1. IEEE P802.22 Wireless RANs Date: 2007-03-9
2018/6/10
Updates on the covariance based and eigenvalue based sensing algorithms
IEEE P Wireless RANs Date:
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Yonghong Zeng, Insitute for Infocomm Research

2. Abstract
Sensing algorithms using properties of the sample covariance matrix are presented
Two statistics are extracted from the received signals and compared to make a decision
The methods can be used without knowledge of the signal, the channel and noise power
Simulation results based on the captured DTV signals and wireless microphone signals are presented
Yonghong Zeng, Insitute for Infocomm Research

3. Principle of the algorithms
The statistics of signal is different from that of noise
The difference is characterized by the eigenvalue distributions or non-diagonal elements of the covariance matrix
Yonghong Zeng, Insitute for Infocomm Research

4. Flow-chart of the maximum-minimum eigenvalue (MME) detection
Choose a smoothing factor and the threshold r
Compute the sample covariance matrix
Transform the sample covariance matrix
Sample and filter the signals
Compute the maximum eigenvalue and minimum eigenvalue of the covariance matrix
Decision: if the maximum eign >r*minimum eign,
signal exists;
Otherwise, signal not exists.
Yonghong Zeng, Insitute for Infocomm Research

5. Flow-chart of the energy with minimum eigenvalue (EME) detection
Choose a smoothing factor and the threshold r
Compute the sample covariance matrix
Transform the sample covariance matrix
Sample and filter the signals
Compute the average energy and minimum eigenvalue of the covariance matrix
Decision: if the energy >r*minimum eign,
signal exists;
Otherwise, signal not exists.
Yonghong Zeng, Insitute for Infocomm Research

6. Flow-chart of the covariance absolute value (CAV) detection
Choose a smoothing factor and the threshold r
Compute the sample covariance matrix
Transform the sample covariance matrix
Sample and filter the signals
Compute the absolute sum of the matrix, T1, and the absolute sum of diagonal elements, T2
Decision: if T1 >r*T2,
signal exists;
Otherwise, signal not exists.
Yonghong Zeng, Insitute for Infocomm Research

7. Flow-chart of the Covariance Frobenius norm (CFN) detection
Choose a smoothing factor and the threshold r
Compute the sample covariance matrix
Transform the sample covariance matrix
Sample and filter the signals
Compute the sum of powers of the matrix elements, T3, and the sum of powers of diagonal elements, T4
Decision: if T3 >r*T4,
signal exists;
Otherwise, signal not exists.
Yonghong Zeng, Insitute for Infocomm Research

8. Threshold setting
The threshold is set based on the Pfa, number of samples and L by using the random matrix theory. The threshold is not related to noise power and signal property. The threshold is fixed for all signals. For examples, the thresholds for the MME and CAV are set respectively as follows (where P0 is the required Pfa).
Yonghong Zeng, Insitute for Infocomm Research

9. Advantages of the algorithms
No signal information is needed (compared to coherent detection)
Robust to multipath propagation (compared to coherent detection)
No synchronization is needed (compared to coherent detection)
No noise uncertainty problem (compared to energy detection)
Good performance (can be better than the ideal energy detection without noise uncertainty)
Yonghong Zeng, Insitute for Infocomm Research

10. Advantages of the algorithms
Same detection method for all signals (DTV, wireless microphone, …)
Same threshold for all signals (the thresholds is independent on the signal and noise power)
Yonghong Zeng, Insitute for Infocomm Research

11. Simulations for wireless microphone signals
FM modulated wireless microphone signal (200 KHz bandwidth)
The source signal is generated as evenly distributed real number in (-1,1). We assume that the signal has been down converted to the IF with central frequency MHz (the same as the captured DTV signal). The sampling rate is MHz (the same as the captured DTV signal). The signal and white noise are passed through the same filter. The passband filter with bandwidth 6 MHz is shown at the next page (provided by Steve Shellhammer). The smoothing factor is chosen as L=10. The threshold is set based on the Pfa, number of samples and L (using random matrix theory) and fixed for all signals. The threshold is not related to noise power and signal.
The MME, CAV and CFN have similar performances and EME is worse, in the following, only results for CAV are given.
Yonghong Zeng, Insitute for Infocomm Research

12. The passband filter
Yonghong Zeng, Insitute for Infocomm Research

13. Probability of misdetection at 4ms sensing time (wireless microphone signal)
Yonghong Zeng, Insitute for Infocomm Research

14. Probability of misdetection at 8ms sensing time (wireless microphone signal)
Yonghong Zeng, Insitute for Infocomm Research

15. Simulations for captured DTV signals
The captured DTV signals in [5] are used in the simulations. The signal and white noise are passed through the same filter. The filter is shown before (provided by Steve Shellhammer). The smoothing factor is chosen as L=10.
The threshold is set based on the Pfa, sensing time and L (using random matrix theory) and fixed for all signals. The threshold is not related to noise power and signal.
The MME, CAV and CFN have similar performances and EME is worse, in the following, only results for CAV are given.
The time slots can be continuous or discontinuous.
Yonghong Zeng, Insitute for Infocomm Research

16. Probability of misdetection at 4ms sensing time (average over 11 DTV signals)
Yonghong Zeng, Insitute for Infocomm Research

17. Probability of misdetection at 8ms sensing time (average over 11 DTV signals)
Yonghong Zeng, Insitute for Infocomm Research

18. Probability of misdetection at 16ms sensing time (average over 11 DTV signals)
Yonghong Zeng, Insitute for Infocomm Research

19. Probability of misdetections for 11 DTV signals at sensing time 16 ms
Yonghong Zeng, Insitute for Infocomm Research

20. Average probability of misdetection at sensing time 16 ms
If we fix the Pmd=0.1, Pfa=0.1 and find the SNRs for the DTV signals to meet this Pmd and then average on the SNRs, we get the average SNR=-16dB.
If we first average the Pmd’s of all the DTV signals at various SNR’s and then find the SNR to meet Pmd=0.1 and Pfa=0.1, we get the average SNR=-15dB.
Yonghong Zeng, Insitute for Infocomm Research

21. Probability of misdetection at 32ms sensing time (average over 11 DTV signals)
Yonghong Zeng, Insitute for Infocomm Research

22. The computational complexity
Filtering the received signals: (K+1)N multiplications and additions, where K is the order of filter and N is the number of samples (if K is large, FFT can be used to reduce the complexity);
Computing the covariance matrix of the received signal: LN multiplications and additions, where L is the smoothing factor;
Transforming the covariance matrix: needs 2L^3 multiplications and additions;
Others: at most L^2 multiplications and additions;
Total: (K+L+1)N+2L^3+L^2 multiplications and additions.
Yonghong Zeng, Insitute for Infocomm Research

23. Conclusions
The covariance based detections do not need any information on signal, the channel, the noise level and SNR
Same detection method for all signals (DTV, wireless microphone, …)
The threshold is set based on sensing time and Pfa. Same threshold for all signals (the thresholds is independent on the signal and noise power)
Filter with better conditional number can be used to increase the performance
Yonghong Zeng, Insitute for Infocomm Research

24. References
A. Sahai and D. Cabric, “Spectrum sensing: fundamental limits and practical challenges,” in Dyspan 2005 (available at:
Steve Shellhammer et al., “Spectrum sensing simulation model”, July 2006.
Suhas Mathur et al., “Initial signal processing of captured DTV signals for evaluation of detection algorithms”, Feb
I.M. Johnstone, “On the distribution of the largest eigenvalue in principle components analysis,” The Annals of Statistics, vol. 29, no. 2, pp. 295—327, 2001.
Victor Tawil, “51 captured DTV signal”, May 2006.
Yonghong Zeng and Ying-Chang Liang, “Eigenvalue based sensing algorithms”,
Yonghong Zeng and Ying-Chang Liang, “Performance of eigenvalue based sensing algorithms for detection of DTV and wireless microphone signals”,
Yonghong Zeng, Insitute for Infocomm Research

25. References
Yonghong Zeng and Ying-Chang Liang, “Performance of eigenvalue based sensing algorithms for detection of DTV and wireless microphone signals”,
Yonghong Zeng and Ying-Chang Liang, “Covariance based sensing algorithms for detection of DTV and wireless microphone signals”,
Yonghong Zeng, Insitute for Infocomm Research