Single FrontSingle Front--end MIMO Architecture end MIMO ... · Single FrontSingle Front--end MIMO...
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Single FrontSingle Front--end MIMO Architecture end MIMO Architecture with Parasitic Antenna Elementswith Parasitic Antenna Elementswith Parasitic Antenna Elementswith Parasitic Antenna Elements
ArakiAraki--SakaguchiSakaguchi LaboratoryLaboratorygg yyMitsuteruMitsuteru YOSHIDAYOSHIDA
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ContentsContents•• BackgroundBackgroundBackgroundBackground•• SFSF--MIMO w/ PAEMIMO w/ PAE
Parasitic antenna elements (PAE)– Parasitic antenna elements (PAE)• Matching problem• Operation problemOperation problem• Performance analysis
– Single Front-end (SF) designg ( ) g
•• Simulation resultsSimulation results•• SummarySummary•• SummarySummary
ℇℇ AbbreviationAbbreviation
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ℇℇ AbbreviationAbbreviation– SF : Single Front-end, PAE : Parasitic Antenna Element– T : Transmitter, P : PAE, R : Receiver
BackgroundBackgroundgg•• MIMO system requires …MIMO system requires …MIMO system requires …MIMO system requires …
– Low spatial correlation in limited space (e.g. mobile terminal)– Transceivers for each branchTransceivers for each branch
•• Novel architecture is neededNovel architecture is needed•• Novel architecture is neededNovel architecture is needed– Mutual coupling effect
• Adaptive beamforming• Adaptive beamforming(e.g. ESPAR)
– Single RF Front-endg• Spatiotemporal conversion• Multiplexing
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SFSF--MIMO w/ PAEMIMO w/ PAE•• Analytical studyAnalytical studyAnalytical studyAnalytical study
– Effect of PAE• Conventional : Empirical studyp y
– Effect of Single Front-end• Switching causes SNR penalty
MIMO f– MIMO performance• Eigenvalue analysis
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SFSF--MIMO w/ PAEMIMO w/ PAE•• Concept of design for MIMO transceiversConcept of design for MIMO transceiversConcept of design for MIMO transceiversConcept of design for MIMO transceivers
– Free space• Stochastic : undesignableg
– Free space + PAE• Quasi stochastic : designable
•• Two designable parametersTwo designable parametersTwo designable parametersTwo designable parameters– Receiver
• Matching problemg p
– Parasitic antenna elements• Operating problem
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Matching problemMatching problemg pg p•• Capacity maximizationCapacity maximizationCapacity maximizationCapacity maximization
– Two independent problems( ) ( )ΗΗΗ +=+ HCCHIHRHI detlogargmaxdetlogargmax ( ) ( )
( )( ) ( )ΗΗΗΗΗΗΗΗΗΗ
Η
+≤+⇒≤⇒≤
⇔=
+=+
CHHCIHCCHICHHCHCCHHHHH
RCCR
HCCHIHRHICHRH
~~detlogdetlog~~~~definite Positive:
detlogargmaxdetlog argmax,,
Q
– Lossless condition( ) ( )+≤+⇒≤⇒≤ CHHCIHCCHICHHCHCCHHHHH detlogdetlog
IΣΣΣΣIΣΣ =+⇒= ΗΗΗ
– Hermitian matching Η= 2211 SΣ
IΣΣΣΣIΣΣ =+⇒= 21211111
( ) ( ) 1SΣSIΣΣH −−=
( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )111
211
112221211
112221211
2222211122
0 ISSSΣSISΣSSISΣΣSIS
SΣSIΣΣΣSISSSSISΣHHSHHΗ−Η−ΗΗΗΗ−Η
−ΗΗ−Η−ΗΗΗΗΗ
≤≥=
−−−−=−
Q
( ) ( ) 21112221 SΣSIΣΣH −=
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( ) ( ) ( ) ( )( ) ( )( ) ( ) ( )( ) 21
111221111
111222121
1222221
2222211122221122222211112221 0
SΣSIΣΣIΣSISSSSIS
ISSSΣSISΣSSISΣΣSIS−ΗΗ−Η−ΗΗ −−−≥−∴
≤≥−−−−−= Q
Matching problem (cont.)Matching problem (cont.)g p ( )g p ( )•• Parasitic antenna elements system modelParasitic antenna elements system modelParasitic antenna elements system modelParasitic antenna elements system model
– Effective free space
( ) ( ) ⎤⎡⎤⎡ −− 1111~~SSΓSSSSΓSSSS ( ) ( )
( ) ( ) ⎥⎥⎦
⎤
⎢⎢⎣
⎡
−+−+−+−+=⎥
⎦
⎤⎢⎣
⎡=→ −−−−
−−
PR1
PP1
PRPRRPT1
PP1
PRPRT
PRPP1
PTPTRPTPP1
PTPTT
RRRT
TRTT ~~~
SSΓSSSSΓSSSSΓSSSSΓSS
SSSSSS
– Hermitian matchingΗ= RR
11R
~SΣ
– Effective channel( ) RT
1
RRRR21R
~~~~ SSSIΣH−Η−=
– Capacity : Equal power allocation
( ) RT
1
RRRRRT~~~~log SSSISI
−ΗΗ −+= γBC
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( ) RTRRRRRTlog SSSISI +γBC
Operating problemOperating problemp g pp g p•• (T,R,P)=(1,1,1)(T,R,P)=(1,1,1)(T,R,P) (1,1,1) (T,R,P) (1,1,1)
– Mobius transform
⎟⎞
⎜⎛ 22 ~~ SS
⎟⎞
⎜⎛ ⎤⎡+Γ
−=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−+
≤Γ≤Γ2
RR
RT
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RR
RT
1 ~1maxarg~1
1logmaxargPP
SSBA
S
S
S
Sγ
Γ is uniquely determined
⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦
⎤⎢⎣
⎡=Δ≥Δ−−+
+Γ+Γ
==Γ PPPR
RPRR22RR
2PP
P
P
1det where01 maxarg
P SSSS
SSDCBA
Q
– ΓP is uniquely determined
P f l iP f l i•• Performance analysisPerformance analysis– No matching (All pass) model ( ) RTRTRT
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RRRRRT~~~~~~ SSSSSIS Η−ΗΗ →−
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IΣOΣ == 21R
11R ,
Performance analysisPerformance analysisyy•• Applying Equal Gain Combining (EGC) analysisApplying Equal Gain Combining (EGC) analysisApplying Equal Gain Combining (EGC) analysisApplying Equal Gain Combining (EGC) analysis
ZYXS
SS
SSSSSS ≡+≡
−+
−+= 2
PTRP2PT
*PPRP
RTmaxRT11
~ ( ) '' 212
*2
1
*1
2
1
2
1
2
1 nrr ++=⎥⎥⎦
⎤
⎢⎢⎣
⎡=⇒⎥
⎦
⎤⎢⎣
⎡+⎥
⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡shh
hh
hh
nn
shh
rr
– X,Y : pseudo branch
SS PPPP 11 21222 ⎥⎦⎢⎣⎦⎣⎦⎣⎦⎣ hhnhr
⎞⎛⎞⎛⎞⎛ 22 2 n
[ ] [ ] ( )( ) ( )22
2222
Y2
Xvarvar,cov,,
YXYXYEXE ≡≡≡ ργγ
( )
( ) ( ) ( ) ( ) ⎪
⎪⎬
⎫
⎪
⎪⎨
⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛+−−⎟
⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟⎠
⎞⎜⎜⎝
⎛+−−⎟
⎟⎠
⎞⎜⎜⎝
⎛×
++
−⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−−=
−
+
−−
+
−
=
∞
=∑∑
12X
12
21
12Y
12Y
12
21
12X
00
22
e
12;
21;
21,
21
1212;
21;
21,
21
12...
...12121
22
21
21
γγγγ
ρρ
knFknF
kn
kn
nn
P
kk
n
k
k
n
n ( ) ( )varvar YX
•• Performance of EGC is quite close to that of MRCPerformance of EGC is quite close to that of MRC
( ) ( ) ( ) ( ) ⎪⎭
⎪⎩
⎟⎠
⎜⎝ ++−⎟
⎠⎜⎝ ++−⎟
⎠⎜⎝ ++−⎟
⎠⎜⎝ ++− YX
2YX
2YX
2YX
2 12222121222212 γγργγργγργγρ
– Exhibiting less than 1dB of power penalty
9•• Noise is added only from 1 branchNoise is added only from 1 branch
Simulation resultsSimulation results•• ConfigurationConfigurationConfigurationConfiguration
– SRT,SPT : Propagation channel (stochastic)• Correlated complex gaussian RVs (CN(0,σ2))p g ( ( , ))• Envelope correlation coefficient by Jakes’ model
⎟⎠⎞
⎜⎝⎛=λπρ dJ 2
0
• Power correlation coefficient
⎟⎠
⎜⎝ λ
ρ 0
( )22( )( ) ( )
2
2PT
2RT
2PT
2RT
varvar
,covρ=
SS
SS
– SRR,SPP,SPR,SRP : Antenna parameters (deterministic)• Calculated by HFSS
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Simulation Simulation resultsresults (cont.)(cont.)( )( )•• Average error probabilityAverage error probability vsvs SNRSNRAverage error probability Average error probability vsvs SNR SNR
⎥⎦
⎤⎢⎣
⎡
×+××−××−××+×
=⎥⎦
⎤⎢⎣
⎡−−−−
−−−−
1111
1111
PPPR
RPRR
1063100510931011109.3101.1106.3109.4
jjjj
SSSS
⎦⎣ ×+×××⎦⎣ PPPR 106.3100.5109.3101.1 jjSS
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Simulation Simulation results (cont.)results (cont.)( )( )•• Average error probabilityAverage error probability vsvs SNRSNRAverage error probability Average error probability vsvs SNR SNR •• Distribution of ΓDistribution of ΓPP
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Simulation Simulation results (cont.)results (cont.)( )( )•• Effect of distance between antenna elementsEffect of distance between antenna elementsEffect of distance between antenna elementsEffect of distance between antenna elements
– Mutual coupling (SRP)– Correlation coefficient
ZYXS
SS
SSSSSS ≡+≡
−+
−+= 2
PP
PTRP2
PP
PT*PPRP
RTmaxRT11
~
Correlation coefficient– E[X2/Y2]
PPPP
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Simulation Simulation results (cont.) results (cont.) ( )( )•• Optimum distanceOptimum distanceOptimum distanceOptimum distance
– Distance gets closer,performance becomes betterp
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Single FrontSingle Front--end end gg•• Spatiotemporal conversionSpatiotemporal conversionSpatiotemporal conversionSpatiotemporal conversion
– PSD of switched signalsin2 ⎞⎛k( )( )
[ ]1,0 wheresin~2
22 ∈⎟
⎠⎞
⎜⎝⎛ −= ∑ k
TnfR
nknkkfR
n ππ
– PSD of white noise (e.g. 3dB penalty where k=1/2)
( )2
2 sin~ kNNnkkfN == ∑ π
– Equivalent channel
( )( ) 002 kNNnk
kfNn
== ∑ π
⎥⎤
⎢⎡
⇒⎥⎤
⎢⎡
=→⎥⎤
⎢⎡
= 111~~~ hhH
hH
ttt
k
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⎥⎦
⎢⎣
⇒⎥⎦
⎢⎣
=→⎥⎦
⎢⎣
=222
~~ hhH
hH
ttt k
Simulation resultsSimulation results•• CapacityCapacityCapacityCapacity
– Optimum
( )Η~~dl
– Sub-optimum at low SNR
( )Η+ HHIΓ
detlogmaxargP
γ
– Sub-optimum at low SNR2~maxarg
PF
HΓ
Th f f i l f tTh f f i l f t d MIMO / PAEd MIMO / PAE
PΓ
•• The performance of single frontThe performance of single front--end MIMO w/ PAE end MIMO w/ PAE is close to that of conventional 2x2 MIMOis close to that of conventional 2x2 MIMO
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SummarySummaryyy•• SFSF--MIMO w/ PAE is proposedMIMO w/ PAE is proposedSFSF MIMO w/ PAE is proposedMIMO w/ PAE is proposed
– Performance of PAE is evaluated analytically– Switching operation can realize MIMO by single RF front-endSwitching operation can realize MIMO by single RF front end
F ibilit f d ti t hi i itF ibilit f d ti t hi i it•• Feasibility of adaptive matching circuitFeasibility of adaptive matching circuit
Th k f ki d tt tiTh k f ki d tt tiThank you for your kind attentionThank you for your kind attention
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