r:
1
£/3(!!/ !lEGS VTC... 973
In Situ Microwave Reflection Coefficient Measurements for Smooth and
Rough Exterior Wall Surfaces
I
I
I
i.
I
Orlando Landron 1, Martin J. Feuerstein 2, and Theodore S. Rappaport 1
[ 1) Mobile and Portable Radio Research Group (MPRG)
Bradley Department of Electrical Engineering
Virginia Polytechnic Institute & State University
Blacksburg, VA 24061
[2] U.S. West Advanced Technologies
Wireless Communication Services
4001 Discovery Drive. Suite 320
Boulder. CO 80303
(perpendicular) to the plane of incidence. as shown in Fig.!. The
properties of each dielectric at the interface is characterized by its
perminivity (E), magnetlc permeability(~) and conductance (0').
The ret1ection coefficients in (!) account only for specular
reflection, which occurs for smooth surfaces. When the surface is
rough, impinging energy will be scattered in angles other than the
specular angle of reflection (i.e. diffuse reflection), thereby reducing
energy in the specularly reflected component. The Rayleigh criterion
[6] is commonly used w; a test for surface roughness. giving the
following critical height (he> of surface protub~rances.
Abstract - Microwave reflection coefficient measurements ut
1.9 GHz and 4.0 GHz are given for u variety of typical smooth
and rough exterior building surfaces. The measurements are
compared to theoretical Fresnel re!lection coetlicients using
Gaussian rough surface scattering models when applicable.
Individual multipaths are resolved temporally using a spread
spectrum sliding correlation system, and spatially using
directional antennas. The measurement test cases included walls
rn11de ol' limestone blocks, glass, and brick. The results indicate
that the Fresnel reflection coetlicients adequately describe the
reflective properties of the glass and brick surfaces. The rough
stone wall meusurement,s ure shown to be bounded by predictions
for a smooth surface model and a Gaussian rough surface model.
The results of this work can be used to estimate rellection
coellicients in ray tracing algorithms for propagation prediction.
h
A
"
= --
(2)
l:lcos8.I
The height (h) of a given rough surface is defined as the minimum
to maximum surface protuberance. A surface is considered smooth if
h <he and rough if h >_he. For the case of rough surfaces, Ament [7]
has derived -a scattenng loss factor (p ) to account for diminished
energy in the specular din:ction of retle~tion given by
INTRODUCTION
Recent studies on ray tracing techniques for propagation
prediction [1-3] have shown promising results 111 predicting channel
parameters such as path loss and RMS delay ::.pread. Ray tracing
approximates electromagnetic waves as discrctc propagating rays
that undergo attenuation, reflection, and scattering phenomena due to
the presence of buildings, walls, and other obstructions. Due to a
lack of dielectric property data on common building materials, ray
tracing techniques often assume a fixed reflection loss for specularly
ret1ected rays, regardless of incident angles, material properti~s and
surface roughness. The Fresnel reflection formulas can be used to
determme the ret1ection loss. provided the dielectric properties of the
mteriace are known.
To provide accurate building ret1ection models, measurements at
1.9 GHz and 4.0 GHz have been made for a variety of typical smooth
and rough surfaces. Using measured dielectric properties [4], th~
empirically measured reflection coefficients are compared with
Fresnel ret1ecuon formulas using a Gaussian rough surface scattering
model when applicable. The results of these comparisons can be
used to develop simple, and empirically accurate, building reflection
models for stte-specitic propagation prediction techniques.
r
(1tO'hcosei)j
(3)
•
A.
where 0' is the standard deviation of the surface height about the
mean sur1ace height. Equation (3) assumes that the surface heights
are Gaussian distributed with negligible sharp edge and shadowing
effects. Using p to modify the reflection coefficients ;, referred as
the Gaussian rough surfa.:e s.;atlenng model, and is writ ..:n as
Ps
(f.L) roug h
= expl-8
....
=P,rl
<fu) roug h
= Psrl,
Boithias [6] reports that the scattenng Joss factor of
agreement with measured results when modilied as
r
(1t'O'h.:osei')1
Ps = expl-8 - - . I.
(3)
(4)
gives better
! (1tO'hcosei)2'"j
.
Jl
/ol8
-
/..
when: / 0 [x] is the muc..lilicJ Ucssd fun.:t1un uf L.eruth urJer. E4ual!Ull~
(3) and (5) are approximately equal when the Bessel function
argument becomes small. causing I 0 to approach unity.
1.9 GHz AND 4.0 GHz MEASUREMENT SYSTEMS
The 1.9 GHz measurements were performed using a wide band
REFLECTION AND SCATTERING MODELS
The Fresnel reflection coefficients ( r) relate the tield reflected
from an infinite ditilectric slab to the incident field, assuming the
Incident field has a planar wavefront with constant phase. Th~
renect!On coefficients are given by
r ·1-
11 2 cos8i-11 1 cos8 1
11 2 cos8i +11 1 cos8 1
r
11
=
11 2 cos8 1 -11 1 cos8 1
11 2 cos8 1 -r 11 1.:os8i
<I>
Where the wave impedances (11) and transmitled wave angh:s (8 1 )
are. complex functions of dielectric material properties, angle of
tns cbtdence ( 8. ), and frequency [5]. The parallel (perpendicular)
U SC ,
'
I
.
npt m (1) refers to the E-field component that is parallel
Figure 1 • Geometry tor Fresnel retlection coetlicicnt calculation
Resear·::ch:;----------------------sponsored by DARPAIESTO and !he MPRG Industrial Affiliates.
0.7803-1266-X/93/$3.00C 1993IEEE
77
spread spectrum sliding correlation system with a 2.047 chip PN
s~uence.
Th1s PN sequence was driven by a 230 Mcps local
oscillator. giving a system resolution of approximately 8.7 ns. The
desired LOS and reflected multipaths were resolved temporally via
the sliding PN code and spatially usmg log-periodic antennas with
60u beamw1dths.
For better spatial resolution. the 4.0 GHz
measurement system used 18.6 dB standard gam horns wllh
measured E-plane and H-plane beamwidths of 17.2° and 14.3°,
respecllvely. For th1s system. a 32.76 7 chip PN sequt:n.:c: wa:.
implemented, which provided superior correlation properties. The
4.0 GHz system used a 240 Mcps sequence clock, giving a system
resolution of approximately 8.3 ns. Detailed specif1cations of this
system are given in [?J. Due to the superior spatial and temporal
resolution of the 4.0 GHz system. most of the measurements were
performed at the higher frequency band, where the surface roughness
etrects are more pronounced.
REFLECTION COEFFICIENT MEASUREMENT
The retlection coefficient measurements were performed using a
two-measurement technique [8] shown in Fig.2. For each transmmer
and receiver location (determined by desired incident and rellected
angles and the system temporal resolution). multiple line-of-sight
(LOS) and ret1ection measurements were made for power averagmg
purposes.
The LOS measurement pr,,\·1des a reference fur
cumpanson with the rece1ved re11ected !'·· ·wer un the re11e.:t!un
measurement. The observed power delay p;·,,file for the reflection
measurement generally contains a LOS and ;·;; r1ected· peak, as shown
in Fig.3. The observed time delay between ·.:.<: two components (i.e.
differential delay) corresponds to the difference in path lengths.
The measured LOS power is taken to be the Friis transmission
value, while the measured reflected power is taken to be the free
space value for the unfolded path length times the reflection loss, or
~
(PR)
=
ref/
PTGTGR')..."
.,
1
1
1fi"
(6)
(41t)- (dl +d2)
Equation (6) implicitly assumes that the rel1ecting boundary is
~'''''''"''''''''''''''''''''''''"''''''''~"'~
LOS Measurement
Rel1ection Measurement
Figure 2 ·Two-measurement technique for
determination
rdl~:ction coellici~:nt
t..•e":Js...,reo :..·:)5 :J...,O We'·e:!e':l v._.rt•O.:''""S 01 5:c,.,eo •O'· ":.:,:,1 :J ...
I • . C ... z
01 ..,6
z .. .
2
o.c.ae
~-0016
1, -o.ueu
:S-o.•••
~ -~ :~~
.;< -- •••
(I
1
!\
~--~co_. ......
\
,, I'
I IiI\
1
·- ... :;· ... • •
... o• .. .
••• .. t•••c-...--·•-••01l<jj,., ... ., ...
,""···.-· ........... -·~ • ;,_'~ ...
,......
1\ I. -
......................
~~-
- (P R ) ref/
1
J;,J
• ' \', \V\~, j,~u~Mf'V'\r"JJW)Jli\.,I\i"~~"~';r~"~,.}
!\JlV
l
Y
-O . .l:l6
infinitely large. which is approximately true when the wall
dimensions are much larger than distances d 1 and d2 in Fig.2 and the
wall surface area is much larger than the illuminated area. Assuming
these conditions are satistied. dividing (6) by the Friis transmission
value for the LOS measurement and solv.ing for the reflection
coefficient yields
dt +d.,J. (PR) fl
lr\ = - - ·
.
dws
Therefore, ·the empirical rel1ection coefficient is determined by the
rauo of the reflected and LOS power measurements, weighted by the
difference in measurement distances (i.e. accounting for the path loss
difference in the two measurements).
The sites for the reflection coefficient measurements included a
rough stone wall· made of limestone blocks, a smooth metallised
glass wall and a brick wall. The chosen sites had relatively
homogenous surface characteristics (i.e. free of clutter. windows,
doors, etc.), and the variation of surface roughness at these sites
ranged from rough stone to smooth glass. Table I lists the estimated
surface roughness parameters and lhe measured dielectric properties
[4) of the limestone and brick surfaces at 4.0 GHz. The roughness
Table 1: Roughness and dielllctric parameters lor the limestone
and brick·wull surfaces at 4.0 GHz. ·
Wall
h (em)
cr h (em)
£r
ll,
cr (S/m)
Limestone
12.7
2.54
7.51
0.95
0.028
Brick
1.27
0.508
4.44
0.99
0.010
parameters for these surfaces are the same for both frequencies, and
the dielectric properties are approximately the same as well. The
dielectric properties for the glass wall were not measured in [4).
MEASUREMENT RESULTS
. Figures 4-7 show the results of the measured reflection
coefficients at the limestone wall site compared to the predicted
values using the Fresnel formulas. Each plotted reflection coefficient
results from an average of multiple reflection coefficient
measurements (typically 10).
The 1.9 GHz measurement results in Figures 4 and 5 are only
compared to the Fresnel rel1ect1on formulas for smooth surfaces and
the Gaussian rough surfa.::t! model using (3). From these figures. the
measured reflection coefi1c1ents are bounded by the smooth and
rough surface predictions. In virtually all cases, Figures 4 and 5
show that simply using the Gaussian rough surface model alone gives
pessimtstlc predicttons to the actual reflection coeflicient values.
F1gures 6 and 7 also show the measured 4.0 GHz rel1ection
coeflicients are bounded by the Fresnel predictions for smooth and
rough surfaces. Again, the Gaussian rough surface model (with
either scattering loss f:~.::turJ tends to give pessimistic predicuons of
the measured reflection coeitic1ent vai:.!~s. However, using the
scattering loss factor in (5) gives improved comparison results.
Figures 4-7 suggest that in the absence oi measured data. an
adequate model for rough building surfaces can be easily computed
by averaging the Fresnel ret1ection coefficients for smooth and rough
surfaces, as a function of incident angle as shown below.
f .!.,II
fAVG:: [f.!.,ll (S;))AVG::
Figure 3. Example retlected path measurements at 4.0 GHz
(time axis has arbitrary zero reference)
78
(7)
re
(PR) LOS
sf.!..II
+p
2
( 1+
= 2
p
s)
f.!.,ll
(&J
Mecsured Reflection Coefficients of Rouqn Stone we:·
("e~"t•co•
' - 1 9 .::;: ..... : <;--> P<etoenoicu•or Polorizot•on
o.,ter,,o oo•or•zCt•O"'J
f -
4
Meosureo Re-tte-ct'c.r·. .:oerf •..:.c-nts ..:>f Rcn... qf"' Stone W.:lll
G,...z <;-- > Peroend•O:~.o~'C' Po•or•Zot•on (vert•C:O' onte,.,no oo•o~'•Zot•O.,J
•o
/
.E.: 6
~ .J.~
~- ~
.g v 3
g.: .:
",.. .. ,, .... o•'I'-'''Oeo••O"
~·~ .... ., . .,,.,, ... ~ D•ao-•·•'1
r • ~ 136 , • .J :;• .. • ; . .;.o
"'C. ... ~'" 'II
:;I·· DO'
:;I,..••••~
' : .. : - . -3~ •
:
~· , _
.,
2~
Mecsure.:l Rei·ectio,.,.
f •
1
1 9
G~""~Z
~oeificie,....!s
; -a
~~
7
~:
6
~.:......,<~P"'
011.011 ... 000" '"''0Cf'
ca._,, .., ... ., .. 'l ........... ,
'- * Gl-1:
;~ ...
1
: :t•c-
0
----------
~ouqn
........ -
.... -
Stone wou
-~~~ ....O"' . . .<INIOC:CII•O"
'----.
I
'\1.-••••"'e'"tP•oc;..l'•h•'
c. •
t••· .. u•• •"''co'•
~::,:~·.o.:,•:;.~"
~o
"?
!a•." •
'"''": •
... , ••., ... •""')" ....... ,., •••
0 O::ll.,. • C.9!1
DO•-·· .. ~
-~--·
. . . · : .. c ...
·~·~·
]v-;
I
·h . . . ~·~-
!
e ....... ,, ..
,i
i
~ 0 ~
/
c
~c::
:5 ....
e.c
~-
§ :..o
~ c.s
~ 0.4
"v'
0
.:..!:1
:: .:..8
~05r------­
.go.J
~~
(oeq'ee~;
.... --> Poroul!• ;:.o•o'•Zot•Or"' tnor•:onto• onte,.,no po•or :ot•O.,J
~
Oc. .. q" .IO"e DO'O,.....el•'t
"• ·;;: :c-
!_
4~
... .::.oerq ,:.,,.,q•e
Meosureo Reflc:-ction CoeHic•ents oi
Stone Wo::
,."'''•...,a•• -o•• •oco••o ..
'S•e-• ~ ... e ... c -· :·r.•·• ...
, . • ., ce. o • c. ~;i. _. • o ~6
"•os .. ••oaco•a
"
Figure 6- Measured rellection coeflicients lor limestone wall at
4.0 GHz (perpendicular polarization)
(--;. Po•olle• coo•o .. •:"O!•on \"O'•::.nlc• ..:nte""'O oo•c• :ot•O"'J
c
£ ~::
..:.:
0
-o
"
~ 0.1
Figure 4 · l'\'leasured retlection cocfth:ients for limestone wall at
1.9 GHz (perpendicular polarization)
/.
0
0
0
·=-
l!
~ ~ . .>
§...:0~
'C.._·
"-'
::::;
c 0'----------------~~---3G
4~ •
o~o..
J.0
Incident At"'qle (degrees)
..:
'J
10
jU
~~
SC
6~
IMC·CI~,t Al"''qle (degrees)
70
sc
90
Figure 5 -l'\'lcasured rdlcction coefficients lt1r limestone wall at
1.9 GHz (parallel polarization)
Figure 7 • 1\leasurcd rcllcl:lion cudlicitmts for limcstonl! wall at
4.0 G Hz tparalll!l polarization)
In. (lSJ. r .1.u is either the perpendicular or parallel polanzauon
rel1ect10n cuc:flkient given in (I) and p s is the s.::attering loss factor
in (3). This simple model is compared to each measured rellection
..:uodlkient 111 Figures 4-7. The error statistiCS of these comparisons.
including mmunum and maximum errors. average error (EuvgJ and
standard deviation (s). are given in Table 2. Table 2 shows that using
measurement results fur vertical and horizontal antenna
polarizations, respe..:uvely. The dielectric properties of clear, nondoped glass are typically quoted as: E = 5. ll = I and cr = 10" 12 S/
m. Since the glass wall is metallised.rthe conductivity will be much
higher than 10" 12 S/m. Bec;tuse the conductivity is unknown. several
Fresnel rellection coeflictents with various conductiVIties (10" 12 to 10
S!m) are plotted in Figures l) and 9. A material having a conductivity
ut' 1U.O S/m woulJ bo: ..:un~tJered a semH:unductur. sim!lar to
seawater or intrinsic germamum [5]. No comparisons with Gaussian
rough surface models were m:.~de in this case.
ln Fig.8. the measureJ rellection coefficients closely agree with
the theoretical Fresnel rel1ection coefticients using cr- 5 Slm.
111di.::ating that it is more r~:tleo.:tive than ordinary. clear glass. For
manv of these me<1surements with e. 2! 45 °, the rellection
.
'
coeflicients are even gre:1ter than that predicted using cr
I 0.0 Slm.
In Fig.9. the comparisons indicate the measured rellection
coefticients are well approx.unated by the Fresnel rellection
coefticients usmg a- 2.5 S/m. Althuugh the ex.a.::t diele.:tru;
properties of thi.; glass :.~re nut known. Figures 8 and 9 indicate th.:tt
the ret1ecuon coeflicielll .:;an be: accurately moJeled using the smooth
surf'-l.:c: Fresnd furmuh~' <llld tht: propt:r o..ltt:lc:.::tn.: properties.
Figures 10 and r I illu~trate llfe !frick wall ro!t1ectJOn coetlicient
results for vertical and hunwntal antenna polarizations. respectively.
The smooth surface unJ Uaussian rutigh surface models were
compared with the measured results. Fur these cases, there is little
Jifference between the s..:attenng lu~~ l<t~oturs of t3J and (5), because
of the small standard deviation of height (a h). The measured
retlection coefficients of the bnck wall are not well bounded by the
Table 2: Error statistics for comparisons of measured rcllcction
cocfticients with simple model ot' (~)
Freq. (GHzJ
Polarization
Em in
Em ax
Eavg
s
1.9
Perpendicular
0.002
0.240
0.096
0.072
1.9
Parallel
0.002
0.103
0.057
0.037
4.0
Perpendicular
0.017
0.3!9
0.146
0.096
4.0
Parallel
0.002
0.184
0.097
0.054
rA \'G
to approximate the measured retlect!On coefficients of the
limestone wall varies in degree of accuracy. In most cases. the: .:rrur
estimates indicate that r A VG giv~s a fairly accurate modd t'~r
surfaces with wndom roughness features wluch is simplt: to
implement and delined by real-world. physic<11 features. In gener<ll.
f:\\'(j giv~~ an Improved t!Stimat~ uver f.l.ll (With or WltlWUt the
s..:auenng luss fa.::tor). A lea.:;t squares .::urve fit or linear regrc:ss1un
.:ould have: been <1pplied to tll~se data to prov1de a more a..:curato::
Jt:,..;npttun. but tlus mudd wuulJ nul bt: rubust 11l that 1t rc:Ljuu·e~
empirical data for different surfaces and matenals.
Figures l) and 9 display the glass wall rel1ection cueffic1ent
=
79
lvleosurea Retlect•on Coeffic•ents of Br•c~oe. Wolf
Meosurec t=<eflect•on Cueffic•ents cf Gloss Wa11
I- 4
1
0
<-->
Pe-rQerHj•cuiOr Po•orozotoon ("'e-rt•cc: .onter'\no ~o•o••zot•onJ
t -
-
0----- -
9 0.6
<.--"'
Perc:>eroa.c ... •or Polorozoticl"' ( ... t!r-t•COI on1ero,.,o polor•zot•on)
~09
•Ooa• ..... OQI"
o..,<lg'~
e ................ q . . . ,. •• .,c-•
~:;::·.o.-G·:;,"'!,"""''•~••-•
k•••• ,, .. ,
.o-·-
o---,;
7
4 CHZ
1()
------_-_--;oe::-_-_~
- : - - -:. : --. -. _.,
~09
.);! 0 8
~0
G...,.z
-
":!-
-
u
~ 0.~
~Q .. •••• 51 .. GO,.I CO"' It' IG("GI•Q"'
•:.-••'i•~<j ......
t l • ~ c '51=..:Q~,Sl.~.,s~Q"';G
a: 0 .
cr•
0
'
~0~
tt• 2
g.o2
G·OS$
~ 0.1
0.0
0
20
'0
30
40
SC
~- -
Meos ..... reu
1.0
.~ 0.9
;;g 0.8
~0.7
c
g u.o
u
C...,.z c.--;,
6C
80
,,.,C•Cle,.,t Ang•e (de';'ees)
Kei•ect•.::.~.
90
(:.::e••·cze.,ts .:;..r C·oss
f-
co .. o•·•-•o..q" •w•••c•
----------
-
·a- - -
a:
0 0 .•
.goJ
..
--- .
0
c
~
---
·~""
""
~0.5
:;
- :.:---·
/,/
~ 0.4
-Q
'
0 . .3
·a 0.2
~0.2
~ 0 ~
~01
""
10
20
30
40
~0
6-
lnc:•Oe-Mt Angle (c:!eq•ees
70
80
co
sc
Figure 9 • Measured reflection coeflicients fur gluss wall ut 4.0
GHz (parallel polarization)
predictions for the smooth and Gaussian rough surfaces. in general.
This is expected since the roughness of the brick surface is such that
the critical heights (he) are greater than the maximum protuberances
for many of the incident angles. Because of this, the Rayleigh
criterion predicts that the surface appears smooth to the incident
radiation and the reflection will be predominantly specular. This is
ev1denced m Figures 10 and 11 since most of the measurements fall
dose to the predicted Fresnel reflection coeflicients for smooth
surfaces.
eo
90
I
I
01 0 . . . . 0 99
•o .. ca .. t. .. ••oc-• ll"O'o""•'•''
"'• 1 17 c.., ""' • 0 ~0.8 c-
-------------. --
o
0
-
\0
-L..__
3~
:7~:
40
50
60
,,.,c•oent Al"ql~ (deqrees)
//
70
eo
90
Figure 11 ·Measured rcllcctiun cuet'ticients l'or brick wall ut 4.0
GHz (parallel polarization)
ACKNOWLEDGMENTS
The authors would like to acknowledge Michael Keitz for his
assistance with the mt:asurement systems, and Amanda Montague.
Hao Men·g and Bhushan Rde for their contributions during the
experimental data collection.
REFERENCES
[lI
R~ppapon.
[21
Symposium on Wir~less Personal Communications. Blacksburg.
VA. June 17-19, 1Y':!2.pp.l6.1-16.27.
Honcharenko. W.. Benoni. H.L.. Dailing. J.L. Yee. H.D.: "Mecfumism-s
CONCLUSION
Microwave rellection coefticient measurements were presented at
1.9 GHz and 4.0 GHz for a variety of typical smooth and rough
building surfaces. The measurement results were compared to the
theoretical Fresnel reflection formulas using Gaussian rough surface
scattering models when applicable. The measurement test cases
include a very rough wall made of limestone blocks. a glass wall, and
a brick wall. The theoretical comparisons show tlwt the Fresnel
reflection formulas for smooth surfaces adequately describe the
rel1ective properties of the glass and brick walls. The rough stone
wall measurements were shown to be bounded by predictwns f~•r a
smooth surTace and the Gaussian rough surface. A simple model to
predict- empirical reflection coeftic1ents for surfaces with random
roughness features was presented. and was shown to adequately
predict the measured results. This model is delined by physical
roughness ieatures and material properties and can be used to further
enhance site-specific propagation prediction models.
70
I
~
? 0.6
u
,,,
~
o.o• ::~ ... - o.99
3~·o~ac-
••-;;::·.
";::·.~:.;:~~·:~~.~:;···;
,, - .... .. c
~u7
'!,•
8
<••n•o••-••
•••'•u ,._.. . ., ""'
WeG • .,•.CIGOiol
~08
a-·---
!IC,
.:.o
~0
60
•n:•Ot:"t Anqle (ceqree5J
. . . -···· .......
1.0
~0.9
-- ·=-
".
Mecsure.::: ~C""C:-~ttcn Coefficr.s-nts of 8rzc~<. ...Vall
"GHz <--> Po,ou.oe· .:>o•cr•zot•on (norizonto• ontenno oo•or•zotion)
v\~P
t
- - - - Q-
••
Figure 10 ·Measured rdl~:ction coefficients for brick wall at 4.0
G Hz tperpcndicular polarization)
r
~0.~
0.0
•o
0
;:.crone• Polo••ZOI•..J,.., l'"'O"::'Or"'IIOI o.,tennc co•O'" :;;ot•oro;
---------
1o .. •
Qli~-J" O"''IJC .. LoG'G ... OIO<O
•·••2"~:,.....
0
5,:.
t.r •
Figure 8 • Measured ret1ection coetlicient.s for glass wull ut 4.0
G Hz (perpendicular polarization)
f- 4
9• c. o••••c•"c o<ag..-•1·••
-- --- --- . -~ -
T.S.. Scu.ld. S. Y.. Schau bach. K.R. : "Site-Specific
Propagt.mon Pretltct/UII fur PCS System Destgn", Virginia Tech's 2ND
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