August 2007

Apurva N. Mody, BAE Systems

Slide 1

doc.: IEEE 802.22-07/0359r1

Submission

Spectrum Sensing of the DTV in the Vicinity of the Pilot Using Higher Order Statistics

IEEE P802.22 Wireless RANs Date: 2007-08-07

Name Company Address Phone email Apurva N. Mody BAE Systems P. O. Box 868,

MER 15-2350, Nashua, NH 03061

1-404-819-0314

apurva.mody@baesystems.com apurva_mody@yahoo.com

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 IEEE’s name any IEEE Standards publication even though it may include portions of this contribution; and at the IEEE’s 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 Chair Carl 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.>

August 2007

Apurva N. Mody, BAE Systems

Slide 2

doc.: IEEE 802.22-07/0359r1

Submission

Abstract• We present an algorithm to detect the DTV Signals in Gaussian noise using DTV Signals in Gaussian noise using

Higher Order Statistics (HOS).Higher Order Statistics (HOS). • The algorithm performs non-Gaussianity check in the frequency domain in the

vicinity of the Pilot• The The AverageAverage results for all the 12 provided DTV Signals results for all the 12 provided DTV Signals: At PFA = 0.04,

– For a capture of 5mS (continuous or staggered) PD = 0.9 at an SNR = -16.6 dB. – For a capture of 10 mS (continuous or staggered), PD = 0.9 at SNR = -18.6 dB – For a capture of 20 mS (continuous or staggered), PD = 0.9 at SNR = -21.6 dB – For a capture of 40 mS (continuous or staggered), PD = 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.

• The proposed algorithm can be used for the detection of wireless microphone as used for the detection of wireless microphone as well as DVB-T signals as well (future contribution)..well as DVB-T signals as well (future contribution)..

August 2007

Apurva N. Mody, BAE Systems

Slide 3

doc.: IEEE 802.22-07/0359r1

Submission

DTV Signal CharacteristicsDTV Signal Characteristics

August 2007

Apurva N. Mody, BAE Systems

Slide 4

doc.: IEEE 802.22-07/0359r1

Submission

DTV Signal Gaussianity Check in Time and DTV Signal Gaussianity Check in Time and Frequency DomainsFrequency 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.

August 2007

Apurva N. Mody, BAE Systems

Slide 5

doc.: IEEE 802.22-07/0359r1

Submission

Signal or Noise Identification Using Higher Order Statistics (HOS)Signal or Noise Identification Using Higher Order Statistics (HOS)

• Use of Higher Order Statistics (HOS)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 = {x0, x1, …, xN-1}, of a random variable x, the rth order Moment of the collection of samples contained in the set (x) may be approximated as

August 2007

Apurva N. Mody, BAE Systems

Slide 6

doc.: IEEE 802.22-07/0359r1

Submission

mr = rth order moment of the random variable x and

cr = rth order cumulant of x.

We can then exploit the relationship between the moments and cumulants to compute the higher order cumulantscumulants as

Signal or Noise Identification Using Higher Order Statistics (HOS)Signal or Noise Identification Using Higher Order Statistics (HOS)

August 2007

Apurva N. Mody, BAE Systems

Slide 7

doc.: IEEE 802.22-07/0359r1

Submission

Signal or Noise Identification Using Higher Order Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis TestingStatistics (HOS) – Hypothesis Testing

• Since 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 thresholdthreshold needs to be set in order to make a decision as to whether the samples belong to Class Signal or Class NoiseClass 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-coherencyTri-coherency etc. tests to determine if the received waveform belongs to the Class Signal or Class Noise.

August 2007

Apurva N. Mody, BAE Systems

Slide 8

doc.: IEEE 802.22-07/0359r1

Submission

Signal Detection for DTV Signals in the Vicinity of the Signal Detection for DTV Signals in the Vicinity of the Pilot – Block Diagram of the AlgorithmPilot – Block Diagram of the Algorithm

August 2007

Apurva N. Mody, BAE Systems

Slide 9

doc.: IEEE 802.22-07/0359r1

Submission

Distribution of Signal and Noise in the Time Distribution of Signal and Noise in the Time Domain after Down-samplingDomain after Down-sampling

Distribution of (Signal + Noise) in the Time Domain

Distribution of Noise in the Time Domain

August 2007

Apurva N. Mody, BAE Systems

Slide 10

doc.: IEEE 802.22-07/0359r1

Submission

Distribution of Signal and Noise in the Frequency Distribution of Signal and Noise in the Frequency Domain after Down-samplingDomain after Down-sampling

Distribution of (Signal + Noise) in the Frequency Domain

Distribution of Noise in the Frequency Domain

August 2007

Apurva N. Mody, BAE Systems

Slide 11

doc.: IEEE 802.22-07/0359r1

Submission

Signal or Noise Identification Using Higher Order Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis TestingStatistics (HOS) – Hypothesis Testing

ALGORITHMALGORITHM• Let RR be the number of moments (mr_real, mr_imaginary) and cumulants (cr_real,

cr_imaginary) of the order greater than two availablegreater than two available for computation of the real and the imaginary parts of each of the segments (XX) of data respectively,

• Choose a Probability Step Parameter 0 < δ < 1; For example let = 0.5 / R = 0.5 / R.

• Let PPSignal_realSignal_real = = PPSignal_imaginarySignal_imaginary = 0.5; = 0.5;

• Choose some γ > 0; γ > 0; typicaltypical = 1 = 1 (Continued)

August 2007

Apurva N. Mody, BAE Systems

Slide 12

doc.: IEEE 802.22-07/0359r1

Submission

Signal or Noise Identification Using Higher Order Statistics Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing(HOS) – Hypothesis Testing

ALGORITHMALGORITHM

• for r = 3 to (R + 2); if |cr_real| < γ|m2_real|r/2, => PSignal_real= PSignal_real - δ, elseif |cr_real | ≥ γ| m2_real |r/2, => PSignal_real= PSignal_real + δ end, if |cr_imaginary| < γ|m2_imaginary|r/2, => PSignal_imaginary= PSignal_imaginary - δ, elseif |cr_imaginary| ≥ γ| m2_imaginary|r/2, => PSignal_imaginary= PSignal_imaginary + δ end,

end

(Continued)

August 2007

Apurva N. Mody, BAE Systems

Slide 13

doc.: IEEE 802.22-07/0359r1

Submission

Signal or Noise Identification Using Higher Order Statistics Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing(HOS) – Hypothesis Testing

ALGORITHMALGORITHM• PPSignal Signal = aP= aPSignal_real Signal_real + bP+ bPSignal_imaginarySignal_imaginary where a and b weight parameters. As an

example a = b = 0.5a = b = 0.5

• if if PPSignalSignal ≥ 0.5 then ≥ 0.5 then XX belongs to Class Signal, and the DTV Signal is belongs to Class Signal, and the DTV Signal is detected.detected.

• if if PPSignalSignal < 0.5 then < 0.5 then XX belongs to Class Noise and the DTV Signal is not belongs to Class Noise and the DTV Signal is not detected.detected.

• The parameter γ is used to make fine adjustments of PFA if needed. As increases PFA decreases and vice-versa. In most cases is kept close to unity.

August 2007

Apurva N. Mody, BAE Systems

Slide 14

doc.: IEEE 802.22-07/0359r1

Submission

Signal Detection for DTV SignalsSignal Detection for DTV Signals

Signal 1 WAS_32_48_06012000_OPT_short

Signal 2 WAS_86_48_07122000_REF_short

Signal 3 WAS_51_35_05242000_REF_short

Signal 4 WAS_68_36_05232000_REF_short

Signal 5 WAS_47_48_06132000_OPT_short

Signal 6 WAS_49_39_06142000_OPT_short

Signal 7 WAS_06_34_06092000_REF_short

Signal 8 WAS_49_34_06142000_OPT_short

Signal 9 WAS_311_35_06052000_REF_short

Signal 10 WAS_3_27_06022000_REF_short

Signal 11 WAS_311_48_06052000_REF_short

Signal 12 WAS_311_36_06052000_REF_short

August 2007

Apurva N. Mody, BAE Systems

Slide 15

doc.: IEEE 802.22-07/0359r1

Submission

Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance for 5 mS Sensing Duration, for 5 mS Sensing Duration, = 0.8 and 1.05, R = 4, a=b=1 = 0.8 and 1.05, R = 4, a=b=1

= 0.8, PD > 0.9 and PFA < 0.05 = 1.05, PD > 0.9 and PFA = 0.01

August 2007

Apurva N. Mody, BAE Systems

Slide 16

doc.: IEEE 802.22-07/0359r1

Submission

Signal Detection for DTV Signals in the Vicinity of the Pilot – Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance for 10 mS Sensing Duration , Performance for 10 mS Sensing Duration , = 0.8 and 1.05, R = 4, a=b=1 = 0.8 and 1.05, R = 4, a=b=1

= 0.8, PD > 0.9 and PFA < 0.05 = 1.05, PD > 0.9 and PFA = 0.01

August 2007

Apurva N. Mody, BAE Systems

Slide 17

doc.: IEEE 802.22-07/0359r1

Submission

Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance for 20 mS Sensing Duration , for 20 mS Sensing Duration , = 0.8 and 1.05, R = 4, a=b=1 = 0.8 and 1.05, R = 4, a=b=1

= 0.8, PD > 0.9 and PFA < 0.05 = 1.05, PD > 0.9 and PFA = 0.01

August 2007

Apurva N. Mody, BAE Systems

Slide 18

doc.: IEEE 802.22-07/0359r1

Submission

Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance Signal Detection for DTV Signals in the Vicinity of the Pilot – Performance for 40 mS Sensing Duration , for 40 mS Sensing Duration , = 0.8 and 1.05, R = 4, a=b=1 = 0.8 and 1.05, R = 4, a=b=1

= 0.8, PD > 0.9 and PFA < 0.05 = 1.05, PD > 0.9 and PFA = 0.01

August 2007

Apurva N. Mody, BAE Systems

Slide 19

doc.: IEEE 802.22-07/0359r1

Submission

Signal Detection for DTV Signals in the Vicinity of the Pilot – Average(PSignal Detection for DTV Signals in the Vicinity of the Pilot – Average(PDD

and Pand PFAFA) for the 12 Provided Signals vs Fine Threshold Adjustment ) for the 12 Provided Signals vs Fine Threshold Adjustment

Parameter (Parameter (, R = 4, a=b=1, R = 4, a=b=1

August 2007

Apurva N. Mody, BAE Systems

Slide 20

doc.: IEEE 802.22-07/0359r1

Submission

ConclusionsConclusions• We presented an algorithm to detect the DTV Signals in Gaussian noise using DTV Signals in Gaussian noise using

Higher Order Statistics (HOS).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 PFA = 0.04,

– For a capture of 5mS (continuous or staggered) PD = 0.9 at an SNR = -16.6 dB.

– For a capture of 10 mS (continuous or staggered), PD = 0.9 at SNR = -18.6 dB

– For a capture of 20 mS (continuous or staggered), PD = 0.9 at SNR = -21.6 dB

– For a capture of 40 mS (continuous or staggered), PD = 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.

• The proposed algorithm can be used for the detection of wireless microphone used for the detection of wireless microphone as well as DVB-T signals as well (future contribution).as well as DVB-T signals as well (future contribution).

August 2007

Apurva N. Mody, BAE Systems

Slide 21

doc.: IEEE 802.22-07/0359r1

Submission

ReferencesReferences

• 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.ppt