micro-Doppler effect in radar V C Chen

Micro-Doppler Effect in Radar: Phenomenon, Model, and Simulation Study VICTOR C. CHEN Naval Research Laboratory FAYIN LI SHEN-SHYANG HO HARRY WECHSLER, Fellow, IEEE George Mason University When, in addition to the constant Doppler frequency shift induced by the bulk motion of a radar target, the target or any structure on the target undergoes micro-motion dynamics, such as mechanical vibrations or rotations, the micro-motion dynamics induce Doppler modulations on the returned signal, referred to as the micro-Doppler effect. We introduce the micro-Doppler phenomenon in radar, develop a model of Doppler modulations, derive formulas of micro-Doppler induced by targets with vibration, rotation, tumbling and coning motions, and verify them by simulation studies, analyze time-varying micro-Doppler features using high-resolution time-frequency transforms, and demonstrate the micro-Doppler effect observed in real radar data. Manuscript received March 1, 2003; revised July 1, 2004 and March 3, 2005; released for publication August 5, 2005. IEEE Log No. T-AES/42/1/870577. Refereeing of this contribution was handled by L. M. Kaplan. This work was supported in part by the Office of Naval Research and the Missile Defense Agency. Authors’ addresses: V. C. Chen, Radar Division, Naval Research Laboratory, Code 5311, 4555 Overlook Ave. SW, Washington, D.C. 20375; F. Li, S-S. Ho, and H. Wechsler, Dept. of Computer Science, George Mason University, Fairfax, VA 22030. 0018-9251/06/$17.00 c° 2006 IEEE I. INTRODUCTION When a radar transmits an electromagnetic signal to a target, the signal interacts with the target and returns back to the radar. Changes in the properties of the returned signal reflect the characteristics of interest for the target. When the target moves with a constant velocity, the carrier frequency of the returned signal will be shifted. This is known as the Doppler effect [1]. For a mono-static radar where the transmitter and the receiver are at the same location, the roundtrip distance traveled by the electromagnetic wave is twice the distance between the transmitter and the target. The Doppler frequency shift is determined by the wavelength of the electromagnetic wave and the relative velocity between the radar and the target: fD =¡2¸V, where ¸= c=f is the wavelength and V is the relative velocity. If the radar is stationary, the relative velocity V will be the velocity of the target along the line of sight (LOS) of the radar, known as the radial velocity. When the target is moving away from the radar, the velocity is defined to be positive, and as a consequence the Doppler shift is negative. If the target or any structure on the target has mechanical vibration or rotation in addition to its bulk translation, it might induce a frequency modulation on the returned signal that generates sidebands about the target’s Doppler frequency shift. This is called the micro-Doppler effect [2—4]. Radar signals returned from a target that incorporates vibrating or rotating structures, such as propellers of a fixed-wing aircraft, rotors of a helicopter, or the engine compressor and blade assemblies of a jet aircraft, contain micro-Doppler characteristics related to these structures. The micro-Doppler effect enables us to determine the dynamic properties of the target and it offers a new approach for the analysis of target signatures. Micro-Doppler features serve as additional target features that are complementary to those made available by existing methods. The micro-Doppler effect can be used to identify specific types of vehicles, and determine their movement and the speed of their engines. Vibrations generated by a vehicle engine can be detected by radar signals returned from the surface of the vehicle. From micro-Doppler modulations in the engine vibration signal, one can distinguish whether it is a gas turbine engine of a tank or the diesel engine of a bus. The micro-Doppler effect was originally introduced in coherent laser systems [3]. A coherent laser radar system transmits electromagnetic waves at optical frequencies and receives the backscattered light waves from targets. A coherent system preserves the phase information of the scattered waves with respect to a reference wave and has greater sensitivity to any phase variation. Because a half-wavelength change in range can cause a 360± phase change, for a coherent laser system with a wavelength of ¸= 2 ¹m, 1 ¹m 2 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 42, NO. 1 JANUARY 2006 variation in range would cause a 360± phase change. In many cases, a target or a structure on the target may have micro-motions, such as vibrations or rotations. The source of rotations or vibrations might be a rotating rotor of a helicopter, a rotating antenna on a ship, mechanical oscillations in a bridge or a building, an engine-induced vibrating surface, or other causes. Micro-motion dynamics produce frequency modulations on the back-scattered signal and would induce additional Doppler changes to the constant Doppler frequency shift of the bulk translational motion. For a target that has only translation with a constant velocity, the Doppler frequency shift induced by translation is a time-invariant function. If the target also undergoes a vibration or rotation, then the Doppler frequency shift generated by the vibration or rotation is a time-varying frequency function and imposes a periodic time-varying modulation onto the carrier frequency. Micro-motions yield new features in the target’s signature that are distinct from its signature in the absence of micro-motions. For a pure periodic vibration or rotation, micro-motion dynamics generate sideband Doppler frequency shifts about the Doppler shifted central carrier frequency. The modulation contains harmonic frequencies that depend on the carrier frequency, the vibration or rotation rate, and the angle between the direction of vibration, and the direction of the incident wave. Because the frequency modulation is a phase change in the signal, in order to extract useful information from the modulation, coherent processing must be used to carefully track the phase change. For a vibration scatterer, if the vibration rate in angular frequency is !v and the maximal displacement of the vibration is Dv, the maximum Doppler frequency variation is determined by maxffDg= (2=¸)Dv!v. As a consequence, for very short wavelengths, even with very low vibration rate !v any micro vibration of Dv can cause large phase changes. As a consequence the micro-Doppler frequency modulation or the phase change with time can be easily detected. A coherent laser radar operating at 1:5 ¹m wavelength, can achieve a velocity precision ¢V better than 1 mm/s, or a Doppler resolution of ¢fD = 2¢V=¸= 1:33 KHz. Because the micro-Doppler effect is sensitive to the operating frequency band, for radar systems operating at microwave frequency bands, the phenomenon may also be observable if the product of the target’s vibration rate and the displacement of the vibration is high enough. For a radar operating at X-band with a wavelength of 3 cm, a vibration rate of 15 Hz with a displacement of 0.3 cm can induce a detectable maximum micro-Doppler frequency shift of 18.8 Hz. If the radar is operated at L-band with a wavelength of 10 cm, to achieve the same maximum micro-Doppler shift of 18.8 Hz at the same vibration rate of 15 Hz, the required displacement must be 1 cm, which may be too large in practice. Therefore, at lower radar frequency bands, the detection of the micro-Doppler modulation generated by vibration may not be possible. The micro-Doppler generated by rotations, such as rotating rotor blades, however, may be detectable because of their longer rotating arms and, thus, higher tip speeds. For example, UHF-band (300—1,000 MHz) radar with a wavelength of 0.6 m, when a helicopter’s rotor blade rotates with a tip speed of 200 m/s, can induce a maximum micro-Doppler frequency shift of 666 Hz that is certainly detectable. To analyze time-varying micro-Doppler frequency features, the Fourier transform, which is unable to provide time-dependent frequency information, is not suitable. An efficient method to analyze time-varying frequency features is to apply a high-resolution time-frequency transform. The contribution of this paper is that 1) a model of the micro-Doppler effect is developed, 2) mathematical formulas of micro-Doppler modulations induced by several typical basic micro-motions are derived and verified by simulation studies, 3) instead of using the conventional Fourier transform, the high-resolution time-frequency transform is used to analyze time-varying micro-Doppler features, and 4) micro-Doppler effect in radar is demonstrated using real radar data. In Section II, we develop a model for analyzing the micro-Doppler effect. In Section III, we briefly introduce high-resolution time-frequency transforms for analyzing time-varying frequency spectrum. In Section IV, we apply the model for analyzing micro-Doppler effect to several typical micro-motions (vibration, rotation, tumbling, and coning) and verify them using simulation studies. In Section V, we demonstrate two examples of micro-Doppler effect in radar observed in real radar data. II. MICRO-DOPPLER EFFECT INDUCED BY MICRO-MOTION DYNAMICS The micro-Doppler effect induced by micro-motions of a target or structures on the target can be derived from the theory of electromagnetic back-scattering field. It can be mathematically formulated by augmenting the conventional Doppler effect analysis using micro-motions. The characteristics of the electromagnetic back-scattering field from a moving or an oscillating target have been studied in both theory and experiment [5—14]. Theoretical analysis indicates that the translation of a target modulates the phase function of the scattered electromagnetic waves. When the target oscillates linearly and periodically, the modulation generates sideband frequencies about the frequency of the incident wave. A far electric field of CHEN ET AL.: MICRO-DOPPLER EFFECT IN RADAR: PHENOMENON, MODEL, AND SIMULATION STUDY 3 Fig. 1. Geometry of translation target in far EM field. a translated target can be derived as [8] ~ET(~r 0) = expfjk~r0 ¢ (~uk ¡~ur)g~E(~r) (1) where k = 2¼=¸ is the wave number, ~uk is the unit vector of the incidence wave, ~ur is the unit vector of the direction of observation, ~E(~r) is the far electric field of the target before moving, ~r = (U0,V0,W0) is the initial coordinates of the target in the radar coordinates (U,V,W), ~r0 = (U1,V1,W1) is the coordinates of the target after translation, and ~r = ~r0+~r0, where ~r0 is the translation vector, as illustrated in Fig. 1. From (1) we can see that the only difference in the electric field before and after the translation is the phase factor expfjk~r0 ¢ (~uk ¡~ur)g. If the translation is a function of time ~r0 =~r0(t) = r0(t)~uT, where ~uT is the unit vector of the translation, the phase factor then becomes expfj©(t)g= expfjkr0(t)~uT ¢ (~uk ¡~ur)g: (2) For back-scattering, the direction of observation is opposite to the direction of the incidence wave, or ~uk =¡~ur and thus expfj©(t)g= expfj2kr0(t)~uT ¢~ukg: (3) If the translation direction is perpendicular to the direction of the incidence wave, the phase function is zero and expf©(t)g= 1. In general, when the radar transmits an electromagnetic wave at a carrier frequency of f, the radar received signal can be expressed as s(t) = expfj2kr0(t)~uT ¢~ukgexpf¡j2¼ftgj~E(~r)j (4) where the phase factor, expfj2kr0(t)~uT ¢~ukg, defines the modulation of the micro-Doppler effect caused by the motion ~r0(t). If the motion is a vibration given by r0(t) = Acos−t, the phase factor becomes a periodic function of the time with an angular vibrating frequency − expfj©(t)g= expfj2kAcos−t~uT ¢~ukg: (5) The phase function can be mathematically formulated by introducing micro-motions to augment the conventional Doppler analysis. Let us represent a target as a set of point scatterers that represent the primary scattering centers on the target. The point scattering model simplifies the analysis while Fig. 2. Geometry of radar and target with translation and rotation. preserving the micro-Doppler features. For simplicity, all scatterers are assumed to be perfect reflectors that reflect all the energy intercepted. As shown in Fig. 2, the radar is stationary and located at the origin Q of the radar coordinate system (U,V,W). The target is described in a local coordinate system (x,y,z) attached to it and has translations and rotations with respect to the radar coordinates. To observe the target’s rotations, a reference coordinate system (X,Y,Z) is introduced, which shares the same origin with the target local coordinates and, thus, has the same translation as the target but no rotation with respect to the radar coordinates. The origin O of the reference coordinates is assumed to be at a distance R0 from the radar. Suppose the target is a rigid body that has translation velocity ~V with respect to the radar and a rotation angular velocity ~!, which can be either represented in the target local coordinate system as ~! = (!x,!y ,!z) T, or represented in the reference coordinate system as ~! = (!X ,!Y,!Z) T. Because the motion of a rigid body can be represented by the position of the body at two different instants of time, a particle P of the body at instant of time t= 0 will move to P 0 at instant of time t. The movement consists of two steps: 1) translation from P to P 00, as shown in Fig. 2, with a velocity ~V, i.e., ¡¡! OO0 = ~Vt, and 2) rotation from P 00 to P 0 with an angular velocity ~!. If we observe the movement in the reference coordinate system, the particle P is located at ~r0 = (X0,Y0,Z0) T, and the rotation from P 00 to P 0 is described by a rotation matrix