Analysis of Radar Data from February 6, 2001

Rick Fisher, NRAO, Green Bank, WV

Contents

Introduction

This page describes some initial analysis of the data recorded from the ARSR-3 Air Surveillance Radar signals at 1292 MHz recorded on the GBT by Galen Watts and myself on February 6, 2001.

Pulse Signature

The radar pulse is a 2-microsecond pulse of the 1292 MHz carrier. This carrier was heterodyned to a frequency of approximately 6 MHz where it was sampled at 20 megasamples/sec using the internal clock of the PDA500 data acquisition board. A typical pulse signature sampled by the 8-bit A/D converter is shown in Figure 1. The pulse was distorted somewhat by the long propagation path of 104 km. A weaker delayed pulse can be seen about 3 microseconds after the main pulse, probably due to scattering near the transmitter or receiver.

Figure 1. Pulse signature sampled by the A/D

The pulse shown in Figure 1 was recorded when the radar beam was several beamwidths away from the direction of Green Bank. The GBT receiver was saturated by pulses received when the beam passed over the GBT. Some saturation can be seen on the negative-going part of the waveform in Figure 1. Even at their strongest, the pulses did not appear to blind the receiver. They just caused clipping of the waveform peaks.

Pulse Repetition Rate

The 5-second data set that began about 1.1 seconds before the radar beam swept over the GBT was searched for pulses that exceeded a threshold of 127 A/D counts. Figure 1 shows that this threshold is well above the baseline noise level. The arrival time of each pulse was recorded as the time of the first data sample that exceeded the threshold. This rough measure tends to bias weak pulses to a slightly later arrival time relative to strong pulses, but the maximum error is the 2-microsecond width of the pulse.

Figure 2 shows the measured pulse arrival times relative to an expected arrival time assuming a repetition rate of 341.42 pulses per second. This rate was derived by adjusting the arrival times to be constant while the pulses were strongest around 1.1 seconds into the data set. The five parallel delay tracks are due to an intentional transmitted pulse time offset of an integer number of 100 microseconds in a repeating sequence of [0, 4, 0, 3, 1, 2, 1, 3]. Presumably, this offset is to resolve ambiguities due to reflections beyond the range interval of 440 km set by the pulse spacing.

Figure 2. Pulse arrival delays

Pulse Filter

Better pulse sensitivity can be obtained by convolving the data with a function that closely matches the pulse signature. An approximation to a pulse filter was derived by a rough fit of a gaussian curve to the power spectrum of the pulse as shown in Figure 3.

Figure 3. Gaussian fit to a pulse for the purpose of deriving a pulse convolution function. spectrum

The full 102 MB data string was then broken into 64 kB blocks, Fourier transformed, multiplied by the frequency domain filter function, and the transformed back to the time domain. The convolved time series of the pulse shown in Figure 1, squared to get power as a function of time, then looks like the data in Figure 4. The filter function can probably be tuned a bit for a better balance between signal-to-noise ratio and pulse resolution.

Figure 4. Pulse in Figure 1 filtered by the function shown in Figure 3.

Pulse Arrival Times

All 5 seconds of the data were then filtered and searched for identifiable separate pulses above most of the highest random noise peaks. The measured arrival times with the 100-microsecond offsets and the average expected pulse arrival time removed are shown in Figure 5. The first part of the data run was found to have a constant pulse arrival time by assuming a pulse repetition rate of 341.4142 pulses per second. The drift in arrival times toward the end of the 5 seconds of data was due to either a drift in the radar timing generator or the internal clock of our data acquisition board of about 60 ppm in frequency. This drift was removed empirically with a polynomial time correction function fitted by eye to the arrival times.

Figure 5. Pulse arrival times for the full 'sweep_minus1s.dat' file data set with the 100-microsecond offsets and the average expected pulse arrival time removed.

At least three features in Figure 5 stand out. First, pulses at constant arrival times are present during the full length of the data set. This is no doubt due to the fact that we are seeing pulses from the radar even when the radar beam is pointed well away from Green Bank. Since the receiver saturated with the beam pointed in our direction, we cannot determine the relative strengths of the sidelobes, but they are at least 30 dB below the main beam.

The second notable feature of Figure 5 is that the earliest pulses are not the most prevalent. The shortest distance, great circle, diffraction path from the radar to the GBT must produce the earliest arriving pulses. Evidently a longer path has a lower propagation loss since the pulses from the radar antenna sidelobes are most apparent at an extra delay of about 40 microseconds. The plots below will show that this lower propagation loss is produced by a reflection from the high mountain ridge about 8 km west of the GBT. A great circle plot of the terrain profile in the direction of the radar shows that the GBT is about 400 meters below the elevation of the nearest diffraction obstacle about 12 km away. The mountain ridge west of the GBT includes Bald Knob, the second highest peak in West Virginia.

The third notable feature of Figure 5 is the cluster of pulses around 1.1 seconds into the data sample. This is when the radar beam passes over Green Bank, and we see reflections from local terrain features in addition to the directly arriving pulse.

Geometric interpretation of Arrival Times

The pulse delay can be interpreted as a physical location of the reflecting object by assuming that only one reflection is involved. The reflection point is then the intersection of three surfaces: the locus of constant delay, which is an ellipsoid with the GBT and the radar antenna at the focii; the vertical plane of the radar beam; and the horizontal plane at the assumed altitude of the reflector. Figure 6 is a map of the intersection point solutions for all of the pulse delays shown in Figure 5, assuming that the reflector altitude is the same as the GBT.

Figure 6. Reflection point locations computed from pulse arrival delays and the radar beam azimuth. The GBT is at the intersection of the two long dotted lines, and the radar is at the small cross near the bottom of the diagram. The radar azimuth sweep during the 5-second data set is from about 325 to 115 degrees.

The heavy ellipse in Figure 6 is the locus of constant delay of about 40 microseconds due to pulses from the radar antenna sidelobes reflecting from the ridge west of the GBT. The weaker inner ellipse is the near-zero-delay locus of the direct path from the radar to the GBT. The cluster of points to the northwest of the GBT is from high terrain in this direction. Other features could be either terrain reflections or aircraft in the area. The small cluster farthest north is almost certainly from an aircraft.

Figure 7 is an expanded plot of the strongest pulses from the area northwest of the GBT. These pulses are more than ten times the intensity of the weakest pulses shown in Figure 6. The band of points running from the lower left corner of Figure 7 to the top center corresponds to the ridge of high peaks shown in the contour map of Figure 8. The ratio of the scales of Figures 7 and 8, in km/cm, is about 1.4:1, at least on the writer's screen. In other words, the total extents of the two maps are about the same. An accurate overlay of the radar returns on the contour map shows that the three clusters of points near the top of Figure 7 correspond nicely to the individual peaks on the ridge.

Since the azimuth of the radar beam and the pulse delay zero point must be inferred from the data, these are two free parameters that have been empirically determined by fitting the point locations in Figure 7 to terrain features in Figure 8. The match of returns to mountain peaks appears pretty convincing, but keep in mid that this is not based on accurate zero-point calibrations.

Figure 7. The geometric interpretation of the delays of the strongest pulses received from locations to the immediate northwest of the GBT.

Figure 8. Contour map of the terrain to the west and north of Green Bank. The GBT is located slightly to the northeast of the 'K' in the large word "GREENBANK" and below the small print "National Radio Astronomy Observatory."

Figures 9 and 10 show the pulse delay maps for the other two data sets that we recorded when the radar beam was sweeping azimuth ranges away from the direction of the GBT.

Figure 9. Pulse reflection map with radar beam sweeping from about 90 to 240 degrees azimuth. The small cluster of points to the south east of the radar is probably an aircraft.

Figure 10. Pulse reflection map with radar beam sweeping from about 180 to 330 degrees azimuth. The isolated dots are probably random noise spikes in the data.

Pulse Intensity Distribution

Relatively strong pulses were seen to be coming from a number of reflection points in the terrain around the GBT so there was not a completely dominant reflection point. Figure 11 shows the pulse intensity as a function of delay from the directly arriving pulse. The pulses at about 43 microseconds saturated the GBT receiver so these were probably 10 to 20 dB higher than measured. The pulses around 5 microseconds delay may also have been saturated but not as severely. Quite strong pulses can be seen out to a delay of 135 microseconds. Most, if not all are from terrain reflections. The group of returns at 430 microseconds is probably from an aircraft.

Figure 11. Pulse intensity as a function of delay from the pulse arriving directly from the radar for the data set shown in Figures 5, 6, and 7.

Figure 12 shows the measured pulse intensities as a function of computed azimuth from the GBT of the reflection points for pulses with delays greater than 50 microseconds. This delay cutoff eliminates the pulses coming from the radar antenna sidelobes that appear to be smeared over a wide range of azimuths as seen in Figure 6. Hence, the directly arriving pulses and the strongest reflected pulses are not shown in Figure 12. The strongest reflection not in this figure is from an azimuth of about -75 degrees.

Because of the distance of the radar antenna the azimuth resolution from the GBT is not terribly good, but the wide distribution of azimuths seen in Figure 12 is real. The azimuth profile of a single reflection point can be seen from the paraboloid-like arcs of points. More distant reflections from the GBT have narrower arcs.

Figure 12. Pulse intensity as a function of inferred azimuth of the radar pulse reflection point for pulse with delays greater than 50 microseconds for the data set shown in Figures 5, 6, 7, and 11. Zero azimuth is north and +90 degrees is east.

Time Window Blanking

Two straightforward blanking techniques were tried on the data set, time window blanking and detected pulse blanking, to determine whether the radar signal can be effectively removed from the spectrum.

In the tests that follow spectra were integrated over chosen intervals in the data by forming spectra with FFT's of overlapping 2048-data-sample sets and accumulating the power spectra. The data-sample sets overlapped by 50% (1024 samples) to reduce the sensitivity loss due to missing correlations between adjacent sample sets. Time window blanking was implemented by not accumulating spectra that had any of their input data extending into the time interval to be blanked.

Figure 13 shows the unblanked spectrum accumulated over the 0.3-second interval when the radar beam was closest to the Green Bank azimuth.

Figure 13. Unblanked spectrum integrated over to time when the radar beam was sweeping over the GBT, between 0.95 and 1.25 seconds into the data. The intensity scale is in units of telescope system noise power.

Figure 14 shows the spectrum accumulated over this same interval but with time window blanking beginning 20 microseconds before and ending 150 microseconds after the first pulses arrive from the radar. About 10% of the spectra were rejected in this integration. This time window can be compared with the time distribution of pulses shown in Figure 11. Figure 14 shows that even with a few weak pulses from aircraft reflections around 430 microseconds included in the spectrum, no trace of the radar signal can be seen. The reference spectrum used to normalize the data in Figures 13 and 14 was an accumulation of spectra over the full 5-second data set that fell outside of a time window from 20 microseconds before to 500 microseconds after the first-arriving pulses. The rms noise amplitude is about what is expected for a 0.3-second integration and 10-kHz spectral resolution.

Figure 14. Spectrum with data blanked for 150 microseconds after the earliest arriving pulses. The spectrum is integrated between 0.95 and 1.25 seconds into the data as in Figure 13. The intensity scale is in units of telescope system noise power.

The robustness of the time window blanking was tested by reducing the window to include more radar pulses in the integration. Evidence of a radar spectral feature did not show up until the end of the time window was reduced to about 100 microseconds after the first-arriving pulse. In Figure 11 you can see that quite a few moderately strong pulses beyond 110 microseconds can be included without distorting the spectrum. Of course, an integration over many radar rotation periods will uncover the spectral signature of these pulses so they do need to be blanked.

Integration of spectra over the full 12-second interval of the radar sweep still needs to reject the weak pulses from the radar antenna sidelobes, as will be seen below, but otherwise these spectra will tend to dilute any residual radar signal coming from pulses outside of the blanking time window. The rejection tests associated with Figure 14 are about the most stringent that we can make with the present data.

Detected Pulse Blanking

We could avoid the problem of continuously measuring radar pulse arrival times to microsecond accuracy to synchronize a blanking window by simply throwing away spectra that contain a detected pulse. To test the effectiveness of this scheme we start with the unblanked spectrum integrated when the radar beam is not pointed very close to the GBT as shown in Figure 15. The fact that we see the radar spectral signature in this spectrum says that we cannot simply blank our spectrometer when the radar beam is pointed near our direction.

Figure 15. Unblanked spectrum integrated over to time when the radar beam was pointed away from the GBT, between 1.6 and 5 seconds into the data. The intensity scale is in units of telescope system noise power.

Now, if we reject all spectra in which we detect a radar pulse with an amplitude greater than 1.5, using the same pulse filtering techniques described above, we get the spectrum shown in Figure 16. Only about 0.4% of the spectra were rejected, and little, if any improvement can be seen in the blanked spectrum. Figure 17 shows the number distribution of measured pulse amplitudes near the tail of the random noise distribution. Further reduction of the rejected pulse cutoff will reject a rapidly increasing fraction of spectra due to random noise. An artificial hole in the spectrum can be created with random noise rejection because spectra with noise peaks at the filtered frequency will be selectively thrown out.

Figure 16. Spectrum with data blanked when a pulse is detected above a level of 1.5 units on the intensity scale shown in Figures 11, 12, and 17. The spectrum is integrated between 1.6 and 5 seconds into the data as in Figure 15. The intensity scale is in units of telescope system noise power.<

Figure 17. Distribution of measured intensity peaks in the data set after filtering as described in connection with Figures 3 and 4. The horizontal scale peak intensity of 1.0 corresponds to 0 dB on the vertical axes of Figures 11 and 12. The square, X, and circle correspond to frequency domain filter center frequencies of 4.7, 5.84 (radar frequency), and 6.5 MHz, respectively.

Figure 18 shows an integration over the 0.3 seconds when the radar beam was pointed close to the GBT using detected pulse blanking only. About 25 db of radar signal rejection is achieved, as can be seen in a comparison with Figure 13, but the low-amplitude pulses that slip under the detection threshold cause an unacceptable radar signal in the spectrum.

Figure 18. Spectrum with data blanked when a pulse is detected above a level of 1.5 units on the intensity scale shown in Figures 11, 12, and 17. The spectrum is integrated between 0.95 and 1.25 seconds into the data as in Figures 13 and 14. The intensity scale is in units of telescope system noise power. Note the change in vertical scale from previous figures.

Detected pulse blanking probably does have a place in radar rejection in combination with time window blanking for rejecting transient pulse reflections that fall outside of the selected time window.

Preliminary Conclusions

From this initial analysis of a small bit of radar data there are a number of points learned that will affect our work on mitigating RFI at the GBT with blanking and canceling techniques:

1. To observe redshifted hydrogen near the radar frequency, simply blanking the receiver when the radar beam passes over Green Bank is not sufficient. A more complex technique of isolating echo-free data between radar pulses is required.

2. Reflections from the highest terrain around Green Bank can produce a stronger signal than the more direct signal path from distant transmitters to the GBT.

3. Any RFI canceling techniques will need to account for multi-path signal propagation arriving from a wide range of azimuths and with differential delays of more than 100 microseconds.

4. Time window blanking does appear to be quite effective, and a large fraction of the time between radar pulses can be used for high sensitivity spectral line measurements.

5. Detected pulse blanking is not a usable technique on its own, but it can be used to reject long-delay pulse reflections that fall outside of the selected blanking time window.

6. Radar pulse timing appears not to be locked to a stable time standard so any time windowing will need to include a pulse tracking capability.

Last modified March 17, 2001

rfisher@nrao.edu

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