Compact and Spherical Range Design, Application and Evaluation

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

3. Critical Range Evaluation 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

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. Direct measurement (field probing) with a small antenna or a small sphere Indirect measurements1,2 (scattering measurements) using a thin long bar Quiet Zone Field Quality 1van de Griendt et al., “Full characterization of the test zone fields using an RCS method,” AMTA, 1995 2B.L. Raghavachari, “Estimation of compact range test zone fields using a RCS method,” M.S. Thesis, The Ohio State University, 1998.

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

7. 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 Indirect Measurements Direct Method is Recommended

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

9. 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 Stray Signal Source Mapping Using Field Probe Data

10. 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, w(m) is a weighting function, r=sosinq, z=socosq. F(r,z) is called the Near Field Spectra. Near Field Focusing

11. 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 q = -20° and has a SNR of 20 dB. The source of the third signal is 20′ from the center of the scanner with q = 15° and has a SNR of 18 dB. Simulated Data

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

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

14. 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. Near Field Focusing (cont.)

15. Near Field Spectra of the Simulated Data Hamming Weights, DPW Subtracted Frequency = 4 GHz Frequency = 2 GHz IMAGE USING NEAR FIELD FOCUSING 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. Let so >>rm, 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 q. F(q) will have a maximum when there is a source along direction q. Near field sources will not focus properly. Beam Forming Technique

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

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

20. 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. Beam Forming Technique (cont.)

21. 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. Direction of Arrival Estimation

22. 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. Time of Arrival (TOA) Estimation

23. 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. Illustrative Example

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

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

26. Hamming weights Sinogram of the Simulated Data

27. 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,q). Then the time of arrival at a probe location r is given by where c is the velocity of light in free space. Making the far field approximation, Time of Arrival Estimation (cont.)

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

30. 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. Data Calibration for TOA Estimation

31. Hamming weights Sinogram of the Experimental Data after Calibration

32. Let the quiet zone fields be probed along a linear scan over a frequency band defined by (f1,f2). Then define where h(f,r) is the probed data at location r, w(f,r) is the weighting function, (r1, r2) define the linear space over which the quiet zone fields are scanned, and H(to, q) will have a local maxima if h(f,r) contains a signal with time delay to and q incidence angel We will define |H(to, q)|2 as the TADOA spectra. Time and Direction of Arrival(TADOA) Spectra (1) (2)

33. |H(t,q)|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. TADOA Spectra (3) (4)

34. TADOA Spectra Calibrated Data Simulated Data Experimental Data

35. Let the quiet zone fields be probed over a frequency band along a linear scan extending from rl to rh. Then define where w(f) is a window function and H(f,r) is the calibrated field probe data. Note that Gr(t) is the range time domain response at probe location r. Next, let where w(r) is another window function, and |I(r0, z0)|2 is called the TDNFF Spectra. Time Domain Near Field Focusing (TDNFF)

36. 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. Experimental Range

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 fences With fences

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

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

42. 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. Stray Signal Source Mapping Using Field Probe Data Summary

43. 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. Range Evaluation Using a Flat Diagonal Plate

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 Length Frequency = 6 GHz

46. RCS Pattern of 1.25’ x 1.25’ Diagonal Plate Mini Range with Absorber Wall 5’ Focal Length Frequency = 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 f = 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