Through the Wall Radar Simulations Using Polarimetric 

Antenna Patterns

by Traian Dogaru and Calvin Le

ARL-TR-5951 March 2012

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Army Research Laboratory 

Adelphi, MD 20783-1197 

ARL-TR-5951 March 2012 

Through the Wall Radar Simulations Using Polarimetric 

Antenna Patterns 

Traian Dogaru and Calvin Le 

Sensors and Electron Devices Directorate, ARL 

Approved for public release; distribution unlimited. 
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Through the Wall Radar Simulations Using Polarimetric Antenna Patterns

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Traian Dogaru and Calvin Le

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14. ABSTRACT

In this report, we analyze the impact of coupling the polarimetric characteristics of antennas and targets on a radar system 

response and performance. We start by formulating the basic equations that govern this interaction and extend them to images 

created by an ultra-wideband (UWB), broad-beam-antenna, strip-map synthetic aperture radar (SAR) system. In the numerical 

example section, we apply this method to the problem of through-the-wall detection of a small weapon based on polarimetric 

differences between SAR images. The scenarios considered involve buildings of various complexities, as well as two families 

of antenna patterns. The results demonstrate a reduction in the weapon detection scheme performance when the radar antenna 

cross-polarization suppression drops under a certain limit. The numerical examples are based on simulated data obtained by the 

AFDTD software (for the radar target signature) and the FEKO software (for the antenna patterns).

15. SUBJECT TERMS

Sensing through the wall, polarimetric radar, computational electromagnetics

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iii

Contents 

List of Figures iv

List of Tables v

Acknowledgments vii

1. Introduction 1

2. Theoretical Formulation 2

2.1 Modeling a SAR Imaging System ...................................................................................2

2.2 Accounting for the Polarization Coupling between Radar Antennas and Target ...........5

2.3 Formulation for a Fully Polarimetric Radar System .......................................................7

2.4 Typical Radar Antenna Patterns ....................................................................................10

2.5 Application to a Simple Polarimetric SAR Imaging Scenario ......................................12

2.6 Limitations and Extensions of the Technique ...............................................................14

3. Numerical Results 15

3.1 Problem Definition and Methodology ...........................................................................15

3.2 Example Involving Simple Antenna Patterns ...............................................................17

3.3 Imaging of a Human in a Simple Room ........................................................................20

3.4 Application to Imaging of a Complex Room ................................................................25

3.5 Examples Involving the SIRE Radar Antennas ............................................................32

4. Conclusions 39

5. References 41

List of Symbols, Abbreviations, and Acronyms 44

Distribution List 45
iv

List of Figures 

Figure 1. Schematic representation of a SAR imaging system geometry in two different 

configuration: (a) spotlight; (b) strip-map. ...............................................................................3

Figure 2. Schematic representation of a bistatic radar scattering scenario, showing generic 

transmitting and receiving radar antennas. ................................................................................5

Figure 3. Schematic representation of a fully polarimetric radar scattering scenario, showing 

the vertically and horizontally polarized, transmitting and receiving radar antennas. ..............8

Figure 4. Three-dimensional representation of the far-field patterns radiated by a rectangular 

waveguide antenna at 4.5 GHz, showing: (a) co-polarization field magnitude; (b) crosspolarization field magnitude. ...................................................................................................11

Figure 5. Two-dimensional, far-field patterns radiated by a rectangular waveguide antenna at 

4.5 GHz, showing: (a) field magnitudes in the  = 5o plane; (b) field magnitudes in the 

= 5o plane. ................................................................................................................................12

Figure 6. Schematic representation of a fully polarimetric two-dimensional SAR imaging 

system, operating monostatically in strip-map configuration. ................................................13

Figure 7. Geometry of the open rectangular waveguide antenna, showing: (a) vertical 

polarization and (b) horizontal polarization. ............................................................................17

Figure 8. Top view of the simple four-wall room with a human carrying an AK-47 rifle and 

placed in the middle of the room, showing a schematic representation of the synthetic 

radar aperture on the left side. ..................................................................................................21

Figure 9. SAR images of the human placed in a middle of a brick wall room, under the plane 

wave assumption, showing: (a) V-V polarization, human unarmed; (b) V-V polarization, 

human with AK-47; (c) H-V polarization, human unarmed; and (d) H-V polarization, 

human with AK-47. .................................................................................................................22

Figure 10. SAR images of the human placed in a middle of a brick wall room, including the 

effects of open waveguide antennas with PRRMS = 20 dB, showing: (a) V-V polarization, 

human unarmed; (b) V-V polarization, human with AK-47; (c) H-V polarization, human 

unarmed; and (d) H-V polarization, human with AK-47. ........................................................23

Figure 11. SAR images of the human placed in a middle of a brick wall room, including the 

effects of open waveguide antennas with PRRMS = 10 dB, showing: (a) V-V polarization, 

human unarmed; (b) V-V polarization, human with AK-47; (c) H-V polarization, human 

unarmed; and (d) H-V polarization, human with AK-47. ........................................................24

Figure 12. The complex room containing humans and furniture objects showing 

(a) perspective view (humans carrying rifles) and (b) top view (humans unarmed). ..............27

Figure 13. SAR images of the complex room under the plane wave assumption showing: 

(a) V-V polarization, all humans unarmed; (b) V-V polarization, all humans with AK-47; 

(c) H-V polarization, all humans unarmed; and (d) H-V polarization, all humans with 

AK-47. .....................................................................................................................................28
v

Figure 14. SAR images of the complex room that include the effects of open waveguide 

antennas with PRRMS = 20 dB showing: (a) V-V polarization, all humans unarmed; (b) VV polarization, all humans with AK-47; (c) H-V polarization, all humans unarmed; and 

(d) H-V polarization, all humans with AK-47. ........................................................................29

Figure 15. SAR images of the complex room that include the effects of open waveguide 

antennas with PRRMS = 10 dB showing: (a) V-V polarization, all humans unarmed; (b) VV polarization, all humans with AK-47; (c) H-V polarization, all humans unarmed; and 

(d) H-V polarization, all humans with AK-47. ........................................................................30

Figure 16. Detection maps for the complex room shown in figure 12, for a SAR system 

equipped with open waveguide antennas with (a) PRRMS = 30 dB and (b) PRRMS = 20 dB. ....31

Figure 17. Detection maps for the complex room in figure 12, for a SAR system equipped 

with open waveguide antennas with PRRMS = 10 dB, showing the cases where (a) all 

humans are unarmed and (b) all humans carry AK-47 rifles. ..................................................31

Figure 18. The SIRE radar antennas for the (a) transmitter and (b) receiver, showing pictures 

of the physical antennas as well as wire-frame meshes used in FEKO simulations................33

Figure 19. The vertical electric field magnitude for the SIRE transmission antenna at  = 0o 

and  = 1o, before and after the smoothing procedure, shown here in: (a) frequency 

domain; (b) time domain. .........................................................................................................34

Figure 20. SIRE antenna patterns in the horizontal plane, at 2 GHz, with antennas at 2o 

elevation tilt, showing: (a) transmitting antenna in vertical polarization; (b) transmitting 

antenna in horizontal polarization; (c) receiving antenna in vertical polarization and 

(d) receiving antenna in horizontal polarization. .....................................................................36

Figure 21. SAR images of the human placed in a middle of a brick wall room, including the 

SIRE antenna effects, showing: (a) V-V polarization, human unarmed; (b) V-V 

polarization, human with AK-47; (c) H-V polarization, human unarmed; and (d) H-V 

polarization, human with AK-47. ............................................................................................37

Figure 22. Cross-polarization (H-V) SAR images of the complex room, including the effects 

of the SIRE antennas tilted at (a) 1o in elevation and (b) 2o in elevation. ................................38

Figure 23. Detection maps for the complex room in figure 12, for a SAR system equipped 

with SIRE antennas tilted at (a) 1o in elevation and (b) 2o in elevation. ..................................38

List of Tables 

Table 1. Comparison of maximum pixel intensity in the human areas within the SAR images 

presented in sections 3.2 and 3.3, in co- and cross-polarization, for the cases with and 

without rifle (all values in dB). ................................................................................................25

Table 2. Detection threshold for the weapon discrimination scheme described in sections 3.4 

and 3.5, for various antenna systems and cross-polarization properties. .................................32
vi 

INTENTIONALLY LEFT BLANK. 
vii 

Acknowledgments 

The authors would like to acknowledge the contributions of Dr. Christopher Kenyon and Dr. 

DaHan Liao, both from the U.S. Army Research Laboratory (ARL). Dr. Kenyon provided the 

FEKO-simulated data for the Synchronous Impulse Reconstruction (SIRE) radar transmitting 

antenna patterns, while Dr. Liao provided the FEKO-simulated data for the SIRE radar receiving 

antenna patterns. 
viii 

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

The Radio Frequency (RF) Signal Processing and Modeling Branch at the U.S. Army Research 

Laboratory (ARL) has been involved in the Army’s development efforts in Sensing through the 

Wall (STTW) radar technology for several years. A significant part of our work consisted of 

modeling radar systems for complex building imaging, with the purpose of understanding the 

radar scattering phenomenology, developing image formation algorithms, and studying design 

parameter trade-offs. A previous technical report (1) suggested a method for detecting behindthe-wall humans carrying small weapons based on polarimetric radar signature. The proposed 

technique was supported by computer models of the radar scattering scenario. However, as 

pointed out in (1), that study contained a number of simplifying assumptions that could have had 

a large impact on the expected performance of such detection method. The current report 

attempts to remedy these shortcomings by bringing more realistic features into the modeling 

scenario. 

One of the major assumptions in most of our electromagnetic (EM) scattering models is that the 

radar targets are placed in the far-field region (2) relative to the transmitter and receiver. As a 

consequence, both the fields incident on the target and the scattered fields observed at the 

receiver are considered plane waves. Additionally, the excitation plane waves have equal 

amplitudes, regardless of the incidence angle. While this model is a very good approximation of 

many radar sensing scenarios, there are situations where the transmitter and receiver antenna 

patterns play an important role. Moreover, the targets may be placed in the transmitter’s or 

receiver’s near-field region, invalidating the far-field assumption. An example of such geometry 

is provided by a ground vehicle-based radar system for building imaging that operates in a sidelooking, strip-map synthetic aperture radar (SAR) mode (3), which is relevant to the STTW radar 

technology currently developed by the Army. This study demonstrates how the far-field, planewave EM computer models can be adapted to closely simulate a strip-map SAR scenario using 

wide-beam antenna patterns. 

An additional complication is introduced by coupling between the polarimetric characteristics of 

the antenna radiation and target scattering. While this issue generally applies to single 

polarization radar, it becomes critical to a fully polarimetric radar system, such as the one 

considered in (1). A similar problem was first investigated in (4) and has subsequently received 

significant attention in the remote sensing community (5–10). Most of these papers deal with the 

issue of polarimetric radar calibration, in which measured radar data are processed to remove the 

antenna cross-polarization contamination, thereby providing a more accurate polarimetric 

characterization of the target. This can be regarded as an inverse problem, in which information 

about the target is extracted from the observed data. Our approach in this report consists of 

solving the forward problem, where we assume we have complete knowledge of the system 
2

parameters, the targets, and the environment around them, and attempt to predict the 

performance of the uncompensated radar system and signal processing algorithms. 

Although the theoretical formulation of the polarimetric coupling between antennas and target 

can be found in many of the references already mentioned, we present a complete derivation of 

the equations that govern this coupling and quantify its importance on the polarimetric 

performance of a radar imaging system. Finally, we apply this formulation to the problem of 

through-the-wall small weapon detection via polarimetric radar and show how the detection 

performance is affected by introducing more realistic assumptions about the radar system and 

geometry. 

The report is organized as follows: in section 2, we develop the theoretical formulation of the 

modeling method for polarimetric radar imaging; in section 3, we present numerical results for 

scenarios with increasing degrees of complexity; in section 4, we draw conclusions and indicate 

possible improvements of the method. 

2. Theoretical Formulation 

2.1 Modeling a SAR Imaging System 

In previous work (11, 12) we discussed the tools and methods used at ARL to model SAR 

systems for STTW building imaging. The computational electromagnetic (CEM) code we rely 

on for most of our EM simulations is AFDTD (13), which was entirely developed at ARL and 

implements the finite-difference time-domain technique. A comprehensive description of the 

underlying computational method for this code can be found in (14). In (11), we also described 

the basic SAR system geometries, namely spotlight and strip-map, and their relationship to the 

numerical scattering models provided by the CEM codes. Thus, we established the fact that the 

far-field geometry assumption of the AFDTD models is generally consistent with most spotlight 

SAR systems and discussed the transformations on these models that are needed in order to 

emulate a strip-map SAR system. In this section, we elaborate further on this topic. 

Let us consider the most basic geometries of spotlight (figure 1a) and strip-map (figure 1b) SAR 

systems. We make a number of simplifying assumptions to our scenarios: the radar and its 

trajectory, the target, and the image are all placed in the horizontal (x-y) plane; the target is in the 

radar’s far-field region; the transmitter and receiver are collocated (monostatic configuration); 

there is no variation of the radar antenna patterns with the elevation angle measured from the 

horizontal plane; the entire configuration is placed in free-space (no physical ground plane); and

we consider only one polarization. Characteristic to the spotlight configuration is that the antenna 

beam always points toward one point in the image (called focus) as the radar moves along the 

synthetic aperture. At the same time, in a strip-map configuration, the antenna beam always 
3

points in the same direction. Ideally, the spotlight radar illuminates the area of interest with plane 

waves (narrow beams), whereas the strip-map radar operates with broad antenna beams.

Figure 1. Schematic representation of a SAR imaging system geometry in two different configuration: 

(a) spotlight; (b) strip-map.

In the following, we assume that the SAR image is created by the back-projection algorithm 

(BPA) (15). We also assume that the imaging algorithm does not compensate for the path loss 

(the variation of the radar return magnitude with range); therefore, the particular shape of the 

radar trajectory along the synthetic aperture is irrelevant. Under these assumptions, for the 

spotlight configuration, the image pixel intensity in the target neighborhood can be written as:

       





N

n

n n n

I x y w s x y

1

,   , , (1)

where 

w

is a post-processing angular window, 

s t n

is the time-domain scattered signal 

received at position n, and 

x y n

 ,

is the propagation delay from the radar position n to the 

image point of coordinates 

x, y

:

 

  

c

R x y

x y

n n n

n

 



2 cos sin

,

 

 , (2)

where Rn and n are the range and angle of the radar position n with respect to the coordinate 

origin of the image. Notice that, consistent with the far-field assumption, all the pixels in the 

image “see” the radar in position n at the same azimuth angle n. For the strip-map configuration, 

the image pixel intensity is given by:

       





N

n

n n n

I x y p s x y

1

,   ,

(3)

(a) (b)
4

where the function 

p  

 describes the antenna pattern (or, more rigorously, the combined 

transmit and receive antenna patterns). It is easy to see that the two formulations (described by 

equations 1 and 3) can be made equivalent if we replace 

w  

by 

p   .

The AFDTD code provides the radar returns 

 tsn

for various incidence and observation angles 

. In previous work (11–12), we considered the spotlight imaging geometry and applied a 

generic angular window 

w  

(such as Hanning [16]), primarily with the purpose of reducing the 

image sidelobes. However, the imaging algorithm based on AFDTD scattering data can be 

adapted to closely emulate the strip-map geometry if we simply consider the antenna pattern 

p  

instead of the window function

w  

, according to equation 3.

The simplifying assumptions introduced earlier in this section can be eliminated at the expense 

of a more cumbersome formulation. Thus, if one considers a bistatic radar configuration, the 

summation in equations 1 and 3 must be performed over all pairs of transmitter-receiver 

locations. Using index n for such a pair location, and 

  R TnTn

,

and 

  R  RnRn

,

for the range and 

angle of the transmitter and receiver, respectively, the propagation delay becomes: 

       

c

yxR yxR

yx

Tn Tn Tn Rn Rn Rn

n

 



cos sin cos sin

,

  



 (4) 

The restrictions regarding the radar aperture, target, and image in the horizontal plane, as well as 

the free-space assumption, can be easily overcome by considering imaging in a slant plane over 

an infinite ground plane (the AFDTD code can readily provide scattering data for such a 

configuration). Additionally, the antenna pattern elevation variation can also be accounted for, 

according to the following equations (valid for monostatic configuration): 

       



N

n

nnnn

zyxspzyxI

1

,,  ,,,

(5) 

    

c

xR y z

zyx

n nn nn n

n





coscos2 cossin sin

,,

  



(6) 

The issue of wave polarization will be considered in the next two sections. However, the 

distinction between near-field vs. far-field geometry cannot be resolved within the framework 

developed in this section. In order to model the near-field scenario rigorously, a near-field EM 

scattering code is required, while the SAR image formation algorithm must be reformulated to 

include the exact Euclidian distance between the image pixel and the radar position coordinates. 

We also need to mention that throughout this report, the SAR images are created with the polar 

format algorithm (PFA) (17) instead of the BPA. However, it can be shown (18) that for a 

spotlight SAR system operating in the far-field, the two formulations are equivalent since they 

both amount to a two-dimensional (2-D) inverse Fourier transform from the frequency-angle 

space to the image space. In light of the previous considerations, we can then model a strip-map 
5

geometry using BPA by applying the antenna patterns to the PFA based on spotlight (or 

AFDTD-modeled) data.

2.2 Accounting for the Polarization Coupling between Radar Antennas and Target

Consider the radar scattering scenario illustrated in figure 2, where, for maximum generality, we 

describe a bistatic configuration. The relative range and angles from the transmitter to the target 

are RT, T, and T, respectively, whereas the relative range and angles from the target to the 

receiver are RR, R, and R (throughout this report we use the T subscript for transmitter and the R

subscript for receiver).

Figure 2. Schematic representation of a bistatic radar scattering scenario, showing generic transmitting 

and receiving radar antennas.

In the previous section, we assumed that the radar antennas transmit and receive only one 

polarization. While most radar antennas are designed to work in one principal polarization (also 

called co-polarization), cross-polarization fields (orthogonal to co-polarization) are also 

generally present in the radiation pattern. Therefore, the far-zone electric field of a radiating 

antenna can be represented as a 2-D vector [(9])

   , 

2 2

, ,

0 0

T T T

jkR

TH T

jkR TV

TH T

TV

T T T T

T T e

R

jZ I

h

h

e

R

jZ I

E

E

R  

 

E   h

 

























 , (7)

where Z0 is the free-space impedance, I is the current at the antenna terminals,  is the 

wavelength, and k is the wavenumber. The vector h, called effective length of the antenna (19,

20), can be decomposed along any two orthogonal directions perpendicular to the uR unit vector. 

Typically, the two components are written as h and h, which are the projections along the unit 

vectors u and u. Throughout this report, we will use the notations hV and hH, whereas by the 
6

subscript V (vertical) we understand the component along u and by the subscript H (horizontal) 

we understand the component along u. Notice that in equation 7, the elements of the vector h

capture entirely the angular dependence of the radiated electric field vector ET.

The polarimetric far-zone electric field scattered by the target that reaches the receiving antenna 

is characterized by the following equation (21):

      TTTTRRTT

R

jkR

RRRR R

R

e

R

R

E ,,  S E ,,,,, 



 , (8) 

or, in matrix form: 







































TH

TV

HV HH

VV VH

R

jkR

RH

RV

E

E

SS

SS

R

e

E

E R

. (9) 

In equation (8), S is called the scattering matrix of the target. Finally, the open-circuit voltage at 

the receiver antenna is given by (19, 20):

      











 

RH

RV

RRRRRRR RV RH E

E

V R ,,, hh

T Eh 

(10) 

where the superscript T stands for the transposed matrix. By combining equations 7, 8 and 10 we 

obtain: 

        TTTRRTTRRRjk RR

RT

RT e

RR

jZ I

V 



,,,,,

2

0 T

Sh h





(11) 

or, in a more explicit form: 

    



























TH

TV

HV HH

VV VH

RV RH

jk RR

RT

h

h

SS

SS

hhe

RR

jZ I

V

RT

 

2

0



(12) 

At this point, we need to examine the factors that appear in the right side of equation (11), their 

dependence on various parameters, and their importance in creating ultra-wideband (UWB) 

broad-beam-antenna SAR images of the target. The relevant parameters for calculating the 

received open-circuit voltage are the ranges (RT and RR), the angles (T, T,R, and R), and the 

frequency (expressed in equation 11 by , but also implicitly by hR, S and hT). The formation of 

far-field SAR images as outlined in section 2.1 involves neglecting the factors containing the 

ranges (including the phase factor 

  RR RT

jk

e



), and keeping only the factors that express the 

dependence on angles and frequency (namely, hR, S and hT and ).

Now let us define the normalized effective length of the antenna as: 

η h

 

 11



























H

V

H

V

h

h

. (13) 
7

Equation 11 becomes: 

        TTTRRTTRRRjk RR

RT

RT e

RR

jZ I

V 



,,,,,

2

0 T

η S η



 . (14) 

Since the received power is proportional to 

2

V

, while the transmitted power is proportional to 

2

I

(with the proportionality factors independent of ranges, angles and frequency), we can write 

the relationship between transmitted and received power as: 

      2

T

2

1

,,,,,

TTTRRTTRRR

RT

TR

RR

CPP 



η S η 















 , (15) 

where the constant C1 does not depend on ranges, angles, or frequency. The classic radar 

equation as formulated in (20) can be written as: 

      2

2

2

,,,,, ˆˆ

RWTTTRRTTRRR

RT

TR G G

RR

CPP ρρ 















 



, (16) 

where GT and GR are the transmitting and receiving antenna gains, respectively,  is the radar 

cross section (RCS), 

ρW

ˆ

is the polarization unit vector of the scattered waves, and 

ρ R

ˆ

is the 

polarization unit vector of the receiving antenna. Notice the close resemblance between 

equations 15 and 16, with the factor 

      2

T

,,,,, η S η  TTTRRTTRRR

accounting for 

antenna gain and polarization and target RCS. In the remainder of this study, the SAR image 

formation algorithms will use the quantity defined by 

       TTTRRTTRRR

,,,,,

T

η S η , 

which captures the entire dependence on the angles T, T, R, and R, together with a frequency 

dependence consistent with the radar equation. 

2.3 Formulation for a Fully Polarimetric Radar System 

A fully polarimetric radar system (19) includes pairs of antennas that can transmit and receive 

both orthogonal polarizations, as shown schematically in figure 3. We use the superscript V to 

indicate a vertically polarized transmitting or receiving antenna and the superscript H for a 

horizontally polarized antenna (here, the terms “vertical” or “horizontal” describe the antenna’s 

principal polarization). In most of our previous modeling work (11, 12) based on AFDTD 

computer simulations, we characterized the radar signature of targets by the matrix S, which 

assumes purely V or H-polarized plane waves both at transmission and reception. However, since 

the antennas generally transmit and receive both co- and cross-polarized fields, the 

characterization of the polarimetric radar system described in figure 3 extends beyond the target 

scattering matrix and must include the antenna polarization properties. 
8

Figure 3. Schematic representation of a fully polarimetric radar scattering scenario, showing the vertically 

and horizontally polarized, transmitting and receiving radar antennas.

For the polarimetric radar system that includes the antennas, we introduce the scattering matrix 

SA defined as:















HV HH

VV VH

SA SA

SA SA

S A , (17)

where, for instance, SAVV stands for the element characterizing vertical antenna polarization at 

both transmission and reception. We also replace the notation for the previously described 

scattering matrix S (that considers plane waves only) with SP. Then, based on the formulation 

developed in section 2.2, we can write:

















































H

TH

V

TH

H

TV

V

TV

HV HH

VV VH

H

RH

H

RV

V

RH

V

RV

HV HH

VV VH

SP SP

SP SP

SA SA

SA SA

 

 

 

 

(18)

or, in a more compact form:

  SA PR SP PT

T

 , (19)

where the matrices PT and PR characterize the pairs of antennas at the transmitter and receiver, 

respectively (these are called “distortion matrices” in [5–7]). The voltages received by the four 

possible polarimetric antenna combinations would then be proportional to the elements of SA. 

Notice that all the quantities involved in equation 18 depend only on angles T, T, R, and R, 

and frequency, but not on ranges.

The SA scattering matrix introduced by equation 19 effectively replaces the original SP

scattering matrix (obtained under the plane-wave assumption) by accounting for the variation of 

the radar return with the relative pairs of angles (T, T, R, and R) between antennas and target. 
9

Importantly, since the  elements are non-dimensional, the SA and SP elements have the same 

dimensionality (namely, meters). 

Antenna-normalized effective lengths of form 

V  V

and 

H  H

characterize the co-polarization fields 

of the antennas, whereas the normalized effective lengths of form 

H  V

and 

V  H

characterize the 

cross-polarization fields of the antennas. In general, we call the ratio between the magnitudes of 

the co- and cross-polarization elements of the vector  of an antenna the polarization ratio PR of 

that antenna. Thus, for the vertically polarized antennas (transmitting or receiving), we have: 

V

H

V

V

PR





 , (20) 

whereas, for the horizontally polarized antennas, we have: 

H

V

H

H

PR







(21) 

Let us rewrite two elements of the matrix described in equation 18 separately: 

V

HH TH

V

RH

V

HV TV

V

RH

V

VH TH

V

RV

V

VV TV

V

SAVV



RV SP  SP  SP  SP 

 (22) 

H

HH TH

V

RH

H

HV TV

V

RH

H

VH TH

V

RV

H

VV TV

V

SAVH



RV SP  SP  SP  SP  . (23) 

By examining equations 22 and 23, we notice that, in each element of SA, all elements of SP

appear coupled by the antenna-normalized effective length vectors . When the polarization 

ratios of the antennas are large, the elements of the matrix SA are closer to the elements of the 

matrix SP (which assumes purely polarized plane waves). In the opposite case, when the 

polarization ratios of the antennas are relatively small (meaning strong cross-polarization 

components in the antenna patterns are present), there is generally a reduction in the polarimetric 

differences between the elements of SA as compared to those of SP. Therefore, a radar system 

that relies on certain particular properties of the target scattering matrix SP may see a reduction 

in performance when it operates with antennas that exhibit low polarization ratios. 

Since the elements of the normalized effective length vector  depend on the angles  and , it 

follows that the polarization ratio of an antenna also depends on these angles. In low-frequency 

(1–4 GHz), UWB strip-map SAR imaging systems used in STTW applications, broad beam 

antennas are typically employed in order to achieve large integration angles and satisfactory 

cross-range resolution (11). Therefore, when we characterize the polarization performance of an 

antenna for these applications, we need to take into account the variation of PR over the angles 

of interest, both in elevation and azimuth. One possible metric for polarization performance is 

the root mean square (RMS) of the polarization ratio: 
10

 

   

 







2

1

2

1

2

1

2

1

2

2

,

,





















dd

dd

PR

cross pol

co pol

RMS

, (24) 

where the integration is performed over the ranges of  and  that are considered in the image 

formation algorithm. 

Additionally, the polarization ratio of an antenna may depend on frequency. In typical antenna 

configurations, PRRMS is large at low frequencies and becomes smaller as the frequency increases 

(20). Since our STTW SAR application involves wide frequency ranges, we will use the PRRMS

in the center of the bandwidth as the final antenna polarization performance metric. 

2.4 Typical Radar Antenna Patterns 

It is useful to illustrate the discussion on polarimetric antenna patterns with a representative 

example. In this section, we plot the 2-D and three-dimensional (3-D) patterns of a hypothetical 

antenna that approximate the free-space, far-field radiation of an open rectangular waveguide 

operating in the TE10 (fundamental) mode, backed by an infinite metallic ground plane (20). The 

equations describing these patterns are given in section 3.2, together with details on the antenna 

geometry. We also assume that the aperture is oriented such that the principal polarization is 

vertical. It should be mentioned that, although this type of antenna is not frequently used in 

practice, the general shape of its patterns is fairly representative for a large number of linearly 

polarized radar antennas, such as the horn or Vivaldi antennas (20, 22).

The 3-D antenna patterns at 4.5 GHz are shown in figure 4, for the co-polarization or vertical 

(figure 4a) and the cross-polarization or horizontal (figure 4b) electric field components, which 

are proportional to the vertical and horizontal components of the vector, respectively. The 

pseudo-color maps represent dB values of the electric field magnitude. The absolute electric field 

intensity values, as well as the conversion factor from electric field to normalized effective 

length is irrelevant for our discussion. In all cases, only the forward-directed (x > 0) patterns 

are plotted. 

Typical for the co-polarization antenna pattern displayed in figure 4a is the main lobe present 

around the boresight direction ( = 0o and  = 0o), while multiple sidelobes of reduced intensity 

extend in both vertical and horizontal directions. The width of the main lobe generally varies 

inverse proportionally with the operating frequency. For the cross-polarization pattern (figure 

4b), we also notice the presence of multiple lobes in both vertical and horizontal directions; 

however, characteristically, there are nulls in this pattern along both the  = 0o and the  = 0o 

planes. Following the usual antenna terminology, the  = 0o (vertical) plane is called the “Eplane,” whereas the  = 0o (horizontal) plane is called the “H-plane” (20). The fact that the cross-
11

polarization fields radiated in the E- and H-planes are null follows from the symmetry properties 

of the antenna geometry and is typical for many idealized radar antenna designs.

To illustrate the behavior of the antenna radiation in the vicinity of the E- and H-planes we 

plotted the 2-D patterns in polar coordinates in figure 5. Thus, figure 5a shows the co- and crosspolarization patterns in the  = 5o plane (close to the E-plane), whereas figure 5b shows the 

patterns in the  = 5o plane (close to the H-plane). Notice that we avoided showing the patterns 

that characterize the exact E- and H-planes, because, in those planes, the cross-polarization fields 

would be null (consequently, the polarization ratio PR would be infinity). The plots in figure 5 

could actually be representative for the vertical and horizontal plane patterns if either an 

unwanted or an intentional misalignment of the antenna’s boresight direction with these planes 

were present. Non-zero cross-polarization fields in the vertical and horizontal planes can also be 

obtained for certain asymmetric antenna designs.

Figure 4. Three-dimensional representation of the far-field patterns radiated by a rectangular waveguide 

antenna at 4.5 GHz, showing: (a) co-polarization field magnitude; (b) cross-polarization field 

magnitude.

(a) (b)
12

Figure 5. Two-dimensional, far-field patterns radiated by a rectangular waveguide antenna at 4.5 GHz, 

showing: (a) field magnitudes in the  = 5o plane; (b) field magnitudes in the  = 5o plane.

Note: The numbers shown as circle radii represent magnitude in dB.

2.5 Application to a Simple Polarimetric SAR Imaging Scenario

In this section we describe how to apply the approach developed in section 2.3 to the 

polarimetric strip-map SAR imaging scenario described in figure 6. The radar is assumed to be in 

the far-field with respect to the target and moves along a one-dimensional trajectory (aperture) in 

the horizontal plane. Furthermore, we assume that the radar configuration is monostatic and all 

antennas (transmitting and receiving, vertical, and horizontal) are collocated. The goal is to form 

a 2-D image of the target in the horizontal plane (although the target may be placed at any height 

with respect to this plane), for each polarization combination.

We assume that the target scattering data are obtained in the far-field through computer 

simulations, using plane-waves propagating at specific angles for both transmission and 

reception. To simplify our analysis, we consider no variation of the antenna patterns with the 

elevation angle. Therefore, in order to create an image in the horizontal plane, we only need the 

far-field target scattering data for propagation at  = 0o (remember, though, that in the vicinity of 

the target we still consider a full 3-D EM field model).

The algorithm for the SAR system simulation would involve the following steps:

• compute the polarimetric target signature under plane-wave transmission/reception (SP

matrix) for all frequencies and azimuth angles of interest;

• obtain the transmitting and receiving antenna patterns in the horizontal plane (matrices PT

and PR), for the range of frequencies and angles of interest, either through computer 

(a) (b)
13

simulations or measurements (this must be performed for both vertically and horizontally 

polarized antennas);

• compute the SA matrix for each frequency and azimuth angle according to equation 19; 

• convert the elements of the SA matrix from the frequency to the time domain via inverse 

Fourier transforms, after applying an appropriate spectral window;

• use equations (1) or (3) to form the SAR image via the BPA for each polarization 

combination.

Alternatively, the last two steps can be combined in one by applying the PFA; in that case, the 

SAR image is obtained directly by taking a 2-D inverse Fourier transform on the SA data.

Figure 6. Schematic representation of a fully polarimetric two-dimensional 

SAR imaging system, operating monostatically in strip-map 

configuration.

In our previous modeling work on radar imaging systems (11, 12), the far-field SAR images 

have always been created from the elements of the SP matrix. In those models, the SP elements 

captured the entire angular variation of the EM scattering phenomena, while leaving the range 

dependence out (see equation 8). In our new approach, the SAR images are based on the 

elements of the SA matrix, which describe the angular dependence of both target scattering and 

antenna transmission/reception. The absolute values of the SA matrix elements are not relevant 

in interpreting the SAR images, where only the relative pixel intensity values are important. 

Moreover, the particular application considered in section 3 (detecting the presence of a weapon 

based on polarimetric image differences) requires taking the pixel intensity ratio of images 

created from different elements of the SA matrix. That case is obviously not affected by any 

extra normalization factors present in equation 19)
14

2.6 Limitations and Extensions of the Technique 

The method of characterizing the performance of a fully polarimetric radar system we have 

outlined links together data specific to target scattering (the scattering matrix SP) with the 

antenna patterns (normalized effective lengths ) in order to obtain a modified version of the 

scattering matrix SA that captures the effect of both. It should be emphasized again that the 

technique applies in particular to low-frequency, strip-map SAR imaging systems, which 

typically use broad beam antennas and UWB waveforms. A spotlight SAR system normally uses 

only fields transmitted and received around the boresight direction, where typical radar antennas 

have very high polarization ratios. Therefore, for that case, the SA matrix closely resembles the 

SP matrix, and the analysis presented in the previous sections becomes irrelevant. The same can 

be said about a high-frequency SAR system (operating in the X-band or higher frequencies), in 

either strip-map or spotlight mode, which uses significantly smaller integration angles (17), 

typically around boresight. 

In section 2.5, we presented a simple SAR imaging geometry that will be followed up with 

numerical examples in section 3. However, the technique does not have to be restricted to that 

particular scenario. Thus, we can easily extend it to a bistatic radar configuration, as outlined in 

section 2.1. Additionally, the transmitting/receiving and vertically/horizontally polarized 

antennas do not have to be identical or collocated. Although the configuration in figure 6 does 

not take into account the antenna patterns in elevation (it assumes they are constant), those could 

also be included in the model as long as they are coupled with the elements of the target SP

matrix for the corresponding elevation angles. Notice that knowledge of the target signature 

variation with elevation, combined with 2-D synthetic aperture geometries, opens up the 

possibility to create 3-D images of the scene. 

The configuration in figure 6 assumes that the aperture and the image are placed in the horizontal 

x-y plane and there is no physical ground plane present in the scene. That allows us to use the 

free-space antenna patterns and target signatures in deriving the polarimetric response of the 

radar system. A more realistic model would place the antennas at a specific height above an 

infinite ground plane. If the antenna is placed at a small height (less than a wavelength), then the 

changes in patterns produced by the ground plane need to be taken into account, together with 

the target signature changes produced by the same. 

As already mentioned in section 2.6, this method cannot be applied to model a near-field 

scenario, since both the antenna patterns and the target signatures considered in equations 1–23

assume a far-field configuration. It is important to emphasize that the near-field antenna patterns, 

as well as the target signatures, may differ significantly from their far-field counterparts. The 

only way to correctly account for the near-field interactions between the radar antennas and the 

targets is to place them together in either a computer simulation or a measurement setup 

designed to evaluate the radar system performance. Currently, our ability to model a near-field 

scenario via computer simulations is limited by the fact that the AFDTD code operates only in 
15

far-field configurations. Interestingly, another CEM code used in radar system simulation at 

ARL, Xpatch (23), offers a “near-field” modeling capability (24), which in effect closely 

resembles the technique outlined in this report (namely, combining far-field antenna patterns and 

target scattering, while the antennas are placed in the near-field of the targets). Given the 

inconsistencies between the two configurations, these models cannot be considered a rigorous 

representation of the near-field problem. Nevertheless, this approach can offer a reasonable 

approximation of the radar system operation in the near-field when other analysis methods are 

not available (25).

It is interesting to consider a formulation that reverses the process outlined in section 2.3. The 

method described so far (which we call the “forward problem”) assumes that we know the 

matrices SP (polarimetric target signature) and P (polarimetric antenna patterns), and compute 

SA according to equation 19. In this approach, the goal is to predict the radar system 

performance in the presence of a known target. In many practical radar imaging applications, one 

needs to obtain a target characterization as accurate as possible based on measured data (the socalled “inverse problem”). The first step in this approach consists of the polarimetric radar 

calibration (4–9), in which one tries to derive the P matrices by measuring SA on a number of 

calibration targets, whose SP matrices are known. The second step involves finding the SP

matrix of the unknown target of interest based on the SA matrix measured by the radar system, 

according to the following equation: 

    T

-1 1

 



S P PR S A PT

. (25) 

In practice, the calibration and compensation procedures involve more complex calculations than 

equation 25 suggests. Details on these techniques can be found in (4–10).

3. Numerical Results 

3.1 Problem Definition and Methodology 

In section 2, we formulated the theoretical approach to modeling the impact of the antenna 

patterns on the SAR images created by a polarimetric radar system. As a numerical application, 

we consider the weapon detection technique based on polarimetric radar image differences 

described in (1). In that report, we established that the ratio of the cross- to co-polarization 

image pixel intensities is significantly enhanced by the presence of a rifle (as compared to the 

case when the rifle is absent). That phenomenological finding enabled us to develop an algorithm 

that discriminates between the presence of an armed human and that of an unarmed human 

placed behind a wall, based on SAR images of the scene created for different polarization 

combinations. Importantly, the images presented in (1) were formed under the plane-wave 

assumption at transmission and reception (the SP matrix as described in section 2.3). In this new 
16

study, we investigate the performance of the same algorithm when the images take into account 

the antenna patterns (the SA matrix). 

The SAR imaging scenario was described in section 2.5, where we established the need to 

evaluate the plane-wave polarimetric radar response for various azimuth angles and frequencies, 

as well as the antenna patterns for the same sets of azimuth angles and frequencies. We obtained 

the former through AFDTD computer simulations, as described in (1). Notice that these were 

large-scale simulations, requiring the high-performance computing (HPC) systems available to 

us at the ARL Defense Supercomputing Resource Center (DSRC) in Aberdeen, MD (26).

The antenna patterns can be evaluated via analytic methods, computer simulations, or anechoic 

chamber measurements. In some simple cases, such as that presented in section 3.2, analytic 

expressions can provide good approximations to the antenna radiation pattern. For more complex 

antenna configurations, either computer simulations or measurements are required. Since 

complete measurement data were not available to us for the specific antennas considered in 

section 3.5, we used modeling data obtained with the FEKO software package (27). It is 

important to emphasize that the data provided by the FEKO models consist of the far-field 

radiated, complex electric field vertical and horizontal components, when the antenna is excited 

by a sinusoid with amplitude 1 V at its terminal, one frequency at a time (28). These field data 

are proportional to the antenna normalized effective lengths required by equation 18. As 

established in section 2.5, this type of data can be directly used in the SAR image formation 

process, without any additional normalization procedure. 

Once the elements of the SA matrix are computed for all azimuth angles and frequencies, SAR 

images of the scene can be created for every polarization combination. In our application, we are 

only interested in the images based on SAVH and SAVV—more specifically, in the pixel-by-pixel 

ratio of those two images (1). By comparing the pixel ratio to a threshold, we decide whether the 

rifle is present or not in the scene. 

The SAR images shown in the following sections are created with the Pioneer RCS software that 

implements the PFA algorithm. We employ a Hanning window in the frequency domain over the 

band of interest; however, unlike the images based on the SP matrix elements, where we used a 

Hanning window in the angular domain, as well, we leave the SA data unchanged with respect to 

angle, consistent with the formulation in section 2.1. 

As suggested in section 2.3, we expect a radar system using antennas with low PR to exhibit 

decreased performance of the weapon detection scheme as compared to the idealized case 

analyzed in (1). In sections 3.2 through 3.4 we consider a set of simple, hypothetical antenna 

patterns that allow incremental changes to the PRRMS parameter and evaluate the impact of these 

changes on the detection scheme performance. By finding the minimum PRRMS value, where we 

notice no significant performance degradation as compared to the idealized case (based on SP

matrix elements), we can make recommendations to the radar system designer in terms of 
17

antenna cross-polarization suppression required by the polarimetric weapon detection scheme to 

work.

3.2 Example Involving Simple Antenna Patterns

In our first numerical example, we consider a set of hypothetical, simple antenna patterns, 

approximating the free-space, far-field radiation of an open rectangular waveguide operating in 

the TE10 (fundamental) mode, backed by an infinite metallic ground plane (20). We emphasize 

that these are not the exact patterns of such antenna, since they are based on the physical optics 

approximation of the equivalent currents along the antenna aperture (20). Moreover, this type of 

antenna is less frequently used in practical radar system implementations than, for instance, the 

horn antenna (20), which generally offers better sidelobe performance. Nevertheless, we use it in 

our analysis since the pattern equations can be written in closed form, and, at the same time, the 

general angular pattern variation is representative for a large number of radar antennas. 

The open waveguide antenna geometry, for vertical and horizontal polarization, respectively, is 

shown in figures 7a and b, where the aperture coincides with the x = 0 plane. We use the same 

antenna geometry for the two polarizations, with the difference that in horizontal polarization the 

structure is rotated by 90o with respect to the x axis, as compared to vertical polarization. We also 

employ the same pairs of antennas for transmission and reception, in monostatic configuration. 

In the numerical calculations, we use a = 0.3 m, b = 0.15 m, which implies that the cutoff 

frequency of the TE10 mode is fc = 0.5 GHz (2). 

Figure 7. Geometry of the open rectangular waveguide antenna, showing: (a) vertical 

polarization and (b) horizontal polarization.

Note: The antenna is backed by an infinite metallic plane, which is not shown in the figure.

For vertical polarization, the components of the electric field radiated by the open rectangular 

waveguide antenna are approximated by (20):

(a) (b)
18

2

sin

2

sin sin

2 4

cossin

2

cossin

cos

cos

2

2

2

0















k b

k b

k a n

k a

R

j abE e

E

jkR

V

V

 















(26) 

2

sin

2

sin sin

2 4

cossin

2

cossin

cos

sinsin

2

2

2

0















k b

k b

k a

k a

R

j abE e

E

jkR

V

H

 















, (27) 

where E0 is the maximum electric field amplitude propagating in the waveguide. Then, the 

components of the  vector can be written as: 

2

sin

2

sin sin

2 4

cossin

2

cossin

cos

cos

2

2 







 

k b

k b

k a

k a

f

f

A

c

V

V

 











 (28) 

2

sin

2

sin sin

2 4

cossin

2

cossin

cos

sinsin

2

2 







 

k b

k b

k a

k a

f

f

A

c

V

H

 











 , (29) 

where the constant A (with dimension meters) does not depend on range, angles, and frequency, 

and, as explained in section 2.5, is irrelevant for the SAR image interpretation. In a plane close to 

horizontal ( close to 0o), we can approximate 

 1cos

and 

  0sin

and write: 

42

sin

2

sin

cos

cos

2

2





 

 













ka

ka

f

f

A

c

V

V

(30) 

42

sin

2

sin

cos

sinsin

2

2





 

 













k a

k a

f

f

A

c

V

H

, (31) 

where  is fixed and  is variable. Notice that the polarization ratio PR depends on the plane tilt 

angle , becoming infinity for  = 0o. Rather than allowing the tilt angle  to determine the 

polarization ratio, we set PRRMS to a specific value and employ the following equations: 
19

42

sin

2

sin

cos

cos

4

2

2

2











 













k a

k a

f

f

c

V

V

(32) 

42

sin

2

sin

cos

sin

4

2

2

2

0











 













k a

k a

f

f

c

V

H

(33) 

 

  





2

1

2

1

2

0

2

0















PR d

d

V

RMS H

V

V

V

H

V

H

. (34) 

Notice that we replaced the constant A by 

2

/4 such that, at the cutoff frequency fc, the maximum 

value of 

V  V

is 1. Another aspect worth mentioning is that, by design, PRRMS does not vary with 

frequency for this antenna (according to equation 34).

For the antenna in horizontal polarization, we can write similar expressions, as in equations 28

and 29, by swapping the  and  angles, as well as the vertical and horizontal components: 

2

sin

2

sin sin

2 4

cossin

2

cossin

cos

sinsin

2

2 







 

k b

k b

k a

k a

f

f

A

c

H

V

 











 (35) 

2

sin

2

sin sin

2 4

cossin

2

cossin

cos

cos

2

2 







 

k b

k b

k a

k a

f

f

A

c

H

H

 











 (36) 

Again, we are interested in evaluating these expressions in a plane close to horizontal ( close to 

0o), by using the following equations: 

2

sin

2

sin sin

0

sin 



 

kb

kb

f

f

c

H

V  (37) 
20

2

sin

2

sin sin

cos 



 

kb

kb

f

f

c

H

H  (38) 

 

  





2

1

2

1

2

0

2

0















PR d

d

H

RMS V

H

H

H

V

H

V

. (39) 

In these equations, PRRMS is set to a specific value (same as for the vertically polarized antenna) 

and the patterns are normalized such that, at the cutoff frequency fc, the maximum value of 

H  H

is 

1 (this is consistent with the maximum value of 

V  V

, since the two must coincide in the boresight 

direction of the vertical and horizontal antennas). 

3.3 Imaging of a Human in a Simple Room 

We apply the antenna patterns developed in the previous section to the relatively simple scenario 

of a human placed in the middle of a four-wall room. The geometry is described in figure 8. The 

room dimensions are 5 m × 3.5 m × 2.2 m (197 in × 138 in × 87 in), with walls made of brick (r

= 3.8,  = 0.03 S/m, thickness 20 cm). The ceiling and floor are represented as 15-cm-thick 

concrete slabs, with r = 6.8,  = 0.1 S/m. The human is represented by the “fit man” model 

described in (29). In the case when he holds an AK-47 rifle, this has a tilt angle of 45o (1). The 

AFDTD grid has a cell size of 5 mm and is comprised of approximately 400 million cells. In 

order to obtain a SAR image, we compute the radar response for angles between –30o and 30o 

azimuth, in 0.5o increments, and frequencies between 0.5 and 3.5 GHz, in 13.3 MHz increments. 

(Notice that, in practice, this antenna could not be used over such a wide frequency band without 

generating higher waveguide propagation modes (2); for the particular aperture dimensions that 

we chose in this example, the TE01 and TE20 modes would start to be generated over 1 GHz). 

Taking into account the windowing procedure, the approximate image resolutions are 10 cm in 

down-range and 14 cm in cross-range. The simulations were run on the Harold system at ARL 

DSRC (26), using 24 cores per angle, for a total of about 25,000 CPU hours per image. 

In figures 9 through 11 we present the SAR images of the human in the simple room, with and 

without the rifle, for various levels of PRRMS. The images represent top-view, 2-D pseudo-color 

maps, with downrange on the x-axis and cross-range on the y-axis. In all images, the human 

faces left, while the radar looks from the left side. The intensity scales are always in dB. For each 

level of PRRMS, we display the images obtained for vertical-vertical (V-V) and horizontal-vertical 

(H-V) polarizations and mark the highest intensity pixel dB value around the human location in 

each case. The key measure for the ability to discriminate between the cases where the human is 
21

armed or unarmed is the ratio (difference in dB) between the cross-polarization (H-V) and copolarization (V-V) pixel intensities.

Figure 8. Top view of the simple four-wall room with a human carrying an AK-47 rifle and 

placed in the middle of the room, showing a schematic representation of the 

synthetic radar aperture on the left side.

y

x
22

Figure 9. SAR images of the human placed in a middle of a brick wall room, under the plane wave 

assumption, showing: (a) V-V polarization, human unarmed; (b) V-V polarization, human with AK47; (c) H-V polarization, human unarmed; and (d) H-V polarization, human with AK-47.

Note: All the numerical values indicated inside the images are in dB.

(a) (b)

(c) (d)

- 21

- 48 - 40

- 25
23

Figure 10. SAR images of the human placed in a middle of a brick wall room, including the effects of open 

waveguide antennas with PRRMS = 20 dB, showing: (a) V-V polarization, human unarmed; (b) V-V 

polarization, human with AK-47; (c) H-V polarization, human unarmed; and (d) H-V polarization, 

human with AK-47.

- 28

- 46

- 28

- 46

(b) (a)

(c) (d)

- 24 - 28

- 46 - 41
24

Figure 11. SAR images of the human placed in a middle of a brick wall room, including the effects of open 

waveguide antennas with PRRMS = 10 dB, showing: (a) V-V polarization, human unarmed; (b) V-V 

polarization, human with AK-47; (c) H-V polarization, human unarmed; and (d) H-V polarization, 

human with AK-47.

We start with the plane-wave model of the SAR imaging system, when PRRMS is infinity, in 

figure 9. This case is identical to the one analyzed in reference (1). It shows a significant gain 

(12 dB) in the cross-to-co-polarization ratio when the rifle is present. Figure 10 takes into 

account the polarimetric antenna patterns with PRRMS = 20 dB. The cross-to-co-polarization ratio 

rifle gain drops to about 9 dB in this scenario. Interestingly, we notice some significant changes 

in the cross-polarization SAR images, particularly the presence of the room corners, which were 

absent from the images in figures 9c and 9d. This is the effect of coupling various elements of 

(a) (b)

(c) (d)

- 22 - 27

- 41 - 39
25

the SP matrix through the antenna patterns, as explained in section 3.3. Figure 11 shows the 

images obtained for PRRMS = 10 dB, where we notice a further drop in the cross-to-copolarization ratio rifle gain down to 7 dB. Table 1 summarizes the relationship between the 

PRRMS and the cross-to-co-polarization ratio gain for PRRMS ranging from infinity to 0 dB. As 

expected, the trend demonstrates that a lower PRRMS level leads to less difference between the 

images of the armed and unarmed human. The impact of the antenna effect on the rifle detection 

scheme based on this difference is examined in section 3.4, where we consider a more complex 

scenario.

Table 1. Comparison of maximum pixel intensity in the human areas within the SAR images presented in sections 

3.2 and 3.3, in co- and cross-polarization, for the cases with and without rifle (all values in dB).

Note: co-polarization denotes the V-V case, whereas cross-polarization denotes the H-V case.

Antenna type PRRMS (dB) or tilt 

angle

Cross-to-co-pol 

ratio, no rifle (dB)

Cross-to-co-pol ratio, 

with rifle (dB)

Gain in ratio with 

rifle (dB)

Open waveguide

Infinity –27 –15 12

30 –23 –13 10

20 –22 –13 9

10 –19 –12 7

0 –17 –12 5

SIRE (TEM-horn and 

Vivaldi)

1o –20 –9 11

2o –14 –7 7

3.4 Application to Imaging of a Complex Room

A model of higher complexity is shown in figure 12, where four humans (each represented by 

the “fit man” model) are placed in a complex room of dimensions 10 m × 7 m × 2.2 m (197 in ×

138 in × 87 in). The room contains furniture and interior walls made of sheetrock. The 

20-cm-thick outer walls are made of brick and are equipped with doors and windows. A detailed 
26

description of the scene, as well as the dielectric properties of the materials, is given in (12). The 

AFDTD grid contains about 1.68 billion cells with 5 mm size. The SAR images are obtained 

with an aperture placed on the left side of the page, with angles between –30o and 30o, in 0.25o 

increments. The frequency varies between 0.5 and 2.5 GHz, in 6.67 MHz increments. The image 

resolutions are 15 cm in down-range and 20 cm in cross-range. The simulations were again run 

on the Harold system, using 64 cores per angle, for a total of 100,000 CPU hours per image. 

Figures 13 through 15 show the SAR images obtained for H-V polarizations, in the cases 

unarmed vs. armed (the humans are either all unarmed or all armed) and various levels of the 

PRRMS parameter. Qualitatively, we notice the same effects of decreasing PRRMS, as in the images 

presented in section 3.3. For this scenario, the antenna coupling (figures 14 and 15) makes a 

large number of vertical corners apparent in the cross-polarization images, including the corners 

formed by the windows and doors with the walls. 

A detection scheme that decides whether the humans are armed or unarmed was presented in (1). 

We apply the same scheme to the scenario considered in this section, for various PRRMS levels. 

Thus, we reduce the image resolution by means of a square moving average filter with size 15-

by-15 pixels in the original SAR images. Then, we eliminate all the “noise” pixels, with 

intensities below a certain threshold (–40 dB for V-V images and –60 dB for H-V images). 

Finally, we form the cross-to-co-polarization ratio of the remaining pixel intensities and compare 

them to a threshold. In general, we increase the detection threshold until we observe no false 

alarms (meaning there are no positive detections for the case when the humans do not carry 

rifles). The final detection maps are shown in figures 16 and 17. For the case shown in figure 

16a, PRRMS = 30 dB, and all the rifle carriers are detected. In figure 16b, we consider PRRMS = 

20 dB and notice that only three out of the four humans carrying rifles are detected. Figure 17 

shows that the detection scheme breaks down for PRRMS = 10 dB, in the sense that we obtain 

numerous false alarms and missed detections. In particular, all the false alarms are created by 

room corners, which, as seen in figure 15, start to show prominently in the cross-polarization 

images. For relatively low PRRMS, the cross-to-co-polarization ratios of these image features 

become larger than those of the humans with rifles, leading to the failure of the discrimination 

algorithm presented above. Notice that varying the detection threshold up or down does not help 

in this case: if the threshold is increased, we miss detecting the rifle carriers, whereas if it is 

decreased we include too many unwanted features as positive detections. The detection threshold 

values used for the cases shown in figures 16 and 17 are listed in table 2. 
27

Figure 12. The complex room containing humans and furniture objects showing (a) perspective view 

(humans carrying rifles) and (b) top view (humans unarmed).

1

2

3

4

(a)

(b)

y

x
28

Figure 13. SAR images of the complex room under the plane wave assumption showing: (a) V-V polarization, all 

humans unarmed; (b) V-V polarization, all humans with AK-47; (c) H-V polarization, all humans 

unarmed; and (d) H-V polarization, all humans with AK-47.

(a) (b)

(c) (d)

-26

-19

-18

-25

-29

-19

-19

-24

-44

-42

-37

-44

-36

-32

-31

-38
29

Figure 14. SAR images of the complex room that include the effects of open waveguide antennas with PRRMS = 

20 dB showing: (a) V-V polarization, all humans unarmed; (b) V-V polarization, all humans with AK47; (c) H-V polarization, all humans unarmed; and (d) H-V polarization, all humans with AK-47.

(a) (b)

(c) (d)

-33

-25

-25

-30

-32

-24

-23

-30

-47

-47

-40

-43

-41

-36

-36

-43
30

Figure 15. SAR images of the complex room that include the effects of open waveguide antennas with PRRMS = 

10 dB showing: (a) V-V polarization, all humans unarmed; (b) V-V polarization, all humans with AK-47; 

(c) H-V polarization, all humans unarmed; and (d) H-V polarization, all humans with AK-47.

(a) (b)

(c) (d)

-39

-35

-33

-38

-42

-40

-37

-37

-33

-24

-24

-29

-31

-23

-22

-29
31

Figure 16. Detection maps for the complex room shown in figure 12, for a SAR system equipped with open 

waveguide antennas with (a) PRRMS = 30 dB and (b) PRRMS = 20 dB.

Notes: In the scenario shown here, all the humans carry AK-47 rifles. The red spots indicate positive detections.

Figure 17. Detection maps for the complex room in figure 12, for a SAR system equipped with open waveguide 

antennas with PRRMS = 10 dB, showing the cases where (a) all humans are unarmed and (b) all humans 

carry AK-47 rifles.

(a) (b)

(a) (b)
32

Table 2. Detection threshold for the weapon discrimination scheme described in sections 3.4 and 3.5, for various

antenna systems and cross-polarization properties.

Antenna type Open waveguide SIRE (TEM-horn and Vivaldi)

Cross-polarization 

metric

PRRMS

(dB) 30 20 10 Tilt angle 1o 2o

Detection threshold 

(dB) –17 –15 –11 –13 –10

Based on the examples shown in this and the previous sections, we draw the broad conclusion 

that antennas with good cross-polarization suppression (of at least 20 dB, but preferably 30 dB, 

as measured by PRRMS) are required in order to successfully employ the cross-to-co-polarization 

ratio in the rifle discrimination technique. Obviously, these numbers are not universally valid for 

all possible scenarios, but depend on the weapon type and orientation, the human body size, 

shape, and orientation, as well as other clutter objects present in the room. It seems that the 

human placed in the upper left corner of the complex room images is more difficult to detect 

when the cross-polarization antenna patterns are taken into account (interestingly, that human is 

rotated by the largest angle in azimuth, namely, 45o with respect to broadside). This result hints 

to a more subtle relationship between target orientation, shape of the antenna pattern, and 

integration angle used by the SAR image formation algorithm. Moreover, these results may 

change if one considers other frequency bands. 

Nevertheless, the figure of about 25 dB for the antenna cross-polarization suppression gives a 

rough guideline to the radar engineer designing an UWB, wide-beam, SAR imaging system that 

attempts to detect targets based on polarimetric differences. Interestingly, our results are 

consistent with the findings in (10), where 30 dB of cross-polarization isolation are 

recommended for a polarimetric SAR application at C-band. Additionally, the method outlined 

in this study allows the analysis of a specific radar antenna design in order to predict the 

performance of the polarimetric target detection scheme for that radar system and scenario, as 

shown in the following section.

3.5 Examples Involving the SIRE Radar Antennas

In this section we apply the technique developed in section 2 to a set of more realistic antenna 

pattern data: the transmitting and receiving antennas of the synchronous impulse reconstruction 

(SIRE) radar (30). The transmitting antenna, shown in figure 18a, is a transversal 

electromagnetic (TEM) horn (31), while at the receiving side the radar uses a Vivaldi notch 

antenna (22), shown in figure 18b. Both are UWB antennas, designed to work in the frequency 
33

range of the SIRE radar (0.5 to 2.5 GHz). In the forward-looking configuration, the SIRE radar 

antenna assembly is made of multiple TEM-horn and Vivaldi elements (30). However, for our 

STTW imaging application, we assume that the radar is configured in the side-looking, strip-map 

SAR mode (3) and only one set of vertically and horizontally polarized antennas is employed for 

both transmission and reception. Moreover, we assume that all the antennas are collocated for 

one radar position along the synthetic aperture, in effect creating a monostatic configuration.

Figure 18. The SIRE radar antennas for the (a) transmitter and (b) receiver, showing pictures of the physical 

antennas as well as wire-frame meshes used in FEKO simulations.

Note: In this figure, both antennas are configured for vertical polarization.

As explained in section 3.1, the patterns of the SIRE transmitting and receiving antennas were 

obtained via FEKO simulations, based on detailed models of the two antenna geometries, for all 

the angles and frequencies of interest. However, further processing of the FEKO output data was 

performed for our application, in order to mitigate possible SAR image artifacts that may arise 

when the antennas are excited with UWB pulses. (Notice that we were not able to include all the 

details of the antenna design in the FEKO models, particularly the areas around the feeding 

points, which are crucial in determining important parameters such as the input impedance and 

S11 [20]). Thus, instead of using complex numbers to represent the normalized effective lengths 

of the antenna, as provided in the FEKO output files, we considered only the magnitude of these 

(a) (b)

Physical 

antenna Physical 

antenna

FEKO model FEKO model
34

numbers, effectively ensuring that the phase center of the antenna does not change its spatial 

position with frequency or propagation angle (this eliminates any issue related to excitation pulse 

dispersion). 

Another modification to the FEKO output data consists of smoothing out the variation of the 

parameters with respect to frequency, in order to eliminate any late-time replicas of the 

excitation pulse that would appear as unwanted echoes in the SAR images (see figure 19). We 

emphasize that the changes in the simulated antenna pattern data are meant only to improve the 

antenna impulse response and should not significantly impact its polarimetric characteristics.

Figure 19. The vertical electric field magnitude for the SIRE transmission antenna at  = 0o and  = 1o, before 

and after the smoothing procedure, shown here in: (a) frequency domain; (b) time domain.

Notes: The original data were obtained via FEKO simulation. The smoothing consists of a cubic polynomial fit. 

The time-domain version was obtained via inverse Fourier transform after applying a Hanning 

window.

The antennas are assumed to have an elevation tilt of 1o or 2o (again, we avoid considering 

perfectly symmetric antennas with no elevation tilt, which would theoretically lead to an infinite 

polarization ratio). After the processing steps previously described, we obtained the following 

PRRMS, at 2 GHz (the center of the pulse spectrum), in the horizontal ( = 0o) plane: 

• for the transmitting antenna with 1o tilt, 21 dB in vertical polarization and 25 dB in 

horizontal polarization; 

• for the transmitting antenna with 2o tilt, 15 dB in vertical polarization and 19 dB in 

horizontal polarization; 

• for the receiving antenna with 1o tilt, 34 dB in vertical polarization and 36 dB in horizontal 

polarization; 

(a) (b)
35

• for the receiving antenna with 2o tilt, 28 dB in vertical polarization and 30 dB in horizontal 

polarization. 

The transmitting and receiving antenna patterns in the horizontal plane for 2o tilt, in both 

polarizations, within the angular span of interest (–30 o to 30 o), at 2 GHz are shown in figure 20. 

It should be noted that, qualitatively, these patterns are very similar to those of the open 

waveguide antenna described in section 3.2. A significant difference is displayed by the 

transmitting antenna in horizontal polarization, for which the fields radiated around ±25o exceed 

those radiated at broadside (0o), for co-polarization. Other aspects worth mentioning with regard 

to the SIRE antennas are the fact that the TEM horn (transmitting) antenna has generally poorer 

polarization ratios than the Vivaldi (receiving) antenna, while the horizontal polarization displays 

larger PRRMS than the vertical polarization (in the horizontal plane). 

Both scenarios described in section 3.3 and 3.4 were re-analyzed using the SIRE radar antenna 

pattern data. Figure 21 shows the SAR images obtained in the simple room case, for V-V and HV polarizations, when the human is armed or unarmed and both SIRE antennas are tilted by 2o. 

In this case, the gain in the cross-to-co-polarization ratio when the rifle is present is 7 dB. If the 

elevation tilt were set to 1o, we would obtain a cross-to-co-polarization gain of 11 dB (a 

summary of these performance metrics can be found in table 1). 

In figure 22, we display the H-V SAR images of the complex room when all the humans are 

armed, for 1o and 2o antenna elevation tilt, respectively. As expected, these images are similar to 

those obtained for the corresponding scenarios in figures 13 and 14. The detection maps obtained 

for those two cases via the procedure outline in section 3.4 are shown in figure 23. For an 

elevation tilt of 1o, all four targets are correctly detected. However, for an elevation tilt of 2o, 

only three out of four targets are detected. The detection thresholds used for these scenarios are 

listed in table 2. Notice that these results are consistent with those obtained in section 3.4, 

showing that polarization ratios of at least 20 dB (preferably 30 dB) are required for the radar 

antennas in order to achieve good weapon detection performance of the polarimetric technique 

outlined in this report. 

We should also mention that the scenarios included in this section are somewhat artificial, in the 

sense that we needed to introduce a small elevation tilt to the antennas in order to illustrate the 

method. However, as a general conclusion we can clearly state that the Vivaldi antenna has much 

better cross-polarization suppression than the TEM horn antenna, exceeding the strong 

requirement of 30 dB polarization ratio for small tilt angles. On the other hand, the TEM horn 

antenna displays marginal cross-polarization properties, with the largest performance 

degradation coming from the vertical polarization configuration. 
36

Figure 20. SIRE antenna patterns in the horizontal plane, at 2 GHz, with antennas at 2o elevation tilt, showing: 

(a) transmitting antenna in vertical polarization; (b) transmitting antenna in horizontal polarization; 

(c) receiving antenna in vertical polarization and (d) receiving antenna in horizontal polarization.

(a) (b)

(c) (d)
37

Figure 21. SAR images of the human placed in a middle of a brick wall room, including the SIRE antenna effects, 

showing: (a) V-V polarization, human unarmed; (b) V-V polarization, human with AK-47; (c) H-V 

polarization, human unarmed; and (d) H-V polarization, human with AK-47.

(a) (b)

(c) (d)

- 21

- 35 - 32

- 25
38

Figure 22. Cross-polarization (H-V) SAR images of the complex room, including the effects of the SIRE 

antennas tilted at (a) 1o in elevation and (b) 2o in elevation.

Note: In both cases, all humans carry AK-47 rifles.

Figure 23. Detection maps for the complex room in figure 12, for a SAR system equipped with SIRE antennas tilted 

at (a) 1o in elevation and (b) 2o in elevation.

Note: In both cases, all humans carry AK-47 rifles.

(a) (b)

-40

-31

-32

-35

-40

-32

-33

-36

(b) (a)
39

4. Conclusions 

In this study, we provided a formulation for characterizing the radar polarimetric scattering 

response by taking into account both the transmission/reception antenna patterns and the target 

radar signature. Subsequently, we applied this formulation to the problem of through-the-wall 

detection of small weapons based on polarimetric differences of radar images. 

In section 2, we derived the polarimetric equations that relate the radar response to the antenna 

characteristics (via the normalized effective length vectors) and the target (via the scattering 

matrix). These equations can be applied to the calculation of the far-field radar response through 

computer models, by separating the evaluation of the antenna radiation and reception from that 

of the target radar signature. Compared to our previous radar performance prediction studies that 

were based on modeling the target signature under pure plane wave excitation and observation, 

the current work replaces the plane-wave-based scattering matrix SP by the antenna-patternbased scattering matrix SA in evaluating the radar system performance. In section 2.3, we 

explained why considering the coupling between the polarimetric characteristics of the antenna 

radiation and target scattering is important in simulating an UWB, broad-beam, strip-map SAR 

imaging system operating at relatively low frequencies (1–4 GHz), typical for STTW 

applications. 

In section 3, we employed this formulation to analyze the performance of a through-the-wall 

small weapon detection system based on polarimetric differences between SAR images. We used 

two different types of radar antenna systems, as well as two different scenes. By assessing the 

influence of the cross-polarization suppression PR of a simple antenna (section 3.2) on the 

weapon detection scheme performance, we derived an approximate lower bound for the PRRMS

parameter required by this technique to work. Subsequently, we repeated the analysis with 

FEKO-simulated patterns of the SIRE transmitting and receiving antennas. 

We should mention that a number of simplifying assumptions were made in our models, many of 

them discussed in section 2.5. Also, the antenna patterns considered in the numerical examples in 

section 3 were somewhat artificial, even when they represented models of the SIRE antenna 

designs. One reason for using antenna pattern models rather than experimental data was the fact 

that complete measurements of the SIRE antenna patterns were not available to us. Additionally, 

the simulated SIRE antenna data went through further processing to make them more suitable for 

UWB pulse excitation (notice that the goal of this study was to assess the polarimetric 

performance, not the UWB characteristics of the antennas). Nevertheless, the technique is readily 

capable of mixing simulation and measurement data on both the antennas and the target. 

As discussed in section 2.5, this formulation can be adapted to solve the “inverse problem” 

(finding the SP matrix based on the measured SA matrix), which first involves performing the 
40

polarimetric calibration of a radar system. Notice that, in this study, we did not attempt to 

compensate for the polarimetric antenna effects in the final SAR images (according to equation 

25). Doing so would have produced “perfect” polarimetric images (identical to those created 

under the plane wave assumption), since all results were obtained via computer modeling, 

without considering any noise or calibration errors. In practice, such “perfect” polarimetric 

images cannot be achieved, even after the calibration and compensation procedures. Our results 

are still useful to the radar system designer, by establishing an upper bound to the polarimetric 

performance (the plane wave transmission and reception case), as well as measuring the 

performance degradation when various levels of antenna cross-polarization isolation are 

considered. 

One shortcoming of the model outlined here is that it cannot be applied to a near-field radar 

scattering scenario. For this purpose, a near-field EM model of the entire scene (including the 

antennas and the target) needs to be developed. In that case, the antenna radiation and reception 

and the target scattering are part of the same simulation, and must not be separated. This type of 

modeling will be the subject of future research. 
41

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44

List of Symbols, Abbreviations, and Acronyms 

2-D two-dimensional 

3-D three-dimensional 

ARL U.S. Army Research Laboratory 

BPA back-projection algorithm 

CEM computational electromagnetics 

DSRC Defense Supercomputing Resource Center 

EM electromagnetic 

H-V horizontal-vertical 

HPC high-performance computing 

PFA polar format algorithm 

RCS radar cross section 

RF radio frequency 

RMS root mean square 

SAR synthetic aperture radar 

SIRE Synchronous Impulse Reconstruction 

STTW sensing through the wall 

TEM transversal electromagnetic 

UWB ultra-wideband 

V-V vertical-vertical
45

NO. OF 

COPIES ORGANIZATION 

 1 ADMNSTR 

 PDF DEFNS TECHL INFO CTR 

 ATTN DTIC OCP 

 8725 JOHN J KINGMAN RD 

 STE 0944 

 FT BELVOIR VA 22060-6218 

 1 US ARMY RSRCH DEV & 

 ENGRG CMND 

 ARMAMENT RSRCH DEV & 

 ENGRG CTR 

 ARMAMENT ENGRG & 

 TECHNLGY CTR 

 ATTN AMSRD AAR AEF T 

 J MATTS 

 BLDG 305 

 APG MD 21005-500

 1 US ARMY TRADOC 

 BATTLE LAB INTEGRATION & 

 TECHL DIRCTRT

 ATTN ATCH B 

 10 WHISTLER LANE 

 FT MONROE VA 23651-5850 

 2 US ARMY RDECOM CERDEC 

 I2WD 

 ATTN RDER IWI MS J CUA

 BLDG 6003 COMBAT DRIVE

 APG MD 21005 

 1 US ARMY INFO SYS ENGRG 

 CMND 

 ATTN AMSEL IE TD A RIVERA 

 FT HUACHUCA AZ 85613-5300

 1 US GOVERNMENT PRINT OFF 

 DEPOSITORY RECEIVING 

 SECTION 

 ATTN MAIL STOP IDAD J TATE 

 732 NORTH CAPITOL ST NW

 WASHINGTON DC 20402 

NO. OF 

COPIES ORGANIZATION 

 16 US ARMY RSRCH LAB 

 ATTN RDRL D 

 ATTN RDRL CIO LT 

 TECHL PUB 

 ATTN RDRL CIO LL 

 TECHL LIB 

 ATTN AMSRD ARL SE RM 

 W O COBURN 

 ATTN AMSRD ARL SE RU 

 A SULLIVAN 

 ATTN AMSRD ARL SE RU C LE 

 ATTN AMSRD ARL SE RU 

 L NGUYEN 

 ATTN AMSRD ARL SE RU 

 D LIAO 

 ATTN AMSRD ARL SE RU 

 C KENYON 

 ATTN AMSRD ARL SE RU 

 K RANNEY 

 ATTN AMSRD ARL SE RU 

 A MARTONE 

 ATTN AMSRD ARL SE RU K KAPPRA 

 ATTN AMSRD ARL SE RU 

 M RESSLER 

 ATTN AMSRD ARL SE RU 

 T DOGARU (2 COPIES) 

 ATTN IMNE ALC HRR 

 MAIL & RECORDS MGMT 

 ADELPHI MD 20783-1197 

TOTAL: 23 (1 ELEC, 22 HCS) 
46

INTENTIONALLY LEFT BLANK.