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Alain SIBILLE ([email protected]), Stéphane FASSETTA*
Laboratoire Electronique-InformatiqueENSTA, 32 Bd Victor, 75739 Paris cedex 15, France
* Now at THALES Communications, Colombes, France
INTERSECTOR CORRELATIONS FOR SWITCHED BEAMS DIVERSITY PERFORMANCE EVALUATION
Outline
context and motivation
antennas
intersector correlations: theory
computations assuming a model scenario
comparison with experimental results
angular vs. spatial diversity
conclusion
Context and motivation
GENERAL CONTEXT: low-complexity beam-switched smart antennas for
terminals, HIPERLAN 2 access points etc …
MOTIVATION: an attempt to quantify the potential benefit brought by beam-
switched antennas prior to any experiment, intended for optimal antenna design.
PARTICULAR CONTEXT: experimental channel measurement campaigns and
antenna design carried out within the European ADAMO project (1998-2000).
Antennas
6 monopoles circular array 4 patches planar array
6 BSSA circular array 13 monopoles array
Antennas
Intersector correlations : theory
)().(/)( ,,, HjHjHiHiHjHiij IEIEIE
dHHI jiHjHi )()( *
,
Hi
Hj
Wideband intersector correlation:
with
i
j
rij is a measure of the diversity performance of a switched beams antenna for wideband radio link (single or multiple carriers)
lllil
llilli
jkDBGF
dkDjgBFH
)exp()()()(
)()exp()()(2
1)(
ml
mlmjlimlHjHi kDkDBBEIE,
**, )()(2)(
l
llili gAfh )(.)()( Discrete multipath channel model:
f(t): receiver filter CIR Ail: path transmittance(Di: receiver antenna radiation pattern)
tl: path delay gl: CIR of environment+ emitter
)( lil kDB
2)()( GF)( : Fourier transform of
Intersector correlations : theory
dDDpIE jiHjHi ).,(),(.),(02)( *,
Di,j: radiation patternsP(): angular power spectrum for omni receiver antenna
Assuming perfect averaging of small-scale fading:
)()(02)( *2
, ljlill
HjHi kDkDBEIE
Continuous approximation of the discrete sum (scenario averaging):
Intersector correlation:
dDpdDp
dDDp
ji
ji
ij
.),(.),(.),(.),(
).,(),(.),(22
*
Intersector correlations : theory
The channel correlation contains the term:
Intersector correlations : theory
)()()()()()( ******ljlljllillilljllil kDBkDBkDBkDBEkDBkDBE
Extension to polarisation-dependent propagation
).,(
).,(),(
p
pXPD
)( ,HjHiIE
)()()()(
)()()()(
****
*2*2
ljlillljlill
ljlilljlil
kDkDBBkDkDBB
kDkDBkDkDBE
dDDp
dDDp
dDDp
ji
ji
ji
).,(),(.),(
).,(),(.),(
).,(),(.),(
*
*
*
),(),,(),,( ppp ),( pgeneralize
),( p is somewhat related to
Continuous approximation:
Computations assuming a V-V model scenario
/2exp2
1)(),( cpp
c
6 BSSA array
0 50 100 150 0
0.2
0.4
0.6
0.8
1
ANGLE (°)
CO
RR
EL
AT
ION
0°/10° 0°/40° 40°/10° 40°/40°
4 patches array
c
Complex vs. Amplitude-only correlations(Phase behavior)
0 50 100 150 0
0.2
0.4
0.6
0.8
1
ANGLE (°)
CO
RR
EL
AT
ION
0°/10° compl 40°/10° compl 0°/10° real
40°/10° real
13 monopoles array
Computations assuming a V-V model scenario
Comparison with experimental results(ADAMO campaign 1, IMST indoor measurements)
x
y
zplotter
table
table
table
locker
table
table
bookshelf
bookshelf
bookshelf
bookshelf
maga
zine rack
1.5 m
2 m
3.5 m
4.5 m
2.5m
a b c
d
zz z
y
x
y
y
x
x
y
z
x
blackbo
ard
Tx
5.25
3 rooms: small , library, hall 6 beams antenna at ceiling levelomnidirectional radiator at desk level5.2 GHz, 120° MHz BW31 locations, small-scale fading averaging every /106 monopoles array and 4 patches array
library
small office
c (°) (°) =60°
=120°
=180°
0 5 0.46 0.13 0.15 0 10 0.46 0.12 0.16 0 20 0.48 0.10 0.16
model:
0 40 0.50 0.07 0.15
20 10 0.56 0.03 0.07 20 20 0.56 0.03 0.07 20 40 0.55 0.02 0.08 30 20 0.60 0.09 0.01 30 40 0.58 0.06 0.04
CAMPAIGN 1 (6 monopoles array) 0.23 0.009 0.05
small office 0.31 0.07 0.07
library 0.25 0.11 0.04
hall 0.46 0.07 0.09
Comparison with experimental results
(ADAMO campaign 1, IMST measurements)
ADDITIONAL SPATIAL DIVERSITY
d
0 50 100 150 0
0.2
0.4
0.6
0.8
1
ANGLE (°)
CO
RR
EL
AT
ION
+0.2 +0.1 0 -0.1 -0.2
6 monopoles array d /
Computations assuming a V-V model scenario
INTERSECTOR CORRELATION: model vs. Experiment(ADAMO campaign 1)
c 60° 120° 180° d/
6Monop exp
0.290 0.069 0.030
6Monop model
0.292 0.071 0.030 40 40 0.18
4Patches exp
0.144 0.037 0.019
4Patches model
0.140 0.027 0.024 35 15 0.38
Comparison with experimental results
expected on account of the Tx-Rx LOS tilt in elevation
Angular vs. spatial diversity
spatial diversity = spatial filtering of faded signals
angular diversity = angular filtering of incoming waves
IS THERE A FUNDAMENTAL DIFFERENCE BETWEEN BOTH ? IS THE
DISTINCTION BETWEEN ANGULAR AND SPATIAL DIVERSITY SO
CLEAR IN PRACTICAL ARRAYS ?
ROLE OF THE PHASE CENTER
Angular vs. spatial diversity
y’
x’
z’
O
P
r
rk
N
M
k
(r, , )
z
y
x
(r, , )
6 points in angular space, used to locally equate to zero the phase differential
r
jkrjA
r
jkrErE O )),(exp(
),()exp(
),(),,( 00
« local » phase center for a given () direction
ROLE OF THE PHASE CENTER
A SIMPLE INTERPRETATION: sectored arrays also exhibit spatial diversity due to sector dependent position of the phase center
phase center
driven monopoles
reactively loaded monopoles
6 MONOPOLES ARRAY
Angular vs. spatial diversity
13 MONOPOLES ARRAY
y ( m m ) phase center
driven monopoles
reactively loaded monopoles 1
reactively loaded monopoles 2
short-circuited monopole
ROLE OF THE PHASE CENTER
Angular vs. spatial diversity
Conclusion
A simple tool has been proposed to evaluate the diversity performance of beam-
switched antennas: intersector correlations assuming a model scenario
Comparison with indoor propagation channel measurements is favorable, on
condition of the presence of extra spatial diversity
Evidence of hybrid spatial angular diversity in beam-switched circular arrays
due to non central position of the phase center.
Perspective: evaluation of correlations for MIMO antennas
Acknowledgements
The authors are grateful to J. Kunisch, M. Schneider, J. Pamp, E. Zollinger, A. Winkelman and M. Gehrt of IMST for supplying CIR measurements
