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Parameter Estimation Employing Parameter Estimation Employing Recursive Recursive EigenvalueEigenvalue DecompositionDecomposition

for MIMOfor MIMO--OFDM Using OFDM Using Maximum Likelihood Detector Maximum Likelihood Detector

with Arraywith Array CombiningCombining

Fan Lisheng, Kazuhiko Fukawa, Hiroshi Suzuki

Tokyo Institute of Technology

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Background

MIMO-OFDM

OFDM + MIMO

MIMO ･･･Improve the system capacity

OFDM ･･･Utilize the spectrum efficiently →high-speed data transmission

Cochannel interference→ Performance is degraded severely

!

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Co-channel interference in the uplink of MIMO-OFDM

Random accessRandom access

Incident angle Incident angle differencedifference

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MLD with Array CombingZF, MMSE, MLD cannot workTo suppress co-channel interference, MLD with the array combing has been proposed

Post-FFT AC PrePre--FFT ACFFT AC

FFT

FFT

Array

combiningMLD

FFTArray

combining MLD

FFT

Array combing: Suppress the co-channel interference

by prewhitening filtering

Pre-FFT AC is superior when using limited preamble symbols

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Motivation

The drawback of Pre-FFT ACLarge complexity in parameter update due to the non-recursive eigenvaluedecomposition (EVD)

A recursive EVD is applied to the parameter estimation of Pre-FFT AC

Reduce the complexity to about 25 percentsSuitable for real-time application

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Pre-FFT ACArray combining

Decision

feedback

Recursive EVD

From desired user

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Error signal in the time domain

: Error signal of the branch metric generatorcaused by the interference and noise

• : AC output- : Coefficient of AC- : Received signal

( , )r by l m ( )lb

H m≅w xlb

w( )mx

( , ) ( , ) ( , )b r b s bl m y l m y l mα = −( , )bl mα

• : Replica signal- : Channel impulse response- : Candidateof the transmitted signal

( , )s by l m ˆ( , ) ( )Hbl m m≅ c s

( , )bl mcˆ( )ms

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whenwhen

Parameter estimation

••To suppress the interference, To suppress the interference, prewhiteningprewhitening filtering is filtering is employed to the error signalemployed to the error signal::

0=

The parameter estimation should be based on EVD

Parameter vector Autocorrelation

matrix

0= b bl l≠

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Comparison between EVD methods

Newton’s iterative search

Low computational complexity

Cyclic Jacobi algorithmLarge computational

complexity

Recursive EVDNonrecursive EVD

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Recursive EVD

Auto-correlation matrix of is

: Forgetting factor

Solve the eigenvalues of the current matrixbased on the EVD result of previous matrix

: Eigenvalues of the previous matrix

: Eigenvectors of the previous matrix

: Eigenvalues of the current matrix: Eigenvectors of the current matrix

( )x mR( 1)x m−R

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Recursively solving the eigenvalues

ext ext( ) ( 1) ( ) ( )Hm m m mλ= − +R R X Xext ( )Hiy m= X p

ext ext{1 ( )[ ( 1) ] ( )} 0Him m m yλ β+ − − =X R I X

( ( ) ) 0i im β− =R I p

ext ext1 ( )[ ( 1) ] ( ) 0Him m mX R I Xλ β+ − − =

0y= ext ( )HjmX p ext ext( ) ( )H

j j m mβ λξ= +X X

0y ≠

Find a accurate root of

ext ext( ) 1 ( )[ ( 1) ] ( )Hf m m mX R I Xβ λ β= + − −

( ) 0f β = 12

( ) 0if β = 1'

( )( )

ii i

i

ff

ηη η

ηββ ββ

+ = −

NewtonNewton’’s iterative search algorithms iterative search algorithm::

: number of iterationsη

Newton’s iterative search

A0λ>

1( ) [ ( ), ( )]i i iβ β β −∈B A A

The interlacing property:Hλ= +B A cc

: Symmetric matrix

1[ , ]i i iβ λξ λξ −∈

Increasement

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Small increasement

'

( ) 0( )

i

i

ff

η

ηββ<

2

ext2

1

( )'( ) 0

( )

HLj

j j

mf β

λξ β=

= >−∑

q X

( )f β

'

( ) 0( )

i

i

ff

η

ηββ>

is a monotone increasing function

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Large increasement

The midpoint of the new intervalThe midpoint of the new interval is is used for the next iterationused for the next iteration

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Flow chart of iterative search

Select the midpoint of the interval

Yes

No

Obtain the next iteration value

Calculate the eigenvectors

Convergence threshold

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The convergence of the search algorithm

Guaranteed to convergenceQuadratic convergent

K. B. Yu, “Recursive updating the eigenvalue decomposition of a covariance matrix”, IEEE Trans. Acoust. Speech Sig. Proc. , vol. 39, pp. 1136-1145, May 1991.

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Simulation conditions

Incident angleDifference:60 DegDeviation: 4 Deg

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Computational complexity

(Dimension of the auto-correlation matrix)

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Average BER versus average CNR

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Average BER versus average CIR

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Average BER versus Doppler Spread

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Conclusion

A recursive EVD based algorithm was applied to the parameter estimation of Pre-FFT ACIt can reduce the total computational complexity to less than 25 percents (More suitable for real-time application)

Pre-FFT AC with recursive EVD can achieve the same performance as that of Pre-FFT AC with the conventional non-recursive EVD

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Thanks a lot for your attention