Reducing Observation Time f for Reliable Cyclostationarity R li bl - PowerPoint PPT Presentation

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 SDR’11-WInnComm 1 DEC 2011 DSP Research Laboratory DSP Research Laboratory

2 Outline Problem Statement and Motivation B Background Material k d M t i l - Cyclostationarity definitions - Robust statistics definitions R b t t ti ti d fi iti - Feature extraction method Simulation Results Si l ti R lt - Second-order first-conjugate observation time requirements - Sixth-order first-conjugate observation time requirements Si th d fi t j t b ti ti i t Conclusion DSP Research Laboratory DSP Research Laboratory

3 Problem Statement and Motivation - Cyclostationarity - Cyclostationarity - interesting feature for detection and classification - many digital signals are inherently cyclostationary - many digital signals are inherently cyclostationary [Gardner-Napolitana-Paura 2006] - feature extraction with minimal pre-processing p p g [Dobre-Abdi-Bar-Ness-Su 2006] - Promising reduction in SNR requirements shown g q when using robust statistics [Malady-Beex 2010] - Drawback: long observation time Drawback: long observation time to be addressed here DSP Research Laboratory DSP Research Laboratory

4 Research Goal Reduce observation time requirements for estimating cyclostationarity features for estimating cyclostationarity features through incorporation of robust statistics DSP Research Laboratory DSP Research Laboratory

5 Background Material Background Material DSP Research Laboratory DSP Research Laboratory

6 Cyclostationarity Definitions Cycle frequency when CTMF nonzero CTMF nonzero 1 Z      j 2 t R ( ) τ lim L t ( , ) τ e CTMF: x n q , x n q , 2 Z 1  Z   t t Z Z [Gardner 1993]   n       t      q * L t ( , ) τ x ( ) ; τ    x n q , j 1 n     j  1 DSP Research Laboratory DSP Research Laboratory

7 Cyclostationarity Estimate T   1  ˆ ( )     j j 2 2 t t R R ( ) τ L L ( , ) ( t τ ) e CTMFE: x n q , x n q , T n  t 0 theoretical estimation variation estimate caused by a finite observation set *CF = 6000/48000 = 0.125 CTMFE nonzero at BPSK non-cycle frequencies DSP Research Laboratory DSP Research Laboratory

8 Cyclostationarity Estimate in the presence of noise BPSK BPSK NO AWGN SNR = 5 dB AWGN further degrades ability to estimate cyclostationarity cyclostationarity Cycle frequency DSP Research Laboratory DSP Research Laboratory

9 Robust Statistic Definitions n CMAD T       j 2 t R R (0) (0) L L ( ,0) ( ,0) t t e e       x n q , n q , x Tc m  t 0       x t ( ) n       j         (*) L L ( , τ ) ( τ ) t t     ; τ ; τ               n q , m 1 1 n x CMAD   m    j 1 Ψ m (x)/a ì ï £ x for x a x/a ï ì ï £ x for x a ï ï ï Y = í Y = í 2 ( ) x 1 ( ) x x = ï = ï m m > > > > a f for x a 0 f for x a ï ï ï ï î ï x ï î ˆ q g  median x | | CMAD DSP Research Laboratory DSP Research Laboratory

10 Improvements from using the Robust CTMFE       Robust Classic 1 x x  m 1 distinct CF CF buried in noise BPSK @ SNR = 0 dB DSP Research Laboratory DSP Research Laboratory

11 Statistical Test for Presence of Cycle Frequencies 1. Search for a peak 1. Search for a peak SSB BPSK |CTMF| |CTMF|  2. Calculate [Dandawade-Giannakis 1994] n q n q , ?     3. 3 n q , DSP Research Laboratory DSP Research Laboratory

12 Robust test vs. Classic Test Estimate robust CTMF Estimate CTMF Identify candidate CFs* Identify candidate CF* At least one peak No peak (l (local max of |CTMFE|) l f |CTMFE|) (global max of |CTMFE|) ( l b l f |CTMFE|) Calculate Calculate     No cyclostationarity No cyclostationarity 2,1 2,1 Compare Compare Compare Compare        2,1 2,1 *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 ) DSP Research Laboratory DSP Research Laboratory

13 Observation Time Requirements Observation Time Requirements DSP Research Laboratory DSP Research Laboratory

14 Simulation Results: Second-Order First-Conjugate Cyclostationarity Detection Cyclostationarity Detection Observation time = 1500 symbols Sample rate = 100 kHz p Symbol rate = 10 kHz DSP Research Laboratory DSP Research Laboratory

15 Simulation Results: Second-Order First-Conjugate Cyclostationarity Detection Cyclostationarity Detection Sample rate = 100 kHz Symbol rate = 10 kHz y Th The robust (solid) curves represent (99;1)% reliability; b t ( lid) t (99 1)% li bilit the classic (dashed) curves represent (90;1)% reliability. DSP Research Laboratory DSP Research Laboratory

16 Simulation Results: Sixth-Order First-Conjugate Cyclostationarity Detection 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 DSP Research Laboratory DSP Research Laboratory

17 Simulation Results: Sixth-Order First-Conjugate Cyclostationarity Detection Cyclostationarity Detection BPSK: m = 1 and m = 2 identical Sample rate = 100 kHz Q QPSK, m=1 (not shown) has 1 dB improvement , ( ) p Symbol rate 10 kHz Symbol rate = 10 kHz Note: 8PSK does not exhibit 6,1* cyclostationarity For classic and robust (99;1)% reliable detection of sixth order For classic and robust (99;1)% reliable detection of sixth-order first-conjugate cyclostationarity. DSP Research Laboratory DSP Research Laboratory

18 Conclusions - Use of robust statistics reduced observation time and/or improved U f b t t ti ti d d b ti ti d/ i d 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 - Dynamic spectrum access D i t - Monitoring DSP Research Laboratory DSP Research Laboratory

19 Questions? Questions? DSP Research Laboratory DSP Research Laboratory

20 References [1] W. Gardner, A. Napolitano, and L. Paura, Cyclostationarity: half a century of research, d li d l i i h lf f h Signal Processing 86 (4), pp. 639–697, 2006. [2] A. C. Malady and A. A. (Louis) Beex, "AMC Improvements from Robust Estimation", Proc. GLOBECOM GLOBECOM, pp. 1-5, 2010. 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 of analog and digital modulations,” Proc. IEEE MILCOM, Washington DC, USA, 2006. [5] [5] P J H ber Rob st Statistics Wile P. J. Huber, Robust Statistics, Wiley, 1981. 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] [7] W A G d W. A. Gardner, Cyclostationarity in Communications and Signal Processing. New York: C l t ti it i C i ti d Si l P i N Y k IEEE Press, 1993. [8] A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, Don Mills, Ont Canada: Addison Wesley 1989 Ont., Canada: Addison-Wesley, 1989. DSP Research Laboratory DSP Research Laboratory