Proposal for Preamble Codes in IEEE 802.15.4ab for Enhanced Data Communications

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This document outlines the proposal for preamble codes aimed at improving data communications in IEEE 802.15.4ab. The technical guidance includes solutions for interference mitigation, coexistence improvements, enhanced link budget, and more. Key considerations involve autocorrelation properties, cross-correlation with legacy devices, and efficiency improvements in the SYNC field length.

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  1. July 2021 doc.: IEEE 15-21-0377-00-04ab Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title: Preamble codes for Data Communications in 802.15.4ab Source: Carlos Aldana (Facebook), Qiyue Zou (Facebook) Address : [1 Hacker Way, Menlo Park, CA 94025] E-Mail: [caldana (at) fb.com] Re: Study Group 4ab: UWB Next Generation Abstract: [preamble code enhancements to 802.15.4z for data communications] Purpose: 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. Carlos Aldana

  2. July 2021 doc.: IEEE 15-21-0377-00-04ab Technical Guidance [1] PAR Objective Safeguards so that the high throughput data use cases will not cause significant disruption to low duty-cycle ranging use cases. Proposed Solution (how addressed) Interference mitigation techniques to support higher density and higher traffic use cases Other coexistence improvement Backward compatibility with enhanced ranging capable devices (ERDEVs). Improved link budget and/or reduced air-time Additional channels and operating frequencies Improvements to accuracy / precision / reliability and interoperability for high-integrity ranging; s Reduce complexity and power consumption; Hybrid operation with narrowband signaling to assist UWB; Enhanced native discovery and connection setup mechanisms; Sensing capabilities to support presence detection and environment mapping; Low-power low-latency streaming higher data-rate streaming allowing at least 50 Mbit/s of throughput. Support for peer-to-peer, peer-to-multi-peer, and station-to-infrastructure protocols; New preamble codes are proposed Infrastructure synchronization mechanisms. Carlos Aldana Slide 2

  3. July 2021 doc.: IEEE 15-21-0377-00-04ab Preamble codes for Data Communications in 802.15.4ab Carlos Aldana

  4. July 2021 doc.: IEEE 15-21-0377-00-04ab Objective Propose preamble codes (SYNC field) candidates for data communications over IEEE 802.15.4a UWB channels [2] Carlos Aldana

  5. July 2021 doc.: IEEE 15-21-0377-00-04ab Background 4 configurations defined 802.15.4z[3] This contribution focuses on the SYNC field Carlos Aldana Slide 5

  6. July 2021 doc.: IEEE 15-21-0377-00-04ab Key Considerations Excellent periodic autocorrelation properties -> improved ranging and channel estimation Good cross-correlation properties with HRP and LRP preambles -> coexist with legacy UWB devices Good periodic cross-correlation properties -> coexist with other data communication UWB devices Reduced SYNC field length -> reduced air time and improved PHY efficiency Carlos Aldana

  7. July 2021 doc.: IEEE 15-21-0377-00-04ab Periodic Autocorrelation Good periodic autocorrelation makes channel estimation easy (via matched filter) Ternary preamble sequences (S1-S32) [4] specified in the UWB standards have perfect periodic autocorrelation function (i.e., out-of-phase autocorrelation = 0) Matched filter output is equal to the channel impulse response plus noise (assuming symbol length Tsym channel duration) IEEE 802.15.4a CM1 CM9 channel models defined in [2] have PDP channel duration in the range 85ns 900ns. All channels except CM6 and CM8 have duration < 330ns Length of Delta Spreading Function Preamble Code Length #Chips Per Symbol Preamble Code Tsym S1-S8 31 16 496 0.994us S1-S8 31 64 1984 3.974us S9 S24 127 4 508 1.018us S25 S32 91 4 364 0.729us Carlos Aldana

  8. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM1) CM1 channel model: residential, LOS channel length = ~120ns Carlos Aldana

  9. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM2) CM2 channel model: residential, NLOS channel length = ~200ns Carlos Aldana

  10. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM3) CM3 channel model: indoor office, LOS channel length = ~130ns Carlos Aldana

  11. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM4) CM4 channel model: indoor office, NLOS channel length = ~120ns Carlos Aldana

  12. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM5) CM5 channel model: outdoor, LOS channel length = ~270ns Carlos Aldana

  13. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM6) CM6 channel model: outdoor, NLOS channel length = ~900ns Carlos Aldana

  14. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM7) CM7 channel model: industrial, LOS channel length = ~85ns Carlos Aldana

  15. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM8) CM8 channel model: industrial, NLOS channel length = ~850ns Carlos Aldana

  16. July 2021 doc.: IEEE 15-21-0377-00-04ab UWB Channel Model (CM9) CM9 channel model: farm channel length = ~330ns Carlos Aldana

  17. July 2021 doc.: IEEE 15-21-0377-00-04ab Periodic Autocorrelation m-sequences have quasi-optimal periodic autocorrelation quasi-optimal -> Out-of-phase autocorrelation = -1 while autocorrelation peak = N Although not perfect , N can be chosen such that N/1 is large and doesn't degrade system performance significantly, e.g., 20*log10(N/1) 20dB m-sequences are bipolar, where only +1 and -1 are transmitted More pulses are transmitted compared to ternary sequences For example, S1 S8 (length = 31) - each sequence has 15 0 s; S9 S24 (length = 127) - each sequence has 63 0 s; S25 S32 (length = 91) - each sequence has 10 0 s Carlos Aldana

  18. July 2021 doc.: IEEE 15-21-0377-00-04ab S9 Length 127 sequence vs m- sequence m-sequence of length 63 M- sequence of length 63 ternary preamble sequence S9 Ternary preamble sequence S9n Carlos Aldana

  19. July 2021 doc.: IEEE 15-21-0377-00-04ab Periodic Cross-Correlation Periodic cross-correlation between different proposed sequences should be small in order to limit the interference within a piconet Goal is to maximize Sidelobe Suppression Ratio (SSR) autocorrelation peak average cross correlation peak) = 20log10( Carlos Aldana

  20. July 2021 doc.: IEEE 15-21-0377-00-04ab Periodic Cross-Correlation of S25 (Length 91) Maximum Sidelobe Suppression Ratio = 20log10(81/15) = 14.65dB Minimum Sidelobe Suppression Ratio = 20log10(81/27) = 9.54dB Average Sidelobe Suppression Ratio = =20*log10(81/21.43) = 11.55dB Consistent with Table in [5] Carlos Aldana

  21. July 2021 Periodic Cross-Correlation of m-sequences of length 63 doc.: IEEE 15-21-0377-00-04ab Maximum Sidelobe Suppression Ratio = 20log10(63/15) = 12.47dB Minimum Sidelobe Suppression Ratio = 20log10(63/23) = 8.75dB Average Sidelobe Suppression Ratio = 20*log10(63/19) = 10.41dB Carlos Aldana

  22. July 2021 doc.: IEEE 15-21-0377-00-04ab Cross-Correlation with HRP and LRP Preambles Cross-correlation between proposed sequences and legacy HRP and LRP preambles needs to be small Binary m-sequences have length 2n -1, i.e., 15, 31, 63, 127, 255, m-sequences of length 31 and 127 have relatively large cross-correlation with length-31 and length-127 legacy preamble sequences (i.e., S1-S8, S9-S24) m-sequences are robust to LRP preambles Therefore, m-sequences of length 15, 63 and 255 are considered Carlos Aldana

  23. July 2021 doc.: IEEE 15-21-0377-00-04ab Shorter Sync Length for Existing Codes sync_length = Tsym Nsync = Tc K L Nsync K L Sync Length (Nsync = 16 Symbols) Sync Length (Nsync = 64 Symbols) (preamble code length) (length of delta spreading function) #Chips Per Symbol Tsym 31 16 496 0.994us 15.897us 63.590us 31 64 1984 3.974us 63.590us 254.359us 127 4 508 1.018us 16.282us 65.128us 91 4 364 0.729us 11.667us 46.667us Carlos Aldana

  24. July 2021 doc.: IEEE 15-21-0377-00-04ab Sync Length for m sequences Short channels do not need long preamble, and short preamble also reduces PPDU duration Smaller Nsync for LOS short-distance channels Nsync 16 for HRP UWB preambles Nsync = 4 or 8 can work for short channels Smaller L for long sequences For long sequences, e.g., m-sequence of length 255, the delta spreading length L can be 1 or 2 L K Sync Length (Nsync = 4 Symbols) Sync Length (Nsync = 8 Symbols) Sync Length (Nsync = 16 Symbols ) (length of delta spreading function) #Chips Per Symbol (preamble code length) Tsym 15 4 60 0.120us 0.481us 0.962us 1.923us 63 2 126 0.252us 1.010us 2.019us 4.039us 63 4 252 0.505us 2.019us 4.039us 8.077us 255 1 255 0.511us 2.043us 4.087us 8.173us 255 2 510 1.022us 4.087us 8.173us 16.346us Carlos Aldana

  25. July 2021 doc.: IEEE 15-21-0377-00-04ab M-Sequences of Length 15 M15_1 -1,-1,-1,1,1,1,1,-1,1,-1,1,1,-1,-1,1 M15_2 -1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1,1,1 Coherent Cross-Correlation Matrix M15_1 23.52 dB 6.62 dB M15_2 6.62 dB 23.52 dB M15_1 15/1 7 M15_2 7 15/1 6.62 = 20*log10(15/7) 23.52 = 20*log10(15/1) M15_1 M15_2 M15_1 M15_2 Sidelobe Suppression Ratio (dB) is computed as 20log10(autocorrelation peak / cross- correlation peak) Carlos Aldana

  26. July 2021 doc.: IEEE 15-21-0377-00-04ab Tx Rx S1 - S8 (length = 31) Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 12.04 dB Min = 3.25 dB Average = 9.28 dB S9 - S24 (length = 127) S25 - S32 (length = 91) m-sequence (length = 15) Cross-correlation: Max = 14.54 dB Min = 7.82 dB Average = 12.05 dB Cross-correlation: Max = 12.04 dB Min = 6.88 dB Average = 10.08 dB Cross-correlation: Max = 14.54 dB Min = 11.02 dB Average = 12.90 dB S1 - S8 (length = 31) Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 18.06 dB Min = 7.50 dB Average = 13.61 dB Cross-correlation: Max = 22.59 dB Min = 16.12 dB Average = 19.49 dB Cross-correlation: Max = 18.34 dB Min = 13.36 dB Average = 16.05 dB Cross-correlation: Max = 21.32 dB Min = 15.30 dB Average = 19.07 dB S9 - S24 (length = 127) Autocorrelation and cross- correlation metrics of m-sequences of length 15 Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 14.65 dB Min = 9.54 dB Average = 11.36 dB Cross-correlation: Max = 23.36 dB Min = 16.96 dB Average = 20.72 dB Cross-correlation: Max = 21.91 dB Min = 15.56 dB Average = 19.16 dB Cross-correlation: Max = 22.61 dB Min = 18.17 dB Average = 20.24 dB S25 - S32 (length = 91) Autocorrelation: Max = 23.52 dB Min = 23.52 dB Average = 23.52 dB Cross-correlation: Max = 6.62 dB Min = 6.62 dB Average = 6.62 dB Cross-correlation: Max = 14.74 dB Min = 10.95 dB Average = 13.45 dB Cross-correlation: Max = 13.98 dB Min = 8.33 dB Average = 11.97 dB Cross-correlation: Max = 11.48 dB Min = 7.26 dB Average = 9.65 dB m-sequence (length = 15) Carlos Aldana

  27. July 2021 doc.: IEEE 15-21-0377-00-04ab M-Sequences of Length 63 M63_ 1 -1,-1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,1,-1,1,-1,-1,- 1,1,1,-1,-1,-1,-1,1 M63_ 2 -1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,1,-1,1,-1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,1,1,- 1,1,-1,1,-1,1,1,1,1,1,1 M63_ 3 -1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,1,1,1,-1,-1,1,1,-1,-1,-1,1,-1,1,-1,1,- 1,-1,1,1,1,1,1,1,-1,1 M63_ 4 -1,-1,-1,-1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,1,1,1,-1,1,1,1,-1,1,-1,1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,- 1,1,-1,-1,-1,-1,1,1,1 M63_ 5 -1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,1,- 1,-1,1,-1,-1,1,1,1,1 Coherent Cross-Correlation Matrix M63_ 6 -1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,- 1,1,1,-1,-1,1,1,1,-1,1,1 M63_1 63/1 15 17 23 17 23 M63_2 15 63/1 23 17 23 17 M63_3 17 23 63/1 15 23 17 M63_4 23 17 15 63/1 17 23 M63_5 17 23 23 17 63/1 15 M63_6 23 17 17 23 15 63/1 M63_1 35.99 dB 12.46 dB 11.38 dB 12.46 dB 35.99 dB 11.38 dB 8.75 dB 8.75 dB 11.38 dB 12.46 dB 35.99 dB 11.38 dB 11.38 dB 8.75 dB 8.75 dB 8.75 dB 11.38 dB 11.38 dB M63_2 M63_3 M63_4 8.75 dB 11.38 dB M63_5 11.38 dB 8.75 dB 8.75 dB M63_6 8.75 dB 11.38 dB 11.38 dB 8.75 dB M63_1 M63_2 M63_3 M63_4 M63_5 M63_6 M63_1 M63_2 M63_3 M63_4 M63_5 M63_6 8.75 dB 35.99 dB 12.46 dB 11.38 dB 35.99 dB 12.46 dB 8.75 dB 12.46 dB 35.99 dB Sidelobe Suppression Ratio (dB) is computed as 20log10(autocorrelation peak / cross-correlation peak) Carlos Aldana

  28. July 2021 doc.: IEEE 15-21-0377-00-04ab Tx Rx S1 - S8 (length = 31) Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 12.04 dB Min = 3.25 dB Average = 9.28 dB S9 - S24 (length = 127) S25 - S32 (length = 91) m-sequence (length = 63) Cross-correlation: Max = 14.54 dB Min = 7.82 dB Average = 12.05 dB Cross-correlation: Max = 12.04 dB Min = 6.88 dB Average = 10.08 dB Cross-correlation: Max = 12.04 dB Min = 6.58 dB Average = 9.68 dB S1 - S8 (length = 31) Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 18.06 dB Min = 7.50 dB Average = 13.61 dB Cross-correlation: Max = 22.59 dB Min = 16.12 dB Average = 19.49 dB Cross-correlation: Max = 18.34 dB Min = 13.36 dB Average = 16.05 dB Cross-correlation: Max = 19.22 dB Min = 12.60 dB Average = 15.95 dB S9 - S24 (length = 127) Autocorrelation and cross- correlation metrics of m-sequences of length 63 Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 14.65 dB Min = 9.54 dB Average = 11.36 dB Cross-correlation: Max = 23.36 dB Min = 16.96 dB Average = 20.72 dB Cross-correlation: Max = 21.91 dB Min = 15.56 dB Average = 19.16 dB Cross-correlation: Max = 19.58 dB Min = 13.31 dB Average = 17.28 dB S25 - S32 (length = 91) Autocorrelation: Max = 35.99 dB Min = 35.99 dB Average = 35.99 dB Cross-correlation: Max = 12.46 dB Min = 8.75 dB Average = 10.41 dB Cross-correlation: Max = 22.92 dB Min = 17.66 dB Average = 20.23 dB Cross-correlation: Max = 20.42 dB Min = 13.54 dB Average = 17.89 dB Cross-correlation: Max = 18.49 dB Min = 11.90 dB Average = 15.87 dB m-sequence (length = 63) Carlos Aldana

  29. July 2021 doc.: IEEE 15-21-0377-00-04ab M-Sequences of Length 255 M255_1 255/1 31 47 63 63 47 63 63 31 63 63 65 65 95 63 31 M255_2 31 255/1 31 63 63 63 65 63 63 63 31 63 95 65 47 47 M255_3 47 31 255/1 63 47 63 95 65 63 31 63 63 65 63 31 63 M255_4 63 63 63 255/1 31 31 63 63 65 65 95 63 31 63 47 47 M255_5 63 63 47 31 255/1 47 63 65 95 63 65 63 63 31 31 63 M255_6 47 63 63 31 47 255/1 31 63 63 95 65 65 63 63 63 31 M255_7 63 65 95 63 63 31 255/1 31 47 63 63 63 31 47 65 63 M255_8 63 63 65 63 65 63 31 255/1 31 63 47 63 47 63 95 31 M255_9 M255_10 M255_11 M255_12 M255_13 M255_14 M255_15 M255_16 31 63 63 65 63 63 31 63 63 31 63 63 65 65 95 63 95 63 65 63 63 95 65 65 47 63 63 63 31 63 47 63 255/1 47 31 63 47 255/1 31 31 31 31 255/1 47 63 31 47 255/1 63 63 63 47 63 47 63 31 65 63 63 31 63 65 63 95 M255_1 M255_2 M255_3 M255_4 M255_5 M255_6 M255_7 M255_8 M255_9 M255_10 M255_11 M255_12 M255_13 M255_14 M255_15 M255_16 65 95 65 31 63 63 31 47 63 63 63 47 95 65 63 63 31 63 47 63 63 47 63 31 31 63 47 31 47 31 63 65 95 65 63 63 31 63 63 31 47 63 47 63 31 63 31 63 65 63 95 63 65 63 255/1 31 63 63 255/1 63 65 255/1 63 255/1 Carlos Aldana

  30. July 2021 doc.: IEEE 15-21-0377-00-04ab M-Sequences of Length 255 M255_1 48.13 18.3 14.69 12.14 12.14 14.69 12.14 12.14 18.3 12.14 12.14 11.87 11.87 8.58 12.14 18.3 M255_2 18.3 48.13 18.3 12.14 12.14 12.14 11.87 12.14 12.14 12.14 18.3 12.14 8.58 11.87 14.69 14.69 M255_3 14.69 18.3 48.13 12.14 14.69 12.14 8.58 11.87 12.14 18.3 12.14 12.14 11.87 12.14 18.3 12.14 M255_4 12.14 12.14 12.14 48.13 18.3 18.3 12.14 12.14 11.87 11.87 8.58 12.14 18.3 12.14 14.69 14.69 M255_5 12.14 12.14 14.69 18.3 48.13 14.69 12.14 11.87 8.58 12.14 11.87 12.14 12.14 18.3 18.3 12.14 M255_6 14.69 12.14 12.14 18.3 14.69 48.13 18.3 12.14 12.14 8.58 11.87 11.87 12.14 12.14 12.14 18.3 M255_7 12.14 11.87 8.58 12.14 12.14 18.3 48.13 18.3 14.69 12.14 12.14 12.14 18.3 14.69 11.87 12.14 M255_8 12.14 12.14 11.87 12.14 11.87 12.14 18.3 48.13 18.3 12.14 14.69 12.14 14.69 12.14 8.58 18.3 M255_9 M255_10 M255_11 M255_12 M255_13 M255_14 M255_15 M255_16 18.3 12.14 12.14 11.87 12.14 12.14 18.3 12.14 12.14 18.3 12.14 12.14 11.87 11.87 8.58 12.14 8.58 12.14 11.87 12.14 12.14 8.58 11.87 11.87 14.69 12.14 12.14 12.14 18.3 12.14 14.69 12.14 48.13 14.69 18.3 12.14 14.69 48.13 18.3 18.3 18.3 18.3 48.13 14.69 12.14 18.3 14.69 48.13 12.14 12.14 12.14 14.69 12.14 14.69 12.14 18.3 11.87 12.14 12.14 18.3 12.14 11.87 12.14 8.58 M255_1 M255_2 M255_3 M255_4 M255_5 M255_6 M255_7 M255_8 M255_9 M255_10 M255_11 M255_12 M255_13 M255_14 M255_15 M255_16 11.87 8.58 11.87 18.3 12.14 12.14 18.3 14.69 12.14 12.14 12.14 14.69 48.13 18.3 12.14 12.14 8.58 11.87 12.14 12.14 18.3 12.14 14.69 12.14 12.14 14.69 12.14 18.3 18.3 48.13 12.14 11.87 12.14 14.69 18.3 14.69 18.3 12.14 11.87 8.58 11.87 12.14 12.14 18.3 12.14 12.14 48.13 12.14 18.3 14.69 12.14 14.69 12.14 18.3 12.14 18.3 12.14 11.87 12.14 8.58 12.14 11.87 12.14 48.13 Sidelobe Suppression Ratio (dB) Carlos Aldana

  31. July 2021 doc.: IEEE 15-21-0377-00-04ab Tx Rx S1 - S8 (length = 31) Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 12.04 dB Min = 3.25 dB Average = 9.28 dB S9 - S24 (length = 127) S25 - S32 (length = 91) m-sequence (length = 255) Cross-correlation: Max = 14.54 dB Min = 7.82 dB Average = 12.05 dB Cross-correlation: Max = 12.04 dB Min = 6.88 dB Average = 10.08 dB Cross-correlation: Max = 11.02 dB Min = 5.49 dB Average = 8.60 dB S1 - S8 (length = 31) Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 18.06 dB Min = 7.50 dB Average = 13.61 dB Cross-correlation: Max = 22.59 dB Min = 16.12 dB Average = 19.49 dB Cross-correlation: Max = 18.34 dB Min = 13.36 dB Average = 16.05 dB Cross-correlation: Max = 17.04 dB Min = 10.55 dB Average = 14.45 dB S9 - S24 (length = 127) Autocorrelation and cross- correlation metrics of m-sequences of length 255 Autocorrelation: Max = Inf dB Min = Inf dB Average = Inf dB Cross-correlation: Max = 14.65 dB Min = 9.54 dB Average = 11.36 dB Cross-correlation: Max = 23.36 dB Min = 16.96 dB Average = 20.72 dB Cross-correlation: Max = 21.91 dB Min = 15.56 dB Average = 19.16 dB Cross-correlation: Max = 17.75 dB Min = 13.31 dB Average = 15.59 dB S25 - S32 (length = 91) Autocorrelation: Max = 48.13 dB Min = 48.13 dB Average = 48.13 dB Cross-correlation: Max = 18.30 dB Min = 8.58 dB Average = 13.03 dB Cross-correlation: Max = 29.29 dB Min = 23.03 dB Average = 26.06 dB Cross-correlation: Max = 26.73 dB Min = 20.09 dB Average = 24.13 dB Cross-correlation: Max = 24.47 dB Min = 18.81 dB Average = 22.15 dB m-sequence (length = 255) Carlos Aldana

  32. July 2021 doc.: IEEE 15-21-0377-00-04ab M-Sequences of Length 255 M255_1 -1,-1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,-1,1,1,1,1,-1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,- 1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1,1,-1,1,1,1,1,-1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,- 1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,1,-1,- 1,-1,1,-1,1,1,1,-1,1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,1,-1,-1,1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,- 1,1,1,1,-1,1,1,-1,-1,1,-1,-1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,1,1,-1,-1,-1,1 M255_2 -1,-1,-1,-1,-1,-1,-1,1,-1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,- 1,1,1,-1,1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,1,1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,-1,1,-1,-1,1,1,- 1,1,1,1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,- 1,1,-1,-1,1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,1,1,1,-1,1,1,1,1,1,-1,-1,-1,-1,- 1,1,1,-1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,1,-1,1,-1,-1,1 M255_3 -1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,-1,-1,- 1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,- 1,1,-1,1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,- 1,-1,1,-1,1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,1,-1,-1,1,-1,- 1,1,1,1,-1,1,-1,1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,1,1,-1,1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1 M255_4 -1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,1,1,-1,-1,1,- 1,-1,1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,-1,1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,-1,1,1,1,1,1,1,-1,-1,1,-1,1,1,-1,- 1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,-1,1,- 1,1,1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,1,1,1,-1,1,-1,-1,1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,- 1,-1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,1,1,1,-1,1 Carlos Aldana

  33. July 2021 doc.: IEEE 15-21-0377-00-04ab M-Sequences of Length 255 M255_5 -1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,1,-1,-1,1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,- 1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,-1,1,-1,1,- 1,1,1,1,1,1,1,1,1,-1,1,1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,-1,-1,- 1,-1,-1,1,-1,-1,-1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,1,-1,-1,1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,- 1,1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,-1,1,1,1,1,1,1 M255_6 -1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,-1,1,1,1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,-1,1,-1,-1,- 1,1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,1,- 1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,1,-1,1,1,1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,-1,1,1,-1,- 1,-1,1,-1,1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,-1,-1,1,-1,- 1,1,1,1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1 M255_7 -1,-1,-1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,1,1,1,1,-1,- 1,1,-1,-1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,- 1,1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,-1,1,-1,1,1,1,-1,1,1,1,1,1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,- 1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1,-1,-1,-1,1,-1,-1,- 1,1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,1,1,1,1,-1,1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,1,-1,-1,1 M255_8 -1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,1,1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,-1,-1,-1,-1,1,-1,1,1,1,1,1,-1,1,-1,-1,1,-1,- 1,1,-1,-1,-1,1,-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,1,-1,1,- 1,-1,1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,-1,-1,- 1,1,1,1,1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,1,1,-1,-1,1,1,-1,1,-1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,1,1,- 1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,-1,1 Carlos Aldana

  34. July 2021 doc.: IEEE 15-21-0377-00-04ab M-Sequences of Length 255 M255_9 -1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,-1,1,-1,-1,1,1,-1,1,1,1,-1,-1,1,-1,- 1,-1,-1,-1,1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1,1,-1,1,1,-1,1,1,1,1,-1,1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,- 1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,- 1,1,1,1,-1,1,1,1,-1,1,1,-1,-1,1,1,1,1,-1,1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,1,1,-1,1,-1,1,- 1,1,-1,1,1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,-1,1,1,-1,1 M255_1 0 -1,-1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,1,-1,1,1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,1,-1,1,-1,1,1,1,- 1,-1,1,-1,-1,1,1,-1,1,1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,1,-1,-1,1,- 1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,1,-1,-1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,1,-1,1,1,- 1,-1,1,-1,1,-1,-1,-1,1,-1,1,1,-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,- 1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1 M255_1 1 -1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,1,1,-1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,- 1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,1,1,1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,-1,- 1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,- 1,1,1,1,1,-1,1,1,-1,-1,1,-1,1,-1,1,1,1,-1,1,-1,1,1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1,- 1,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,1,-1,1 M255_1 2 -1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,-1,1,-1,1,-1,-1,1,1,-1,1,-1,1,1,-1,-1,-1,- 1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,1,1,-1,1,1,1,1,-1,- 1,1,-1,1,-1,1,1,1,-1,1,1,1,1,1,1,1,1,-1,1,1,-1,1,-1,-1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,1,1,-1,1,1,- 1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,- 1,1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,1,1,1,1,-1,-1,1,1 Carlos Aldana

  35. July 2021 doc.: IEEE 15-21-0377-00-04ab M-Sequences of Length 255 M255_1 3 -1,-1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,-1,-1,-1,- 1,1,-1,1,-1,1,1,1,1,1,1,1,1,-1,-1,1,-1,1,1,1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,1,-1,- 1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,- 1,1,1,-1,1,-1,-1,1,1,1,1,1,1,-1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,- 1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,-1,-1,1,1,1,1,1 M255_1 4 -1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,-1,-1,-1,1,-1,1,-1,-1,- 1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1,-1,-1,1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,-1,-1,- 1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,1,-1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,1,1,-1,-1,1,1,-1,1,1,- 1,1,1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,- 1,1,1,1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,-1,-1,1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,-1,1,1,-1,1,1 M255_1 5 -1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,1,1,1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,- 1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,- 1,1,1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,-1,1,-1,1,1,-1,1,1,1,1,1,1,1,1,-1,1,1,1,-1,1,-1,1,- 1,-1,1,1,1,1,-1,1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,1,-1,-1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,1,1,-1,-1,-1,1,1,- 1,-1,-1,-1,1,1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,1,1 M255_1 6 -1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,-1,-1,-1,- 1,1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,1,-1,1,-1,1,1,-1,-1,1,1,-1,1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,- 1,1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,- 1,-1,1,-1,1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,1,-1,-1,- 1,1,-1,-1,1,-1,-1,1,-1,1,1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,-1,-1,-1,1,-1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,1 Carlos Aldana

  36. July 2021 doc.: IEEE 15-21-0377-00-04ab Conclusions m-sequences could be used as preamble codes for 802.15.4ab data communications Good autocorrelation and cross-correlation properties m-sequences of length 15 could be applied to short-distance LOS channels m-sequences of length 63 and 255 could be applied to longer-distance or NLOS channels Sync Length can be reduced by using shorter delta spreading function (L=1, 2) and fewer number of preamble symbols (e.g. Nsync = 8, 16) Carlos Aldana

  37. July 2021 doc.: IEEE 15-21-0377-00-04ab References [1] 15-21-297-01 15.4.ab Technical Guidance Doc [2] A.F. Molisch et al., IEEE 802.15.4a Channel Model - Final Report, IEEE TG802.15.4a, 15-04-0662-08-004a, November, 2004. [3] IEEE Std 802.15.4z-2020 [4] V. P. Ipatov, Ternary sequences with ideal autocorrelation properties Radio Eng. Electron. Phys., vol. 24, pp. 75 79, Oct. 1979. [5] 15-21-152-00 802.15.4z - HRP UWB PHY - HPRF mode preamble sequence cross-correlation properties [6] 15-05-737-01 Length 127 Preamble codes for 500 MHz and 1500 MHz bands Carlos Aldana Slide 37

  38. July 2021 doc.: IEEE 15-21-0377-00-04ab Questions? Carlos Aldana Slide 38

  39. July 2021 doc.: IEEE 15-21-0377-00-04ab APPENDIX Carlos Aldana Slide 39

  40. July 2021 doc.: IEEE 15-21-0377-00-04ab CM1 Channel peak is normalized to 0dB Significant components of CM1 channels have delay < 120 ns preamble symbol length Tsymneeds to 120 ns 60 chips for channel estimation Carlos Aldana

  41. July 2021 doc.: IEEE 15-21-0377-00-04ab Channel Estimation matched filter correlates 1 preamble symbol matched filter correlates 4 consecutive preamble symbols Matched filter output is equal to the channel impulse response plus noise (assume symbol length channel length) Carlos Aldana

  42. July 2021 doc.: IEEE 15-21-0377-00-04ab Channel Estimation matched filter correlates 1 preamble symbol matched filter correlates 4 consecutive preamble symbols 4 preamble symbol is used for channel estimation m-sequences can perform well as the ternary sequences in matched- filter based channel estimation Carlos Aldana

  43. July 2021 doc.: IEEE 15-21-0377-00-04ab Channel Estimation 1 preamble symbol is used for channel estimation 4 preamble symbol is used for channel estimation Performance of channel estimation can be improved by using least squares Carlos Aldana

  44. July 2021 doc.: IEEE 15-21-0377-00-04ab LRP Modes LRP base mode (1 Mb/s) Tsym = 1us, Tchip = 1us, 1 chip per symbol Each pulse is much shorter than Tchip Preamble: a continuous stream of pulses with length 16 128 at the base mode PRF of 1 MHz Carlos Aldana

  45. July 2021 doc.: IEEE 15-21-0377-00-04ab LRP Modes LRP extended mode (250 kb/s) Tsym = 4us, Tchip = 1us, 4 chips per symbol Preamble: a continuous stream of pulses with length 16 256 Carlos Aldana

  46. July 2021 doc.: IEEE 15-21-0377-00-04ab LRP Modes LRP long-range mode (31.25 kb/s) Tsym = 32us, Tchip = 0.5us Preamble consists of 3 parts: Part 1: a continuous stream of 1024 - 8192 pulses Part 2: - - - P - P - - P - - P P P - P ( P pulse; - no pulse) Part 3: a stream of 16 64 1 symbols Carlos Aldana

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