1. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 1 Spectrum Sensing of the DTV in the Vicinity of the Pilot Using Higher Order Statistics IEEE P802.22 Wireless RANs Date: 2007-08-07 Authors: Notice: This document has been prepared to assist IEEE 802.22. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor grants a free, irrevocable license to the IEEE to incorporate material contained in this contribution, and any modifications thereof, in the creation of an IEEE Standards publication; to copyright in the IEEEs name any IEEE Standards publication even though it may include portions of this contribution; and at the IEEEs sole discretion to permit others to reproduce in whole or in part the resulting IEEE Standards publication. The contributor also acknowledges and accepts that this contribution may be made public by IEEE 802.22. Patent Policy and Procedures: The contributor is familiar with the IEEE 802 Patent Policy and Procedures http://standards.ieee.org/guides/bylaws/sb-bylaws.pdf including the statement "IEEE standards may include the known use of patent(s), including patent applications, provided the IEEE receives assurance from the patent holder or applicant with respect to patents essential for compliance with both mandatory and optional portions of the standard." Early disclosure to the Working Group of patent information that might be relevant to the standard is essential to reduce the possibility for delays in the development process and increase the likelihood that the draft publication will be approved for publication. Please notify the Chairhttp://standards.ieee.org/guides/bylaws/sb-bylaws.pdf Carl R. StevensonCarl R. Stevenson as early as possible, in written or electronic form, if patented technology (or technology under patent application) might be incorporated into a draft standard being developed within the IEEE 802.22 Working Group. If you have questions, contact the IEEE Patent Committee Administrator at patcom@iee.org.patcom@iee.org >

2. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 2 Abstract DTV Signals in Gaussian noise using Higher Order Statistics (HOS).We present an algorithm to detect the DTV Signals in Gaussian noise using Higher Order Statistics (HOS). The algorithm performs non-Gaussianity check in the frequency domain in the vicinity of the Pilot The Average results for all the 12 provided DTV SignalsThe Average results for all the 12 provided DTV Signals: At P FA = 0.04, –For a capture of 5mS (continuous or staggered) P D = 0.9 at an SNR = -16.6 dB. –For a capture of 10 mS (continuous or staggered), P D = 0.9 at SNR = -18.6 dB –For a capture of 20 mS (continuous or staggered), P D = 0.9 at SNR = -21.6 dB –For a capture of 40 mS (continuous or staggered), P D = 0.9 at SNR = -23.7 dB We use a 2048 point FFT to implement the algorithm which may be used for Spectrum Sensing as well as OFDMA demodulation. Because of the Constant False Alarm Rate (CFAR) nature of the detector, the threshold is built into the technique and NO Presetting is required. Fine adjustment is possible if needed. used for the detection of wireless microphone as well as DVB-T signals as well (future contribution)..The proposed algorithm can be used for the detection of wireless microphone as well as DVB-T signals as well (future contribution)..

3. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 3 DTV Signal Characteristics

4. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 4 DTV Signal Gaussianity Check in Time and Frequency Domains Our technique relies on the non-Gaussianity of a signal to separate it from the Gaussian noise. In the Time Domain, DTV Signals show a Gaussian characteristic. However, in the Frequency Domain they are non-Gaussian. We will exploit this characteristic to detect the signals in AWGN.

5. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 5 Signal or Noise Identification Using Higher Order Statistics (HOS) Higher Order Statistics (HOS)Use of Higher Order Statistics (HOS) is an efficient metric for detecting non-Gaussian signals at low SNRs. In particular, if we assume the noise to be a Gaussian random process, then all the Cumulants of Order greater than 2 are supposed to be nearly zero. Given a set of N samples x = {x 0, x 1, …, x N-1 }, of a random variable x, the r th order Moment of the collection of samples contained in the set (x) may be approximated as

6. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 6 m r = r th order moment of the random variable x and c r = r th order cumulant of x. cumulants We can then exploit the relationship between the moments and cumulants to compute the higher order cumulants as Signal or Noise Identification Using Higher Order Statistics (HOS)

7. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 7 Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing threshold Class Signal or Class NoiseSince our data record for the determination of the HOS is not infinitely long, the cumulants of Order Greater than 2 may not be exactly zero. Hence, some threshold needs to be set in order to make a decision as to whether the samples belong to Class Signal or Class Noise. For our case, we compare the higher order cumulants with the power of second order moment. This is also known as Bi-coherency Tri-coherency etc. tests to determine if the received waveform belongs to the Class Signal or Class Noise.

8. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 8 Signal Detection for DTV Signals in the Vicinity of the Pilot – Block Diagram of the Algorithm

9. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 9 Distribution of Signal and Noise in the Time Domain after Down-sampling Distribution of (Signal + Noise) in the Time Domain Distribution of Noise in the Time Domain

10. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 10 Distribution of Signal and Noise in the Frequency Domain after Down-sampling Distribution of (Signal + Noise) in the Frequency Domain Distribution of Noise in the Frequency Domain

11. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 11 Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing ALGORITHM R greater than two available XLet R be the number of moments (m r_real, m r_imaginary ) and cumulants (c r_real, c r_imaginary ) of the order greater than two available for computation of the real and the imaginary parts of each of the segments (X) of data respectively, = 0.5 / RChoose a Probability Step Parameter 0 < δ < 1; For example let = 0.5 / R. P Signal_real = P Signal_imaginary = 0.5;Let P Signal_real = P Signal_imaginary = 0.5; γ > 0; typical = 1Choose some γ > 0; typical = 1 (Continued)

12. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 12 Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing ALGORITHM for r = 3 to (R + 2); if |c r_real | P Signal_real = P Signal_real - δ, elseif |c r_real | γ| m 2_real | r/2, => P Signal_real = P Signal_real + δ end, if |c r_imaginary | P Signal_imaginary = P Signal_imaginary - δ, elseif |c r_imaginary | γ| m 2_imaginary | r/2, => P Signal_imaginary = P Signal_imaginary + δ end, end (Continued)

13. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 13 Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing ALGORITHM P Signal = aP Signal_real + bP Signal_imaginary a = b = 0.5P Signal = aP Signal_real + bP Signal_imaginary where a and b weight parameters. As an example a = b = 0.5 if P Signal 0.5 then X belongs to Class Signal, and the DTV Signal is detected.if P Signal 0.5 then X belongs to Class Signal, and the DTV Signal is detected. if P Signal < 0.5 then X belongs to Class Noise and the DTV Signal is not detected.if P Signal < 0.5 then X belongs to Class Noise and the DTV Signal is not detected. The parameter γ is used to make fine adjustments of P FA if needed. As increases P FA decreases and vice-versa. In most cases is kept close to unity.

14. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 14 Signal Detection for DTV Signals Signal 1WAS_32_48_06012000_OPT_short Signal 2WAS_86_48_07122000_REF_short Signal 3WAS_51_35_05242000_REF_short Signal 4WAS_68_36_05232000_REF_short Signal 5WAS_47_48_06132000_OPT_short Signal 6WAS_49_39_06142000_OPT_short Signal 7WAS_06_34_06092000_REF_short Signal 8WAS_49_34_06142000_OPT_short Signal 9WAS_311_35_06052000_REF_short Signal 10WAS_3_27_06022000_REF_short Signal 11WAS_311_48_06052000_REF_short Signal 12WAS_311_36_06052000_REF_short

15. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 15 Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance for 5 mS Sensing Duration, = 0.8 and 1.05, R = 4, a=b=1 = 0.8, P D > 0.9 and P FA < 0.05 = 1.05, P D > 0.9 and P FA = 0.01

16. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 16 Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance for 10 mS Sensing Duration, = 0.8 and 1.05, R = 4, a=b=1 = 0.8, P D > 0.9 and P FA < 0.05 = 1.05, P D > 0.9 and P FA = 0.01

17. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 17 Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance for 20 mS Sensing Duration, = 0.8 and 1.05, R = 4, a=b=1 = 0.8, P D > 0.9 and P FA < 0.05 = 1.05, P D > 0.9 and P FA = 0.01

18. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 18 Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance for 40 mS Sensing Duration, = 0.8 and 1.05, R = 4, a=b=1 = 0.8, P D > 0.9 and P FA < 0.05 = 1.05, P D > 0.9 and P FA = 0.01

19. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 19 Signal Detection for DTV Signals in the Vicinity of the Pilot – Average(P D and P FA ) for the 12 Provided Signals vs Fine Threshold Adjustment Parameter (, R = 4, a=b=1

20. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 20 Conclusions DTV Signals in Gaussian noise using Higher Order Statistics (HOS).We presented an algorithm to detect the DTV Signals in Gaussian noise using Higher Order Statistics (HOS). The algorithm performs non-Gaussianity check in the frequency domain in the vicinity of the Pilot The average results for all the 12 provided DTV SignalsThe average results for all the 12 provided DTV Signals: At P FA = 0.04, –For a capture of 5mS (continuous or staggered) P D = 0.9 at an SNR = -16.6 dB. –For a capture of 10 mS (continuous or staggered), P D = 0.9 at SNR = -18.6 dB –For a capture of 20 mS (continuous or staggered), P D = 0.9 at SNR = -21.6 dB –For a capture of 40 mS (continuous or staggered), P D = 0.9 at SNR = -23.7 dB We used a 2048 point FFT to implement the algorithm which may be used for Spectrum Sensing as well as OFDMA demodulation. Because of the Constant False Alarm Rate (CFAR) nature of the detector, the threshold is built into the technique and NO Presetting is required. Fine adjustment is possible if needed. used for the detection of wireless microphone as well as DVB-T signals as well (future contribution).The proposed algorithm can be used for the detection of wireless microphone as well as DVB-T signals as well (future contribution).

21. doc.: IEEE 802.22-07/0359r1 Submission August 2007 Apurva N. Mody, BAE SystemsSlide 21 References S. K. Shanmugan, A. M. Breipohl, Random Signals, Detection Estimation and Data Analysis, John Wiley and Sons, 1988. S. M. Kay, Fundamentals of Statistical Signal Processing, Detection Theory, Prentice Hall Signal Processing Series, 1993. S. M. Kay, Fundamentals of Statistical Signal Processing, Estimation Theory, Prentice Hall Signal Processing Series, 1993. IEEE 802.22 Contribution 22-07-0359-00-0000 at http://grouper.ieee.org/groups/802/22/Meeting_documents/2007_July/22-07-0359-00- 0000_mody_spectrum_sensing_hos_1.ppt22-07-0359-00-0000 http://grouper.ieee.org/groups/802/22/Meeting_documents/2007_July/22-07-0359-00- 0000_mody_spectrum_sensing_hos_1.ppt