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Adaptive Multitaper Spectral Detector for Wideband Spectrum Sensing in Strong Interference

EnvironmentStudent: Jung-Mao Lin

Advisor: Danijela Cabric and Hsi-Pin Ma

March 12, 2010

Jung-Mao Lin

Outlines

• Introduction• System Design

– Wideband Sensing– Narrowband Sensing

• Simulation Results• Future Works• Conclusions

Jung-Mao Lin

Introduction

Jung-Mao Lin

• Spectrum sensing – Matched-filter detection [1], [2]

• Resistant to noise but prior knowledge of primary user (PU) is required

– Energy detection [3], [4]• Simplest method but vulnerable to noise

– Autocorrelation- and cyclostationary-based detection [5]−[7]

• Without knowing noise level but periodic or cyclic features are required in the transmitted signal

Motivation (1/2)

Jung-Mao Lin 5

Motivation (2/2)

-2005 Haykin (Guidelines & Concepts) [10]

-2007 Erpek, Leu, and Mark (TV bands) [11]

-1982 Thomson (Multitapter Spectral Estimation, MTSE)

[9]

-1978 Slepian (Discrete Prolate Spheroidal Sequence,

DPSS) [8]

?

Jung-Mao Lin 6

Discrete Prolate Spheroidal Sequence (DPSS)N=256, NW=4

1st order

3rd order

2nd order

4th order

Jung-Mao Lin

Strong Interference in Wideband Environment

7

Jung-Mao Lin

System Design

Jung-Mao Lin

System Block Diagram

9

Jung-Mao Lin

Adaptive Multitaper Spectral Estimation (AMTSE)

∑

∑

=

== K

tt

K

t

mttt

fd

fSfdfS

1

2

1

)(2

)(

)(ˆ)()(ˆ

{ })()(ˆ)(ˆ

)(fBfS

fSfd

kk

kt E+

=λ

λ

21

0

2)( ][][)(ˆ ∑−

=

−⋅⋅=N

n

nfjt

mtt enhnxfS π

( )∑−

=

−1

0

2 1][N

nknx λ 1

1

42

1

2 )()(2−

==⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡= ∑∑

K

tt

K

tt fdfdν

DPSS windows

Input time sequence

Degree of Freedom (DoF)

∑=

=K

t

mtt

ini fSK

fS1

)()( )(ˆ1)(ˆ

10

Jung-Mao Lin

Wideband Locally Most Powerful Detector (LMPD) (1/6)

• Let Y1, Y2, … , YN be a stationary m-dependent sequence with finite variance

where

Then,

( )[ ]ilkmt

i

N

iiN fSYYS +

−

=

==∑ ,)(

1

0

ˆln ,

( ) 2,,

)( )(~ˆ

νχνlk

lkmt fS

fS

Sampled PSD

Chi-Square

( )2 ,~ σμ NNS YN Ν

( )[ ]{ } ( )[ ] ( ) ( )

( )[ ] ( )ν

νψνμ

gfS

fSfS

k

kkmt

Y

+=

⎟⎠⎞

⎜⎝⎛++−==

ln 2

2lnlnlnˆlnE )(

Digamma Function

11

Jung-Mao Lin

20

201

200

2 22 mσσσσ ++≈

{ } { }( ) ( ) ( ) ( )

( ) ( ){ } ( ) ( )[ ] ( )νρννχχ

μχν

χν

μσ

νν

νν

gg

fSfS

YYYYCov

iill

ilk

lk

illilli

Y

Y

′−=+−⋅=

−⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡+⎟⎠⎞

⎜⎝⎛

⎥⎦

⎤⎢⎣

⎡+⎟⎠⎞

⎜⎝⎛=

−⋅==

+

+

++

22,

2,

22,

2,

220

lnlnlnE

lnlnlnlnE

E,

( )[ ]{ } ( ) ( ) ⎟⎠⎞

⎜⎝⎛′=

⎭⎬⎫

⎩⎨⎧

+⎟⎠⎞

⎜⎝⎛==

2lnlnVarˆlnVar 2

,)(2

00νψχ

νσ ν l

kk

mt fSfS

TrigammaFunction

( )[ ] ( )[ ]νρνρνψσσσσ gg mm ′−+′−+⎟

⎠⎞

⎜⎝⎛′=++≈ 22

222 12

0201

200

2

Wideband Locally Most Powerful Detector (LMPD) (2/6)

If for simplicity, assume mρρρρ ≈≈= 21

( )[ ] νηρνρνψσ ,2 22

2 mmgm +=′−+⎟⎠⎞

⎜⎝⎛′≈⇒

12

Jung-Mao Lin

• Binary hypothesis test :

• Log Likelihood Ratio Test (LLRT) :

Wideband Locally Most Powerful Detector (LMPD) (3/6)

( ) ( ) ( )

( ) ( ) ( ) 2,

)(1

2,

)(0

)(~ˆ ; :

)(~ˆ ; :

ν

ν

χν

χν

kRxlk

mtkRxk

knlk

mtknk

fSfSfSfSH

fSfSfSfSH

=

=

( ) ( )( )

( )[ ]( )[ ]⎩

⎨⎧

====

=⇒kRxkRx

knkn

N

NNG SfS

SfSHSpHSpSL

,1

,0

00

11

lnln

,;,;

θθ

ξθθ

( ) [ ] ( )

( )[ ] ( ) ( )[ ]( ){ }( )ν

ν ηρνηρπ

μσ

πσθ

,

2

,

22

2

22ln22ln

21

212ln

21,;ln

mi

kiNmi

iNi

iiiN

mNfSgNSm

NSN

NHSp

++−

−+−≈

−−−=⇒

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Jung-Mao Lin

• LMP Test

Wideband Locally Most Powerful Detector (LMPD) (4/6)

( ) ( ) ( ) ( ) ( )

00

2

2

001

LMP;lnE , ;ln

θθθθ θθθθ

θθ

=

−

=⎥⎦

⎤⎢⎣

⎡∂

∂−=⋅

∂∂

= NNN

SpIISpST

( ) ( )[ ]νηρ

ν

,2;ln

m

kN

k

kN

mSgNS

SSSp

++−

=∂

∂

( )νηρ ,

2

2

2;ln

mk

kN

mN

SSSp

+−

=∂

∂

( ) ( )[ ]N

mm

SgNSST m

m

knNN

ν

ν

ηρηρ

ν ,

,

,LMP

22

++++−

=⇒

Test Statistic

14

Fisher Information Matrix

Jung-Mao Lin

Wideband Locally Most Powerful Detector (LMPD) (5/6)

• Assume (Asymptotically Performance)∞→N

( ) ( )( )( )( )

, 1 ,IN , 1 0,N

~1010

0LMP

⎩⎨⎧

−⇒

HH

ST N θθθ

( ){ } ( ) ( )FA1

0LMPFA Pr PQQHSTP N−=⇒=>=⇒ ξξξ

( ){ } ( )( )

( ) ( )[ ] ( )[ ]( )

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛+

+−=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=>=⇒

−

−

SNR1ln2

lnln2

1I

Pr

,FA

1

,FA

1

0101LMPD

ν

ν

ηρ

ηρ

θθθξξ

m

knkRxm

N

mNPQQ

fSfSm

NPQQ

QHSTP

( )( ) SNR1 Assume +=

kn

kRx

fSfS

( )ννψη ν gmm ′−⎟⎠⎞

⎜⎝⎛′= 2

2, 15

Jung-Mao Lin

• Detection performance

• Minimum required observations

( )( )[ ]

( )⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+′−+⎟

⎠⎞

⎜⎝⎛′

−= − SNR1ln2

2

FA1

D

νρνψ gm

NPQQP

Monotonically Decreasing

Monotonically Decreasing

( )[ ] ( ) ( )[ ]( )[ ]2

2D

1FA

1

SNR1ln2

2 +−

⎭⎬⎫

⎩⎨⎧ ′−+⎟

⎠⎞

⎜⎝⎛′=

−− PQPQgmN νρνψ

Wideband Locally Most Powerful Detector (LMPD) (6/6)

Jung-Mao Lin

NW=3, K=1~5FFT=1024,

BW=500 MHz( ) ( ){ }( ) ( ) ( )

( ) ( )

( ) ( )

( ) ( ) ( ) ( )

( ) ( )( )

21

0

22

2

21

0

222

22

2*

,0,

assume and ,0 Since

,

*

ˆ,ˆcov

∑

∑

∫

−

=

−

−

=

−

=≡

+≈=

≡=

≈

⋅−+⋅−≈

+

N

t

tjt

N

t

tjt

(mt)(mt)

ehfRfRR

fSfSfSfR

fRehfS

HHfS

duuSufHufH

fSfS

πη

πη

ηη

η

η

η

η

η

Decimation in Frequency

Narrowband Sensing (1/4)

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Jung-Mao Lin

• Setand assume all the are independent and identically distributed (i.i.d.)

• Assume TLRT is Gaussian distributed according to Central Limit Theorem

Test Statistic

Narrowband Sensing (2/4)

( )( ) ( )[ ] ξ ˆln fˆ1

0

)()(LRT ∑

−

=

=N

kk

mtmt fST S

( )( ) ( )( )

, ,N , ,N

~fˆ1

211

02

0)(LRT

0

⎩⎨⎧

⇒HH

T mt

σμσμ

S

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Jung-Mao Lin

Narrowband Sensing (3/4)

( )( ){ } ( ) ( ) ( )[ ]∑−

=

+⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛++−==

1

00

)(LRT0 ln

22lnln ;fˆ E

N

kkn

mt fSNHT νψνμ S

( )( ){ } ( ){ } ⎟⎠⎞

⎜⎝⎛′⋅=== ∑

−

= 2lnV ;fˆ V

1

0

20

)(LRT

20

νψχσ ν NarHTarN

k

mtS

( )( ){ } ( ) ( ) ( )[ ]∑−

=

+⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛++−==

1

01

)(LRT1 ln

22lnln ;fˆ E

N

kkRx

mt fSNHT νψνμ S

( )( ){ } ( ){ } ⎟⎠⎞

⎜⎝⎛′⋅=== ∑

−

= 2lnV ;fˆ V

1

0

21

)(LRT

21

νψχσ ν NarHTarN

k

mtS

19

Jung-Mao Lin

( )[ ]( ) ( )[ ]

( )[ ]22

D1

FA1

2 SNR1ln2

SNR1ln2

+

⎟⎠⎞

⎜⎝⎛′

∝−+

⎟⎠⎞

⎜⎝⎛′

= −−

νψνψPQPQN

• Detection performance

• Minimum required observations

( ) ( )⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+⋅⋅

⎟⎠⎞

⎜⎝⎛′

−= − SNR1ln

2

1FA

1D NPQQP

νψ

Narrowband Sensing (4/4)

Jung-Mao Lin

• The noise uncertainty model [12]

• Detection performance

• Minimum required observations

Noise Uncertainty

SNR Wall

Jung-Mao Lin

Simulation Results

Jung-Mao Lin

Narrowband DetectionPU = WGN

N=8, SNR=0dB PFA=10-3

[5][4]

[4]

[5]

Jung-Mao Lin

Wideband DetectionPU = QPSK, Fs=64MHz, FFT=128

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of False Alarm (PFA)

Pro

babi

lity

of D

etec

tion

(PD

)

AMTSE Det. (theo.), NW=3, K=2AMTSE Det. (sim.), NW=3, K=2AMTSE Det. (theo.), NW=3, K=3AMTSE Det. (sim.), NW=3, K=3

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of False Alarm (PFA)

Pro

babi

lity

of D

etec

tion

(PD

)

AMTSE Det. (theo.), NW=3, K=2AMTSE Det. (sim.), NW=3, K=2AMTSE Det. (theo.), NW=3, K=3AMTSE Det. (sim.), NW=3, K=3

N=16, SNR=0dB, BW=1M, m=1

N=16, SNR=0dB, BW=2M, m=1

Jung-Mao Lin

Minimum Required Observations (W/ Noise Uncertainty)

-40 -35 -30 -25 -20 -15 -10 -5 010

0

102

104

106

108

1010

1012

1014

1016

SNR (dB)

Min

imum

Req

uire

d S

ampl

e P

oint

s (lo

g10

N)

Energy.(anal.)Prop.(anal.), K=2Prop.(anal.), K=4Prop.(anal.), K=2, noise uncertaintyProp.(anal.), K=4, noise uncertaintyEnergy.(anal.), noise uncertainty

x=1dB

x=0.001dB

x=0.1dB

PD=PFA=10-3

Jung-Mao Lin

Future Works

• Fine sensing– Mixer, low pass filter, and AMTSE narrowband detector– Strong interference suppression

• Whole wideband sensing system construction– Two stages detection– Performance evaluation

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Jung-Mao Lin

• A wideband AMTSE detector based on LMP test and a narrowband AMTSE detector, including mathematical formulation and numerical analysis, is presented.

• By providing a higher order degree of freedom (DoF) from multitaper gain, the provided AMTSE detector is more reliable in detection performance or has less required observations compared to others.

• By taking advantage of multitaper estimation, the provided detector can achieve a non-parametric detection without the prior knowledge of PU.

Conclusions

Jung-Mao Lin

References

[1] D. Middleton, “On the detection of stochastic signals in additive normal noise -Part I,” IEEE Trans. Inf. Theory, vol. 3, pp. 86–121, June 1957.

[2] T. Yucek and H. Arslan, “Spectrum characterization for opportunistic cognitiveradio systems,” in Proc. IEEE MILCOM ’06, Washington, DC, Oct. 2006, pp.1–6.

[3] T. Ikuma and M. Naraghi-Pour, “A comparison of three classes of spectrumsensing techniques,” in Proc. IEEE GLOBECOM ’08, New Orleans, LO, Nov.2008, pp. 1–5.

[4] S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory.Englewood Cliffs, NJ: Prentice-Hall PTR, 1998.

Jung-Mao Lin

[5] S. Chaudhari, V. Koivunen, and H. V. Poor, “Distributed autocorrelation-basedsequential detection of OFDM signals in cognitive radios,” in Proc. IEEECrownCom ’07, Singapore, May 2008, pp. 1–6.

[6] W. Gardner, “Signal interception: A unifying theoretical framework for featuredetection,” IEEE Trans. Commun., vol. 36, pp. 897–906, Aug. 1988.

[7] J. Lunden, V. Koivnen, A. Huttunen, and H. V. Poor, “CollaborativeCyclostationary Spectrum Sensing for Cognitive Radio Systems,” IEEE Trans.Signal Process., vol. 57, no. 11, pp. 4182–4195, Dec. 1992.

[8] D. Slepian, “Prolate spheroidal wave functions, Fourier analysis anduncertainty – V: The discrete case,” Bell Syst. Tech. J., vol. 57, pp. 1371–1429, 1978.

[9] D. J. Thomson, “Spectrum estimation and harmonic analysis,” Proc. IEEE,vol. 20, pp. 1055–1096, Sep. 1982.

[10] S. Haykin, “Cognitive radio: Brain-empowered wireless communications,”IEEE J. Sel. Areas Commun., vol. 23, no. 3, pp. 201–205, Feb. 2005.

Jung-Mao Lin

[11] T. Erpek, A. Leu, and B. L. Mark, “Spectrum sensing performance in TV bands using the multitaper method,” in Proc. IEEE 15th Signal Processing and Communication Applications Conf., Eskisehir, Turkey, Jun. 2007, pp. 1–4.

[12] R. Tandra and A. Sahai, “SNR walls for signal detection,” IEEE J. Sel. Topics Signal Process., vol. 2, no. 1, pp. 4–17, Feb. 2008.

Jung-Mao Lin

Appendix

Jung-Mao Lin

Noise Uncertainty

32