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SFD Design for SUN FSK

This presentation discusses two SFD proposals for SUN FSK, including an optimization metric for SFD design and the computation of false alarm probability.

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SFD Design for SUN FSK

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  1. Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title: [SFD Design for SUN FSK] Date Submitted: [March 2010] Source: [Tim Schmidl, Khanh Tuan Le, Trond Rognerud] Company [Texas Instruments] Address [12500 TI Blvd, Dallas, TX 75243 USA] Voice:[+1 214-480-4460], FAX: [+1 972-761-6966], E-Mail:[schmidl@ti.com] Abstract: [This presentation gives two SFD’s for SUN FSK] Purpose: [For information] 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. Tim Schmidl, Texas Instruments Inc.

  2. SFD Proposals Evaluated • Three proposals for SFD pairs (Plan A, B, C) are given in 15-10-0112-01-004g-sfd-and-fec-proposal.pdf • This document proposes Plan D: Tim Schmidl, Texas Instruments Inc.

  3. Optimization Metric for SFD Design • Plans A, B, and C are optimized by minimizing rms. Problems with rms include: • Correlation of 6 is weighted the same as correlation of -6, while correlation of 6 is much more likely to cause a false alarm • Highest rms value occurs with correlation of -16, which is largest distance away from the SFD and the least likely to cause a false alarm • Weights for rms do not vary much from correlation of 6 to correlation of 4, while the probability of false alarm varies greatly • Plan D was found by directly optimizing the probability of false alarm, so this gives a low probability of false alarm • False alarm probability is what affects system performance Tim Schmidl, Texas Instruments Inc.

  4. 11 same bits 5 different bits Correlation = 6 2 bit errors cause a false alarm 13 same bits 3 different bits Correlation = 10, FALSE ALARM Computation of False Alarm Probability for a Single Shift with Correlation = 6 • Assumption is that the threshold is set at a correlation of 10, which means that out of 16 bits there are 13 matching bits and 3 different bits • Correlation of 6 means that 11 bits match and 5 bits differ. If 2 of the 5 different bits are received in error, then there is a false alarm • False Alarm Probability = (5 Choose 2)p2 (1-p)14 = 10p2(1-p)14, where p = prob. of a bit error • Assuming i.i.d. errors, for p = 0.01 ( SNR of 4 dB), FA probability = 8.710-4 Tim Schmidl, Texas Instruments Inc.

  5. False Alarm Probability for Each Correlation Value • Correlation values of 6 is ~50 times more likely to cause false alarms than correlation values of 4 Tim Schmidl, Texas Instruments Inc.

  6. RMS is not the same as False Alarm Probability • The rms metric treats the correlation of -16 as the worst case even though it is the best case because all 16 bits differ from the correct SFD and 13 bit errors would be required to generate a false alarm. The rms metric is not appropriate for estimating false alarm when the false alarm probabilities can be directly calculated Tim Schmidl, Texas Instruments Inc.

  7. Textbook Method of Finding Probability of Error dmin dmin Probability of error is dominated by the minimum distance to the nearest neighbor and the number of nearest neighbors Tim Schmidl, Texas Instruments Inc.

  8. RMS Method Does Not Give Probability of Error d2 d1 darb d3 d4 Select arbitrary distance darb and then find rms from darb. Distances from darb are minimized, but this does not necessarily minimize probability of error. Tim Schmidl, Texas Instruments Inc.

  9. Preamble for 802.15.4d/g • The preamble is repeated bytes of “01010101”. • The receiver can detect that a preamble is present, but it needs to detect the SFD to determine the start of the frame • Once the “01010101” pattern is detected, the receiver knows that the SFD must start on an even position, where the 0 positions are even. Therefore it can search only on even start positions in order to lower the false alarm probability. • For images a “10101010” pattern is received, so the receiver can again search for the SFD on even positions where the 0 positions are defined as even. Tim Schmidl, Texas Instruments Inc.

  10. Simulation Assumptions • The received sequence is a 32 bit preamble followed by an SFD. The receiver is assumed to detect the preamble and start searching for the SFD immediately thereafter • The receiver correlates with both of the defined SFD’s to determine which one was received • For the image, the received sequence is inverted so that 0 maps to 1 and 1 maps to 0 Tim Schmidl, Texas Instruments Inc.

  11. Preamble Detector Types • Type 0: The correlation values for all start positions are searched. This is the so-called “conventional” detector. • Type 1: The correlation values for only even start positions are searched because these are the only positions that can contain a valid SFD Tim Schmidl, Texas Instruments Inc.

  12. 105 * False Alarm Rates at 4 dB SNR Type 0: Conventional detector Plan D average false alarm rate = 7.1e-4 Plan B average false alarm rate = 7.0e-4 Tim Schmidl, Texas Instruments Inc.

  13. 105 * False Alarm Rates at 4 dB SNR Type 1: Search even positions Tim Schmidl, Texas Instruments Inc.

  14. Average False Alarm Rates at 4 dB SNR Type 1: Search even positions • Full correlation values for all shifts are shown in backup slides About a factor of 10 higher false alarm rate with Plan B versus Plan D! Tim Schmidl, Texas Instruments Inc.

  15. Conclusion • Probability of false alarm for each shift position can be calculated directly from the correlation value • Plans A, B, and C each contain a shift position with a correlation of 6 which leads to high false alarm rates • Plan B will have poor coexistence with 802.15.4d since high correlations with the 15.4d SFD are found for both SFD1 and SFD2 • Plan B and Plan D have almost the same false alarm probability with the Type 0 conventional detector (7.0e-4 versus 7.1e-4), but Plan D offers about 10x lower false alarm probability when the preamble structure information is utilized with the Type 1 detector (4.9e-4 versus 5.2e-5) • Plan D offers the best correlation properties and should be selected as the 802.15.4g SFD’s Tim Schmidl, Texas Instruments Inc.

  16. Backup Tim Schmidl, Texas Instruments Inc.

  17. Correlation with Plan A SFD’s Correlation with 0xF68D Correlation with 0x7BC9 Tim Schmidl, Texas Instruments Inc.

  18. Correlation with Plan B SFD’s Correlation with 0x6F4E Correlation with 0x904E Tim Schmidl, Texas Instruments Inc.

  19. Correlation with Plan C SFD’s Correlation with 0x21F6 Correlation with 0xC9C2 Tim Schmidl, Texas Instruments Inc.

  20. Correlation with Plan D SFD’s Correlation with 0x632D Correlation with 0x7A0E Tim Schmidl, Texas Instruments Inc.

  21. SFD Selection Criteria • The criteria for the selection of 2 SFD’s is given in 15-10-0051-01-004g-fsk-sub-group-resolution-update.pdf • Process to select the SFD values: • 1. Will be selected based on the following prioritized criteria: • a. Autocorrelation and cross correlation to the other pattern • b. Good image rejection (low correlation against the image) • c. Correlation relative to the preamble (low side lobes against the preamble) • 2. The following prioritized differentiators will be used to select SFD values if multiple solutions are found with identical performance. Supporting data for item 2a shall be provided by all proposals. • a. The selected code should have good orthogonality against the existing 802.15.4d SFD. (Co-existence with 802.15.4d is imperative) • 3. Timeline: • a. Harada-san: proposals provided within one month (no later than 2/22 midnight PST) and exchanged among subgroup participants. Proposals will be emailed to Harada-san and copied to all members of the SFD subgroup. Harada-san will send an email to all SFD participants. • b. There will be a conference call the week of 2/22 to review the proposals. Harada-san will schedule the conference call for 2/25 (we propose using the normal 4g call time) Tim Schmidl, Texas Instruments Inc.

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