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1 Reducing Observation Time f for Reliable Cyclostationarity R li bl C l i i Feature Extraction Feature Extraction Amy C. Malady and A.A. (Louis) Beex DSPRL Wireless@VT ECE Department Blacksburg, VA 24061-0111 SDR11-WInnComm

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SLIDE 1

1

Reducing Observation Time f R li bl C l i i for Reliable Cyclostationarity Feature Extraction Feature Extraction

Amy C. Malady and A.A. (Louis) Beex

DSPRL – Wireless@VT – ECE Department Blacksburg, VA 24061-0111

DSP Research Laboratory DSP Research Laboratory

SDR’11-WInnComm 1 DEC 2011

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SLIDE 2

Outline

2

Problem Statement and Motivation B k d M t i l Background Material

  • Cyclostationarity definitions

R b t t ti ti d fi iti

  • Robust statistics definitions
  • Feature extraction method

Si l ti R lt Simulation Results

  • Second-order first-conjugate observation time requirements

Si th d fi t j t b ti ti i t

  • Sixth-order first-conjugate observation time requirements

Conclusion

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SLIDE 3

Problem Statement and Motivation

3

  • Cyclostationarity
  • Cyclostationarity
  • interesting feature for detection and classification
  • many digital signals are inherently cyclostationary
  • many digital signals are inherently cyclostationary
  • feature extraction with minimal pre-processing

[Gardner-Napolitana-Paura 2006]

p p g

  • Promising reduction in SNR requirements shown

[Dobre-Abdi-Bar-Ness-Su 2006]

g q when using robust statistics

  • Drawback: long observation time

[Malady-Beex 2010]

Drawback: long observation time

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to be addressed here

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SLIDE 4

Research Goal

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Reduce observation time requirements for estimating cyclostationarity features for estimating cyclostationarity features through incorporation of robust statistics

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SLIDE 5

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Background Material Background Material

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SLIDE 6

Cyclostationarity Definitions

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Cycle frequency when CTMF nonzero

CTMF:

2 , ,

1 ( ) lim ( , ) 2 1

Z j t x n q x n q Z t Z

R L t e Z

   

   τ τ

CTMF nonzero

 

 

* , 1

( , ) ( ) ;

n q x n q j n

L t x t            

τ τ 

t Z 

[Gardner 1993]

1 j

 

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SLIDE 7

Cyclostationarity Estimate

7

2

1 ˆ ( ) ( )

T j t

R L

 

2 , ,

( ) ( , )

n

j t x n q x n q t

R L t e T

  

  τ τ

CTMFE:

theoretical estimate

estimation variation caused by a finite

  • bservation set

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BPSK

*CF = 6000/48000 = 0.125

CTMFE nonzero at non-cycle frequencies

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SLIDE 8

Cyclostationarity Estimate in the presence of noise

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BPSK BPSK NO AWGN SNR = 5 dB

AWGN further degrades ability to estimate cyclostationarity cyclostationarity

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Cycle frequency

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SLIDE 9

Robust Statistic Definitions

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 

2

(0) ( ,0)

n T j t

CMAD R L t e

  

   

 

, , (*) 1

(0) ( ,0) ( ) ( τ) ;τ

m

x n q n q x t n j

R L t e Tc x t L t   

 

             

 

 

 

, 1 1

( ,τ) ;τ

m

n q m n x j

L t CMAD  

 

          

Ψm(x)/a

1( ) m

x for x a x x a for x a

=

ì ï £ ï ï ï Y = í ï > ï

x/a

2( ) m

x for x a x for x a

=

ì ï £ ï Y = í ï > ï

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f x > ï ï ï î f > ï î

ˆ | |

CMAD

median x  q g

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SLIDE 10

Improvements from using the Robust CTMFE

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Robust

 

1 x

 Classic

 

1 m

x

distinct CF CF buried in noise

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BPSK @ SNR = 0 dB

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SLIDE 11

Statistical Test for Presence of Cycle Frequencies

11

  • 1. Search for a peak
  • 1. Search for a peak

SSB BPSK

|CTMF| |CTMF|

  • 2. Calculate

n q

[Dandawade-Giannakis 1994]

3

, n q ?

 

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3.

, n q

 

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SLIDE 12

Robust test vs. Classic Test

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Estimate CTMF Estimate robust CTMF Identify candidate CFs* (l l f |CTMFE|) Identify candidate CF* ( l b l f |CTMFE|) At least one peak No peak Calculate (local max of |CTMFE|) (global max of |CTMFE|) Calculate No cyclostationarity

 

Compare Compare No cyclostationarity

2,1

2,1

Compare Compare

2,1

  

2,1

   

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*Two methods to identify candidate CFs: local max and global max. Local max criteria: |CTMFE| at least ~4 times larger than “nearest neighbors.” (10000 bins in FFT, used nearest ~400 neighbors)

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SLIDE 13

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Observation Time Requirements Observation Time Requirements

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SLIDE 14

Simulation Results: Second-Order First-Conjugate Cyclostationarity Detection

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Cyclostationarity Detection

Observation time = 1500 symbols Sample rate = 100 kHz p Symbol rate = 10 kHz

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SLIDE 15

Simulation Results: Second-Order First-Conjugate Cyclostationarity Detection

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Cyclostationarity Detection

Sample rate = 100 kHz Symbol rate = 10 kHz y

Th b t ( lid) t (99 1)% li bilit

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The robust (solid) curves represent (99;1)% reliability; the classic (dashed) curves represent (90;1)% reliability.

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SLIDE 16

Simulation Results: Sixth-Order First-Conjugate Cyclostationarity Detection

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Cyclostationarity Detection

Observation time = 1500 symbols Sample rate = 100 kHz p Symbol rate = 10 kHz Note: 8PSK does Note: 8PSK does not exhibit 6,1* cyclostationarity

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SLIDE 17

Simulation Results: Sixth-Order First-Conjugate Cyclostationarity Detection

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Cyclostationarity Detection

Sample rate = 100 kHz Symbol rate = 10 kHz BPSK: m = 1 and m = 2 identical QPSK, m=1 (not shown) has 1 dB improvement Symbol rate 10 kHz Q , ( ) p Note: 8PSK does not exhibit 6,1* cyclostationarity

For classic and robust (99;1)% reliable detection of sixth order

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For classic and robust (99;1)% reliable detection of sixth-order first-conjugate cyclostationarity.

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SLIDE 18

Conclusions

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U f b t t ti ti d d b ti ti d/ i d

  • Use of robust statistics reduced observation time and/or improved

reliability for second-order first-conjugate CS feature detection

  • Sixth-order first-conjugate CS feature detection also quicker and/or

more reliable when using robust statistics

  • Compared performance of two different influence functions
  • Performance vs complexity trade-off

e o a ce vs co p e y ade o

  • Applications in detection and classification problems

D i t

  • Dynamic spectrum access
  • Monitoring

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Questions? Questions?

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References

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d li d l i i h lf f h [1]

  • W. Gardner, A. Napolitano, and L. Paura, Cyclostationarity: half a century of research,

Signal Processing 86 (4), pp. 639–697, 2006. [2] A. C. Malady and A. A. (Louis) Beex, "AMC Improvements from Robust Estimation", Proc. GLOBECOM 1 5 2010 GLOBECOM, pp. 1-5, 2010. [3] T. Biedka, L. Mili, and J. H. Reed, “Robust estimation of cyclic correlation in contaminated Gaussian noise”, Proc. 29th Asilomar Conference on Signals, Systems and Computers, pp. 511 515 Pacific Grove CA 1995 511-515, Pacific Grove, CA, 1995. [4]

  • O. A. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Cyclostationarity based blind classification
  • f analog and digital modulations,” Proc. IEEE MILCOM, Washington DC, USA, 2006.

[5] P J H ber Rob st Statistics Wile 1981 [5]

  • P. J. Huber, Robust Statistics, Wiley, 1981.

[6] A. V. Dandawade and G. B. Giannakis, “Statistical tests for presence of cyclostationarity,” IEEE Trans. SP, vol. 42, pp. 2355- 2369, 1994. [7] W A G d C l t ti it i C i ti d Si l P i N Y k [7]

  • W. A. Gardner, Cyclostationarity in Communications and Signal Processing. New York:

IEEE Press, 1993. [8] A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, Don Mills, Ont Canada: Addison Wesley 1989

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Ont., Canada: Addison-Wesley, 1989.