A Time Domain Atmospheric Noise Level Analysis

1. A Time Domain Atmospheric Noise Level Analysis Lee Boyce International Loran Association Boulder, CO 7 November 2003

2. Lightning • Cloud to Ground • Preliminary breakdown • Stepped leader • Attachment • First return stroke • J & K process • Dart leader • Subsequent return stroke • Intra-Cloud Discharge • J & K process • Q noise

3. Time Histories Return Preliminary Breakdown Stepped Leader Unipolar & Bipolar K-Process ~400us

4. Time Histories (cont)

5. Noise E-Field of a Typical Day

6. Noise Model

7. Clipping and Hole-Punching Clipping Unfiltered Hole-Punching (Blanking)

8. Hole-Punching

9. Key Question • How do we claim credit for hole-punching over linear processing? • Past work • Feldman 12dB-17dB improvement (on severe days) using two channels for a communication receiver. • Spaulding & Middleton LOBD 30dB, but there are many caveats. • Qualitative explanation • Usually performance will be a function of the level at which the Non-Gaussian component takes over. • Can come up with an estimate based on “hole-punching” that is not too bad.

10. Goals • Calculate a bound for noise analysis that is better than linear processing • Use available data (CCIR, measurements) • Hole-punch out large non­Gaussian impulses • Calculate Gaussian residual • Develop a model for atmospheric noise

11. CCIR • Used the ARN-2 Radio Noise Recorder • 16 Stations around the globe • Average noise power at each of eight frequencies for fifteen minutes each hour • 13 kHz, 11kHz, 250kHz, 500kHz, 2.5MHz, 5MHz, 10MHz, and 20MHz • 1957-1961 (4 years) → 8640 15-minute measurements → 99.98% • Tracked filtered noise envelope not instantaneous noise • Took high speed data to obtain APDs (400Hz) • Sectioned the year into seasons and time blocks • Four 90-day seasons • Six 4-hour time blocks • Tracked external antenna noise factor, Fa • Power received through a loss-free antenna Fa = 10*log10(Pn/KToB) • Lists the median value hourly value for each time block, Fam, at 1 MHz • Lists the upper decile (90%) level Du • Calculate noise E-field from Fa, BW, frequency • Use normal or log-normal statistics and graphs to adjust values • Limitations • Average background noise, local thunderstorms not included • If power averaged over several minutes, it’s a constant, except when there are local thunderstorms • Noise BW is wider than Rx BW

12. CCIR (cont) • Noise Factor, Fa • Determines absolute measure Erms (uV/m) • Varies with location • Bandwidth independent • Voltage deviation, Vd • Determines APD curve • Uncorrelated to Noise Factor • APD gives strength relative to RMS value, parameterized by Vd • Enoise(%) = Erms(Fa) + APD(Vd)

13. APD Review • Amplitude Probability Distributions or Apriori Probability Distributions • APD = 1 - CDF • Shows the percentage of time that a given envelope voltage level is exceeded • Envelope, A, is Rayleigh = Sqrt(Gaussian12 + Gaussian22) • Rayleigh Distribution is a Line • Values relative to RMS (0 dB) • Parameterized by Voltage Deviation, Vd • Vd = 20*log10(RMS Voltage / Avg Voltage) • High amplitude samples dominate Vd D = A - Arms 0 0.0001% 36% 99% P [D Exceeded]

14. 60 50 40 30 20 10 0 -10 -20 -30 -40 • CCIR uses these • Large database over 4 years • APD referenced to RMS value • Parameterized by Vd • Noise BW is wider than Rx 0dB = ARMS D = A - Arms Vd = 1.05 Vd=30 12 14 0.01 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.001 0.1 P [D Exceeded] 0.0001

15. 60 50 40 30 20 10 0 -10 -20 -30 -40 • Atmospheric noise is Non-Gaussian overall but has a strong Gaussian component, hence Rayleigh Envelope • Vd coupled amount of time that the signal is Rayleigh • Hole Punch whenever the Noise Level is more than 3dB above the Rayleigh component • Get measure of signal suppression D = A - Arms Rayleigh Vd = 1.05 3dB Hole Punched “Suppressed” Vd = 10 Rayleigh “Available” 0.01 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.001 0.1 P [D Exceeded] 0.0001

16. Hole Punch Signal Suppression Loss or Signal Suppression [dB]

17. 60 50 40 30 20 10 0 -10 -20 -30 -40 • Vd coupled to the strength of Rayleigh Component • Measured how far below RMS value Rayleigh component was • Get measure of Rayleigh signal strength • Reduces the noise numbers D = A - Arms Rayleigh Level Relative to RMS Rayleigh -20dB Vd = 1.05 Vd = 10 0.01 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.001 0.1 P [D Exceeded] 0.0001

18. Difference between RMS and Rayleigh Level

19. Noise Model • Break up Atmospheric Noise into two parts • Hole Punch non-Rayleigh (non­Gaussian) noise out • Increases Noise • Reduce noise level from RMS value to Rayleigh level • Decreases Noise

20. Total Effect of Hole Punch and Vd on Noise Level

21. Median 95% Level of Erms

22. Median 95% Effective Noise Level

23. Summary of Noise 1 Summer 18h Worst Case 2 Spring 18h Worst Case

24. July 9, 2002 Upland, IN>10kA Strikes 1600-2259 UTC (10:00a – 4:59p CDT) Click on map for animation

25. Taylor Univ. - Upland, Indiana • 300Hz-40kHz BW • 100kS/s • Filter BW wide enough to contain interference

26. Results of Processing • Less signal suppression than predicted • Lower difference between Vrms and Rayleigh Level • Median 50% E-field @ Taylor 20kHz BW 40kHz = 75 dB uV/m

27. 1620h Taylor, IN

28. 2220h Taylor, IN

29. Simulation • Try to keep 1st Order Statistics (APD) • Get the flavor of the time structure • Use two continuous Markov processes to describe close and far discharges

30. Markov Chain for Discharges Local Remote

31. Data Comparison Data Simulation

32. Simulated and Actual Data APD

33. Summary • Non-linear processing analysis should give goals for real design. • Have the makings of a good atmospheric noise model. • 1st order statistics preserved • Adequately show time dependency • Need data from Midwest or Gulf during peak times with Loran Rx to verify analysis.

34. Acknowledgements • Mitch Narins FAA Program Manager • John Cramer & Ken Cummins, Vaisala Inc • Umran Inan & Troy Wood, Department of Electrical Engineering, Stanford University

35. Backup Slides

36. Before Storm 16:20 (UTC)

37. Before Storm Data

38. During Storm 22:20 (UTC)

39. During Storm Data

40. Lines up well

41. Pulse Shape Comparison

42. Data Wiping Before Storm

43. Data Wiping During Storm

44. Captured and Missed Pulses

45. What is the correct N in SNR? • Need to estimate the noise and the processing gains correctly. • Frequency domain estimate will kill us. • Is there structure in the time domain that we may exploit? • Model as Gaussian + impulsive noise? 110 90 70 50 30 10 -10 -30 E-Field (dB uV/m) Courtesy of Weidman et al 1981

46. Sept 2001 Data Night Day High Activity Low Activity +22dB to Noise and +15dB to Vd due to BWR

47. Median 95% Level of Erms

48. Median 95 % Gaussian Noise Level

49. Median 95% Effective Noise Level

50. Median 99% Level of Erms