ARL-TR-8045 ● JUNE 2017

US Army Research Laboratory

Study of the Bistatic Radar Cross Section of a 

155-mm Artillery Round

by Christopher Kenyon and Traian Dogaru

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Destroy this report when it is no longer needed. Do not return it to the originator.
ARL-TR-8045 ● JUNE 2017

US Army Research Laboratory

Study of the Bistatic Radar Cross Section of a 

155-mm Artillery Round

by Christopher Kenyon and Traian Dogaru

Sensors and Electron Devices Directorate, ARL

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1. REPORT DATE (DD-MM-YYYY)

June 2017

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Technical Report

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Sep 2016–Apr 2017

4. TITLE AND SUBTITLE

Study of the Bistatic Radar Cross Section of a 155-mm Artillery Round

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Christopher Kenyon and Traian Dogaru

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US Army Research Laboratory

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Adelphi, MD 20783-1138

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ARL-TR-8045

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

This report investigates the bistatic radar signature of a 155-mm artillery round in 4 radar frequency bands, L, S, C, and X, 

using computer models. The radar cross section (RCS) calculations are performed by 2 different methods, implemented by the 

FEKO and AFDTD electromagnetic simulation software packages, over all the possible aspect angles. The solutions obtained 

by the 2 methods are compared for accuracy validation, showing excellent agreement between the 2. We also include a 

discussion of the RCS results, which underscores the complexity of bistatic radar scattering phenomenology. Particular 

emphasis is given to the forward and specular scattering directions, which display much larger target signatures than other 

geometries, including that of a monostatic radar system.

15. SUBJECT TERMS

computational electromagnetics, radar signature, bistatic radar, radar cross section, RCS, EM

16. SECURITY CLASSIFICATION OF:

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28

19a. NAME OF RESPONSIBLE PERSON

Traian Dogaru

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(301) 394-1482

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iii

Contents

List of Figures iv

1. Introduction 1

2. Description of the Target, Computational Methods, and 

Terminology 2

3. Comparison of FEKO and AFDTD Bistatic RCS Predictions 5

4. Discussion of the Bistatic RCS of a 155-mm Round 12

5. Conclusions 15

6. References 17

List of Symbols, Abbreviations, and Acronyms 18

Distribution List 19
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iv

List of Figures

Fig. 1 Representation of the computational mesh of the 155-mm artillery 

round considered in this study, together with the Cartesian coordinate 

system and the incidence and scattering angles relevant to the bistatic 

radar geometry .......................................................................................2

Fig. 2 Schematic diagram of 3 radar scattering geometries, showing the a) 

backscattering configuration, b) forward scattering configuration, and 

c) specular scattering configuration.......................................................4

Fig. 3 Schematic diagram of 2 angle sweeping configurations, showing a) inplane scattering and b) out-of-plane scattering......................................4

Fig. 4 In-plane bistatic RCS of a 155-mm round in the S band computed by 

AFDTD and FEKO for a) θi = 30°, b) θi = 60°, c) θi = 90°, d) θi = 

120°, and e) θi = 150°. In most cases, the lines obtained by the 2 

methods are on top of one another.........................................................6

Fig. 5 In-plane bistatic RCS of a 155-mm round in the X band computed by 

AFDTD and FEKO for a) θi = 30°, b) θi = 60°, c) θi = 90°, d) θi = 

120°, and e) θi = 150°. In most cases, the lines obtained by the 2 

methods are on top of one another.........................................................7

Fig. 6 Out-of-plane bistatic RCS of a 155-mm round in the S band computed 

by AFDTD and FEKO for V-V polarization and a) θi = 30°, b) θi = 

60°, c) θi = 90°, d) θi = 120°, and e) θi = 150°. The line plots were 

obtained by AFDTD, while the marker plots were obtained by FEKO. 

The plots are color-coded as follows: blue θs = 30°, red θs = 60°, green 

θs = 90°, black θs = 120°, and cyan θs = 150°........................................8

Fig. 7 Out-of-plane bistatic RCS of a 155-mm round in the S band computed 

by AFDTD and FEKO for H-H polarization and a) θi = 30°, b) θi = 

60°, c) θi = 90°, d) θi = 120°, and e) θi = 150°. The line plots were 

obtained by AFDTD, while the marker plots were obtained by FEKO. 

The plots are color-coded as follows: blue θs = 30°, red θs = 60°, green 

θs = 90°, black θs = 120°, and cyan θs = 150°........................................9

Fig. 8 Out-of-plane bistatic RCS of a 155-mm round in the S band computed 

by AFDTD and FEKO for H-V polarization and a) θi = 30°, b) θi = 

60°, c) θi = 90°, d) θi = 120°, and e) θi = 150°. The line plots were 

obtained by AFDTD, while the marker plots were obtained by FEKO. 

The plots are color-coded as follows: blue θs = 30°, red θs = 60°, green 

θs = 90°, black θs = 120°, and cyan θs = 150°......................................10

Fig. 9 Out-of-plane bistatic RCS of a 155-mm round in the S band computed 

by AFDTD and FEKO for V-H polarization and a) θi = 30°, b) θi = 

60°, c) θi = 90°, d) θi = 120°, and e) θi = 150°. The line plots were 

obtained by AFDTD, while the marker plots were obtained by FEKO. 

The plots are color-coded as follows: blue θs = 30°, red θs = 60°, green 

θs = 90°, black θs = 120°, and cyan θs = 150°......................................11
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v

Fig. 10 Bistatic RCS of a 155-mm round in the forward and specular 

directions as a function of θi, showing a) L-band, V-V polarization; b) 

L-band, H-H polarization; c) S-band, V-V polarization; and d) S-band, 

H-H polarization ..................................................................................14

Fig. 11 Bistatic RCS of a 155-mm round in the forward and specular 

directions as a function of θi, showing a) C-band, V-V polarization; b) 

C-band, H-H polarization; c) X-band, V-V polarization; and d) Xband, H-H polarization.........................................................................15
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vi

INTENTIONALLY LEFT BLANK.
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1

1. Introduction

The US Army has been developing radar technology for the detection and tracking 

of artillery rounds grouped under the generic category of rockets, artillery, and 

mortar. The electromagnetic (EM) modeling team at the US Army Research 

Laboratory (ARL) is contributing to these efforts by undertaking a systematic study 

of the radar signature of these targets, based on computer models. Our findings have 

already been published in a series of technical reports.

1–3 In those studies, we 

analyzed the radar cross section (RCS) of several types of projectiles for sensing 

scenarios involving monostatic radar. In this new report, we investigate the 

scattering signature obtained in bistatic radar configurations. 

There has been little material published in the open literature on the subject of 

bistatic radar. Besides Willis’ book,

4 which represents a good, systematic 

introduction to the topic, several other texts include chapters or research articles on 

bistatic radar.

5,6 However, the subject of bistatic RCSs is very briefly treated in all 

of these books. As discussed by many authors, one of the potential advantages of 

using bistatic radar is that, for many targets, the RCS in the forward and specular 

directions can be much larger (by orders of magnitude) than in the backscatter 

direction (where a monostatic radar operates). This can have a significant effect in 

improving the radar detection performance. However, these bistatic radar 

configurations also present serious drawbacks regarding the radar measurement of 

various target parameters4; therefore, the bistatic radar overall performance analysis 

always involves some engineering tradeoffs. 

Our goal in this study is to understand the phenomenology of the bistatic radar 

scattering from a 155-mm artillery round, while limiting our analysis to scenarios 

amenable to an open-source publication. Specifically, we use computer simulations 

to calculate the bistatic RCS of this target placed in a fixed, upright position, 

without any reference to specific radar implementations or operational scenarios. 

As with our previous similar investigations, we use the AFDTD simulation 

software7 to evaluate the RCS for all possible bistatic radar geometrical 

configurations, as well as 4 different radar frequency bands. As a preliminary step, 

we perform a validation of the AFDTD results with the commercial FEKO EM 

simulation software.

8

This report is organized as follows. In Section 2, we present the target under 

investigation and the numerical methods used in computing the radar signature; 

additionally, we explain the geometry, notations, and terminology employed 

throughout the rest of the study. Section 3 compares the accuracy of the 2 EM 

modeling software packages used in this work. In Section 4, we discuss the relevant 
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2

phenomenology related to the bistatic RCS of the target as a function of aspect and 

frequency. We end with conclusions in Section 5.

2. Description of the Target, Computational Methods, and 

Terminology

The radar target under investigation in this report, a 155-mm artillery round, is

shown in Fig. 1. This is the same target used in our previous work on monostatic 

radar signatures.

1 As in that work, the projectile shell material is modeled as a 

perfect electric conductor. The closest simple geometrical shape, whose signature 

is discussed in some bistatic radar references,

4,9 is a circular cylinder of a diameter 

much smaller than its length. Knott includes a discussion of the physical optics 

solution to the radar scattering from a cylindrical target; however, that solution has 

a limited range of validity is terms of aspect angles and frequencies. Willis presents 

bistatic scattering patterns for a cylinder based on method of moments calculations, 

which were validated by measurements. The results in these references constitute a 

useful baseline for our investigation. Nevertheless, we expect the bistatic RSC of a 

155-mm round to differ from that of a cylinder at certain aspect angles, given the 

nose taper characteristic of the former.

Fig. 1 Representation of the computational mesh of the 155-mm artillery round considered 

in this study, together with the Cartesian coordinate system and the incidence and scattering 

angles relevant to the bistatic radar geometry

Two different EM modeling programs were used in this study: FEKO and AFDTD. 

FEKO is a commercial software package that includes several methods of solving 
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3

general EM wave propagation problems, including radar scattering. In this work, 

we used the surface integral equation (SIE) solver (also known as the method of 

moments) for the RCS calculation of the targets of interest. AFDTD is an EM 

modeling software package developed in-house at ARL specifically for radar 

signature simulation. It is based on the finite-difference, time-domain (FDTD) 

method10 and has been employed and validated in many radar system modeling 

applications of interest to the Army. 

The AFDTD code was parallelized and designed to run on high-performance 

computing platforms at the Defense Supercomputing Resource Centers (DSRCs). 

For this investigation, the following platforms have been used: Excalibur (Cray 

XC40) at the ARL DSRC,11 and Lightning (Cray XC30) at the US Air Force 

Research Laboratory DSRC.

12 The typical number of cores used in each simulation 

was 4. FEKO was run on desktop PCs under the Windows operating system, using 

a maximum of 4 cores at a time and with a memory limit of 96 GB. A more 

extensive comparison between the capabilities, limitations, and efficiency of the 2 

software packages, relevant to the simulations presented in this study, was 

discussed in a previous report1 and is not repeated here. An additional feature of 

both codes, which makes them particularly efficient to the current analysis, is the 

fact that they are capable of computing the bistatic RCS over the entire range of 

scattering angles, in one run. Nonetheless, the main purpose of employing 2 

different simulation methods in this report is to validate the accuracy of their

bistatic radar scattering calculations (this is performed in Section 3).

In reference to Fig. 1, we need to be specific about the way we define the incidence 

and scattering angles. Note that this report designates these angles in a manner 

consistent with the EM modeling codes (both AFDTD and FEKO), which may be 

different from other authors’ notation. Thus, the target is placed at the origin of the 

Cartesian coordinate system and the radar transmitter (Tx) and receiver (Rx) are 

both placed in the far-field region. The pair of incidence angles( ) i i φ ,θ represents 

the direction of the Tx location, while the pair of scattering angles ( ) s s φ ,θ

represents the direction of the Rx location, both starting from the origin 

(see Fig. 1). The propagation directions of the incident and scattered plane waves 

are given by the following unit vectors:





















−

−

−

=

i

i i

i i

i

θ

φ θ

φ θ

cos

sin sin

cos sin

kˆ 





















=

s

s s

s s

s

θ

φ θ

φ θ

cos

sin sin

cos sin

kˆ (1)
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4

Notice that the φ angles are allowed to vary around the clock (from 0° to 360°), 

whereas the θ angles are limited to the interval between 0° and 180°. The 

backscattering configuration (encountered in monostatic radar) involves the 

following relations: s i φ = φ and s i θ = θ . Other important bistatic scattering configurations are forward scattering, when s i φ −φ = 180° and i s θ +θ = 180°; and specular 

scattering, when s i φ = φ and i s θ + θ = 180° (note that the term “specular” is used 

here in reference to the vertical axis of the target). These configurations are illustrated 

in Fig. 2. When the Tx, the target, and the Rx are all in the same vertical plane 

(meaning s i φ − φ = 0° or 180°), we talk about “in-plane” scattering (Fig. 3a). When 

φs −φi takes any other values, the scattering geometry is called “out-of-plane”

(Fig. 3b).

(a) (b) (c)

Fig. 2 Schematic diagram of 3 radar scattering geometries, showing the a) backscattering 

configuration, b) forward scattering configuration, and c) specular scattering configuration

(a) (b) 

Fig. 3 Schematic diagram of 2 angle sweeping configurations, showing a) in-plane 

scattering and b) out-of-plane scattering 

The simulation space for a bistatic radar signature is much larger than in the case 

of monostatic radar. Thus, when we characterize the RCS in the most general case, 

we have to deal with 5 variables: the 4 angles i s i s φ ,φ ,θ ,θ and frequency. In our 
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5

case, we take advantage of the target symmetry to reduce the dimensionality of the 

simulations and results. Thus, given the rotational symmetry with respect to the z

axis, we can fix the angle φi (by taking = 0° i φ ) and vary the angle φs from 0° to 

180°, in 6° increments. Nevertheless, both θ angles must be swept from 0° to 180°

in the simulations—we use 1° increments in this process. Another interesting result 

allowing us to reduce the simulation space is that the θi and θs angles are 

interchangeable (meaning that if we swap the values of θi and θs we obtain the same 

RCS)—this is a consequence of the reciprocity theorem in EM.

9

In terms of frequencies, we perform the calculations at 1.3 GHz (corresponding to 

the L band), 2.4 GHz (to the S band), 5.6 GHz (to the C band), and 9.5 GHz (to the 

X band). For each band, the RCS results are averaged over a 200-MHz subband 

centered at the frequencies previously mentioned (similar to our previous work).1,2

Additionally, we consider all polarization combinations: vertical-vertical (V-V), 

horizontal-horizontal (H-H), horizontal-vertical (H-V), and vertical-horizontal (VH). The simulation results are typically presented as the variation of RCS in decibel

square meters versus one angle.

3. Comparison of FEKO and AFDTD Bistatic RCS Predictions

In this section, we present the results of the AFDTD and FEKO simulations for the 

target introduced in Section 2. A discussion of these results is included in 

Section 4. In Figs. 4 and 5, we compare the in-plane bistatic RCS obtained by the 

2 methods, for V-V and H-H polarizations, in the S and X bands, respectively. For 

these simulations, we consider several incidence directions (θi = 30°, 60°, 90°, 

120°, 150°) and let the θs angle vary around the clock. Notice that in Figs. 4 and 5, 

when the θs angle is positive (between 0° and 180°), we take φs = 180°, whereas 

when θs is negative (between 0° and –180°), we take φs = 0°. The arrows in these 

figures help the reader locate the backscatter, specular, and forward scattering 

directions in each case.

In Figs. 6–9, we compare the out-of-plane bistatic RCS obtained by the 2 methods. 

This time, we show only the S-band results, but consider all 4 polarization 

combinations (V-V, V-H, H-V, and H-H). In these figures, the pick the same 5 

incidence directions (θi = 30°, 60°, 90°, 120°, 150°), as well as 5 different values 

of θs (θs = 30°, 60°, 90°, 120°, 150°), and let the angle φs vary from 0° and 180° (by 

symmetry, the other half of the circular range for φs would yield the same results). 

In Figs. 6–9, all the line plots were obtained with AFDTD, while the marker plots 

were obtained with FEKO. The specific values for θs in each plot of a graph are 

color-coded, as explained in the captions. In all cases, the match between the 

AFDTD and FEKO results is remarkably good.
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6

(a) (b) 

(c) (d) 

(e) 

Fig. 4 In-plane bistatic RCS of a 155-mm round in the S band computed by AFDTD and 

FEKO for a) θi = 30°, b) θi = 60°, c) θi = 90°, d) θi = 120°, and e) θi = 150°. In most cases, the 

lines obtained by the 2 methods are on top of one another. 

-150 -100 -50 0 50 100 150

s (degrees)

-40

-30

-20

-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

specular

backscatter

forward

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s (degrees)

-40

-30

-20

-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

backscatter

specular

forward

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s (degrees)

-40

-30

-20

-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

specular and

backscatter

forward

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s (degrees)

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0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

backscatter

specular

forward

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s (degrees)

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-30

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-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

specular

backscatter

forward
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7

(a) (b) 

(c) (d) 

(e) 

Fig. 5 In-plane bistatic RCS of a 155-mm round in the X band computed by AFDTD and 

FEKO for a) θi = 30°, b) θi = 60°, c) θi = 90°, d) θi = 120°, and e) θi = 150°. In most cases, the 

lines obtained by the 2 methods are on top of one another. 

-150 -100 -50 0 50 100 150

s (degrees)

-40

-30

-20

-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

specular

backscatter

forward

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s (degrees)

-40

-30

-20

-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

specular

backscatter

forward

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s (degrees)

-40

-30

-20

-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

forward

specular and

backscatter

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s (degrees)

-40

-30

-20

-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH

backscatter

specular

forward

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s (degrees)

-40

-30

-20

-10

0

10

20

RCS (dBsm)

AFDTD VV

FEKO VV

AFDTD HH

FEKO HH specular

forward

backscatter
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8

(a) (b) 

(c) (d) 

(e) 

Fig. 6 Out-of-plane bistatic RCS of a 155-mm round in the S band computed by AFDTD 

and FEKO for V-V polarization and a) θi = 30°, b) θi = 60°, c) θi = 90°, d) θi = 120°, and

e) θi = 150°. The line plots were obtained by AFDTD, while the marker plots were obtained by 

FEKO. The plots are color-coded as follows: blue θs = 30°, red θs = 60°, green θs = 90°, black 

θs = 120°, and cyan θs = 150°.

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-50

-40

-30

-20

-10

0

10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-50

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-10

0

10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-50

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0

10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

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0

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RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-50

-40

-30

-20

-10

0

10

RCS (dBsm)
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9

(a) (b) 

(c) (d) 

(e) 

Fig. 7 Out-of-plane bistatic RCS of a 155-mm round in the S band computed by AFDTD 

and FEKO for H-H polarization and a) θi = 30°, b) θi = 60°, c) θi = 90°, d) θi = 120°, and

e) θi = 150°. The line plots were obtained by AFDTD, while the marker plots were obtained by 

FEKO. The plots are color-coded as follows: blue θs = 30°, red θs = 60°, green θs = 90°, black 

θs = 120°, and cyan θs = 150°.

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-50

-40

-30

-20

-10

0

10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-50

-40

-30

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-10

0

10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-50

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-10

0

10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

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-10

0

10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-50

-40

-30

-20

-10

0

10

RCS (dBsm)
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10

(a) (b) 

(c) (d) 

(e) 

Fig. 8 Out-of-plane bistatic RCS of a 155-mm round in the S band computed by AFDTD 

and FEKO for H-V polarization and a) θi = 30°, b) θi = 60°, c) θi = 90°, d) θi = 120°, and

e) θi = 150°. The line plots were obtained by AFDTD, while the marker plots were obtained by 

FEKO. The plots are color-coded as follows: blue θs = 30°, red θs = 60°, green θs = 90°, black 

θs = 120°, and cyan θs = 150°.

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-55

-50

-45

-40

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-25

-20

-15

-10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

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-45

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RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

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-45

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-15

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RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

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RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

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-50

-45

-40

-35

-30

-25

-20

-15

-10

RCS (dBsm)
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11

(a) (b) 

(c) (d) 

(e) 

Fig. 9 Out-of-plane bistatic RCS of a 155-mm round in the S band computed by AFDTD 

and FEKO for V-H polarization and a) θi = 30°, b) θi = 60°, c) θi = 90°, d) θi = 120°, and

e) θi = 150°. The line plots were obtained by AFDTD, while the marker plots were obtained by 

FEKO. The plots are color-coded as follows: blue θs = 30°, red θs = 60°, green θs = 90°, black 

θs = 120°, and cyan θs = 150°.

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

RCS (dBsm)

0 20 40 60 80 100 120 140 160 180

s (degrees)

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

RCS (dBsm)
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12

4. Discussion of the Bistatic RCS of a 155-mm Round

In this section, we discuss some of the bistatic signature results from Section 3 and 

make a comparison of the bistatic RCS over the 4 frequency bands mentioned in 

Section 2. Although the simulations were run over the entire angular ranges 

mentioned in Section 2, we must limit the presentation of results to a relatively 

small number of scenarios. In previous work,

1,2 the comparison among frequency 

bands was performed by computing monostatic RCS averages over the scattering 

elevation angle. We attempted a similar procedure for the bistatic RCS: for 

instance, one could fix the θi and θs angles, and compute averages over φs – φi. 

However, we found out that such averages are clearly dominated by 2 angular 

configurations (corresponding to forward and specular scattering), where the RCS 

is typically at least an order of magnitude larger than in other directions. 

Consequently, we think that the RCS averages over certain angular ranges are less 

meaningful for our investigation; instead, we decided to simply compare the 

scattering strengths in the forward and specular directions among the 4 frequency 

bands.

The bistatic RCS results for in-plane scattering (Figs. 4 and 5) show, as expected, 

2 peaks, in the forward and specular directions. Notice that the difference between 

these 2 peaks becomes larger as the incidence direction gets closer to normal to the 

target (θi = 90°). For θi = 90°, the forward scattering configuration reaches the 

absolute maximum in terms of RCS. For smaller θi (or incidence direction closer 

to the z axis), the peaks are not very pronounced: in that case, the target geometry 

as seen by the radar Tx departs the ideal long cylindrical shape and the contribution 

of the projectile’s ends to the scattering response becomes more significant. The 

peaks in the forward and specular directions become narrower as the frequency is 

increased (compare the plots in the S and X bands), meaning that, at high frequency, 

the scattering is more directional. 

More interesting are the RCS results for out-of-plane bistatic scattering. By 

analyzing the plots in Figs. 6–9, we concluded (again, as expected) that 

configurations for which s i θ +θ = 180° (which contain both the forward and 

specular directions) display the largest RCS at any azimuth angle. However, when 

one tries to compare the RCS in the general “forward scattering hemisphere” 

(where 90° ≤ φ s −φi ≤ 180°) with that in the “backward scattering hemisphere” 

(where 0° ≤ φ s −φi ≤ 90°), the results are less clear-cut. Thus, for configurations 

where s i θ +θ = 180°, the RCS in the forward hemisphere is generally larger than 

that in the backward hemisphere. However, for θ s +θ i ≠ 180°, there are 
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13

configurations where the opposite is true. Another striking result is the fact that, in 

the backward hemisphere, the bistatic RCS generally does not vary much with the 

azimuth angle (φs – φi), typically within a range of no more than 5 dB. This effect 

is more evident as the incidence gets closer to normal to the target (θi = 90°).

So far, the discussion involved only the 2 co-polarized scattering configurations, 

V-V and H-H. The in-plane cross-polarization (i.e., V-H and H-V) bistatic signature 

is theoretically null due to the target symmetry—consequently, we did not display 

it graphically in this report. However, as shown in Figs. 6–9, the out-of-plane crosspolarization RCS can be quite significant—at some scattering angles, especially as 

φs approaches 90o, it exceeds the co-polarization RCS. This result is important for 

radar systems that measure fully polarimetric data and may open the door to 

interesting applications of polarimetric processing for bistatic radar. Another 

interesting fact is that the signatures are different between V-H and H-V 

polarizations for bistatic radar configurations. This is unlike for a monostatic radar, 

where the 2 cross-polarization combinations yield the same signature. This means 

that as far as polarization goes, the bistatic radar is an example where the reciprocity 

principle cannot be applied.

Finally, we compare the bistatic RCS in the forward and specular directions among 

the 4 frequency bands in Figs. 10 and 11, for V-V and H-H polarizations, 

respectively. The angle variable in the graphs in Figs. 10 and 11 is θi. For θi = 0° 

or 180°, the specular and forward scattering directions are identical. In the forward 

direction, the RCS always has a peak for normal incidence, when θi = 90°; however, 

the specular RCS does not display the same variation with θi, but is relatively flat. 

Interestingly, a simple analytic formula gives an approximate value of a target RCS 

in the forward scattering direction4

:

F i

A θ

λ

σ π 2

2

2

= 4 sin (2)

where A is the target’s shadow area (in our case, the cross-section area in a vertical 

plane going through its middle) and λ is the radar wavelength. This formula 

becomes more accurate as we approach the “optical” (or high-frequency) regime. 

To test its accuracy, we plotted it alongside the AFDTD-computed values in 

Figs. 10 and 11 (note: for the 155-mm round, we have A = 0.0765 m2). By 

comparing the graphs, we conclude that the analytic prediction is fairly close to the 

exact (AFDTD) solution, except for incidence near nose-on or bottom-on 

orientations (within 30° from the z axis). The analytic formula’s accuracy is better 

at high frequencies (X band) than at low frequencies (L band), and for H-H 
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14

polarization than for V-V polarization, but the errors never exceed 3 dB within the 

angular range already mentioned.

(a) (b)

(c) (d)

Fig. 10 Bistatic RCS of a 155-mm round in the forward and specular directions as a function 

of θi, showing a) L-band, V-V polarization; b) L-band, H-H polarization; c) S-band, V-V 

polarization; and d) S-band, H-H polarization
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15

(a) (b)

(c) (d)

Fig. 11 Bistatic RCS of a 155-mm round in the forward and specular directions as a function 

of θi, showing a) C-band, V-V polarization; b) C-band, H-H polarization; c) X-band, V-V 

polarization; and d) X-band, H-H polarization

Regarding the frequency dependence, we notice larger forward and specular RCS 

values as the frequency increases. However, this does not necessarily mean that the 

RCS generally increases with frequency for all bistatic angle configurations. As 

previously discussed, the plots in Figs. 3–6 show that, as the frequency is increased, 

the forward and specular peaks become both narrower and larger in amplitude, 

leaving open the question whether the average bistatic RCS increases or decreases 

with frequency. For now, we can state that the answer to this question depends on 

the specific bistatic radar sensing scenario and geometry and will be the subject of 

a future study.

5. Conclusions

This report performed an investigation of the RCS of 155-mm artillery round for 

bistatic radar configurations. As mentioned in the Introduction, very little 

information has been published in the open literature on the bistatic radar signature 
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16

of targets beyond some very basic shapes and approximate signature analysis 

methods. To obtain accurate bistatic RCS data on the target of interest, we 

employed exact EM modeling techniques, based on FDTD and the SIE methods. 

The software packages employed in our simulations were AFDTD and FEKO. The 

results obtained by the 2 codes are in very good agreement, as demonstrated in 

Section 3—this makes us confident to use them in future investigations related to 

this radar technology.

The bistatic RCS analysis in Section 4 suggests that the phenomenology of bistatic 

radar scattering is very complex and does not lend itself to simple generalizations, 

particularly for out-of-plane configurations. This is consistent with the findings of 

other authors; thus, Willis4 warns against drawing simplified conclusions regarding 

the scattering signature of radar targets and clutter for bistatic geometries. 

Moreover, the target considered in this report has a particular shape displaying

cylindrical symmetry; consequently, we need to clearly state that some results in 

Section 4 cannot be extended to the bistatic signature of other targets with different 

shape factors and symmetry characteristics. 

Nevertheless, certain general conclusions can be drawn from our study regarding 

the bistatic RCS of the 155-mm round. Most importantly, there are 2 configurations, 

the forward and specular scattering, where the target signature is much larger (by 

at least an order of magnitude) than in any other geometries. Therefore, a bistatic 

radar system could potentially present a rather large advantage over a monostatic 

system in terms of radar signature. Nonetheless, multiple other issues related to the 

bistatic radar technology,

4 which are not discussed in this report, could either negate 

this advantage or make the bistatic radar implementation impractical. Follow-up 

investigations will attempt to further our understanding of these issues as they relate 

to practical radar detection problems of interest to the Army. 
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17

6. References

1. Kenyon C, Dogaru T. Numerical computation of the radar cross section of 

rockets and artillery rounds. Adelphi (MD): Army Research Laboratory (US); 

2015 Sep. Report No.: ARL-TR-7468.

2. Kenyon C, Dogaru T. Numerical computation of the radar cross section of a 

120-mm mortar. Adelphi (MD): Army Research Laboratory (US); 2015 Nov. 

Report No.: ARL-TN-0716.

3. Dogaru T, Kenyon C. Numeric computation of the radar cross section of inflight Projectiles. Adelphi (MD): Army Research Laboratory (US); 2016 Nov. 

Report No.: ARL-TR-7895.

4. Willis N. Bistatic radar. Norwood (MA): Artech; 1991.

5. Skolnik M. Radar handbook. New York (NY): McGraw Hill; 2008.

6. Melvin W, Scheer J. Principles of modern radar – radar applications. Raleigh:

SciTech Publishing; 2014.

7. Dogaru T. AFDTD user’s manual. Adelphi (MD): Army Research Laboratory 

(US); 2010 Mar. Report No.: ARL-TR-5145.

8. FEKO EM Simulation Software Web page. Tory (MI): Altair Engineering; 

2015. [accessed 2016 Oct]. http://www.feko.info.

9. Knott E, Shaeffer J, Tuley M. Radar cross section. Norwood (MA): Artech; 

1993.

10. Taflove A, Hagness S. Computational electrodynamics: The finite-difference 

time-domain method. Norwood (MA): Artech; 2000.

11. ARL DSRC Web page. Aberdeen Proving Ground (MD): Army Research 

Laboratory (US); 2016 Oct 18 [accessed 2017 May]. http://www.arl.hpc.mil.

12. AFRL DSRC Web page. Wright Patterson Air Force Base (OH): Air Force 

Reearch Laboratory (US); 2015 Aug 5 [accessed 2017 May]. 

http://www.afrl.hpc.mil.
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List of Symbols, Abbreviations, and Acronyms

ARL US Army Research Laboratory

DSRC Defense Supercomputing Resource Center

EM electromagnetic

FDTD finite difference, time domain 

H-H horizontal-horizontal

H-V horizontal-vertical

PC personal computer

RCS radar cross section

Rx receiver

SIE surface integral equation

Tx transmitter

V-H vertical-horizontal

V-V vertical-vertical
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1 DEFENSE TECH INFO CTR

(PDF) ATTN DTIC OCA

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(PDF) RDRL SER U 

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