Compact and Spherical Range Design, Application and Evaluation

Walter D. Burnside and Inder J. Gupta

The Ohio State UniversityElectroScience Laboratory

1320 Kinnear RoadColumbus, Ohio 43212

(614) 292-5747 and (614) 292-5951

Presented on September 21-22, 2005 for Raytheon (Tucson, AZ).

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)

Inder (Jiti) Gupta

ElectroScience LaboratoryDept. of Electrical and Computer Engineering

The Ohio State University1320 Kinnear Road, Columbus, OH 43212

Phone: (614) 292-5951Fax: (614) 292-7297

Email: gupta.11@osu.edu

Critical Range Evaluation

What Range Evaluation Involves

Quiet zone field quality

–amplitude taper–phase uniformity–ripple in the fields–cross-polarization level

Stray signal source mapping

Quiet Zone Field Quality

• Direct measurement (field probing)– with a small antenna or a small sphere

• Indirect measurements1,2 (scattering measurements)– using a thin long bar

1van de Griendt et al., “Full characterization of the test zone fields using an RCS method,” AMTA, 19952B.L. Raghavachari, “Estimation of compact range test zone fields using a RCS method,” M.S. Thesis, The Ohio State University, 1998.

Direct Measurement

Advantage–No processing required

–Suitable for antenna as well as radar ranges

Disadvantages–Requires special equipment

–Depends on the probe quality

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

Stray Signal Source Mapping

Using field probe data

Using flat diagonal plate

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

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,

= sosin, z = socos.

F(,z) is called the Near Field Spectra.

2

1

( , )m

M j sm

m o

sF z m h m e

s

1

2 22 ,m ms z

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.

Simulated Data, 3 Incident Signals

Frequency = 2 GHz Frequency = 4 GHz

Near Field Spectra of the Simulated Data

Hamming Weights

Frequency = 2 GHz Frequency = 4 GHz

IMAGE USING NEAR FIELD FOCUSING IMAGE USING NEAR FIELD FOCUSING

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.

Near Field Spectra of the Simulated Data

Hamming Weights, DPW Subtracted

Frequency = 2 GHz Frequency = 4 GHz

IMAGE USING NEAR FIELD FOCUSING IMAGE USING NEAR FIELD FOCUSING

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.)

Beam Forming Technique

Let so >>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.

2

sin

1

, ,m

M j

om

F z F s w m h m e

s inm o ms s

DOA Spectra Obtained Using Beam Forming Technique

Hamming Weights, Simulated Data

Frequency = 2 GHz Frequency = 4 GHz

DOA Spectra Obtained Using Beam Forming Technique

Hamming Weights, Simulated Data – Smoothed Data

Frequency = 2 GHz Frequency = 4 GHz

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.

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.

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.

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.

Simulated Data vs. Frequency

Four incident signals

Probe Location = 0.0 inch Probe Location = 18.0 inch

TOA Plots for the Simulated Data

Probe Location = 0.0 inch Probe Location = 18.0 inch

Hamming weights

Sinogram of the Simulated DataHamming weights

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,

1 22 22 sino

R R Rt t

c

sinot t

c

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.)

Sinogram of the Experimental DataHamming weights, No calibration performed

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.

Sinogram of the Experimental Data after CalibrationHamming weights

Time and Direction of Arrival(TADOA) Spectra

Let the quiet zone fields be probed along a linear scan over a frequency band defined by (f1,f2). 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(to, ) will have a local maxima if h(f,) contains a signal with time delay to and incidence angel

We will define |H(to, )|2 as the TADOA spectra.

2 2

1 1

2, , ,f j f t

o ffH t w f h f e d d

sin.ot t

c

(1)

(2)

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.

2

1

2( , ) , of j f t

o fH t h f e df %

2

1

2 sin

, , , .f

jch f w f h f e d

%

(3)

(4)

TADOA SpectraCalibrated Data

Simulated Data Experimental Data

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, z0)|2 is called the TDNFF Spectra.

2,l

fh j f t

fG t w f H f e df

0 0 0 0, , ,h

l

I z w G t z d

0 0 0 0 0 0

1, , , , , .t z R z R z

c

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.

A Drawing of the Experimental Test Range

A Photograph of the 30-meter Outdoor Range

Field Probe Data along the Vertical Scan. HP

No Calibration

No fences With fences

Field Probe Data along the Vertical Scan. HP

After Calibration

No fences With fences

Field Probe Data along the Vertical Scan. HP

No fences With fences

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

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.

AdvantageVery suitable for scattering ranges.Strong to medium stray signals can be directly

identifiedLarge dynamic range

Plate SizeThe stray signals should be in the far zone of

the plate.

Range Evaluation Using a Flat Diagonal Plate

RCS Pattern of 1.25’ x 1.25’ Diagonal Plate

Mini Range

5’ Focal Length Frequency = 6 GHz

RCS Pattern of 1.25’ x 1.25’ Diagonal Plate

Mini Range with Absorber Wall

5’ Focal Length Frequency = 6 GHz

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

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)

Scattered Fields of 9’ x 9’ Diagonal Plate

No Stray Signal -70 dB Stray Signal at 40°

UTD (Uniform Theory of Diffraction) Solution

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

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

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.

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 data10° to 30° aspect angle

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 data10° to 30° aspect angle

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.

Diagonal Plate in OSU Compact Test Range

Top View of the Range ISAR Image at 155°

Diagonal Plate in OSU Compact Test Range

Top View of the RangeWith 6” Sphere

ISAR Image at 155°With 6” Sphere

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

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

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.

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