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

1

RRRRRT~~~~~~ SSSSSIS Η−ΗΗ →−

8

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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