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

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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

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

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4 Time Histories (cont)

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5 Noise E-Field of a Typical Day

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6 Noise Model

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

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8 Hole-Punching

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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.

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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

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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, 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

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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 )

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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 1 2 + 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]

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14 12 14 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.0001 0.1 0.01 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 V d Noise BW is wider than Rx = A - A rms V d = 1.05 0.001 V d =30 0dB = A RMS P [ Exceeded]

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15 V d = 10 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.0001 0.1 0.01 60 50 40 30 20 10 0 -10 -20 -30 -40 = A - A rms P [ Exceeded] V d = 1.05 0.001 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”

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

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17 V d = 10 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.0001 0.1 0.01 60 50 40 30 20 10 0 -10 -20 -30 -40 = A - A rms P [ Exceeded] V d = 1.05 0.001 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

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18 Difference between RMS and Rayleigh Level

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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

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20 Total Effect of Hole Punch and V d on Noise Level

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21 Median 95% Level of E rms

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22 Median 95% Effective Noise Level

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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 95 1 80600 99 1 9070- 10 99.9 2 10080- 20 99.99 2 11090- 30 1 Summer 18h Worst Case 2 Spring 18h Worst Case

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

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

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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

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27 1620h Taylor, IN

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28 2220h Taylor, IN

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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

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30 Markov Chain for Discharges Local Remote

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31 Data Comparison Simulation Data

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32 Simulated and Actual Data APD

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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.

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

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35 Backup Slides

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36 Before Storm 16:20 (UTC)

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37 Before Storm Data

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38 During Storm 22:20 (UTC)

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39 During Storm Data

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40 Lines up well

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41 Pulse Shape Comparison

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42 Data Wiping Before Storm

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43 Data Wiping During Storm

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44 Captured and Missed Pulses

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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) 110 90 70 50 30 10 -10 -30

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

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47 Median 95% Level of E rms

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48 Median 95 % Gaussian Noise Level

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49 Median 95% Effective Noise Level

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50 Median 99% Level of E rms

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51 Median 99% Effective Noise Level

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52 Median 99% Effective Noise Level (Spring)

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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.

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54 Median 99.9% Effective Noise Level (Summer)

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55 Median 99.9% Effective Noise Level (Spring)

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56 Median 99.99% Level of E rms

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57 Median 99.99% Effective Noise Level

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58 Median 99.99% Effective Noise Level

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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

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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

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61 NLDN Data DateStart HourEnd Hour< 30 [km]30 - 300 [km] 2002/07/0920:20:2821:20:2861955 2002/07/0921:20:2922:20:272574009 2002/07/0922:20:2823:20:274684864 2002/07/0923:20:2823:59:59574499 2002/07/2616:00:0516:59:5963542 2002/07/2617:00:0117:59:59553641 2002/07/2618:00:0019:00:001421055 2002/08/2222:00:0122:59:5902677 2002/08/2223:00:0023:59:593942779 2002/08/2300:00:0001:00:002333208 2002/08/2301:00:0501:59:591173255 2002/08/2302:00:0102:59:59183451 2002/08/2303:00:0004:00:0012378 2002/08/2319:00:0119:59:591491780 2002/08/2320:00:0220:59:593313326 2002/08/2321:00:0121:59:592513772 2002/08/070 2002/08/080 2002/08/090 Noisy Days Quiet Days < 500 [km]

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62 Experiment ARI

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63 July 9, 2002 Upland, IN >10kA Strikes 0820-2359 UTC (3:20a – 8:59p CDT)

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

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

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66 95% Signal Available

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67 40% Signal Available

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68 Pre-IF Filter (Bad Day)

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69 Post-IF Filter (Bad Day)

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70 Post-IF Filter (Good? Day)

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71 12 14 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.0001 0.1 0.01 60 50 40 30 20 10 0 -10 -20 -30 -40 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 = 1.05 0.001 V d =30

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72 August 8, 2002 Upland, IN >10kA Strikes 0000-2359 UTC (7:00p – 8:59p CDT)

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73 Post-IF Filter (Good? Day)

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74 August 8, 2002 Upland, IN >10kA Strikes 0000-2359 UTC (7:00p – 8:59p CDT)

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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

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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.

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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

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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

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79 Loran Aperture-RF-IF

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80 Reception Probabilities ≡ Strike/GRI

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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 25.0 - 50.0 sec between valid updates

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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

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

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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

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85 Class B Model

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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.

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88 Another Blanking Example

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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 –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)

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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

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91 F am for Summer 20-24h

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