Characterization of UWB Radar Targets: Time Domain vs. Frequency Domain Description Elena Pancera, Thomas Zwick, Werner Wiesbeck Institut für Hochfrequenztechnik und Elektronik Karlsruhe Institute of Technology (KIT) Karlsruhe, Germany
[email protected] Abstract—In this paper a characterization of UWB Radar targets is provided, both in the frequency domain and in the time domain. This is done by firstly giving a mathematical description of the Radar target in the UWB case, then providing measurement results. The proposed characterization allows for discerning and classifying UWB targets. Moreover, in this paper a full polarimetric analysis is taken into account.
I.
INTRODUCTION
recovered time domain signal. The proposed analysis is performed full polarimetric. II.
In this section, the mathematical description of the target for a UWB impulse Radar system is provided, both in the frequency domain and in the time domain. The analyzed scenario is illustrated in Fig. 1.
In recent time Ultra Wideband (UWB) technology has assumed more and more interest due to its high data rate and huge bandwidth. This last characteristic permits to obtain high resolution and hence the possibility of highly discern among different objects. Because of that, the utilization of Radar with large bandwidth has assumed increasing interest. In fact, in Radar application, where in most cases the target is observable only for a limited time, the best choice for improving the system capacity is expanding the signal bandwidth. Therefore, in recent years, ultra wideband Radar has become an important topic [1]. In the UWB Radar case, specific tools and methods to recognize, characterize and classify the detected object have to be applied. Differently form classical narrowband Radars, where targets are characterized through their Radar Cross Section (RCS) at the particular frequency under use, in the UWB case a wideband characterization is required, i.e. the target behavior has to be known on a large spectral range. From this point of view, in the UWB Radar case, differently from the narrowband case, easy identification and characterization can be made directly in the time domain. Hence, specific tools for time domain description has to be used. In literature there are firsts examples of target characterization in the time domain, which has been done analyzing the time domain back reflected signal from the target [2]-[4].
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In this paper a complete mathematical description and characterization of UWB Radar targets is presented, both in the frequency domain and in the time domain. In particular, in the time domain specific characterization tools are introduced and methods are derived for target classification basing on the
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UWB RADAR TARGET DESCRIPTION
Figure 2. UWB time domain Radar link.
A. Frequency Domain Description Let [Ei(f)] be the electric field impinging on the target and [Er(f)] the electric field back reflected by the target at a distance r from the target itself. Both these matrices are 2x2 since the polarimetric polarization components are considered. It is usual to define the scattering matrix in the following way [5]
[E r ( f )] =
1 4 "r 2
[SSc ( f )] # [E i ( f )]
(1)
The matrix [SSc(f)] is independent form the distance r, i.e. it is object oriented and its dimensions are meters. Moreover, it is frequency-dependent. In the frequency domain the scattering behavior of a target is expressed by its Radar Cross Section (RCS) [σ Sc(f)] [6]. The fully polarimetric scattering behavior is expressed by a 2 × 2 matrix as (in the following, for simplicity and without loss of generality, the vertical v and horizontal h polarization components are considered, but the
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same equations can be written for two arbitrary orthogonal polarizations)
[" Sc ( f )]
#" Schh ( f ) " Schv ( f )& 2 = % vh ( = 4 ) * [SSc ( f )] = vv $" Sc ( f ) " Sc ( f )' # S hh ( f ) 2 S hv ( f ) 2 & ( Sc ) ( Sc ) ( = 4) * % %( SScvh ( f )) 2 ( SScvv ( f )) 2 ( $ ' (2)
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where the different polarization components have been explicitly written (with the apex ij the component for a j polarization of the receive antenna and an i polarization of the transmit antenna is indicated). It has to be noticed that the scattering matrix [SSc(f)] coincides with the transfer function matrix [HSc(f)] and it is dependent on the frequency [6]. From that observation it derives that the absolute value of each component |σScij(f)| of the RCS matrix is directly proportional to the absolute value of the scatter’s transfer function |HScij(f)|2 and hence it describes the power distribution in the frequency domain. B. Time Domain Description ! Let [hSc(t)] denote the impulse response matrix of the scatterer, defined as hh hv % "IFT{HSc hh hv % "hSc IFT{HSc } }' hSc $ [hSc ] = $ vh vv' = IFT{[HSc ]} = vh vv $#IFT{HSc } IFT{HSc }'& #hSc hSc &
(3)
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where IFT denotes the Inverse Fourier Transform. The dimensions of [hSc(t)] are hence m/s. Recalling the equivalence between the scattering matrix and the transfer function matrix [SSc(f)] = [HSc(f)], it is turned out that the time domain equivalent [σ Sc(t)] of RCS matrix [σ Sc(f)] can be written as
[" Sc (t)]
2 2 (( % % hh hv ' IFT{( HSc ( f ))} '&IFT{( HSc ( f ))} *)* = 4# $ ' 2 2 (* % vh vv IFT H ( f ) * ' IFT{( HSc ( f ))} ( ) { } Sc &' )*) & % h hh (t) 2 h hv (t) 2 ( [ Sc ] [ Sc ] * 2 = 4 # $ [hSc (t)] = 4 # $ ' '[ hScvh (t)] 2 [ hScvv (t)] 2 * & )
[ [
] ]
(4)
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It has to be observed that the absolute value of each term |σScij(t)| is directly proportional to the absolute value of the scatter’s impulse response |hScij(t)|2 and hence it describes the power distribution in the time domain.
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Hence, in order to characterize the target completely in the time domain, it is necessary to know its impulse response matrix. Consequently, a calibration procedure in the time domain has to be used.
C. UWB Target characterization basing on time domain properties Once the impulse responses of a target have been calibrated for each polarization, it is possible to characterize the target itself based on its time domain signature. Classical methods for classifying targets are based on frequency domain signatures [3], [7]. In the following, a time domain method is introduced. This method is based on the fidelity of the signal backscattered from the target with a reference template. Let hijSc,id(t) be the ideally expected target’s impulse response for the ij polarization and let hijSc(t) be the target’s impulse response for the same polarization obtained from a calibrated measurement. The fidelity F for the ij polarization component between hijSc,id(t) and hijSc(t) can be calculated as [8], [9] +%
F ij =max & "
%$ij hSc (t +" ) ij (t ) hSc 2
#
ij hSc,id (t ) ij hSc,id (t )
(5)
dt 2
where ||.||2 is the 2-norm. Through the calculation of the fidelity between hijSc,id(t) and hijSc(t) it is possible to determine the amount of distortion between the two impulse responses. The following step consists in constructing a database containing the information about the ideally expected impulse response for each polarization for different targets. Hence, applying the previously described procedure for each polarization component, by calculating the fidelity between the measured calibrated impulse response and the one stored in the database, it is possible to determine the unknown target. III.
EXAMPLE OF UWB TARGET CHARACTERIZATION
In this section the presented UWB characterization is shown for a particular object. The considered target is a dihedral corner reflector (symmetrical to its fold line) whose dimensions are 17.5 x 17.5 cm2 and positioned with a 0° offset from the vertical. It has been positioned vertically, with the incident ray path perpendicular to its fold line. It has only copolarized components, which are equal in amplitude but outof-phase. A. Frequency Domain Characterization Since the dihedral corner reflector has only co-polarized and out-of-phase polarimetric components, its scattering matrix [SDi,0°(f)] is [6]
$1
[SDi,0° ( f )] = SDi,0° ( f ) " &0 %
0' ) #1(
(6)
where SDi,0°(f) is [6]
#" & f SDi,0° ( f ) =4 " absin% ( $ 4 ' c0
(7)
with a, b the dihedral dimensions and c0 the velocity of light.
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B. Time Domain Characterization According to the presented characterization, in the time domain the dihedral can be represented through its impulse response matrix [hDi,0°(t)], namely
$1
[hDi,0° (t)] = hDi,0° (t) " &0 %
0' ) #1(
(8)
being hDi,0°(t) the inverse Fourier transform of SDi,0°(f).
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C. Measurement Results The measurement scenario at the transmitter side is composed by a pulse generator (Pico Second Pulse Lab PSPL 3600, pulse duration 80 ps (at the Full Width at Half Maximum) and pulse peak 5.5 V) and a transmit antenna (dual polarized horn antenna, Model 6100). The output signal of the pulse generator fed the vertical v or the horizontal h polarization of the transmit antenna. At the receiver side by a receive antenna (dual polarized horn antenna, Model 6100 as for the transmitter side) and an oscilloscope (Agilent Infinium DCA, 12 GHz bandwidth, 40 GSs/s). The oscilloscope is directly connected to a laptop for data acquisition and data processing. A trigger (Tektronix, Arbitrary Waveform Generator) permits the synchronization of the pulse generator and the oscilloscope. A quasi-monostatic case has been investigated. The signal to noise ratio of the signal recorded by the receive antenna is improved by averaging on 128 measurements. This permits to decrease the statistical errors [10]. The data are acquired for a time duration of 50 ns, recovering 2001 points per measurement. The measurements have been taken in an anechoic chamber in order to minimize the reflections from the surrounding. The target object has been placed in the anechoic chamber at a distance of 2.9 m from the two antennas at the same height and in the main radiation direction.
2 co- and 2 cross-polarized measurements have been taken. Moreover, a calibration procedure has been applied in order to eliminate the antennas influence and the coupling between the antennas and the co- and cross- polarized channels. The obtained target impulse responses, after calibration, are illustrated in Fig. 2 for each polarization component. In order to characterize the measured object, for each polarization component the fidelity between the measured impulse response and the ideally expected impulse response of the target has been calculated according to eq. (5). In Tab. I, for each polarimetric component, the fidelity F between the actually measured impulse response of the investigated dihedral and the ideally expected one have been reported. TABLE I.
FIDELITY BETWEEN MEASUREMENT RESULTS AND IDEALLY EXPECTED IMPULSE RESPONSES Polarization
Fidelity F
HH
0.9047
VV
0.8986
HV
0.9431
VH
0.8335
However, the fidelity itself gives information only on the shape of the considered impulse responses but not on their peak values [8]. Hence, together with the fidelity results, for a complete, ultra wideband characterization of the target, also the peak value of the impulse responses for each polarization component has to be taken into account.
Figure 2. Calibrated measured dihedral impulse responses for the different polarization components.
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IV.
CONCLUSIONS
In this paper a complete mathematical characterization for UWB Radar target has presented, both in the frequency domain and in the time domain. This characterization has been done full polarimetric. Moreover, a classification method based on the time domain correlation properties of UWB targets has been presented. Measurement results have also been provided. ACKNOWLEDGMENT This work was supported by COST Action IC0803 “RF/Microwave communication subsystems for emerging wireless technologies” (RFCSET). REFERENCES [1] [2]
[3]
M.G.M. Hussain, “Ultra-Wideband Impulse Radar-an Overview of the Principles”, IEEE AES Systems Magazine, pp. 9-14, Sept. 1998. W.A. van Cappellen, R.V. de Jongh, L.P. Ligthart, “Potentials of UltraShort-Pulse Time-Domain Scattering Measurements”, IEEE Antennas and Propagation Magazine, vol. 42, no. 4, Aug. 2000. Y. Chevalier, Y. Imbs, B. Beillard, J. Andrieu, M. Jouvet, B. Jecko, M. Le Goff, E. Legros, “UWB Measurements of Canonical Targets and
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RCS Determination”, Ultra Wideband Short-Pulse Electromagnetic 4, Heyman et al. ed., Kluwer Academic, New York, 1999. [4] S.R. Cloude, P.D. Smith, A. Milne, D. M. Parkes, K. Trafford, “Analysis of Time Domain Ultrawideband Radar Signals”, UltraWideband, Short-Pulse Electromagnetics, H. Bertoni et al. ed., Plenum Press, 1993. [5] H.Mott, Antennas for Radar and Communications, a Polarimetric Approach, J.Wiley and Sons, New York, 1992. [6] G.T.Ruck, ed., Radar Cross Section Handbook, Plenum Press, New York, 1970. [7] G.C.Gaunaurd, H.C.Strifors, S.Abrahamsson, B.Brusmark, “Scattering of Short EM-Pulses by Simple and Complex Targets Using Impulse Radar”, Ultra-Wideband, Short Pulse Electromagnetics, H.Bertoni ed., Plenum Press, pp.437-444, 1993. [8] E.Pancera, T.Zwick, W.Wiesbeck, “Correlation Properties of UWB Radar Target Impulse Responses”, IEEE Radar Conference 2009, RadarCon09, Pasadena, CA, USA, May, 2009. [9] D.Lamensdorf, L.Susman, “Baseband-pulse-antenna techniques”, IEEE Antennas and Propagation Magazine, vol.36, no.1, Feb. 1994. [10] W.Wiesbeck, S.Riegger, “A Complete Error Model for Free Space Polarimetric Measurements”, IEEE Trans. on Antennas and Propagations, vol.39, no.8, pp. 1105-1111, Aug. 1991.
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