IEEE P802.22 Wireless RANs Date: 2007-03-21 2018/5/24 Updates on the covariance based and eigenvalue based sensing algorithms IEEE P802.22 Wireless RANs Date: 2007-03-21 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. > Yonghong Zeng, Insitute for Infocomm Research

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

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

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

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

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

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

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

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

Advantages of the algorithms Same detection method for all signals (DTV, wireless microphone, analog TV, …) Same threshold for all signals (the thresholds is independent on the signal and noise power) Can use continuous or discontinuous time slots for sensing Yonghong Zeng, Insitute for Infocomm Research

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 5.381119 MHz (the same as the captured DTV signal). The sampling rate is 21.524476 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. SNR is measured in 6MHz bandwidth. The central frequency location of the microphone signal is unknown. 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

The passband filter (provided by Steve Shellhammer) Yonghong Zeng, Insitute for Infocomm Research

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

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

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. 12 captured DTV files are tested: WAS-047/48/01, WAS-311/48/01, WAS-311/35/01, WAS-311/36/01, WAS-086/48/01, WAS-006/34/01, WAS-003/27/01, WAS-051/35/01, WAS-049/39/01, WAS-032/48/01, WAS-068/36/01, WAS-049/34/01. Yonghong Zeng, Insitute for Infocomm Research

Probability of misdetection at 4ms sensing time (average over 12 DTV signals) Yonghong Zeng, Insitute for Infocomm Research

Probability of misdetection at 8ms sensing time (average over 12 DTV signals) Yonghong Zeng, Insitute for Infocomm Research

Probability of misdetection at 16ms sensing time (average over 12 DTV signals) Yonghong Zeng, Insitute for Infocomm Research

Probability of misdetections for 12 DTV signals at sensing time 16 ms Yonghong Zeng, Insitute for Infocomm Research

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

Probability of misdetection at 32ms sensing time (average over 12 DTV signals) Yonghong Zeng, Insitute for Infocomm Research

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

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) Can use continuous or discontinuous time slots for sensing (same performance), which allows flexible sensing time slots allocation Yonghong Zeng, Insitute for Infocomm Research

Conclusions Can reach Pfa=0.1 and Pmd=0.1 at SNR=-20dB and sensing time less than 100ms Filter with better conditional number can be used to improve the performance or reduce sensing time Yonghong Zeng, Insitute for Infocomm Research

References A. Sahai and D. Cabric, “Spectrum sensing: fundamental limits and practical challenges,” in Dyspan 2005 (available at: www.eecs.berkeley.edu/∼sahai), 2005. Steve Shellhammer et al., “Spectrum sensing simulation model”, http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_July/22-06-0028-07-0000-Spectrum-Sensing-Simulation-Model.doc, July 2006. Suhas Mathur et al., “Initial signal processing of captured DTV signals for evaluation of detection algorithms”, http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_Oct/22-06-0158-06-0000-Intial-Signal-Processing-for-DTV-Signal-Files.doc, Feb. 2007. 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”, http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_May/Informal_Documents, May 2006. Yonghong Zeng and Ying-Chang Liang, “Eigenvalue based sensing algorithms”, http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_July/22-06-0118-00-0000_I2R-sensing.doc Yonghong Zeng and Ying-Chang Liang, “Performance of eigenvalue based sensing algorithms for detection of DTV and wireless microphone signals”, http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_Sept/22-06-0186-00-0000_I2R-sensing-2.doc Yonghong Zeng, Insitute for Infocomm Research

References Yonghong Zeng and Ying-Chang Liang, “Performance of eigenvalue based sensing algorithms for detection of DTV and wireless microphone signals”, http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_Sept/22-06-0187-00-0000_I2R-sensing-2.ppt Yonghong Zeng and Ying-Chang Liang, “Covariance based sensing algorithms for detection of DTV and wireless microphone signals”, http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_Nov/22-06-0187-01-0000_I2R-sensing-2.ppt Yonghong Zeng, Insitute for Infocomm Research