Numerical Computation of the

Radar Cross Section of the

ZSU-23-4

ARL-MR-430 April 1999

Ronald Chase, H. Bruce Wallace, and Thomas Blalock

Approved for public release; distribution unlimited.
The findings in this report are not to be construed as an

official Department of the Army position unless so

designated by other authorized documents.

Citation of manufacturer’s or trade names does not

constitute an official endorsement or approval of the use

thereof.

Destroy this report when it is no longer needed. Do not

return it to the originator.
ARL-MR-430 April 1999

Army Research Laboratory

Adelphi, MD 20783-1197

Numerical Computation of the

Radar Cross Section of the

ZSU-23-4

Ronald Chase, H. Bruce Wallace

Sensors and Electron Devices Directorate, ARL

Thomas Blalock

Defense Intelligence Agency Missile and Space Intelligence Center

Approved for public release; distribution unlimited.
A computer geometry model of the ZSU-23-4 (a quad 23-mm

self-propelled antiaircraft gun) was obtained in Ballistic Research

Laboratory-Computer Aided Design (BRL-CAD), a combinatorial solid

geometry-based modeling system. The BRL-CAD file served as input

to a software package (ECLECTIC) that generated a flat, triangular,

all-metal facet representation of the ZSU exterior structure, containing

approximately 78,000 facets. The facet model served as input to Xpatch,

a high-frequency signature prediction code based on the shooting and

bouncing ray (SBR) technique. Xpatch was run at the Defense

Intelligence Agency, High Performance Computing Center with

several Silicon Graphics, Inc. (SGI), Origin, Onyx, and Challenge

machines that used 426 CPUs and 60 Gflops of computing power. The

configuration parameters for the ZSU model, both with and without a

perfect metal ground plane, included two depression angles (12° and

30°), both polarizations, 256 frequencies (about each center frequency),

and azimuth steps of 0.05° (for X-band) and 0.015° (for Ka-band). The

configuration parameters were selected based on measurement data

taken on a ZSU vehicle at the U.S. Army Research Laboratory

Aberdeen Proving Ground test facility. The model predictions will

include radar cross-section data as a function of polarization and angle

and synthetic aperture radar images. This report details the

Abstract

preliminary results from the computer modeling.

ii
1

1. Introduction

The U.S. Army Research Laboratory (ARL) is participating in a North

Atlantic Treaty Organization (NATO) research study group (RSG20) with

a focus on the military applications of millimeter-wave (MMW) imaging.

RSG20 conducted an experiment at Swynnerton, UK, that involved the

use of airborne synthetic aperture radar (SAR) systems to collect imagery

of a military location. The experiment assessed the applicability of MMW

imaging for locating and engaging ground vehicles and other fixed

targets. One of the ground vehicles used in this test was a ZSU-23-4, a

quad 23-mm self-propelled antiaircraft weapon system (see fig. 1). ARL

conducted a series of measurements at the outdoor signature research

facility at Aberdeen Proving Ground (APG), MD, in August 1996 to

characterize the MMW signature of this vehicle for comparison to similar

measurements obtained at Swynnerton. As an adjunct to the original

intent of comparing measurements, the participants agreed to perform

radar cross-section (RCS) predictive modeling using this target as a

baseline. The United States agreed to provide a flat, triangular facet

representation of the exterior structure of the ZSU that would be suitable

for RCS calculations. The parameters used in the modeling would be the

same as those used in the measurements at ARL. The aim was to allow

direct comparison of model results with a standard set of signature

visualization tools.

The fully polarimetric instrumentation radars at the ARL signature

research facility were used to collect data on the ZSU vehicle at both

X-band and Ka-band. Table 1 summarizes the main characteristics of the

measurement instrumentation in figure 2.

A full description of the operation of the radar and data acquisition

system can be found in Stratton et al.* Measurements made with this

system are taken with the radar mounted on an elevator on a 125-ft-high

tower. The radar is pointed at an in-ground turntable 153 ft away. The test

*Suzanne R. Stratton, H. Bruce Wallace, Robert L. Bender, and Ann E. M. Brodeen, A Comparison of Radar

Cross-Section (RCS) Measurements of 11 T72M1 Tanks at 35 GHz, U.S. Army Research Laboratory, ARL-TR1421 (July 1997).

Figure 1. ZSU-23-4

vehicle at APG

measurement facility.
2

Figure 2. X-, Ka-, and

W-band polarimetric

ISAR.

Parameter X-band Ka-band W-band

Center frequency (GHz) 9.25 34.25 94.25

RF bandwidth (MHz) 1511.64 1511.64 1511.64

Frequency step (MHz) 5.928 5.928 5.928

Peak transmit power (dBm) +27 +20 +13

Pulsewidth (ns) 100 100 100

PRF (MHz) 1.0 1.0 1.0

3 dB beam-width (°) 8.5 8.5 8.5

Polarization isolation (dB) 30 35 35

System noise figure (dB SSB) 7 9 11

Minimum detectable signal –80 –80 –80

Transmitted polarization: vertical and horizontal

Received polarization: vertical and horizontal

Table 1. X-, Ka-, and

W-band polarimetric

ISAR instrumentation

data.

vehicle sits on this turntable. Figure 1 shows the ZSU vehicle at the APG

facility. Target rotation is always counterclockwise; thus, 90° is always on

the left side of the vehicle when looking at it head-on. A complete rotation

for frequency measurements at 34 GHz takes about 10 min. A fully calibrated RCS plot can be ready 10 min after the measurement is completed.

A series of inverse synthetic aperture radar (ISAR) images displayed on a

CRT as a movie is available 25 min after the measurements are completed.

Table 2 displays the measurement conditions that were replicated in the

ZSU modeling work.

Parameter X-band Ka-band

Nominal center frequency (GHz) 9 34

Start frequency (GHz) 8.00000 33.48836

Stop frequency (GHz) 9.51164 35.00000

Step frequency (MHz) 5.928 5.928

Number of frequencies 256 256

Depression angles (°) 12 and 30 12 and 30

Angle sampling interval (°) 0.05 0.015

Measured polarizations: vertical/vertical, vertical/horizontal, horizontal/

vertical, horizontal/horizontal

Table 2. ZSU

measurement

parameters.
3

2. Development of the Facet Model

The computer modeling of the ZSU-23-4 began with the development of a

geometric representation of the exterior of the vehicle in some suitable

format. An existing geometry model of the ZSU was found at ARL-APG.

This geometry model was created with the Ballistic Research LaboratoryComputer Aided Design (BRL-CAD) software package. These BRL-CAD

models were originally developed to analyze various physical properties

(such as center of mass, moments of inertia) and vulnerability, but in

recent years they have been used for optical, radar, and infrared (IR)

signatures.

BRL-CAD software development started in 1979 as a task to provide an

interactive graphics editor for the BRL vehicle description database. The

software package includes a solid geometric editor; the ray-tracing library; different lighting models; and many image handling, data comparison, and other supporting utilities. This software package now totals

more than 500,000 lines of C source code and undergoes continuous

development (the current version is 4.4). It runs under UNIX and is

supported by more than a dozen product lines from Sun Microsystems

workstations to Silicon Graphics, Inc. (SGI), supercomputers. BRL-CAD

supports a variety of geometric representations, including an extensive

set of traditional combinatorial solid geometry (CSG) primitive solids

such as blocks, cones, and tori; solids made from closed collections of

uniform B-spline surfaces as well as nonuniform rational B-spline

(NURBS) surfaces; purely faceted geometry; and n-manifold geometry

(NMG). All these geometric objects may be combined using Boolean set

theory operations such as union, intersection, and subtraction. All the

geometric entities provide different material representations. The software is an unpublished work that is only available through the terms of a

limited-distribution agreement. BRL-CAD is licensed at nearly 800 sites

worldwide.

The BRL-CAD representation of the ZSU vehicle contains both interior

and exterior feature details. This representation is not suitable as input to

the software selected to perform the RCS calculations, Xpatch. Xpatch

requires either a triangular facet representation or an international graphics exchange specification (IGES) representation of the exterior structure

of the vehicle. Several geometry format conversion packages are available

that will accept a BRL-CAD input file and produce facet and/or IGES

formats. In addition, Xpatch software includes a utility for this process. A

facet representation of the model was generated, since Xpatch can compute the required RCS data about four times faster for a facet input file

than for an equivalent IGES input file. The speed difference is related to

the ray-tracing algorithm in the software.

Initially, a utility in Xpatch called Cifer was applied to convert the BRLCAD file into a facet representation. This attempt failed because the ZSU

CAD representation was too large to process in a single step. It would

have been necessary to edit the CAD model (with a BRL-CAD editor) to

divide the original model into three or four segments, facetize each
4

segment, and recombine the faceted segments. The next attempt employed a software converter—a pre-release version of ECLECTIC—that

was developed by the Army Tank and Automotive Command (TACOM).

ECLECTIC is an extension of an earlier converter called Facet Region

Editor (FRED) that was also developed at TACOM to generate flat, triangular facet representations from BRL-CAD models to support IR signature analysis on computers. ECLECTIC generates facet models in several

stages by identifying and facetizing geometry primitives, separately

handling intersections of primitives (edges), and determining interior and

exterior elements of the model. Several levels of facet size refinement are

available in the code, from coarse to relatively fine (designated 1 to 10).

Plans were made to examine the ZSU model at several different facet

sizes to compare the resulting representations for quality (facet skewness), uniformity, and number of facets. However, the need for an unexpected early release of the model to the NATO participants forced the use

of the facet representation existing at that time. The model facet size used

in this program was four, slightly higher than the default value in the

software. We believe that it is appropriate to comment here that even if

the facet level in the software were set to the highest level (i.e., 10) the

facet model would still consist of the same order of magnitude of individual facets. The conversion software discussed here cannot produce a

“high resolution” facet model of the ZSU like the one discussed later in

this report. The facet size level relates more to the capability of the software to handle geometry intersections and small features in the model.

The facet model generated by this software contains listings of the nodes,

their interconnections, the normal vector for each facet, and extensive

listings of the facets by regions and elements directly referenced to the

BRL-CAD file.

Another software package used by our organization—ACAD, developed

by the Lockheed Fort Worth Company—can also be employed to read in

and convert BRL-CAD representations into facet representations. ACAD,

which is supported by the Electromagnetic Code Consortium (EMCC),

includes a stand-alone CAD development capability that is an alternative

to BRL-CAD for electromagnetic (EM) model development. EMCC is a

group of individuals from government, academia, and industry who have

been very active in shaping the development of EM analysis software

used in high-performance supercomputers over the last decade. Two of

the authors are active members of this organization. It is interesting to

note that the BRL-CAD converters employed by Xpatch and ACAD are

slightly different versions of the TACOM software FRED. The version of

FRED included in the Xpatch utility (Cifer) is a formula translator (FORTRAN) programming language implementation with hard-coded limits

on array sizes. Cifer could not produce a facet representation of the ZSU

model because the number of nodes in the model exceeded the array size

limit. However, ECLECTIC, which uses the same basic algorithms as

FRED to generate the facet representation as Cifer, was able to convert the

entire ZSU model. ECLECTIC is coded in C language and employs

dynamic memory allocation for arrays, so the hard-coded limits associated with older FORTRAN versions were avoided.
5

The ZSU facet model used in this work consists of a flat, triangular facet

representation of the exterior structure of the vehicle. The model contains

40,037 nodes and 77,955 facets, with each facet representing metal material. Because of the number of facets and their inconsistent size and

uniformity, the model is categorized as a coarse representation. Figures

3(a) through 3(d) show the ZSU facet model as it would appear sighted

along the boresight axis of the APG radar. Figures 3(a) and 3(b) depict a

depression angle for the radar measurements of 12°, with azimuth angles

of 45° and 225°, respectively. Figures 3(c) and 3(d) depict a depression

angle of 30°, with azimuth angles of 30° and 260°, respectively. The use of

flat, triangular facets to represent curved features on the ZSU model will

always result in some “discretization” error. Small facets minimize this

error to a large degree, considering the additional approximations inherent in the modeling software. The inconsistent size and uniformity of the

facets in the model introduced modeling errors associated with Xpatch

software and numerical machine precision, and these are discussed in

section 3.
6

Figure 3. ZSU facet

model as it appears to

APG radar

measurement facility

looking down

boresight of radar.

Configuration shows

a 12° depression angle

and (a) 45° and

(b) 225° azimuth

angle.

(a)

(b)
7

Figure 3 (cont’d). ZSU

facet model as it

appears to APG radar

measurement facility

looking down

boresight of radar.

Configuration shows

a 30° depression angle

and (c) 30° and

(d) 260° azimuth

angle.

(d)

(c)
8

3. Xpatch Software

The first version of Xpatch was developed in 1988 at the University of

Illinois in Urbana-Champaign. The code remained largely unused for

several years. In late 1991, the code was adopted as a signature computation tool by the Air Force. Xpatch currently enjoys Department of Defense

(DoD) support for feature enhancement and distribution under the

software development activity that is included in the Defense High

Performance Computer Modernization Program. One goal of this activity

is the porting of Xpatch software to all parallel computer architectures

supported in the program. DEMACO, Inc., and the Center for Computational Electromagnetics at the University of Illinois are responsible for

current development of the software. The latest version of the software

(version 2.4d, released March 1997) is supported on most SGI and SUN

computer platforms.

Xpatch is a high-frequency radar signature prediction code based on the

shooting and bouncing ray (SBR) technique. With the SBR technique, a

dense grid of rays is shot from the radar toward the target. Rays are

traced according to geometrical optics theory as they bounce around

within the target. The tracing includes the effects of polarization, ray

divergence, and layered material transmission and/or reflection. At the

point where the ray exits the target, a physical optics integration is performed to calculate the scattered far field from the target. All single and

multiple bounce contributions are included in the geometrical or physical

optics (PO) theory. Current versions of Xpatch allow for first-order edge

diffraction to be included in the computations. This software consists of

three parts: (a) electromagnetics: XpatchF and XpatchT for frequency

domain and time domain calculations, (b) CAD and visualization tools,

and (c) a graphical user interface (GUI). The code is written in FORTRAN,

C, and C++ languages. The EM portion and the ray tracer consist of

approximately 0.6 million lines of code, and the tools and GUI account for

0.8 million lines of code. Table 3 describes some of the differences between the two EM domain computations in Xpatch.

The distribution of the Xpatch computer code and its documentation is

subject to export control laws. Xpatch is generally available to U.S. government agencies and contractors performing work for the government.

Capabilities XpatchF XpatchT

Computation domain Frequency Time

Target geometry Facet/IGES/CSG Facet/IGES/CSG

Coatings/materials Yes Approximate

First-bounce PO/z-buffer/SBR z-buffer/SBR

Higher-bounce SBR SBR

Edge diffraction Metal Metal

Best for RCS/range-profile SAR/range-profile

Table 3. Comparison

of XpatchF and

XpatchT.
9

The accuracy of Xpatch for RCS calculations depends on many factors;

one is the facetization representation of the model. Extremely narrow

facets can generate numerical instabilities in the Xpatch ray tracer. The

actual criterion used to disqualify a facet is a complex expression in

geometrical terms. Facets with very small interior angles (less than 0.002°)

and side ratios in excess of 10 to 1 have a good chance of being rejected by

the code. A utility in Cifer checks and reports “bad” facets in the facet

model. There were three bad facets identified in the current ZSU model.

These facets are simply ignored by the code. Any rays that intersect these

facets disappear into the interior of the model and are not accounted for

in the far-field determinations. The size and locations of the bad facets

were such that they were judged to be insignificant for the accuracy of the

calculations performed in this work. Other issues related to facetization—

such as verification of a closed, connected, continuous outer surface

(except for the three bad facets)—were checked with other Cifer utilities.

There are significant concerns about Xpatch software when considerations of verification arise for cases in the higher frequency ranges of 35

and 95 GHz. Xpatch was originally designed for the X-band frequency

range; hence its name. Although the software is increasingly being used at

the higher frequency ranges, a significant body of verified data does not

exist to warrant a high confidence level in the results.

The current versions of Xpatch have known limitations that can cause

measurable errors if they are not considered in the interpretation of the

computer results. For instance, the existence of cavities and large seams in

the modeled object cannot be treated in the present versions of the code.

Therefore, little confidence can be placed in results at very low depression

angles where the wheels/tracks of the vehicle are illuminated and would

form a set of large cavities. In addition, there is no present capability to

consider the effects of surface roughness on the vehicle. Finally, while

there is a provision to incorporate material properties in Xpatch as part of

the model, layered materials and uncertainty in material properties

require experience in the interpretation of Xpatch data.
10

4. Computer Resources

The Xpatch computations using the ZSU model were performed on the

high-performance computers at the Missile and Space Intelligence Center

(MSIC) of the Defense Intelligence Agency (DIA) at Redstone Arsenal in

Alabama. MSIC has the mission for the intelligence community of computing, storing, cataloging, and disseminating radar signature data on

foreign assets. It has an extensive database of RCS measurements and

validation data obtained with state-of-the-art RCS calculation software.

MSIC is the leader in the development of high-fidelity CAD model representations of assets, employing proprietary digital three-dimensional

(3-D) laser scanning tools to generate CAD models of targets. MSIC’s

high-performance computer system is the largest computer system in the

intelligence community. The system has logged more than 115 years of

central processing unit (CPU) hours for radar signatures. The CPU hours

needed to perform the ZSU computations that were completed are presented in table 4.

The amount of time is determined in large part by the type of computer

system on which the model runs. On the networked computers at MSIC,

any particular computation shown in table 4 would have been distributed

to different platforms depending on the current machine loads. Figure 4

shows an example of the variation in the computational times involved

on the different platforms for a 12° depression angle, with ground plane,

run at X-band. The computation at Ka-band, with a 30° depression angle

including the ground plane had not begun to run at the time that these

data were generated. It is estimated, based on the previous runs, that this

computation will take about 84 days to complete and use more than

double the CPU hours required for the similar computation with the 12°

depression angle.

Condition Without ground plane With ground plane

12° depression angle

X-band 296 1,339

Ka-band 5,737 25,046

30° depression angle

X-band 233 2,620

Ka-band 6,661 (Not completed)

Totals 12,927 29,005

Table 4. CPU hours for

ZSU computations.
11

Figure 4. Example of

variation in run times

for one type of

computation at MSIC.

1200000

1000000

800000

600000

400000

200000

0

Shorter

runs on

new

Longer

runs

on older

CPU time vs aspect angle for ARL’s ZSU-23

12° elevation with ground plane – X-band

0 30 60 90 120 150 180 210 240 270 300 330 360

Aspect angle (°)

CPU (s)
12

5. Data Format and Analysis

The computed data (monostatic RCS as a function of frequency and

angle) were received from MSIC on 4-mm digital audio tapes separated

according to each computation that was completed. The computer runs

were divided into eight groups corresponding to frequency range (Xband and Ka-band), depression angle (12° and 30°), and whether or not a

ground plane was present. Each group was divided into 360 files, with

each file containing the data for one azimuth angle. All the data were in

compressed ASCII format. Each X-band group contained 84 MB in compressed format, which expanded to 920 MB when uncompressed. Each

Ka-band group contained 280 MB in compressed format, which expanded

to 3.1 GB when uncompressed. Seven of the eight groups were completed

and delivered to ARL. As mentioned above, the Ka-band computations at

30° depression angle including the ground plane had not begun to run at

the time that the rest of these data were provided to ARL.

All the computed Xpatch data were converted into the data format of the

ARL-APG radar measurement system (raw) data. This would allow the

calculated data to be processed in precisely the same manner as the

measured data. This also would provide for a direct one-to-one

comparison between measured and computed results. This direct

comparison will extend to the format of the data output plots and ISAR

image presentations/movies since the signal/data processing software

will be the same for both measured and computed data. This common

processing software includes the data analysis tools developed and

verified over the years at a production radar measurement facility. Further, all the standard statistical parameters used to characterize the measurement data are automatically available in the software and can be

applied to the computed data. At APG, a standard format is used for all

RCS polar plots, allowing the computed ZSU data to be directly compared against data from other vehicles measured at the APG facility.

While the benefits to this data conversion were evident, there were still

challenges to implementing it. The least of these involved the actual data

conversion. The ARL-APG radar data set consists of an ASCII header

portion that describes the specifics of the measurement conditions. An

ASCII data block follows with specifics on the data format. Finally, arrays

of 2-byte integers containing the real and imaginary parts (I, Q values) of

the calculated fields as a function of frequency and angle for each measurement channel complete the data set. The only interesting feature that

occurred here involved the requirement to write the 2-byte integer values

in the reverse of the “normal” byte order on most systems.

Modern radars include a complex signal-processing pipeline that acts on

the raw data to account for many factors (including channel imbalance,

image rejection, clutter elimination, etc). This signal-processing pipeline

at APG uses a set of five reference/calibration files that “correct” the raw

data based on reference measurements and calibration factors. The

converted, computer-generated Xpatch data must flow down this

signal-processing pipeline when they are processed by the APG radar
13

software. Xpatch data are “perfect” since all the above corrections to the

APG measurement data are not necessary, with the exception of scaling

the computer data to the final magnitude. The challenge was to generate

five reference/calibration files that approximate a perfect radar system by

not altering the computer data (scaling the exception). Fortunately, with

expertise from H. Bruce Wallace (one of the authors, as well as the system

designer and software developer), the needed reference/calibration files

were developed. At present, there is still a slight discrepancy (a factor of

the square root of two—too small) in the magnitude of the cross polarization channels that was not corrected by the reference/calibration files.

This discrepancy does not substantially affect the data comparisons

presented in section 6.
14

6. Data Comparisons

To present an introduction to comparisons of the measured and computed data, we decided to focus on an interesting feature that was noticed

in the computer-generated data but that was missing from the corresponding measured data, yet that appeared in related measured data at a

different frequency. We will also present a comparison of the data obtainable from a high-fidelity, high-resolution facet model of the ZSU (developed for another program) to indicate why such models are of great

utility for RCS calculations.

Figures 5 through 7 show comparisons between Xpatch data and the

corresponding APG measured data. The data presented in these figures

are the average over the frequency of the RCS values (in dBsm) plotted at

every 0.5° in azimuth. The data were generated by software used at APG,

with the same processing conditions applied for the computed and

measured data values. While the details in any individual figure could

change slightly if all (or a different part of) the azimuth values in the data

set were used, the comparison is still quite good since both the measurement data and computer data are processed in exactly the same manner.

Figure 5 presents the comparisons of measured and computed data at

X-band for a 30° depression angle, representing the cross-polarized

component of electric field and the vertical transmit and horizontal

receive conditions. Notice the peak in the Xpatch data at about 290° in

azimuth and the absence of a corresponding peak in the APG data. The

comparison between the two data plots is poor—mainly because the

Xpatch results were taken from the calculations of the ZSU without a

ground plane (i.e., as if the vehicle were floating in free space).

Consider figure 6, which shows the same conditions as above, but where

the Xpatch data were computed with the vehicle on a metal ground

plane. There is a significantly better agreement of the computed data with

the measurement data. Thus, we can infer that the earth response is a

very important contribution to the RCS for ground vehicles. It is also

interesting that the comparison is so good, considering that the measurements include the response from an “earth” ground, while the computed

data involve a metal plane. In addition, the cross-polarization Xpatch data

are slightly lower in amplitude for all azimuth angles because our data

analysis approach is not finalized. For reference, the size of the ground

plane used by Xpatch is approximately 10 times greater than the size of

the largest dimension of the modeled object (a general “rule of thumb”

requirement).

Figure 7 shows measurement conditions identical to the previous two

figures with the exception that the center frequency of interest here is at

Ka-band. We note that the APG measurement data show a peak response

near 290° azimuth that did not appear at X-band. The Xpatch data in

figure 7 are for the case without a ground plane, which again accounts for

the poor agreement between the two plots. Unfortunately, the computation with the ground plane and at this depression angle had not yet been

run.
15

Figure 5. Comparison

of Xpatch and APG

RCS data for ZSU

measurement at X-band, 30°

depression angle,

cross-polarized field

components (vertical

transmit, horizontal

receive). Xpatch

results are for a

vehicle without a

ground plane.

Figure 6. Comparison

of Xpatch and APG

RCS data for ZSU

measurement at X-band, 30°

depression angle,

cross-polarized field

components (vertical

transmit, horizontal

receive). Xpatch

results are for a

vehicle with a ground

plane.
16

The actual feature on the vehicle that is responsible for the prominent

peak value in the RCS data appears to be related to the indentation on the

front left side of the vehicle (see fig. 8). To confirm this suspicion, one

could look at the ISAR image data for this case (near 290° azimuth angle),

or look further at the RCS polar plot data under circular polarization

conditions. This type of analysis is planned for our more complete future

report on the ZSU computed versus measured data comparisons.

The previous data were generated from a facet model with approximately

80,000 facets. For a vehicle of the size and complexity of the ZSU, this

facet model is considered coarse. The visual representation of the model

shows many abutting planes, poor representation of curved surfaces, and

absence of “small” details. At X-band, coarse models have been considered adequate based on comparisons with measurements and code

limitations. At Ka-band, or especially at W-band, the predictions from

coarse resolution facet models become more suspect. Theory indicates

that the lack of sufficient details in the model at these higher frequencies

will affect the predictive results. The degree of error at these higher

frequencies is strongly model-dependent (or geometry-dependent) and

also related to code limitations (such as edge diffraction) that play a role

even at X-band. High-fidelity CAD models, with a factor of 10 or more

greater numbers of facets than the ZSU model, are becoming more common for RCS prediction. The geometric representation of detail is much

greater, bad facets are absent, and the model appears much more visually

realistic (see fig. 9). Experience with high-fidelity models shows that they

can yield significantly better results not only at high frequencies where

Figure 7. Comparison

of Xpatch and APG

RCS data for ZSU

measurement at

Ka-band, 30°

depression angle,

cross-polarized field

components (vertical

transmit, horizontal

receive). Xpatch

results are for a

vehicle without a

ground plane.
17

sufficient detail is needed, but also at X-band. Consider the SAR image

comparison presented in figure 10 for the ZSU model used in the NATO

research study group versus the high-fidelity model of the ZSU generated

for another program. The SAR image from the high-fidelity model provides a better representation. Another measure of model performance

that better highlights the results from a comparison of the two levels of

model resolution is shown in figure 11. This figure indicates that the highfidelity model provides a greater feature recognition capability from RCS

radar data, to the degree that it becomes possible to separate and distinguish between different vehicles from Xpatch data sets. In the current

model, the ZSU could be distinguished from similar vehicles using

Xpatch data at only one azimuth angle (0°) over the 360° range. Using the

high-fidelity model, the ZSU could be distinguished from other similar

vehicles at over 25 different azimuth angles.

High-fidelity models do produce better results, but these come at a price.

The development of these models from CAD packages takes longer and

requires significantly greater resources than for low-fidelity models. The

high-fidelity facet model of the ZSU took over 3 months to develop

starting from the same CAD description as the coarse model. In addition,

the computational resources and the time required to run these models

are greatly extended (quantitative data on the ZSU high-fidelity model

are not yet available). The modeler must decide when the information

required from the model warrants the additional investment of time and

resources to pursue the high-fidelity approach.

Figure 8. Facet model

of the ZSU at 30°

depression angle and

290° in azimuth angle.
18

Figure 10. ISAR data

comparisons between

coarse resolution ZSU

model and highfidelity ZSU model.

Elevation: 30°

Azimuth: –135°

–35 –20 –5 10

Radar cross section (dBsm)

Current model Measured data New high-fidelity model

Source: Missile and Space Intelligence Center.

Figure 9. Comparison

of (a) current ZSU

facet model with

(b) high-fidelity facet

model.

Current model New geometrically exploited

high-fidelity model

Facets: 77,950

Parts: 763

Facets: 852,803

Parts: 3,943

ZSU-23 virtual target models

Source: Missile and Space Intelligence Center.
19

Figure 11. Value of

using high-fidelity

models, even at Xband.

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Elevation: 30°

–180 –135 –90 –45 0 45 90 135 180

Azimuth (°)

Validation error metric

M2 BTR-70 ZSU

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Validation error metric

–180 –135 –90 –45 0 45 90 135 180

Azimuth (°)

Source: Missile and Space Intelligence Center.

Current model Current model New high-fidelity model
iii

Contents

1. Introduction ....................................................................................................................................... 1

2. Development of the Facet Model ................................................................................................... 3

3. Xpatch Software ................................................................................................................................ 8

4. Computer Resources ....................................................................................................................... 10

5. Data Format and Analysis ............................................................................................................. 12

6. Data Comparisons ........................................................................................................................... 14

Distribution ............................................................................................................................................ 21

Report Documentation Page ................................................................................................................ 23

Figures

1. ZSU-23-4 vehicle at APG measurement facility.............................................................................. 1

2. X-, Ka-, and W-band polarimetric ISAR ........................................................................................... 2

3. ZSU facet model as it appears to APG radar measurement facility looking down

boresight of radar ................................................................................................................................ 6

4. Example of variation in run times for one type of computation at MSIC .................................11

5. Comparison of Xpatch and APG RCS data for ZSU measurement at X-band, 30°

depression angle, cross-polarized field components ................................................................... 15

6. Comparison of Xpatch and APG RCS data for ZSU measurement at X-band, 30°

depression angle, cross-polarized field components ................................................................... 15

7. Comparison of Xpatch and APG RCS data for ZSU measurement at Ka-band, 30°

depression angle, cross-polarized field components ................................................................... 16

8. Facet model of the ZSU at 30° depression angle and 290° in azimuth angle ........................... 17

9. Comparison of current ZSU facet model with high-fidelity facet model ................................. 18

10. ISAR data comparisons between coarse resolution ZSU model and high-fidelity ZSU

model .................................................................................................................................................. 18

11. Value of using high-fidelity models, even at X-band .................................................................. 19

Tables

1. X-, Ka-, and W-band polarimetric ISAR instrumentation data ..................................................... 2

2. ZSU measurement parameters .......................................................................................................... 2

3. Comparison of XpatchF and XpatchT .............................................................................................. 8

4. CPU hours for ZSU computations .................................................................................................. 10
21

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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Numerical Computation of the Radar Cross Section of

the ZSU-23-4

April 1999 Interim, July–September 1998

A computer geometry model of the ZSU-23-4 (a quad 23-mm self-propelled antiaircraft gun) was

obtained in Ballistic Research Laboratory-Computer Aided Design (BRL-CAD), a combinatorial solid

geometry-based modeling system. The BRL-CAD file served as input to a software package

(ECLECTIC) that generated a flat, triangular, all-metal facet representation of the ZSU exterior

structure, containing approximately 78,000 facets. The facet model served as input to Xpatch, a

high-frequency signature prediction code based on the shooting and bouncing ray (SBR) technique.

Xpatch was run at the Defense Intelligence Agency, High Performance Computing Center with

several Silicon Graphics, Inc. (SGI), Origin, Onyx, and Challenge machines that used 426 CPUs and 60

Gflops of computing power. The configuration parameters for the ZSU model, both with and without

a perfect metal ground plane, included two depression angles (12° and 30°), both polarizations, 256

frequencies (about each center frequency), and azimuth steps of 0.05° (for X-band) and 0.015° (for

Ka-band). The configuration parameters were selected based on measurement data taken on a ZSU

vehicle at the U.S. Army Research Laboratory Aberdeen Proving Ground test facility. The model

predictions will include radar cross-section data as a function of polarization and angle and synthetic

aperture radar images. This report details the preliminary results from the computer modeling.

radar cross section, ZSU, Xpatch

Unclassified

ARL-MR-430

8NE6K2

622705.H94

AH94

62705A

ARL PR:

AMS code:

DA PR:

PE:

Approved for public release; distribution

unlimited.

28

Unclassified Unclassified UL

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U.S. Army Research Laboratory

Attn: AMSRL-SE-RE rchase@arl.mil

U.S. Army Research Laboratory

23

Ronald Chase, H. Bruce Wallace (ARL), Thomas Blalock

(Defense Intelligence Agency Missile and Space Intelligence Center)

email:

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Adelphi, MD 20783-1197
DEPARTMENT OF THE ARMY

U.S. Army Research Laboratory2800 Powder Mill RoadAdelphi, MD 20783-1197

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