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Extended high resolution range profile-jet engine modulation analysis with signal eccentricity.

1. INTRODUCTION

Inverse synthetic aperture radar (ISAR) imaging [1-4] has been widely employed as a representative radar target recognition method. However, for a few types of radar targets, the ISAR image may be limited by its cross-range dimension, which totally depends on the relative target rotation. Recently, the concept of high resolution range profile in conjunction with jet engine modulation (HRRP-JEM) for aircraft targets with jet engines was introduced [5,6] as another radar imaging method for target recognition. HRRP-JEM, also known as the combined HRR-JEM, uses a radar waveform with both high range resolution and high frequency resolution. By high range resolution, the information on the aircraft structure can be obtained from the HRRP. With high frequency resolution, the JEM [6-11], one of the micro-Doppler phenomena induced by a rotating jet engine compressor, can show its unique spectrum affected by several characteristics of the jet engine. Thus, an HRRP-JEM image composed of range and frequency axes is considered as an independent means for radar target recognition by localizing the equipped jet engine installed on the aircraft [5,6,12]. However, most literature dealing with radar imaging has not placed great emphasis on HRRP-JEM analysis.

In our previous work [12], an algorithm for automatically determining the jet engine location was proposed and basically postulated that after eliminating frequency components around the zero-frequency, the range cell related to the jet engine location had higher amplitude than other cells by the remaining 1st chopping harmonic of the JEM spectrum [10,11]. However, this non-parametric approach does not consider the inherent signal characteristics, and ambiguity can arise from the threshold for discriminating the frequency range to be removed. Hence, this work should be extended by focusing on more quantitative analysis. In addition, the JEM component containing jet engine features needs to be further extracted for enhanced target recognition.

With a simple parametric model of the range cell data, this paper employs signal eccentricity [13-15] to quantitatively determine the jet engine location. For a limited dwell time, the eccentricity is expected to be useful for measuring the micro-Doppler contribution of each range cell. Then, we adopt complex empirical mode decomposition (CEMD) [16-20] to further extract the JEM component. Apart from existing criteria, the eccentricity also serves as a supplementary means for the CEMD-based micro-Doppler extraction. The rest of the paper is organized as follows: In Section 2, we briefly introduce the range cell data model and propose basic techniques for extended HRRP-JEM analysis. In Section 3, we examine the HRRP-JEM data obtained from virtual aircraft framework (VIRAF, by IDS inc.) simulations of realistic aircraft models. Finally, conclusions and future work are discussed in Section 4.

2. BASIC TECHNIQUES FOR EXTENDED HRRP-JEM ANALYSIS

2.1. Simple Parametric Model of Radar Cell Data

The signal in the range cell of the HRRP-JEM image is modelled on the basis of point scatterers [17, 21-23] and the problem geometry with related parameters is shown in Fig. 1. Q and P are the scattering points on the target with bulk rotation angle, [theta](t) and on the rotating subordinate part, respectively. After the range tracking and the translational motion compensation, the radar received signal from Q with a wavelength of X is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [[omega].sub.Q] denotes the angular frequency, and [R.sub.Q] is the distance between the target geometrical center O and Q. After ignoring the initial angle [[theta].sub.Q], [S.sub.Q](t) becomes the form of linear phase modulation by the small accumulation angle assumption, namely [[omega].sub.Q]t [much less than] 1. Hence, the instantaneous frequency of Q is time-invariant. The radar signal from P is represented by the sinusoidal phase modulation such that

sp (t)=exp [j [4[pi][R.sub.p]/[lambda] sin([omega]pt)] (2)

where [[omega].sub.p] is the angular speed of the rotating part and [R.sub.p] the rotation radius. Note that the small accumulation angle assumption is not valid here since [[omega].sub.pt] is not generally small in relation to 1 [17,23] and up is much greater than [[omega].sub.Q] in the HRRP-JEM imaging scenario ([[omega].sub.] [much less than] [[omega].sub.p]). Consequently, the range cell data can be expressed by the sum of the body returned component [s.sub.Q](t) and the micro-Doppler component Sp(t) as follows:

s(t)= sp(t)+[As.sub.Q](t)=exp [j [4[pi][R.sub.p]/[lambda]] sin ([omega]pt)]] + Aexp [4[pi][R.sub.Q]/[lambda]] [omega][Q.sub.t]] (3)

where A is the weight that makes the body returned component account for a relatively large portion of s(t). This is because sp(t) may become weaker than [s.sub.Q](t) if there is emphatic scattering from aircraft structures.

2.2. Signal Eccentricity and Its Application to Estimating Jet Engine Location

Signal eccentricity e measures how far a complex-valued signal deviates from circularity with respect to the central axis of the complex plane [13-15]. By definition, it is expressed by main and minor axes of elliptical geometry when the signal s(t) = s is projected onto the 2D complex plane. However, since deterministically calculating the lengths of these axes is not always possible for an arbitrary data set, we use another mathematical expression based on the statistical characteristic of s such that [15]

[epsilon] = [square root of [absolute value of P/C/] = [square root of [absolute value of E[s x [s.sup.T]/E[s x [s.sup.H]] (4)

where P is the pseudo-covariance, C the covariance, and E[*] the expectation operator.

The eccentricity ranges between 0 for pure circular polarization and 1 for pure linear polarization. In (3), both signal components theoretically have 0 eccentricity values because they all have circularly rotating natures in the 3D complex domain composed of real, imaginary and time axes. However, in reality, the eccentricity cannot be 0 since the dwell time for radar imaging is within tens of milliseconds [6, 12, 17]. Thus, it can be highly dependent on the signal rotating behavior in the given dwell time. Since the body returned component sq (t) slowly rotates compared to the micro-Doppler sp(t) ([[omega].sub.Q] [much less than] [[omega].sub.p]) [5, 6,12], [s.sub.Q](t) will appear to be linearly polarized as shown in Fig. 2(a) as opposed to sp(t), which will retain its circularity along the central axis of the complex plane as shown in Fig. 2(b). Table 1 gives background information on the signal components illustrated in Fig. 2. The large value of [omega]p considers a scattering point on a propeller blade rotating at a rate of 6000 RPM.

Figure 3 shows eccentricity values of s(t) for different A. If A is less than 1, the micro-Doppler contribution becomes dominant and s(t) has a low eccentricity value. However, when A increases, the rotating behavior of s(t) starts to deviate from circularity with respect to the central axis of the complex plane. Therefore, the signal eccentricity is feasible for assessing the micro-Doppler contribution to the range cell data. To further develop our discussion on localization of the jet engine, the eccentricity concept will be applied to HRRP-JEM images. Since the JEM micro-Doppler contribution will be maximized at the engine location, the corresponding range cell is expected to be found by investigating the eccentricity of each range cell.

2.3. Micro-Doppler Extraction via CEMD Incorporated with Signal Eccentricity

Once the range cell indicating the jet engine location is found, the JEM component can be further extracted from the range cell data, which still contains the body returned component. In this paper, we adopt CEMD [16], an extension of real-valued EMD [24], as an extraction method. Its underlying idea is to regard the complex-valued signal as rapidly rotating components superimposed on slowly rotating components. Thus, CEMD successively separates zero-mean rotating components from the original signal by projecting it in uniformly spaced directions along a unit circle. Each decomposed component is referred to as the complex intrinsic mode function (IMF). Since CEMD has fully data-driven characteristics, namely, it makes no prior assumption on the given data, many researchers have demonstrated its effectiveness in a variety of applications [17-20]. Since the detailed algorithm has been presented in many papers, we will not repeat it here to keep this paper concise.

We use (3) again to illustrate the CEMD-based micro-Doppler extraction. A is given as 50 to imitate the range cell data in which the body returned component strongly overlaps with the micro-Doppler. The CEMD with 127 projection directions is applied to s(t) and 3 complex IMFs are obtained. Since the micro-Doppler can be reconstructed by combining appropriate IMFs, a standard for IMF selection needs to be set up. In [17], Bai et al. proposed the number of zero-crossings as a standard for IMF discrimination to separate the micro-Doppler from the body Doppler in ISAR imaging. It can be a physically intuitive means because it basically assumes that the micro-Doppler varies much more rapidly than the body Doppler. However, the zero-crossing threshold may not be clear if there is no rapid change in the number of zero-crossings. Furthermore, in contrast to our situation dealing with the HRRP-JEM data, the micro-Doppler discussed in [17] accounts for a substantial portion of the range cell data. Therefore, we propose the eccentricity as a new complementary means to consider the rotating behavior of the reconstructed signal.

Figure 4 shows the number of zero-crossings and the energy ratio of each extracted IMF. The first two IMFs have numerous zero-crossings while their energy values are at least 30 dB lower than that of the 3rd IMF. Thus, it can be anticipated that these IMFs contain the micro-Doppler component. To clarify this observation, we then calculate the eccentricity for IMF combinations: [r.sub.1](t), [r.sub.2](t) and [r.sub.3](t). Here, [r.sub.n] (t) is given by

[r.sub.n] (t) = [n.summation over (i=1)[c.sub.i](t) (5)

where [c.sub.i](t) is the ith IMF, and IMFs are combined by the ascending order in accordance with the degree of rotation. Note that [r.sub.n](t) becomes identical with the original signal when n is equal to the number of extracted IMFs. The eccentricity of each [r.sub.n] (t) is 0.1576, 0.1099 and 0.8577, respectively. The eccentricity value of [r.sub.3] (t) quantitatively reveals that the last IMF denotes the body returned component as predicted from Fig. 4. After separating the 3rd IMF, [r.sub.2](t) with the minimum eccentricity is regarded as best characterizing the micro-Doppler component and is designated as the reconstructed micro-Doppler component. Since the 2nd IMF has relatively low energy, [r.sub.1] (t) is allowed to be selected despite its relatively high eccentricity. Therefore, the signal eccentricity does not severely restrict the IMFs to be used but indicates the desirable IMF combination.

Figure 5 presents the spectrograms of s(t) and [r.sub.2](t). Even though Fig. 5(a) exhibits an almost constant frequency line, Fig. 5(b) depicts a time-dependent frequency and shows quite a good match with the theoretical micro-Doppler frequency, which can be derived from the phase term in (2) as follows:

f (t) = [1/2[pi]] [d/dt] [4[pi][R.sub.p]/[lambda] sin([omega]pt) = 2/[lambda][R.sub.p[omega]p] cos([omega]pt) (6)

3. APPLICATION OF PROPOSED TECHNIQUES TO HRRP-JEM IMAGES

3.1. Estimation of Jet Engine Location

To verify the proposed techniques, this section examines the 2D RCS data set [12] obtained from VIRAF simulations of two realistic aircraft models. These aircraft models are equipped with jet engines as shown in Fig. 6 and were assumed to be stationary for typical HRRP-JEM images without cross-range dimensions. Table 2 gives electromagnetic simulation parameters and relevant geometrical and dynamic characteristics.

Figure 7 shows Fourier-based HRRP-JEM images of the aircraft models. In the Global Hawk, the head and tail positions can be observed at the 4th and 18th range cells in accordance with the projected length. In addition, broad spectra are shown at the 11th-14th range cells. Although these spectra suggest the existence of the JEM harmonic spectrum, it is difficult to determine the range cell indicating the actual jet engine location.

For discrimination accuracy, some range cells are excluded in the eccentricity computation when they do not overlap with the effective aircraft range or their maximum RCS values do not reach the predetermined small value of -20dBsm as shown in Fig. 8(a). This is because the JEM-related spurious components existent throughout the ranges can also give a small eccentricity even if they do not have a real influence on the HRRP-JEM image. Fig. 8(b) exhibits the eccentricity values calculated for the rest of range cells, and the 13th range cell shows the lowest eccentricity. Since there are 9 cells between the head and the engine, the estimated range cell corresponds to the real location at which the distance to the head is 8.46 m. If the range resolution of 1 m is further improved by the wide bandwidth, more accurate localization can be performed. The eccentricity also confirms that the 11th and 12th range cells with high eccentricity denote the scattering from the aircraft structure.

In the B-1B Bomber, the tail position is not clear, as depicted in Figs. 7(b) and 9(a). Thus, the jet engine location is estimated with respect to the head position at the 2nd range cell. Although there are two JEM-like broad spectra at the 27th-29th range cells and at the 34th-36th range cells, we cannot clearly conclude which range cell denotes the real jet engine location. Fig. 9(b) shows the eccentricity of the range cells with RCS values greater than -20dBsm. It can be shown that the 34th range cell with the minimum eccentricity is identified as the jet engine location from which the distance to the head is 31.51m. Other JEM-like spectra at the 27th-29th range cells are shown to be mainly contributed to by the body returned component. This section demonstrated that the eccentricity could facilitate the quantitative estimation of the jet engine location.

3.2. Extraction of JEM Component

Figure 10(a) shows the spectrogram of the 13th range cell data in the Global Hawk. The spectrogram confirms that the strong body returned component still exists around the zero frequency. The CEMD with 127 directions decomposed the data into 9 IMFs, and their numbers of zero-crossings and the energy ratio are shown in Fig. 10(b). Although the number of zero-crossings of the 1st IMF is much more than the others, most of the energy lies in the 2nd IMF except for the 9th IMF, which obviously coincides with the strong zero-frequency component. Hence, it is not clear which IMF should be included for accurate JEM extraction. As evident from Table 3, the eccentricity values of reconstructed signals ([r.sup.1] (t) ~ [r.sub.8] (t)) do not sharply increase until the last 9th IMF is added. Based on the minimum eccentricity, [r.sub.8](t) is selected as the extracted JEM component.

Figure 11 depicts the spectrogram of [r.sub.8](t) where the JEM component is more concentrated than in the spectrogram of Fig. 10(a). From Fig. 11(b), we can obtain a variety of information, such as the chopping rate, the blade length, and the blade parity (whether the number of blades is even or odd). The chopping rate [6,11], the period when a blade moves to its neighbor position, can be calculated as 0.435 ms. The blade length is estimated using the Doppler span [8,10,11] along the frequency axis. The slanted waveforms marked with white lines suggest the odd number of blades for which the blades alternately approach and recede [8].

Figure 12(a) shows the spectrogram of the 34th range cell data in the B-1B Bomber. Although it presents the relatively strong micro-Doppler by simultaneous scattering from 4 engines, further processing is needed for more accurate JEM analysis. Table 3 supports that [r.sub.1](t) is designated as the extracted JEM component. One remarkable characteristic of the auto-correlation of [r.sub.1](t) shown in Fig. 12(b) is the spool rate(full rotation period), one of the typical JEM characteristics. The outstanding peaks associated with the spool rate exist among surrounding peaks related to the chopping rate. Thus, using the time intervals of the auto-correlation, the number of blades can be calculated as 17. From Figs. 12(c) and 12(d), it is noteworthy that the refined spectrogram of [r.sub.1](t) exhibiting slanted lines leads to the more distinct even/odd check of the blade number than Fig. 12(a).

4. CONCLUSION

This paper presents an extended HRRP-JEM analysis with signal eccentricity: the estimation of the jet engine location and the extraction of the JEM component via CEMD. Based on the range cell data model, we employed the eccentricity as a metric for assessing the micro-Doppler contribution. Rather than the non-parametric approach, the signal eccentricity served as a reliable indicator by facilitating more quantitative jet engine localization. In addition, further application of eccentricity could provide a new supplementary means for the CEMD-based JEM extraction. Future studies should focus on examining the measured data where the clarity of HRRP JEM images would be degraded by the aircraft motion. To maintain the quality of HRRP-JEM images, not only the aircraft target but also the rotating jet engines need to be continuously tracked by the radar during the dwell time. Although this paper dealt with HRRP-JEM images with one JEM line, more than two jet engines can be illuminated by the radar signal and can be located at different range cells. Therefore, HRRP-JEM images with more than two JEM lines can also provide later research direction. However, the fundamental principles of this research can be followed because the eccentricity was proven to be effective for evaluating the micro-Doppler contribution. The extended HRRP-JEM analysis described in this paper is expected to be useful for advanced radar target recognition with HRRP-JEM.

ACKNOWLEDGMENT

This research was supported by Samsung Thales Co., Ltd..

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Ji Hoon Park (1), *, Woo Yong Yang (1), Jun Woo Bae (2), Seong Cheol Kang (2), and Noh Hoon Myung (1)

(1) Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 335 Gwahangno, Yuseong-gu, Daejeon 305-701, Korea

(2) Samsung Thales, Sampyong-Dong, Bundang-Gu, Seongnam 463-400, Korea

Received 1 August 2013, Accepted 12 September 2013, Scheduled 16 September 2013

* Corresponding author: Ji Hoon Park (dydynoel@kaist.ac.kr).

Table 1. Parameters of signal components depicted in Fig. 2.

       parameters                                        value
radar wavelength [lambda]                               0.03 m
   sampling frequency                                   80 kHz
       dwell time                                        20 ms
  parameters related to         [R.sub.p],       0.25 m, 200n [pi]ad/s
         P and Q             [[omega].sub.p]     5.0 m, 0.05 rad/s, 50
                                [R.sub.Q],
                            [[omega].sub.Q], A

Table 2. Electromagnetic simulation parameters for HRRP-JEM
imaging and geometrical and dynamic characteristics of two aircraft
models with jet engines.

                        aircraft model      Global Hawk   B-1B Bomber

  electromagnetic       electromagnetic     shooting and bouncing
    simulations         analysis method       rays (SBR) [25,26]

                         radar center                  10 GHz
                           frequency

                           bandwidth               150 MHz (range
                                                 resolution = 1 m)

                      frequency interval      7.5 MHz        3 MHz

                           number of            21            51
                        frequency steps

                       pulse repetition       80 kHz        20 kHz
                        frequency (PRF)

                          dwell time             20 ms (frequency
                                               resolution = 50 Hz)

                        incident angle      70[degrees]   100[degrees]
                       (azimuth [PHI] =
                          0[degrees])

characteristics of     projected length       13.34 m       47.96 m
two aircraft models    by incident angle
 with jet engines
                      projected distance      8.46 m        31.51m
                      from head to engine

                      number of equipped         1             4
                          jet engines

                         engine model         AE3007         F101

                      full rotation speed              6000 RPM

                      number of blades in       23            17
                        1st rotor stage

                       length of blades       0.491m        0.385 m
                      in 1st rotor stage

Table 3. Calculated eccentricity for IMF combinations of two aircraft
cases.

              [r.sub.1](t)   [r.sub.2](t)   [r.sub.3](t)

Global Hawk      0.3513         0.3721         0.3262
B-1B Bomber      0.2820         0.4140         0.4667

              [r.sub.4](t)   [r.sub.5](t)   [r.sub.6](t)

Global Hawk      0.3174         0.3149         0.3136
B-1B Bomber      0.4487         0.4355         0.4363

              [r.sub.7](t)   [r.sub.9](t)   [r.sub.9](t)

Global Hawk      0.3135         0.3135         0.7193
B-1B Bomber      0.7711           --             --
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Author:Park, Ji Hoon; Yang, Woo Yong; Bae, Jun Woo; Kang, Seong Cheol; Myung, Noh Hoon
Publication:Progress In Electromagnetics Research
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Date:Oct 1, 2013
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