Channel Dynamic Range vs Energy Capture Ratio

1. Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title: Channel Dynamic Range vs. Energy Capture Ratio Date Submitted: 19 July, 2002 Source: Marcus Pendergrass, Time Domain Corporation 7057 Old Madison Pike, Huntsville, AL 35806 Voice:256-428-6344 FAX: [256-922-0387], E-Mail: Marcus.Pendergrass@timedomain.com Re: Ultra-wideband Channel Models IEEE P802.15-02/208r0-SG3a, 17 April, 2002, Abstract: The extraction of channel impulse responses from channel measurement data requires a threshold of some sort to determine when the channel extraction process is complete. This report examines two thresholding techniques: energy capture ratio thresholding, and path amplitude thresholding. It is shown that these two techniques are not equivalent, in the sense that the path amplitude threshold that results in the same extracted CIR as a given energy capture threshold varies from channel to channel. A recommendation is made to use energy capture thresholding whenever possible. Purpose: The information provided in this document is for consideration in the selection of a UWB channel model to be used for evaluating the performance of a high rate UWB PHY for WPANs. Notice: This document has been prepared to assist the IEEE P802.15. 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 acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P802.15. Marcus Pendergrass Time Domain Corporation (TDC)

2. Channel Dynamic Range vs. Energy Capture Ratio • 18 July 2002 • Marcus Pendergrass • Marcus.Pendergrass@timedomain.com • Time Domain Corporation References Channel model submission, July 2002, Vancouver BC http://grouper.ieee.org/groups/802/15/pub/2002/Jul02/02240r1p802-15_SG3a-Empirically_Based_UWB_Channel_Model.ppt Channel model presentation, July 2002, Vancouver BC http://grouper.ieee.org/groups/802/15/pub/2002/Jul02/02294r0p802-15_SG3a-Empirically_Based_Statistical_Ultra-Wideband_Channel_Model.ppt Marcus Pendergrass Time Domain Corporation (TDC)

3. Brief Recap of Data Processing Methodology • Data extracted with CLEAN algorithm. • Energy capture stopping criteria used • CLEAN stops extracting impulses out of a scanned waveform when the current CIR either • captures at least x% of the energy in the scanned waveform (x is called the energy capture ratio); or • contains 200 impulses • Energy capture targets of x = 80%, 85%, 90%, and 95% used in analysis. Marcus Pendergrass Time Domain Corporation (TDC)

4. Original scan Error vector s s-r r CLEAN approximation to original scan (reconstructed scan) Linear space of all possible reconstructed scans Energy Capture Ratio and Relative Error When the sum of the relative error and the energy capture ratio is 1, the CLEAN algorithm is returning a least-squares approximation of the scanned waveform. Energy Capture Ratio: Relative Error: Least Squares Condition: Marcus Pendergrass Time Domain Corporation (TDC)

5. a0 mmin t0 t1 tk tn t an - mmax max {|ai| : i = 1, 2, …, n} mmax = min {|ai| : |ai| > 0, i = 1, 2, …, n} mmin = = 20 log10(mmax/mmin) CIR Dynamic Range CIR Dynamic Range Ratio of the maximum and minimum non-zero magnitudes of the CIR Marcus Pendergrass Time Domain Corporation (TDC)

6. Path Amplitude Thresholding and CIR Dynamic Range • Path amplitude thresholding halts the CIR extraction process when the returned path is less than a certain fraction of the peak path in magnitude. • Typical threshold values used are 10 dB, 20 dB. • CIR dynamic range is precisely the minimum path amplitude threshold that would have resulted in the extraction of the given CIR. • Plots that follow show the equivalent path amplitude threshold for 429 channels that were extracted using the energy capture threshold method. Marcus Pendergrass Time Domain Corporation (TDC)

7. CIR Dynamic Range vs. Energy Capture Ratio Marcus Pendergrass Time Domain Corporation (TDC)

8. CIR Dynamic Range vs. Energy Capture Ratio Marcus Pendergrass Time Domain Corporation (TDC)

9. CIR Dynamic Range vs. Energy Capture Ratio Marcus Pendergrass Time Domain Corporation (TDC)

10. Comments • The path amplitude threshold that would result in the same extracted CIR as a given energy capture threshold varies from channel to channel. • Over 10 dB of variation in all cases • Since data collection SNR varies from channel to channel, a rigorous application of path amplitude thresholding would require a different threshold for each channel. • Energy capture thresholding accomplishes this automatically. Marcus Pendergrass Time Domain Corporation (TDC)

11. Conclusions/Recommendations • Energy capture thresholding and path amplitude thresholding are not equivalent methods of CIR extraction. • Energy capture thresholding is grounded in the mathematics of least squares approximation. • Recommend using energy capture thresholding whenever possible for CIR extraction. Marcus Pendergrass Time Domain Corporation (TDC)