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 Preliminary Breakdown Stepped Leader Return 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 Unfiltered Clipping 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 – (4 years) → 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, F a –Power received through a loss-free antenna F a = 10*log 10 (P n /KT o B) –Lists the median value hourly value for each time block, F am, 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 E rms (uV/m) –Varies with location –Bandwidth independent Voltage deviation, V d –Determines APD curve –Uncorrelated to Noise Factor –APD gives strength relative to RMS value, parameterized by V d E noise (%) = E rms (Fa) + APD(V d )

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(Gaussian Gaussian 2 2 ) Rayleigh Distribution is a Line Values relative to RMS (0 dB) Parameterized by Voltage Deviation, V d –V d = 20*log 10 (RMS Voltage / Avg Voltage) –High amplitude samples dominate V d 99%0.0001%36% 0  = A - A rms P [  Exceeded]

CCIR uses these Large database over 4 years APD referenced to RMS value Parameterized by V d Noise BW is wider than Rx  = A - A rms V d = V d =30 0dB = A RMS P [  Exceeded]

15 V d =  = A - A rms P [  Exceeded] V d = Rayleigh 3dB Atmospheric noise is Non-Gaussian overall but has a strong Gaussian component, hence Rayleigh Envelope V d 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 Rayleigh “Available” Hole Punched “Suppressed”

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

17 V d =  = A - A rms P [  Exceeded] V d = Rayleigh -20dB V d 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 Rayleigh Level Relative to RMS

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 V d on Noise Level

21 Median 95% Level of E rms

22 Median 95% Effective Noise Level

23 Summary of Noise Percentage Fa (Availability) E rms Noise Level [dB  V/m] Effective Noise Level [dB  V/m] SNR Assuming 60 dB  V/m Summer 18h Worst Case 2 Spring 18h Worst Case

24 July 9, 2002 Upland, IN >10kA Strikes 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% Taylor 20kHz BW 40kHz = 75 dB uV/m

h Taylor, IN

h Taylor, IN

29 Simulation Try to keep 1 st 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 Simulation Data

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. –1 st 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? Courtesy of Weidman et al 1981 E-Field (dB uV/m)

46 Sept 2001 Data Low Activity High Activity +22dB to Noise and +15dB to V d due to BWR DayNight

47 Median 95% Level of E rms

48 Median 95 % Gaussian Noise Level

49 Median 95% Effective Noise Level

50 Median 99% Level of E rms

51 Median 99% Effective Noise Level

52 Median 99% Effective Noise Level (Spring)

53 Cross-over for Worst Case Spring Du is larger than for Summer. In the low-probability (>99.9%) conditions, the Spring 18h Fa exceeds Summer 18h value.

54 Median 99.9% Effective Noise Level (Summer)

55 Median 99.9% Effective Noise Level (Spring)

56 Median 99.99% Level of E rms

57 Median 99.99% Effective Noise Level

58 Median 99.99% Effective Noise Level

59 Current Work Obtained & processed NLDN data for July & August 2002 –Rated days as noisy or quiet based on number of lightning strikes within 30 km (16 NM) or 300 km (160 NM) –Only a few bad days in 2 months Obtained & processed some days of Upland, IN data –Worst times and worst days not available –Some bad times for worst day is available

60 NLDN Data –Range of days from July 9 to August 27, 2002 –Rated days as noisy or quiet based on number of lightning strikes within 30 km (16 NM) or 300 km (160 NM) –Only a few bad days in 2 months Upland, IN data –Worst times and worst days not available –Some bad times for worst day is available

61 NLDN Data DateStart HourEnd Hour< 30 [km] [km] 2002/07/0920:20:2821:20: /07/0921:20:2922:20:  2002/07/0922:20:2823:20:  2002/07/0923:20:2823:59: /07/2616:00:0516:59:  2002/07/2617:00:0117:59:  2002/07/2618:00:0019:00:  2002/08/2222:00:0122:59:  2002/08/2223:00:0023:59:  2002/08/2300:00:0001:00:  2002/08/2301:00:0501:59:  2002/08/2302:00:0102:59:  2002/08/2303:00:0004:00:  2002/08/2319:00:0119:59:  2002/08/2320:00:0220:59:  2002/08/2321:00:0121:59:  2002/08/ /08/080  2002/08/090 Noisy Days Quiet Days < 500 [km]

62 Experiment ARI

63 July 9, 2002 Upland, IN >10kA Strikes UTC (3:20a – 8:59p CDT)

64 APDs of 1 Minute Samples (Pre-IF Filter) Storm getting nearer 180  V/m 16h 22h

65 Normalized APD (Post-IF) Storm getting nearer 16h 22h

66 95% Signal Available

67 40% Signal Available

68 Pre-IF Filter (Bad Day)

69 Post-IF Filter (Bad Day)

70 Post-IF Filter (Good? Day)

APD referenced to RMS value Calculated V d =10 Offset probably due to clipping Overlays between 12 < V d < 14  = A - A rms P [  Exceeded] V d = V d =30

72 August 8, 2002 Upland, IN >10kA Strikes UTC (7:00p – 8:59p CDT)

73 Post-IF Filter (Good? Day)

74 August 8, 2002 Upland, IN >10kA Strikes UTC (7:00p – 8:59p CDT)

75 For Further Study Make sure number of strikes/GRI will never completely wipe out availability Validate curves for higher Vd Get large dynamic range measurements without clipping Take data within a large storm tied to NLDN Agree on extent of variances Availability implies 50% Levels

76 Use of CCIR Data RMS Value + APD = Total Noise Strength (absolute) (relative to rms) Given a center frequency of 100kHz with a 30kHz BW we get V d.

77 National Lightning Detection Network Privately run Real-Time data collection Mostly detection and high level data Some waveform data Can use newer analytical field models

78 Progress II Atmospheric Models –Hall/Feldman Simple analytical description Empirically derived parameters Captures atmospheric noise reasonably well Unbounded second moment: infinite energy –Middleton Almost all physically derived parameters Works for a wide range of noise processes Class A model works great Class B model only half works Bounded second moment, unlike Hall May be useful for UWB –Weibull Semi-physical parameters Works for some Class B noise, but doesn’t seem to capture intermediate statistics Bounded second moment Models allow analytical calculation of moments and simulation

79 Loran Aperture-RF-IF

80 Reception Probabilities ≡ Strike/GRI

81 Conclusion Want 500 – 1000 “good” signals = 63 – 125 GRIs = 6.3 – 12.5 sec If we use the binomial distribution with probability, p ≡ Strike/GRI/100, at worst case (p=0.3) need ~4x number of signals. Need to integrate for sec between valid updates

82 Middleton’s Assumptions Source locations and emission times are Poisson distributed in space Narrow-band receiver condition Δf ARI ≪ f ₀ –The characteristic function is independent of phase "Local Stationarity" –No changes in average source numbers and emission properties during the observation period T

83 Class A –  F N <<  F R –Clearly seen noise –Threshold on amplitude Class B –  F N >>  F R –Infinite duration –Poisson amplitudes

84 Class B Parameters A B ≡ Avg. rate of signal generation * Avg. duration A α = The “effective” impulse index, which depends on the α-moment of the basic envelope of the output of the IF. α = the spatial density-propagation parameter. It provides and "effective" measure of the average source density with range. Thus we can calculate the power law for the source. This provides information on the emitting source. Ω 2B = The intensity of the "impulsive" component Γ B ≡ σ G ²/Ω 2B = The ratio of the intensity of the independent Gaussian component σ G ² to Ω 2B the intensity of the "impulsive" non-Gaussian N I = the scaling factor which insures that the pdfs match up and yield the correct mean square envelope. ε B = the empirically seen “bend-over” point

85 Class B Model

86

87 Future Work Develop Hall Model Produce curve of V d vs. % Time and V d vs. Gaussian level for different seasons Use numbers to re-run probability analysis to determine required time for inertial system.

88 Another Blanking Example

89 What is CCIR 322-2? Reported background atmospheric noise levels Evolved into ITU P372-7 –Included man-made and galactic noise –Removed technical background 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 – (4 years) → minute measurements → 99.98% –Tracked filtered noise envelope not instantaneous noise –Took high speed data to obtain APDs (400Hz)

90 What is CCIR 322-2? (cont) Sectioned the year into seasons and time blocks –Four 90-day seasons –Six 4-hour time blocks Tracked external antenna noise factor, F a –Power received through a loss-free antenna F a = 10*log 10 (P n /KT o B) –Lists the median value hourly value for each time block, F am, 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

91 F am for Summer 20-24h