24.0 dB
2.0 dB As I-Path Fades, Degradation Decreases
Desired Path Fade Increments - In dB
Sum of Incremental Times Below Solid Line Gives
Time Below I-Adjusted Threshold, Or Outage Time
Sum of All Incremental Time Entries Below 26 dB
Represent Time Faded Below 26 dB Percentage -
Assumed No-I Threshold of Desired Path
Robert Ferguson - WorldCom Robert.Ferguson_at_wcom.co
m [phone]
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Possible Data Exchange Flow - Breakpoints
(For Discussion Only)
Verify Accuracy
Simulation Program
Fading Matrices Database
Data Reduction Program
Simulation Parameters
Processed Data
Common Access Functions
Design Programs
Robert Ferguson - WorldCom Robert.Ferguson_at_wcom.co
m [phone]
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Discussion and Conclusion
Discussion Does The Problem Need To Be Solved
? Is Standardization of A Process Realistic
? Intra-Company Vs. Inter-Company Usage
Interference Criteria - Time or dB or ?
IEEE 802.16 / NSMA ? Next Steps Conclusion
Robert Ferguson - WorldCom Robert.Ferguson_at_wcom.co
m [phone]
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Addendum