2014 27 27 1

: Beamformer Correlated Signal

.

Affine Projection Algorithm

. Affine Projection

Algorithm .

Beamformer Affine

Projection Algorithm ,

.

: Adaptive Beamformer, Generalized

Sidelobe Canceller, Affine Projection Algorithm

.Adaptive Beamformer

Enhance

Suppressing Array Output Signal to

Interference plus Noise Ratio (SINR)

[1][2]. Adaptive Beamformer

Radar, Sonar, Microphone Array Speech Processing,

Wireless Communications

[3].

Linearly Constrained Minimum Variance (LCMV)

Adaptive Beamformer Criterion

. Pass Output

signal-to-interference-plus-noise ratio (SINR)

. Generalized Sidelobe Canceller (GSC)

LCMV Beamformer

[4].

Beamforming

GSC Weight Adaptive Algorithm

Update .

Algorithm Least-mean-square (LMS)

Normalized LMS . LMS Algorithm

. LMS Algorithm Input Signal

Highly correlated

[5][6].

Affine Projection Algorithm

(GSC-APA) [7][8]. LMS-based GSC

update Input Signal

GSC – APA K Input Signal

.

GSC-APA

. GSC-APA

Beamforming APA K

.

GSC-APA .

. Generalized Sidelobe Canceller – Affine

Projection Algorithm

M Sensor Array

Desired Signal

Interference Signal Array Received

Signal .

1

0 01

( ) ( )L

i l l il

s i s ix a a n(1)

( 1)1Tj j Me ea

Steering Vector ,

2 sindd

Sensor , Signal .

Beamformer Output*( ) iy i w x

LCMV

Output Signal Minimization

.

* *min . . s txww R w C w f (2)

C Constraint , f

Response Vector . GSC LCMV

Alternative Formulation . 1

GSC . Weight

Decomposition .

q aw w Bw (3) LCMV Constrained Minimization

- 1 -

2014 27 27 1

Problem Unconstrained Minimization

Problem . *

mina

q a q axww Bw R w Bw (4)

Optimum Weight . 1* *o

a qx xw B R B B R w (5)

Optimum Weight input correlation

matrix .

Input Correlation Matrix

Weight Adaptive Algorithm Update

.

Correlated Input Signal

GSC-APA . GSC-APA

Update .

1* *

, , 1a i a i i i i iw w V VV e (6)

, 1, ,i i i a i i i q i ie d Vw d X w V X B

Blocking Matrix Output K Weight

Update .

1. GSC

. GSC-APA

GSC-APA

.

GSC-APA K

Term .

Section Beamformer Measure

Excess Mean Square Error (EMSE) SINR

.

GSC-APA

Update Weight Error Recursion

.

, ,

1* *, 1

1* *, 1

1* *,

oa i a a i

a i i i i i

i i i i a i

i i i opt i

w w w

w V VV e

I V VV V w

V VV e(7)

,o

opt i i i ae d Vw Optimum residual error

. Expectation

2 Term .

,

, 1

1* *,

,0

1 1* *,

0

a i

i a i

i i i opt i

ii a

i pi i i i opt i

p

E

E E

E

E E

E E

w

I P w

V VV e

I P w

I P V VV e

(8)

. Term

Step-size 0 .

max

20iE P

(9)

Term Term

.

1* *,

0

11 * *,

pi i i i opt i

p

i i i i opt i

b E E

E E

I P V VV e

P V VV e

(10)

Weighted Variance Relation

.

2 2 2 *

, , 1 , ,

1 1* * * *, , 12Re

a i a i opt i i opt i

opt i i i i i i i i a i

E E E

E

w w e A e

e VV V I V VV V w

(11)

2 *i i i i iE E EP P V A V

1 1* * *i i i i i i iA VV V V VV .

Weighted Variance Relation

Vec{} Operator

. Vec{} MxM Matrix

M2x1 Column Vector Operator .

2 2 2 * * 2 *

, , min 1 2vec veca a FE E Jw w

(12)

1* * * 1min opt optJ x xw R w f C R C f

Minimum

error ,=vec , =vec

,

Term .

- 2 -

2014 27 27 1

2* *vec i i i iE V VV V ,

1 1* * * * *1 , ,=vec opt i i i i i i i opt ibE E be VV V V VV e

1 1* * * *,

2 1 1* * * * *,

veci i i i opt i i i i

i i i opt i i i i i

E b

E b

V VV V e VV V

V VV e V VV V

(13)

EMSE SINR

.

2 12 * * 2 *

, min 1 2EMSE= = vecaE J I Fv

vRw R

min

SINR=EMSE+

s s

I n s

P PP P J P

(14)

GSC-APA

.

.

8 Sensor Array Desired

Signal 0 , Interference Signal

, -25°, 45°, 65 .

Signal-to-Noise Ratio 0dB ,

Interference-to-Noise Ration 30dB . 200

Independent trial

.

2 Step-size EMSE

Simulation

. K=1

Simulation

Step-size

. K=2, 4 Simulation

.

Step-size 3dB

.

3 SINR .

SINR .

K=1 EMSE

. SINR

Step-size

.

. Beamformer Correlated Signal

.

GSC-APA . GSC-APA

.

GSC-APA K

,

.

GSC-APA .

GSC-APA

. EMSE SINR

3dB

.

2. Step-size EMSE

3. Step-size SINR

Acknowledgements

This work was supported by the National research

Foundation of Korea (NRF) grant funded by the

Korea government (MEST)

(2012R1A2A2A01011112) and in part by the Ministry

of Science, ICT & Future Planning (MSIP), Korea,

under the Convergence Information Technology

Research Center (CITRC) support program

(NIPA-2014-H0401-14-1001) supervised by the

National IT Industry Promotion Agency (NIPA).

[1] C. Godara, ” Applications of antenna arrays to

mobile communications, Part II: Beam-forming

and direction-of-arrival considerations,” Proc.

IEEE, vol. 85, pp.1195-1245, Aug. 1997.

[2] G. V. Tsoulos, Adaptive Antennas for Wireless

- 3 -

2014 27 27 1

Communications, Wiley-IEEE, New York, 2001.

[3] O. L. Frost III, ” An algorithm for linearly

constrained adaptive array processing,” Proc.

IEEE, vol. 60, no. 8, pp.926-935, Aug. 1972.

[4] L. J. Griths and C.W. Jim, Alternative approach

to linear constrained adaptive beamforming,”

IEEE Transactions on AntennasPropag., vol.

AP-30, pp.27-34, Jan. 1982.

[5] S. Haykin, Adaptive Filter Theory, 4th ed. Upper

Saddle River, NJ: Prentice Hall, 2002

[6] A. H. Sayed, Fundamentals of Adaptive Filtering,

New York: Wiley, 2003

[7] Y.R. Zheng and R.A. Goubran,” Adaptive

beamforming using affine projection

algorithms,” in Proc. IEEE Int. Conf. Signal

Process., vol.3, pp.1929-1932, 2000.

[8] Yoganathan V.,” Switched Gri_ths-Jim

beamformer using the affine projection

algorithm,” Mechatronics and Machine Vision

in Practice,15th International Conference on,

pp.391-396, 2008.

- 4 -