July 2006

Steve Shellhammer, Qualcomm

Slide 1

doc.: IEEE 802.22-06/0134r0

Submission

Performance of the Power Detector with Noise Uncertainty

IEEE P802.22 Wireless RANs Date: 2006-07-17

Name Company Address Phone email Steve Shellhammer Qualcomm 5775 Morehouse Dr

San Diego, CA 92121 (858) 658-1874 Shellhammer@ieee.org

Rahul Tandra Qualcomm 5775 Morehouse Dr San Diego, CA 92121

(858) 845-1970 rtandra@qualcomm.com

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.>

July 2006

Steve Shellhammer, Qualcomm

Slide 2

doc.: IEEE 802.22-06/0134r0

Submission

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

July 2006

Steve Shellhammer, Qualcomm

Slide 3

doc.: IEEE 802.22-06/0134r0

Submission

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”

July 2006

Steve Shellhammer, Qualcomm

Slide 4

doc.: IEEE 802.22-06/0134r0

Submission

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

July 2006

Steve Shellhammer, Qualcomm

Slide 5

doc.: IEEE 802.22-06/0134r0

Submission

How Much Noise Uncertainty?

• Noise power spectral density (PSD) is given by

• Where Kb is Boltzmann constant, and T is the temperature is degrees Kelvin

• Let us see how much the PSD changes with a change in temperature.

TKN b0

)(10)(10)(10)(10 12120 TLogTLogTKLogTKLogN bb

July 2006

Steve Shellhammer, Qualcomm

Slide 6

doc.: IEEE 802.22-06/0134r0

Submission

How Much Noise Uncertainty?

• The change in PSD is given by,

• Let the temperature increase 20 degrees

1

20 10

T

TLogN

dBLogN 28.0300

320100

July 2006

Steve Shellhammer, Qualcomm

Slide 7

doc.: IEEE 802.22-06/0134r0

Submission

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

dBg 2.0)01.0(20

July 2006

Steve Shellhammer, Qualcomm

Slide 8

doc.: IEEE 802.22-06/0134r0

Submission

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

Initial Estimate Error 0.22 dB

July 2006

Steve Shellhammer, Qualcomm

Slide 9

doc.: IEEE 802.22-06/0134r0

Submission

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.

dB7.0

dB1y UncertantNoise

July 2006

Steve Shellhammer, Qualcomm

Slide 10

doc.: IEEE 802.22-06/0134r0

Submission

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

July 2006

Steve Shellhammer, Qualcomm

Slide 11

doc.: IEEE 802.22-06/0134r0

Submission

Robust Statistics Approach

• The robust statistics approach can be though of as the worst case scenario

• Average PSD

• Range of PSD

HzdBmNN /16311174110

HzdBmNN /163

July 2006

Steve Shellhammer, Qualcomm

Slide 12

doc.: IEEE 802.22-06/0134r0

Submission

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

July 2006

Steve Shellhammer, Qualcomm

Slide 13

doc.: IEEE 802.22-06/0134r0

Submission

Robust Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 14

doc.: IEEE 802.22-06/0134r0

Submission

Robust Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 15

doc.: IEEE 802.22-06/0134r0

Submission

Robust Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 16

doc.: IEEE 802.22-06/0134r0

Submission

Robust Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 17

doc.: IEEE 802.22-06/0134r0

Submission

Robust Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 18

doc.: IEEE 802.22-06/0134r0

Submission

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”

July 2006

Steve Shellhammer, Qualcomm

Slide 19

doc.: IEEE 802.22-06/0134r0

Submission

SNR Wall

SNR Wall Power Wall

0.5 dB -6.4 dB -101.6 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 -98.5 dBm

July 2006

Steve Shellhammer, Qualcomm

Slide 20

doc.: IEEE 802.22-06/0134r0

Submission

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

HzdBmNN /

Otherwise0

)()()2/(1)(

NnNnf N

July 2006

Steve Shellhammer, Qualcomm

Slide 21

doc.: IEEE 802.22-06/0134r0

Submission

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

July 2006

Steve Shellhammer, Qualcomm

Slide 22

doc.: IEEE 802.22-06/0134r0

Submission

Bayesian Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 23

doc.: IEEE 802.22-06/0134r0

Submission

Bayesian Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 24

doc.: IEEE 802.22-06/0134r0

Submission

Bayesian Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 25

doc.: IEEE 802.22-06/0134r0

Submission

Bayesian Statistics Approach

July 2006

Steve Shellhammer, Qualcomm

Slide 26

doc.: IEEE 802.22-06/0134r0

Submission

Bayesian Statistics Approach

• The results for the Bayesian Statistics approach are similar to that of the Robust Statistics approach.

• The PMD curves are smoother since we are averaging over the a priori distribution of the noise PSD

July 2006

Steve Shellhammer, Qualcomm

Slide 27

doc.: IEEE 802.22-06/0134r0

Submission

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 -96.45 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]

July 2006

Steve Shellhammer, Qualcomm

Slide 28

doc.: IEEE 802.22-06/0134r0

Submission

Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

July 2006

Steve Shellhammer, Qualcomm

Slide 29

doc.: IEEE 802.22-06/0134r0

Submission

Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

July 2006

Steve Shellhammer, Qualcomm

Slide 30

doc.: IEEE 802.22-06/0134r0

Submission

Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

July 2006

Steve Shellhammer, Qualcomm

Slide 31

doc.: IEEE 802.22-06/0134r0

Submission

Performance with Noise Uncertainty, Shadow Fading and Multiple Sensors

July 2006

Steve Shellhammer, Qualcomm

Slide 32

doc.: IEEE 802.22-06/0134r0

Submission

• 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

July 2006

Steve Shellhammer, Qualcomm

Slide 33

doc.: IEEE 802.22-06/0134r0

Submission

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

July 2006

Steve Shellhammer, Qualcomm

Slide 34

doc.: IEEE 802.22-06/0134r0

Submission

1. Steve Shellhammer, Performance of the Power Detector, IEEE 802.22-06/0075r0, May 2006

2. Steve Shellhammer and Gerald Chouinard, Spectrum Sensing Requirements Summary, IEEE 802.22-06/0089r4, June 2006

3. Rahul Tandra, Fundamental Limits of Detection in Low SNR, Masters Thesis, University of California Berkeley, Spring 2005

4. Steve Shellhammer, Victor Tawil, Gerald Chouinard, Max Muterspaugh and Monish Ghosh, Spectrum Sensing Simulation Model, IEEE 802.22-06/0028r6, June 2006

References