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**IEEE P802.22 Wireless RANs Date: 2006-09-18**

Performance of eigenvalue based sensing algorithms for detection of DTV and wireless microphone signals IEEE P Wireless RANs Date: Authors: Notice: This document has been prepared to assist IEEE 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 Patent Policy and Procedures: The contributor is familiar with the IEEE 802 Patent Policy and Procedures 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 Working Group. If you have questions, contact the IEEE Patent Committee Administrator at > Yonghong Zeng, Insitute for Infocomm Research

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Abstract Sensing algorithms using the eigenvalues of the sample covariance matrix are presented 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 Comparisons with the energy detection are given Yonghong Zeng, Insitute for Infocomm Research

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**Principle of the algorithms**

The statistics of signal is different from that of noise The difference is characterized by the eigenvalue distributions of the covariance matrix Yonghong Zeng, Insitute for Infocomm Research

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**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

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**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

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**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

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**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

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**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 passband filter with bandwidth 6 MHz is the raised cosine filter with 89 tapes. The signal and white noise are passed through the same filter. Sensing time is 9.30 mili seconds (ms). The smoothing factor is chosen as L=10. The threshold is set based on the required Pfa=0.1 (using random matrix theory) and fixed for signals. The threshold is not related to noise power. Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (wireless microphone signals, sensing time 9**

Probability of detection (wireless microphone signals, sensing time 9.30 ms) Yonghong Zeng, Insitute for Infocomm Research

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**Probability of false alarm (filtered noise, sensing time 9.30 ms)**

EG-2dB EG-1.5dB EG-1dB EG-0.5dB EG-0dB (no uncertainty) EME MME 0.497 0.496 0.483 0.108 0.081 0.086 EG-xdB: energy detection with xdB noise uncertainty. Yonghong Zeng, Insitute for Infocomm Research

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**Simulations for captured DTV signals**

Based on the “Spectrum sensing simulation model”. The captured DTV signal is passed through a raised cosine filter (bandwidth 6 MHz, rolling factor ½, 89 tapes). White noises are added to obtain the various SNR levels. The number of samples used is (corresponding to ms). The smoothing factor is chosen as L=10. The threshold is set based on the required Pfa=0.1 (using random matrix theory) and fixed for all signals. The threshold is not related to noise power. Yonghong Zeng, Insitute for Infocomm Research

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**Probability of false alarm (white noise, sensing time 18.60 ms)**

EG-2dB EG-1.5dB EG-1dB EG-0.5dB EG-0dB (no uncertainty) EME MME 0.496 0.491 0.481 0.095 0.029 0.077 EG-xdB: energy detection with xdB noise uncertainty. Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-311/48/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-311/35/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-311/36/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-086/48/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-006/34/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-003/27/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-051/35/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-049/39/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-032/48/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-068/36/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Probability of detection (WAS-049/34/01)**

Yonghong Zeng, Insitute for Infocomm Research

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**Summary of the simulations**

11 of the 12 DTV signals in the “proposed subset of captures” (by Victor) were tested. (signal WAS-047/36/01 not found) 9 of them obtain Pd >= 0.9 at SNR lower than -20 dB Average Pd = 0.87 at SNR -20 dB Best case is Pd > 0.9 at SNR lower than -22 dB Worst case is Pd > 0.9 at SNR -18 dB Yonghong Zeng, Insitute for Infocomm Research

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Conclusions The eigenvalue 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, …) Same threshold for all signals (the thresholds is independent on the signal and noise power) Performance is comparable to ideal energy detection (can be better than if over-sampled) Yonghong Zeng, Insitute for Infocomm Research

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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. Steve Shellhammer, “Numerical spectrum sensing requirements”, July 2006. 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, Insitute for Infocomm Research

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