1. IEEE P802.22 Wireless RANs Date: 2007-07-12
Month Year
doc.: IEEE yy/xxxxr0
July 2007
Spectrum Sensing of the DTV in the Vicinity of the Video Carrier Using Higher Order Statistics
IEEE P Wireless RANs Date:
Authors:
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Apurva N. Mody, BAE Systems
John Doe, Some Company

2. Month Year
doc.: IEEE yy/xxxxr0
July 2007
Abstract
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 Video Carrier
The 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 = dB.
For a capture of 10 mS (continuous or staggered), PD = 0.9 at SNR = dB
For a capture of 20 mS (continuous or staggered), PD = 0.9 at SNR = dB
For a capture of 40 mS (continuous or staggered), PD = 0.9 at SNR = 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 Signals as well (Future Contribution)..
Apurva N. Mody, BAE Systems
John Doe, Some Company

3. DTV Signal Characteristics
July 2007
DTV Signal Characteristics
Apurva N. Mody, BAE Systems

4. DTV Signal Gaussianity Check in Time and Frequency Domains
July 2007
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.
Apurva N. Mody, BAE Systems

5. Signal or Noise Identification Using Higher Order Statistics (HOS)
July 2007
Signal or Noise Identification Using 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 = {x1, x2, …, 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
Apurva N. Mody, BAE Systems

6. Signal or Noise Identification Using Higher Order Statistics (HOS)
July 2007
Signal or Noise Identification Using Higher Order Statistics (HOS)
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 cumulants as
Apurva N. Mody, BAE Systems

7. July 2007
Signal or Noise Identification Using Higher Order Statistics (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 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.
Apurva N. Mody, BAE Systems

8. July 2007
Signal Detection for DTV Signals in the Vicinity of the Video Carrier – Block Diagram of the Algorithm
Apurva N. Mody, BAE Systems

9. July 2007
Distribution of Signal and Noise in the Time Domain after Down-sampling
Distribution of Noise in the Time Domain
Distribution of (Signal + Noise) in the Time Domain
Apurva N. Mody, BAE Systems

10. July 2007
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
Apurva N. Mody, BAE Systems

11. July 2007
Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing
ALGORITHM
Let R be the number of moments (mr_real, mr_imaginary) and cumulants (cr_real, cr_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,
Choose a Probability Step Parameter 0 < δ < 1; For example let d = 0.5 / R.
Let PSignal_real = PSignal_imaginary = 0.5;
Choose some γ > 0; gtypical = 1
(Continued)
Apurva N. Mody, BAE Systems

12. July 2007
Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing
ALGORITHM
for r = 2 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
(Continued)
Apurva N. Mody, BAE Systems

13. July 2007
Signal or Noise Identification Using Higher Order Statistics (HOS) – Hypothesis Testing
ALGORITHM
PSignal = aPSignal_real + bPSignal_imaginary where a and b weight parameters. As an example a = b = 0.5
if PSignal ≥ 0.5 then X belongs to Class Signal, and the DTV Signal is detected.
if PSignal < 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 PFA if needed. As g increases PFA decreases and vice-versa. In most cases g is kept close to unity.
Apurva N. Mody, BAE Systems

14. Signal Detection for DTV Signals
July 2007
Signal Detection for DTV Signals
Signal 1
WAS_32_48_ _OPT_short
Signal 2
WAS_86_48_ _REF_short
Signal 3
WAS_51_35_ _REF_short
Signal 4
WAS_68_36_ _REF_short
Signal 5
WAS_47_48_ _OPT_short
Signal 6
WAS_49_39_ _OPT_short
Signal 7
WAS_06_34_ _REF_short
Signal 8
WAS_49_34_ _OPT_short
Signal 9
WAS_311_35_ _REF_short
Signal 10
WAS_3_27_ _REF_short
Signal 11
WAS_311_48_ _REF_short
Signal 12
WAS_311_36_ _REF_short
Apurva N. Mody, BAE Systems

15. July 2007
Signal Detection for DTV Signals in the Vicinity of the Video Carrier – Performance for 5 mS Sensing Duration, g = 0.8, R = 4, a=b=1
Apurva N. Mody, BAE Systems

16. July 2007
Signal Detection for DTV Signals in the Vicinity of the Video Carrier – Performance for 10 mS Sensing Duration , g = 0.8, R = 4, a=b=1
Apurva N. Mody, BAE Systems

17. July 2007
Signal Detection for DTV Signals in the Vicinity of the Video Carrier – Performance for 20 mS Sensing Duration , g = 0.8, R = 4, a=b=1
Apurva N. Mody, BAE Systems

18. July 2007
Signal Detection for DTV Signals in the Vicinity of the Video Carrier – Performance for 40 mS Sensing Duration , g = 0.8, R = 4, a=b=1
Apurva N. Mody, BAE Systems

19. July 2007
Signal Detection for DTV Signals in the Vicinity of the Video Carrier – Average(PD and PFA) for the 12 Provided Signals vs Fine Threshold Adjustment Parameter (g), R = 4, a=b=1
Apurva N. Mody, BAE Systems

20. July 2007
Conclusions
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 Video Carrier
The 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 = dB.
For a capture of 10 mS (continuous or staggered), PD = 0.9 at SNR = dB
For a capture of 20 mS (continuous or staggered), PD = 0.9 at SNR = dB
For a capture of 40 mS (continuous or staggered), PD = 0.9 at SNR = 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 Signals as well (Future Contribution).
Apurva N. Mody, BAE Systems

21. July 2007
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.
Apurva N. Mody, BAE Systems