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Generalized SZ Phase Codes

Generalized SZ Phase Codes. Sebastián Torres CIMMS/NSSL. Data Quality MOU – Technical Interchange Meeting Fall 2008. Outline. Generalized phase codes Results on simulated data Data with no phase errors ( recap ) Data with phase errors Results on real data Test VCP Summary/Future Work.

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Generalized SZ Phase Codes

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  1. Generalized SZ Phase Codes Sebastián Torres CIMMS/NSSL Data Quality MOU – Technical Interchange Meeting Fall 2008

  2. Outline • Generalized phase codes • Results on simulated data • Data with no phase errors (recap) • Data with phase errors • Results on real data • Test VCP • Summary/Future Work

  3. Beyond SZ(8/64) • SZ(8/64) is optimum (NSSL Report #2, 1997) • Is this really the case for every overlaid case? • How does SZ(8/64) compare to other phase codes? • Is there a phase code that can be used to recover overlaid echoes beyond the 4th trip?

  4. Generalized SZ(n/64) Codes • SZ(n/64) phase code: • SZ(n/64) exploits WSR-88D phase shifter resolution to the maximum • Phase shifter in the WSR-88D has 7 bits • Phase resolution is 2p/128 = p/64 • SZ(n/64) leads to M = 2k • Not such an issue nowadays • SZ-2 can handle these codes with minor software changes

  5. Evaluation of SZ(n/64) Codes • Weak-trip velocity recovery depends on • Phase code • PNF notch width • Performance can be quantified in terms of the size of the “recovery region” • On the S1/S2 vs svS plane,this is the number of cases for which SD(vW) meets requirements • SD(vW) ≤ 2 m/s@ svS = 4 m/s

  6. Performance of SZ(n/64) CodesNo Phase Errors Size of Recovery Region Overlaid Case 1 Overlaid Case 1 Overlaid Case 2 382 Overlaid Case 3 Overlaid Case 4 1

  7. Performance of SZ-2 vs. Best CodesNo Phase Errors Size of Recovery Region Overlaid Case 1 Overlaid Case 2 SZ(56/64) SZ(28/64) 8 8 48 32 SZ(62/64) Overlaid Case 3 Overlaid Case 4 SZ(3/64) 8 8 32 48

  8. Origin of Phase Errors • Phase errors can be due to • Phase shifter • Constant: quantization error • NSSL Report 7 • Random: jitter, voltage fluctuations, signal path • NSSL Report 2, NSSL Report 7 • Burst pulse measurement • Random • Others?

  9. Mathematics of Phase Errors • First-trip time series (strong): V1 • Second-trip time series (weak): V2 • Tx switching code: Y= exp(jy) • Received time series: V = V1Y1 + V2Y2 • Rx switching code: Y’ • Strong-trip cohered time series: • V1’ = V1Y1Y’1* + V2Y2Y’1* • If Y = Y’, V1’ = V1 + V2Y2Y1* • If Y = Y’ = SZ(8/64), V1’ = V1 + V2F • My simulation: • Y = SZ(8/64), Y’ = SZ(8/64) + Ye • arg(Ye) is uniformly distributed in [-0.5, 0.5] deg Perfect Modulation Code

  10. Performance of SZ-2 vs. Best CodesNo Phase Errors Size of Recovery Region Overlaid Case 1 Overlaid Case 2 Overlaid Case 3 Overlaid Case 4

  11. SZ-2 PerformanceNo Phase Errors Size of Recovery Region

  12. SZ-2 PerformancePhase Errors Size of Recovery Region

  13. SZ-2 PerformancePhase Errors Size of Recovery Region

  14. SZ-2 PerformanceNo Phase Errors Size of Recovery Region

  15. Best SZ(n/64) CodesNo Phase Errors • For overlaid signals with one trip difference, the best code is SZ(8/64) • For overlaid signals with more than one trip difference, the best code is not SZ(8/64) • There is no single code that is optimum for all overlaid cases

  16. Best SZ(n/64) CodesPhase Errors • For overlaid signals with one trip difference, the best code is SZ(10/64) • Not SZ(8/64)! • PNF notch width is narrower if there are phase errors • There is no single code that is optimum for all overlaid cases

  17. SZ-2 vs. Best CodesNo Phase Errors SZ(8/64)

  18. SZ-2 vs. Best CodesNo Phase Errors Best Codes

  19. SZ-2 vs. Best CodesPhase Errors SZ(8/64)

  20. SZ-2 vs. Best CodesPhase Errors Best Codes

  21. Best Overall SZ(n/64) CodeNo Phase Errors • What is the best single code considering overlaid cases 1, 2, and 3? (1st – 4th trips) • SZ(4/64) is the optimum code for recovery of up to 4th trip overlaid echoes • For a trip difference of 1, SZ(4/64) is 10% worse • For a trip difference of 2, SZ(4/64) is ~30% better • For a trip difference of 3, SZ(4/64) is ~50% better Bonus!

  22. Best Overall SZ(n/64) CodePhase Errors • What is the best single code considering overlaid cases 1, 2, and 3? (1st – 4th trips) • SZ(4/64) is the optimum code for recovery of up to 4th trip overlaid echoes • For a trip difference of 1, SZ(4/64) is ~5% better • For a trip difference of 2, SZ(4/64) is ~15% better • For a trip difference of 3, SZ(4/64) is ~50% better Bonus!

  23. SZ-2 vs. Best Overall CodeNo Phase Errors SZ(8/64)

  24. SZ-2 vs. Best Overall CodeNo Phase Errors SZ(4/64)

  25. SZ-2 vs. Best Overall CodePhase Errors SZ(8/64)

  26. SZ-2 vs. Best Overall CodePhase Errors SZ(4/64)

  27. Real Data Collection • SZ(3/64) and SZ(4/64) added to the RRDA • Test VCP 2052 created • Two elevations: 0.5 and 1.5 deg • For each elevation: • Surveillance scan • Non-phase-coded Doppler scan • SZ(8/64), SZ(4/64), and SZ(3/64) phase-coded Doppler scans • Data collected on 09/11/08 • VCP 2052 and stationary antenna • Looking for overlaid cases 2 and 3 • SZ-2 modified to process SZ(n/64) • PNF notch widths • Recovery regions (I did not change them)

  28. 20:47 UTC 11 September 08 - Reflectivity

  29. SZ-2 Velocity – SZ(8/64)

  30. SZ-2 Velocity – SZ(4/64)

  31. Strong/Weak Trip Locations Strong Weak

  32. Strong-Weak Trip Differences

  33. Strong-Weak Trip Differences

  34. SZ-2 Velocity – SZ(8/64)

  35. SZ-2 Velocity – SZ(4/64)

  36. Summary and Future Work • SZ(8/64) is optimum only for overlaid signals with a one-trip difference and no phase errors • SZ(4/64) is the optimum code for the recovery of up to 4th trip overlaid echoes • Limited evidence: • Simulated data with no phase errors • Simulated data with phase errors (one case) • Need to examine other types/levels of phase errors • One “so-so” case of real data • Need to collect data with more gates exhibiting case 2 or 3 overlay • Future work • More simulation and real-data analyses • Is this something we want to pursue any further?

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