1. Compact and Spherical Range Design, Application and Evaluation Walter D. Burnside and Inder J. Gupta The Ohio State University ElectroScience Laboratory 1320 Kinnear Road Columbus, Ohio 43212 (614) 292-5747 and (614) 292-5951 Presented on September 21-22, 2005 for Raytheon (Tucson, AZ).

2. Course Outline  Basic Range Design Guidelines (Burnside)  Compact Range Reflector Design (Gupta)  Absorber Design and Layout (Burnside)  Critical Range Evaluation (Gupta) Second Half Day First Full Day  R-Card Fences for Outdoor Ranges (Gupta)  Summary of Range Design Issues (Burnside)

3. Inder (Jiti) Gupta ElectroScience Laboratory Dept. of Electrical and Computer Engineering The Ohio State University 1320 Kinnear Road, Columbus, OH 43212 Phone: (614) 292-5951 Fax: (614) 292-7297 Email: gupta.11@osu.edu Critical Range Evaluation

4. What Range Evaluation Involves  Quiet zone field quality – amplitude taper – phase uniformity – ripple in the fields – cross-polarization level  Stray signal source mapping

5. Quiet Zone Field Quality Direct measurement (field probing) –with a small antenna or a small sphere Indirect measurements 1,2 (scattering measurements) –using a thin long bar 1 van de Griendt et al., “Full characterization of the test zone fields using an RCS method,” AMTA, 1995 2 B.L. Raghavachari, “Estimation of compact range test zone fields using a RCS method,” M.S. Thesis, The Ohio State University, 1998.

6. Direct Measurement  Advantage – No processing required – Suitable for antenna as well as radar ranges  Disadvantages – Requires special equipment – Depends on the probe quality

7. Indirect Measurements  Advantages – Very suitable for scattering ranges – No special equipment required – No spatial filtering – Large dynamic range  Disadvantages – Not suitable for antenna ranges – Data processing required – Difficult to measure and isolate scattering from a long straight edge Direct Method is Recommended

8. Stray Signal Source Mapping  Using field probe data  Using flat diagonal plate

9. Stray Signal Source Mapping Using Field Probe Data  Near Field Focusing  Beam Forming Technique  Direction of Arrival Estimation  Time of Arrival Estimation  Time and Direction of Arrival (TADOA) Spectra  Time Domain Near Field Focusing

10. Near Field Focusing  Let the quiet zone be probed along a linear scan at M points at the frequency of interest.  Then define where h(m) is the field probe data,  (m) is a weighting function,  = s o sin , z = s o cos .  F ( , z ) is called the Near Field Spectra.

11. Simulated Data  Three incident signals.  The desired plane wave (DPW) is incident from 0° and has a SNR of 50 dB.  The source of the second signal is 40′ from the center of the scanner with  = -20° and has a SNR of 20 dB.  The source of the third signal is 20′ from the center of the scanner with  = 15° and has a SNR of 18 dB.

12. Simulated Data, 3 Incident Signals Frequency = 2 GHzFrequency = 4 GHz

13. Near Field Spectra of the Simulated Data Hamming Weights Frequency = 2 GHz Frequency = 4 GHz IMAGE USING NEAR FIELD FOCUSING

14. Near Field Focusing (cont.)  The desired plane wave (DPW) limits the performance of the near field focusing technique.  One can estimate and then subtract the DPW from the field probe data to enhance the performance of the near field focusing.  The weighted average (smoothing) of the field probe data can be used to estimate the DPW.

15. Near Field Spectra of the Simulated Data Hamming Weights, DPW Subtracted Frequency = 2 GHz Frequency = 4 GHz IMAGE USING NEAR FIELD FOCUSING

16.  Limited resolution in the down range direction (perpendicular to the scanner).  Computationally inefficient in that one has to calculate the function over the whole plane.  In general, not recommended. Near Field Focusing (cont.)

17. Beam Forming Technique Let s o >>  m, m = 1, 2… M Then, and  This is called the Beam Forming Technique. Note that F needs to be calculated only as a function of   F (  ) will have a maximum when there is a source along direction .  Near field sources will not focus properly.

18. DOA Spectra Obtained Using Beam Forming Technique Hamming Weights, Simulated Data Frequency = 2 GHz Frequency = 4 GHz

19. DOA Spectra Obtained Using Beam Forming Technique Hamming Weights, Simulated Data – Smoothed Data Frequency = 2 GHz Frequency = 4 GHz

20. Beam Forming Technique (cont.)  At low frequencies, one may not have enough resolution to separate various signals in the angle domain  Two stray signals coming from the same direction but associated with different mechanisms cannot be differentiated.

21. Direction of Arrival Estimation  The beam forming technique, as pointed out earlier, basically estimates the DOA of the incident signals.  One can use Capon’s method, MUSIC algorithm and its variants, maximum likelihood estimator, etc. for DOA estimation.  For narrow band field probe data, the incident signals are correlated with each other  Stray signals do not have planar wavefront.  The amplitude of the stray signal varies significantly over the probed aperture.  DOA estimation is carried out using a portion of the probed aperture.  At low frequencies where the probed aperture is already small (electrically), these techniques do not provide any advantage over the beam forming technique.

22. Time of Arrival (TOA) Estimation  Let the quiet zone fields be probed over a frequency band at each probe location.  Then one can transform the frequency domain data at each probe location to time domain.  Inverse Fourier Transform (IFT) can be applied to the frequency domain data for time of arrival estimation.  Since the probe is a small antenna (point source), various peaks in the time domain will yield the relative TOA of the incident signals.

23. Illustrative Example  Probe data over 72” linear scan in 0.5” increments.  2-6 GHz frequency band.  Four incident signals.  DPW at 0° with 50 dB SNR.  Two signals incident from -20° with 15 dB and 20 dB SNR, respectively.  Another signal is incident from 15° and has 18 dB SNR.  The relative (with respect to DPW) TOA of the three stray signals at the center of the quiet zone are -10 nsec, 2 nsec and 3 nsec, respectively.

24. Simulated Data vs. Frequency Four incident signals Probe Location = 0.0 inchProbe Location = 18.0 inch

25. TOA Plots for the Simulated Data Probe Location = 0.0 inchProbe Location = 18.0 inch Hamming weights

26. Sinogram of the Simulated Data Hamming weights

27. Time of Arrival Estimation (cont.)  Slopes of the various lines in a sinogram are linked with the location of the incident signal sources.  Let the source be located at (R,  ). Then the time of arrival at a probe location  is given by where c is the velocity of light in free space.  Making the far field approximation,

28.  In practice, the magnitude of the probed data varies with frequency and its phase also displays non-linear variation.  Variations in magnitude are due to – gain of the feed antenna – gain of the probe antenna – losses in the cable and various connectors  Non-linear variation in phase can be due to – dispersion in the microwave components – phase center of the probe antenna – connectors  The probed data should be calibrated. Time of Arrival Estimation (cont.)

29. Sinogram of the Experimental Data Hamming weights, No calibration performed

30. Data Calibration for TOA Estimation  One needs another set of measurements for data calibration.  For field probe data, another set of measurements is not available.  We propose to use the DPW component of the probe data as the calibration signal.  Since the DPW is normal to the probe scanner, one can spatially smooth the probe data at each frequency to estimate the DPW component.  Then the DPW component at the center of the scanner can be used for the calibration of probe data at that frequency.

31. Sinogram of the Experimental Data after Calibration Hamming weights

32. Time and Direction of Arrival (TADOA) Spectra  Let the quiet zone fields be probed along a linear scan over a frequency band defined by ( f 1, f 2 ). Then define where h ( f,  ) is the probed data at location , w ( f,  ) is the weighting function, (  1,  2 ) define the linear space over which the quiet zone fields are scanned, and  H ( t o,  ) will have a local maxima if h ( f,  ) contains a signal with time delay t o and  incidence angel  We will define | H ( t o,  )| 2 as the TADOA spectra. (1) (2)

33. TADOA Spectra  | H ( t,  )| 2 involves the computation of a 2-D integration, and thus can be inefficient.  To increase the computational efficiency, one can use an FFT to carry out the integration over frequency.  (1) can be written as where  (4) is the DOA spectra at frequency f. (3) (4)

34. TADOA Spectra Calibrated Data Simulated DataExperimental Data

35. Time Domain Near Field Focusing (TDNFF)  Let the quiet zone fields be probed over a frequency band along a linear scan extending from  l to  h. Then define where w ( f ) is a window function and H ( f,  ) is the calibrated field probe data. Note that G  ( t ) is the range time domain response at probe location .  Next, let where w (  ) is another window function, and  | I (  0, z 0 )| 2 is called the TDNFF Spectra.

36. Experimental Range  30 meter long,  Radar antenna height is 60 cm,  Center of target zone is 3 meters above ground,  6-18 GHz frequency band,  Six R-card fences,  Fences are tilted 20° towards the feed.

37. A Drawing of the Experimental Test Range

38. A Photograph of the 30-meter Outdoor Range

39. Field Probe Data along the Vertical Scan. HP No Calibration No fencesWith fences

40. Field Probe Data along the Vertical Scan. HP After Calibration No fencesWith fences

41. Field Probe Data along the Vertical Scan. HP No fencesWith fences

42. Stray Signal Source Mapping Using Field Probe Data  Various techniques for mapping stray signal sources in far-field antenna/RCS ranges were presented.  These techniques use the quiet zone field probe data at a single frequency or band of frequencies.  Relative merits and drawbacks of various mapping methods were also discussed.  It was shown that relatively simple processing of the field probe data can be used effectively for mapping of the stray signal sources. Summary

43. Range Evaluation Using a Flat Diagonal Plate  A diagonal flat plate is positioned in the quiet zone and a portion of the chamber is scanned by rotating the plate.  The scattered fields from the plate are measured over the frequency band of interest at various plate orientations (rotation angle).  The stray signal response will peak up when the plate is oriented such that the stray signal is specularly reflected back in the DPW direction.  The measured scattered field data is processed to locate the sources of stray signals.

44. Advantage  Very suitable for scattering ranges.  Strong to medium stray signals can be directly identified  Large dynamic range Plate Size  The stray signals should be in the far zone of the plate. Range Evaluation Using a Flat Diagonal Plate

45. RCS Pattern of 1.25’ x 1.25’ Diagonal Plate Mini Range 5’ Focal LengthFrequency = 6 GHz

46. RCS Pattern of 1.25’ x 1.25’ Diagonal Plate Mini Range with Absorber Wall 5’ Focal LengthFrequency = 6 GHz

47. Diagnosis Tools  Raw data as a function of plate orientation at fixed frequency  Finite impulse response (TOA) at a set of aspect angles.  Inverse synthetic aperture radar (ISAR) images. Range Evaluation Using a Flat Diagonal Plate

48.  9’ x 9’ flat square plate.  Signal scenario consists of two signals.  One of the signals, referred to as the plane wave, is mono-statically scattered by the plate.  The other signal, referred to as the stray signal, is bistatically scattered by the plate.  The two signals are incident in  = 45° plane.  The angular separation between the two signals is kept fixed at (40°).  The stray signal has fixed time delay with respect to the plane wave and is 70 dB below the plane wave level Range Evaluation Using a Flat Diagonal Plate (Illustrative Example)

49. Scattered Fields of 9’ x 9’ Diagonal Plate No Stray Signal -70 dB Stray Signal at 40° UTD (Uniform Theory of Diffraction) Solution

50. Time Domain Response of 9’ x 9’ Diagonal Plate No Stray Signal -70 dB Stray Signal With15 ns Delay 0.5 GHz to 1.5 GHz scattered field data

51. Time Domain Response of 9’ x 9’ Diagonal Plate -70 dB Stray Signal With 5 ns Delay-70 dB Stray Signal With10 ns Delay 0.5 GHz to 1.5 GHz scattered field data

52. TOA Estimation Using Diagonal Flat Plate  The sinogram of the scattered fields from a diagonal plate provides an estimate of the direction of arrival as well as the time delay of the stray signals.  The time delay is the time difference between the plane wave and the stray signal assuming the return path of the scattered signals is the same  The time delay can be used to identify very weak stray signals if and only if the time delay is large  ISAR images are studied next.

53. ISAR Images of 9’ x 9’ Diagonal Plate No Stray Signal Stray Signal With15 ns Delay  0.5 GHz to 1.5 GHz scattered field data  10° to 30° aspect angle

54. ISAR Images of 9’ x 9’ Diagonal Plate Stray Signal With 5 ns DelayStray Signal With10 ns Delay  0.5 GHz to 1.5 GHz scattered field data  10° to 30° aspect angle

55. Example from the Ohio State University Compact Range  Scattered fields from a 3’ x 3’ diagonal flat plate.  2-18 GHz frequency band in 10 MHz frequency increments.  ISAR images using 20° aspect region with 0.1° angular increments.  The compact range reflector has an elliptical rolled edge.

56. Diagonal Plate in OSU Compact Test Range Top View of the RangeISAR Image at 155°

57. Diagonal Plate in OSU Compact Test Range Top View of the Range With 6” Sphere ISAR Image at 155° With 6” Sphere

58.  Measured scattered fields off a flat diagonal plate can be used effectively to evaluate the performance of a range.  The measured data can be used for stray signal source mapping.  Sinogram (time of arrival spectra at various plate orientations) can be used to identify stray signals with large time delays.  ISAR images obtained from the measured data are also effective in mapping stray signal sources  Sources of very weak stray signals can be mapped. Critical Range Evaluation Summary

59.  Various methods for critical range evaluation were discussed.  These methods include probing of the quiet zone fields as well as measuring the scattered fields from specific targets (long bar, diagonal plate, etc.).  Many signal processing methods that can be used with the field probe data and/or scattered field data for range diagnosis were presented. Summary Critical Range Evaluation

60. References for Critical Range Evaluation  D.R. Koberstein, “Near field synthetic aperture imaging of probe data for scattering studies of the ElectroScience compact range,” M.S. Thesis, The Ohio State University, 1986.  E.K. Walton, “Compact range spurious signal mapping using probe data,” Technical Report 719627-12, The Ohio State University ElectroScience Laboratory, December 1987.  T.P. Delfeld and F.C. Delfeld, “Use of the MUSIC algorithm in the analysis of compact range field probe data,” AMTA’89, Monterey, CA, October 1989.  A. Moghaddar, E.K. Walton and W.D. Burnside, “Imaging of compact range stray signal sources using parametric modeling of the field probe data,” Technical Report 312884-21, The Ohio State University ElectroScience Laboratory, March 1990.  A. Moghaddar and E.K. Walton, “Imaging of low level signals in a compact range,” AMTA ’90, Philadelphia, PA, October 1990.  I.J. Gupta and W.D. Burnside, “Imaging of compact range probe data,” AMTA ’90, Philadelphia, PA, October 1990.  I.J. Gupta, “Performance of superresolution techniques in imaging compact range probe data,” AMTA ’91, Boulder, CO October 1991.  I.J. Gupta, T.-H. Lee and W.D. Burnside, “Study of the flat plates to map weak stray signals in compact ranges,” Technical Report 312496-4, The Ohio State University ElectroScience Laboratory, February 1991.

61.  T. Lee, T. Clark, W. Burnside and I. Gupta, “Critical range evaluation using a diagonal flat plate,” IEEE Transactions on Antennas and Propagation, vol. 40, pp 966-974, Aug. 1992.  A. van der Merwe and D.J. Janse van Rensburg, “Main-beam reduction for compact range imaging,” IEE Proceedings, Part H, vol. 141, pp.461-463, December 1994.  I.J. Gupta and A. van der Merwe, “Compact range evaluation at low frequencies,” AMTA ’95, Williambsurg, VA, November 1995.  I.J. Gupta, E.K. Walton and W.D. Burnside, “Time and direction of arrival estimation of stray signals in a RCS/antenna range,” AMTA ’96, Seattle, WA, October 1996.  M.A.J. van de Griendt et al., “Full characterization of the test zone fields using an RCS method,” AMTA ’95, Williamsburg, VA, November 1995.  B.L. Raghavachari, “Estimation of compact range test zone fields using a RCS method,” M.S. Thesis, The Ohio State University, 1998.  T.D. Moore and I.J. Gupta, “Calibration of range probe data for stray signal analysis,” AMTA 2000 Philadelphia, PA, October 2000.  I.J. Gupta, “Time domain near field focusing to map stray signals in spherical ranges,” AMTA ’02, Cleveland, OH, November 2002.  I.J. Gupta, “Stray signal source location in far-field antenna/RCS ranges,” IEEE Antennas and Propagation Magazine, vol. 46, pp.20-29, June 2004. References for Critical Range Evaluation