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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 1 Performance of the Power Detector with Noise Uncertainty 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 IEEEs name any IEEE Standards publication even though it may include portions of this contribution; and at the IEEEs 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 Chairhttp://standards.ieee.org/guides/bylaws/sb-bylaws.pdf Carl R. StevensonCarl 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 >

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 2 Introduction At the May IEEE Session we made a presentation on the performance of the Power Detector for Spectrum Sensing [1] In this presentation the results of the previous presentation are extended to consider the effect of noise uncertainty

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 3 What is Noise Uncertainty? In the power (energy) detector it was assumed that then noise power level was know exactly. This made it possible to detect a very weak signal (negative SNR) since the detector was able to detect the small increase in power due to the sum of the noise and signal power However, we never know the noise power exactly, even if we calibrate the system So we call this lack of knowledge noise uncertainty

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 4 How Much Noise Uncertainty? Some preliminary estimates of the noise uncertainty are given in Appendix A in [2]. Some of those calculations are repeated here for broader review The purpose of these calculations are to get an idea of the magnitude of the noise uncertainty There are several factors that effect noise uncertainty –Calibration error –Thermal noise change due to temperature change –Amplifier gain change due to temperature change –Interference during calibration

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 5 How Much Noise Uncertainty? Noise power spectral density (PSD) is given by Where K b is Boltzmann constant, and T is the temperature is degrees Kelvin Let us see how much the PSD changes with a change in temperature.

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 6 How Much Noise Uncertainty? The change in PSD is given by, Let the temperature increase 20 degrees

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 7 How Much Noise Uncertainty? The gain in the LNA also changes with temperature. I was able to find a UHF LNA with a specification for gain changes due to temperature change. The specification was 0.01 dB/ C If the temperature changes 20 degrees we get the following change in amplifier gain

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 8 How Much Noise Uncertainty? There is an initial calibration error. If the power estimator used during calibration operates for 1 ms then the standard deviation of the initial calibration is, Of course the error can exceed the standard deviation, but this gives an idea of the calibration error

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 9 How Much Noise Uncertainty? Combining these errors we see that the noise uncertainty, without considering the effects of interference during calibration, is at least Rounding up we can say the noise uncertainty without considering interference is, With interference the noise uncertainty may be much larger.

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 10 How to Model the Effects of Noise Uncertainty There are two approaches we used to model noise uncertainty –Use Robust Statistics and consider the worst case in noise uncertainty –Use Bayesian Statistics and assume an a priori distribution on the noise PSD We took both approaches so we could see how they compared

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 11 Robust Statistics Approach The robust statistics approach can be though of as the worst case scenario Average PSD Range of PSD

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 12 Robust Statistics Approach Use upper limit of PSD to calculate Probability of False Alarm Use lower limit of PSD to calculate the Probability of Misdetection As was done previously the theoretical results are shown on the plots with lines and the simulation results are show with discrete points

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 13 Robust Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 14 Robust Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 15 Robust Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 16 Robust Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 17 Robust Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 18 Robust Statistics Approach As you can see from the plots, even for very large sampling time, there is a limit to the SNR under which the power detector gives acceptable misdetection probability This phenomenon was predicted in [3] and is referred to as the SNR Wall

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 19 SNR Wall SNR WallPower Wall 0.5 dB-6.4 dB dBm 1.0 dB-3.3 dB-98.5 dBm So we see that for a noise uncertainty of 1 dB the power detector cannot detect below dBm

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 20 Bayesian Statistics Approach Assume an a priori distribution on the noise PSD Given no other information than the bounds on the noise uncertainty we selected a uniform distribution on the noise PSD

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 21 Bayesian Statistics Approach Calculate the probability of false alarm and the probability of misdetection by averaging over the a priori distribution on the noise PSD

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 22 Bayesian Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 23 Bayesian Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 24 Bayesian Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 25 Bayesian Statistics Approach

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 26 Bayesian Statistics Approach The results for the Bayesian Statistics approach are similar to that of the Robust Statistics approach. The P MD curves are smoother since we are averaging over the a priori distribution of the noise PSD

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 27 Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors As was done in [1] we consider the effects of shadow fading and the use of multiple sensors As per [4] the average noise power at the edge of the keep-out region is dBm The standard deviation of the shadow fading is 5.5 dB The local detector threshold is selected to obtain the specified global false alarm rate Each local sensor sends a one bit decision to the base station which logically ORs together these decisions to obtain a global decision, as in [1]

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 28 Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 29 Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 30 Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 31 Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 32 We can make the following observations –With noise uncertainty the single sensor power detector does not work. In no way does it meet the requirements or give decent results in the simulation scenarios –With noise uncertainty you need many independent sensors, possibly more than are available, for the power detector to give decent results –You cannot fix the effects of noise uncertainty by sensing longer –We do not yet have a well researched value for the noise uncertainty, which could also be effected by interference, so it may be larger than the 1 to 2 dB used in these simulations Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 33 Conclusions The effects of noise uncertainty were studied for the power detector The effect of noise uncertainty prevents the single sensor power detector from meeting the sensing requirements, even for very long sensing times With noise uncertainty the number of independent sensors required to give reasonable performance may be larger than the number of available independent sensors

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doc.: IEEE /0134r0 Submission July 2006 Steve Shellhammer, QualcommSlide 34 1.Steve Shellhammer, Performance of the Power Detector, IEEE /0075r0, May Steve Shellhammer and Gerald Chouinard, Spectrum Sensing Requirements Summary, IEEE /0089r4, June Rahul Tandra, Fundamental Limits of Detection in Low SNR, Masters Thesis, University of California Berkeley, Spring Steve Shellhammer, Victor Tawil, Gerald Chouinard, Max Muterspaugh and Monish Ghosh, Spectrum Sensing Simulation Model, IEEE /0028r6, June 2006 References

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