micromotion characteristic acquisition based on wideband radar phase

3650 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 6, JUNE 2014

Micromotion Characteristic AcquisitionBased on Wideband Radar Phase

Yongxiang Liu, Member, IEEE, Dekang Zhu, Xiang Li, Member, IEEE, and Zhaowen Zhuang

Abstract—A novel method of precise radial range measurementbased on wideband radar phase is presented in this paper formicromotion characteristic acquisition. The advantage of thismethod is the high precision with root-mean-square error valuesat subwavelength levels, while its difficulties are phase extractionfrom wideband radar echoes and resolution of ambiguous phase.After the analysis of the principle of radial range measurementbased on radar phase, the method of extracting the Doppler phasefrom wideband radar echoes is proposed, following a comprehen-sive technical diagram for micromotion characteristic synthesisbased on the wideband radar phase. Some restraint conditionsfor the resolution of the ambiguous phase are analyzed system-atically according to the different characteristics of micromotionand radar parameters. The method provides a more precise toolto acquire the micromotion characteristic than the traditionalDoppler frequency methods, and the experiments have shownthe performances of wideband radar phase extraction and itsambiguity resolution.

Index Terms—Doppler phase, micromotion, phase-derivedrange, wideband radar.

I. INTRODUCTION

M ICROMOTION is the mechanical dynamics of a targetor any structure on the target in addition to bulk mo-

tion, including rotation, vibration, tumbling, precession, and soon. Characteristic analyses of radar targets with micromotionshave gotten more and more attention in the radar community[1], [2]. There have been numerous research works conductedin recent years [3], [4], such as the modulation mechanicsof micromotions on electromagnetic waves, radar imaging oftargets with micromotions, extraction of micromotion features,estimation of micromotion parameters, and so on. Micromotioncharacteristic acquisition is a key technical challenge amongthese research works because of its weakness in radar echoes,particularly under conditions such as small amplitude of mi-cromotions, low working frequency of radar, or inaccuratecompensation of bulk translation.

Manuscript received October 23, 2012; revised March 10, 2013; acceptedJune 13, 2013. Date of publication September 4, 2013; date of current versionFebruary 27, 2014. This work was supported in part by the National ScienceFoundation of China under Contracts 61025006 and 60872134.

The authors are with the College of Electronic Science and Engineering,National University of Defense Technology, Changsha 410073, China (e-mail:[email protected]; [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2013.2274478

As far as micromotion characteristic acquisition based onradar is concerned, the highly precise measurement of range orvelocity is a necessary precondition. It has been indicated thatthe current X-band radar in missile defense systems could havea highly precise measurement capability of range and velocity,and this superprecision at subwavelength level will ensure thesystem to acquire the micromotion characteristic of ballistictargets [5]. Reviewing the technology development of highlyprecise range measurement in the past 40 years, a range mea-surement method based on a narrow-band coherent radar phasenamed Range Vernier (RV) was developed in the 1970s [6]and a range measurement method based on radar phase namedPhase-Derived Range (PDR) was applied to missile defensesystems in 1983 [5], [7]. Some applying patents about highlyprecise measurement based on wideband radar have shownthat the PDR technology was used in X-band radar, whichhas proven the capability of estimating precession parametersand acquiring precession features [8], [9]. A research projectnamed Discrimination via PDR was sponsored [10], [11] inorder to discriminate the dynamic details of a target for radarimaging and micromotion acquisition. Some research works onmicromotion analysis based on wideband/ultrawideband radarhave been conducted in recent years [12]–[15] for widebandradar systems can provide both the micro-Doppler signatureand high range resolution profile (HRRP) signatures, permittinga 3-D domain output of joint range–time–frequency repre-sentation, and these combined features are useful in severalapplications for human sensing, through-wall sensing, multiple-object detection, target localization, real-time target tracking,target classification, and so on. The highly precise measurementof range or velocity based on radar phase has shown greatacademic and applicable values during the past several decades,and there are still some technical difficulties needed to resolve,such as phase extraction from wideband radar echoes andresolution of ambiguous phase.

In this paper, a novel method of highly precise range mea-surement based on wideband radar phase is presented, wheretwo technical cores are focused on phase extraction from wide-band radar and the resolution of ambiguous phase consideringdifferent conditions. The works are organized as follows. Thebasic principle of radial range measurement based on radarphase is analyzed in Section II, and the technique of phaseextraction from wideband radar is developed in Section IIIfollowing an entire technical diagram. In Section IV, somerestraints for the resolution of ambiguous phase are consid-ered and analyzed. The experimental results are presented inSection V, showing the performance of the method on wide-band radar phase extraction and its ambiguity resolution.

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LIU et al.: MICROMOTION CHARACTERISTIC ACQUISITION BASED ON WIDEBAND RADAR PHASE 3651

II. PRINCIPLE OF RADIAL RANGE MEASUREMENT

BASED ON RADAR PHASE

For a coherent narrow-band radar, its Doppler phase (theso-called Doppler phase means the phase of the target withmotions, and the Doppler frequency induced by motions willhave effects on the radar phase) between the transmitted andechoed pulses is θ = f0τ , where f0 is the carrier frequency andτ is the time delay. It is obvious that we can get highly preciseradial range measurements with error values at subwavelengthlevel if the radar can provide the accurate Doppler phase θ. Infact, only the ambiguous Doppler phase measurement θ̃m canbe provided by the radar

θ̃m = θm − 2πKm + εm (1)

where m denotes the mth echoed pulse, θm is the Dopplerphase corresponding to the mth echoed pulse, Km is an in-teger to ensure 0 ≤ θm − 2πKm ≤ 2π, and εm is the mea-surement error of Doppler phase θm. Let Dm = θm+1 − θmbe the Doppler phase delta between the mth and (m+ 1)thechoed pulses and the corresponding ambiguous measurementof Doppler phase delta

d̃m = θ̃m+1 − θ̃m = Dm − 2Nmπ + εm+1 − εm (2)

where Nm = Km+1 −Km and this parameter is the exactnumber for resolutions of ambiguous Doppler phase. The cor-responding measurement of Doppler phase delta D̃m can beobtained as

D̃m = d̃m + 2πNm. (3)

In order to obtain the successive measurements, we need toaccumulate the measurements of Doppler phase delta D̃m(1 ≤m ≤ n− 1)

S̃n = D̃1 + D̃2 + · · ·+ D̃n−1. (4)

Using the aforementioned equations yields

S̃n = θn − θ1 + εn − ε1 = Sn + εn − ε1 (5)

where Sn = θn − θ1 is the true value of S̃n. This shows thatthe ambiguous Doppler phase measurements θ̃m and errorsεm(1 < m < n) vanish in the sum procedure due to mutualcancellation. The measurement error of the Doppler phase deltais dependent only on the Doppler phase measurement errors ofthe first and last pulses, i.e., ε1 and εn, which ensures that themethod can realize the high precision of range measurement.The radial range variation of the target during the first and nthpulses is

R̃n =λ

4πS̃n =

λ

4πSn +

λ

4π(εn − ε1) = Rn +

λ

4π(εn − ε1).

(6)

This indicates that the principle of radial range measurementbased on radar phase is to convert the Doppler phase delta toradial range change, i.e., to get the precise radial range deltaof the target relative to the initial radial position at the instantthe first pulse occurred. As far as the initial radial position

Fig. 1. Process of radial range measurement based on radar phase.

is concerned, it can be obtained by the ranging subsystem inradar; in fact, it is not a necessary parameter for describing themicromotion characteristic of the target. Then, the radial rangemeasurement based on radar phase can be realized, as shownin Fig. 1.

The precise radial range delta can provide the information ofmicromotion, and the key point is to resolve the ambiguity ofthe Doppler phase delta, i.e., to determine the number Nm in(3). An ambiguity resolution method based on the estimationof the Doppler phase delta was provided in 1970s, named RV[6]. It uses the integral of the Doppler frequency in the pulseDoppler radar system during the period of successive pulses tocalculate Dm, the estimation of Doppler phase delta Dm

Dm = 2π

tm+1∫tm

fd(t)dt ≈ π[f̃d(m) + f̃d(m+ 1)

]· Tr (7)

where f̃d(m) denotes the measurement of the Doppler fre-quency from the mth pulse and Tr denotes the pulse repetitiontime. Let

Dm/2π = Nm + qm (0 ≤ qm < 1). (8)

Consider the difference between the estimated and measuredDoppler phase delta values

Cm = qm −[d̃m/2π

](9)

where d̃m = θ̃m+1 − θ̃m is the ambiguous phase delta mea-surement of two successive pulses. In fact, Cm ∈ (−1, 2) isa factor for modifying the estimation based on measurement,as |d̃m| < 2π and 0 ≤ qm < 1. Because the ambiguous phaseis the true Doppler phase modulo 2π, the modifying valueΔNm determined by Cm is shown in Fig. 2 and the correctinteger cycles for the Doppler phase delta can be yielded asNm = Nm +ΔNm.

III. EXTRACTION OF THE DOPPLER PHASE

FROM WIDEBAND RADAR

The precise radial range can be obtained by the Dopplerphase measurement in the narrow-band coherent radar inSection II. Using the radar phase ranging method, the narrow-band radar can only provide a precise range of target as a whole(i.e., bulk translation) rather than enough information for target


Fig. 2. Modifying values in the resolution of ambiguous phase.

micromotion analysis due to the limitation of target resolution.The wideband radar has been paid much attention because ofits capability to resolve the individual scatters in the target withHRRP, which will provide the potential foundation to describethe micromotion characteristic precisely by the method inSection II. The first technical challenge of applying the radarphase range method is the difficulty to extract the Dopplerphase f0τ from the wideband radar echoes, which is the maintask tackled in this section. Unlike the narrow-band radar echofrom which the Doppler phase can be measured directly, thewideband linear frequency modulated (LFM) signal has a linearincreasing instantaneous frequency, leading to the fact that wecannot measure the Doppler phase directly. However, consid-ering the instantaneous frequency as having two parts, whichare an initial carrying frequency f0 and a modulated frequencydelta added, respectively, we can estimate the Doppler phaseterm f0τ from phase measurements of compressed echo bycompensating unwanted phase terms.

Wideband chirp waveforms are commonly used because oftheir ease of generation and processing in the radar receiver.Consider a wideband radar transmitting LFM signal, and themth transmitted pulse is

St(t) = rect(t̂/T ) exp[j2π(f0t+ γt̂2/2)

](10)

where T denotes the pulsewidth, f0 denotes the carrier fre-quency, γ denotes the slope of frequency modulation, t̂ denotesthe fast time from the instance of pulse starting and 0 < t̂ < T ,Tr denotes the pulse repetition time, and tm denotes the slowtime, where tm = m · Tr and t = tm + t̂.

The dynamic characteristic of a radar target with micromo-tions can be divided into two parts: One is the radial bulk trans-lation with radial velocity v, and the other is the micromotionwith radial range r(tm). In fact, the change of v in the fast timeperiod cannot be ignored if v has a big value (for example,orbit target, ballistic target, and so on); meanwhile, r(tm) isa small value reflecting micromotions and its change in fasttime periods can be ignored. In addition, the relation betweenR(tm) and r(tm) during the period of two successive pulses isillustrated in Fig. 3.

Fig. 3. Relation between R(tm) and r(tm) during the period of two succes-sive pulses.

The dynamic characteristic of a radar target with micromo-tions is given by

R(t, t̂) = R(tm) + vt̂+ r(tm). (11)

The corresponding time delay is

τ̂(t) = 2R(t, t̂)/c = 2 ·(R(tm) + vt̂+ r(tm)

)/c

= τ(tm) + 2vt̂/c (12)

where c is the speed of light, τ(tm) = 2 · (R(tm) + r(tm))/cdenotes the corresponding time delay that the mth transmittedpulse returns from the target, briefing as τ , and the correspond-ing echo is

Sr(t, t̂) = rect{[(1− 2v/c)t̂− τ

]/T

}·exp

{j2π

[f0(t−τ−2vt̂/c)

+1

2γ((1−2v/c)t̂−τ

)2]}. (13)

Let τ0(tm) be the reference time delay corresponding to themth echoed pulse in the dechirping processes, briefing as τ0.The echo can yield after the dechirping processes [16]

Sif(t, t̃) = rect{[

t̃− 2(RΔ + vτ0)/c]/T

}· exp

{−j2π[ϕ1 + ϕ2 + ϕ3t̃+ ϕ4t̃

2]}

(14)

where t̃ = t̂− τ0, RΔ = c(τ − τ0)/2, and 1− 2v/c ≈ 1because of v � c

ϕ1=− γ(2R2

Δ+4vRΔτ0)/c2 ϕ2=f0τ + f0τ0(2v/c− 1)

ϕ3=2RΔγ/c+2v(τ0γ + f0)/c ϕ4=2vγ

c. (15)

After compensating the phase term ϕ4 by the fast method ofdechirping, the Fourier transform is applied with t̃ in (14) toobtain (16) where the amplitude is the 1-D HRRP in the fre-quency domain. By multiplying c/(2γ), the frequency domaincan translate to the relative range domain with the referencerange cτ0/2

Sif(t, f) =T sin c [T (f+ϕ3)]

×exp {−j2π [ϕ1+ϕ2+2(f + ϕ3)

× (2RΔ + vτ0)/c)]} . (16)


Fig. 4. Acquisition of micromotion characteristic based on wideband radarphase.

This indicates that the peak of the HRRP lies at f = −ϕ3

and the phase term Δϕ should be compensated to extract theDoppler phase f0τ from the phase term ϕ2

Δϕ = 2π [ϕ1 + f0τ0(2v/c− 1)] . (17)

The aforementioned compensated phase term can be simpli-fied with (15)

Δϕ = 2π[−γ

(2R2

Δ/c2 + 4vRΔτ0/c

2)+ f0τ0(2v/c− 1)

].

(18)Furthermore, with the relationship between ϕ3 and RΔ in

(15), RΔ/c = ϕ3/(2γ)− vτ0/c− vf0/(cγ)

Δϕ = 2π [−(ϕ3/2γ − vτ0/c− vf0/cγ)

×(ϕ3 − 2vγτ0/c− 2vf0/c) + f0τ0(2v/c− 1)] . (19)

After phase compensation, the complex signals of the peakof the HRRP become S(τ, tm) = T exp{−j2πf0τ} and thescatter corresponding to the peak of the HRRP has an am-biguous Doppler phase θ̃ = mod(2πf0τ, 2π) according to themth transmitted pulse or at the instant tm. This method isapplied in HRRP iteratively, and the ambiguous Doppler phasescorresponding to the scatters in the HRRP can be obtained.Furthermore, a similar procedure is applied to every widebandradar echo, and using the technology of scatter association (thistechnology is to ensure that the peaks in different HRRPs comefrom the same scatter in the target) [17], we can get the ambigu-ous Doppler phase of every scatter under successive widebandradar echoes, and then, the precise radial range measurementsof scatters in the target can be realized, which can be used toacquire the characteristic of micromotions. This procedure isshown in Fig. 4.

In practice, the velocity variation during the period betweentwo successive pulses is not significant and the Doppler phasedelta estimation based on the measured velocities is preciseenough for ambiguity resolution. Thus, the bulk velocity duringthe period between two successive pulses can be assumed asconstant, i.e., ignoring the acceleration and change of accel-eration, which can bring the conveniences in the mathematicdevelopment and experiments.

IV. SOME RESTRAINTS FOR RESOLUTION

OF AMBIGUOUS PHASE

As mentioned in Section I, one of the technical challenges forthe radar phase ranging method is the restraints for resolutionof ambiguous phase. In Section II, the estimation of Dopplerphase delta Dm is introduced to resolve the phase ambiguity;in fact, the method needs a necessary condition [6]

|δDm − δD̃m| < π (20)

where δDm is the error of Dm and δD̃m is the error of D̃m.With this condition, we hope to get the restraint relationshipbetween the resolution of the ambiguous phase and the param-eters of the radar measurements.

Based on the estimation of the Doppler phase delta in (7), theestimation error is

δDm = (Δωd(tm+1) + Δωd(tm)) · Tr/2 (21)

where Δωd(t) denotes the measurement error of the Dopplerfrequency in the radar. Let σωd

denote the root mean square(RMS) error of the Doppler frequency and Δωd ∼ N(0, σ2

ωd)

due to radar system characteristic, where N(·) means thenormal distribution. Assume that the Doppler frequency mea-surements at tm and tm+1 are independent

(Δωd(tm+1) + Δωd(tm)) ∼ N(0, 2σ2

ωd

). (22)

So

δDm ∼ N(0, T 2

r σ2ωd/2). (23)

Considering δD̃m = εm+1 − εm, let σD denote the rms ofthe Doppler phase measurement error and δD̃ ∼ N(0, 2σ2

D)

δDm − δD̃m ∼ N(0, T 2

r σ2ωd/2 + 2σ2

D

). (24)

To meet the necessary conditions in (20), the 3σ principle(i.e., in a sample set with normal distribution, the sampleswhose variations are less than 3σ from the mean value willoccupy more than 99%, where σ is the rms of the normaldistribution) is introduced here. Then, the comprehensive re-straint relationship among the rms of the Doppler frequencymeasurement error, the rms of the phase measurement error,and the pulse repetition time is

3√

T 2r σ

2ωd/2 + 2σ2

D < π (25)

which provides the restraint conditions for the radar measure-ments for ambiguous phase resolution.


As shown in (11), the motions of the radar target can bedivided into bulk translation and micromotions, and the charac-teristic of micromotions is the focus of our technical attention.In fact, the micromotions have great influence on the resolutionof ambiguous Doppler phases, and this section will analyze thecorresponding influence in the different situations. Consideringthe Doppler phase delta Dm of some scatter in the targetbetween the mth and m+ 1th echoed pulses, it can be dividedinto two parts: One is the Doppler phase delta induced bybulk translation DBm, and the other is the Doppler phase deltainduced by micromotions DMm, i.e., Dm = DBm +DMm.

A. Ambiguity Resolution When Micromotions are Ignored

The estimation error of the Doppler phase δDm = δDBm +DWm because we estimate the Doppler phase by the bulkDoppler measured. Referring to (20)∣∣∣δDm − δD̃′

m

∣∣∣ = |δDBm +DMm − δD̃m| < π

(26)

|δDBm +DMm − δD̃m| < |δDBm − δD̃m|+ |DMm| < π.

(27)

Finally, we can get

|DMm| < π − 3√

T 2r σ

2ωd/2 + 2σ2

D. (28)

This means that when the Doppler phase delta induced bymicromotions between two successive pulses satisfies (26), theresolution of the ambiguous phase can be realized by onlyusing the estimation of the Doppler phase delta induced by bulktranslation. Equation (26) means that when the phase caused bymicromotion falls into the gap between π and |δDBm − δD̃m|,we can get the correct resolution result, but it will contributeto the error of the measured ambiguous phase which eventuallypollutes the range measurement.

B. Ambiguity Resolution When Micromotions Are Considered

When the Doppler frequency value induced by micromotionsis large and DMm does not meet the condition in (26), theresolution of the ambiguous phase should consider the influenceof DMm. Then, the estimation of the Doppler phase deltaconsists of the estimation of the Doppler phase delta induced bybulk translation and the estimation of the Doppler phase deltainduced by micromotions. The estimation of the Doppler phasedelta induced by micromotions can be approximated as

DMm = (ω̃M (tm) + ω̃M (tm+1)) · Tr/2 (29)

where ω̃M denotes the Doppler angular frequency induced bymicromotions, the so-called micro-Doppler angular frequency.

With (20)

|δDm − δD̃m| = |δDBm + δDMm − δD̃m| < π. (30)

Referencing (24), we can get

δDBm+δDMm−δD̃m∼N(0, T 2

r

(σ2ωB

+σ2ωM

)/2+2σ2

D

)(31)

where σωBand σωM

denote the rms errors of the Dopplerfrequency measurements induced by bulk translation and mi-cromotions, respectively. With the principle of 3σ, we can getthe constraint for the resolution of the ambiguous Dopplerphase delta

3√T 2r

(σ2ωB

+ σ2ωM

)/2 + 2σ2

D < π. (32)

When the micromotion character does not fit the requirementin (26) and with the indication of (32), the Doppler phase deltashould be the sum of the Doppler phase delta induced by bulktranslation and that by micromotion

Dm = DBm +DMm (33)

where DMm=∫ tm+1

tmωM(t)dt≈(ω̃M(tm)+ω̃M(tm+1))·Tr/2

and ω̃M(m) can be estimated from the time–frequency repre-sentations of the range bins containing the scatter in the HRRPsequences.

C. Performance of Ambiguous Phase ResolutionConsidering SNR

Equation (25) provides the restraint conditions for the radarmeasurements for ambiguous phase resolution, such as therms of the Doppler frequency measurement error, rms of theDoppler phase measurement error, and pulse repetition time.With the radar handbook in [18], the Cramer–Rao Low Bound(CRLB) values of the phase and Doppler frequency measure-ments in the radar system are

σ2D ≥ 1/(N · SNR) =σ2

D̂(34)

σ2ωd

≥ 1/(N · SNR · τ2s rms

)=σ2

ω̂d(35)

where N is the number of pulses accumulated and τ2s rms =∫ +∞−∞ t2s2r(t)dt/

∫ +∞−∞ s2r(t)dt is the rms duration of signal

sr(t). Substituting (34) and (35) into (25), we can developthe restraint condition of the signal-to-noise ratio (SNR) forambiguous phase resolution, as in (36). The first term in theright-hand side of the inequality is caused by the Doppler phasemeasurement error, and the second one is caused by the Dopplerfrequency measurement error

SNR > 18/π2 + 9T 2r /

(2Nπ2τ2s rms

). (36)

V. EXPERIMENTS AND ANALYSIS

A. Radial Range Estimation With Wideband Radar Data ofTarget With Micromotions

This section intends to validate the algorithm performanceusing the radar measurement data of a cone target with preces-sion, including the extraction of the Doppler phase from thewideband radar and the resolution of ambiguous phase.


Fig. 5. Configuration of cone target with precession and its radarmeasurement.

Fig. 6. Time–frequency representations of K-band radar returns from preces-sion cone.

The precession is a typical kind of micromotions for spacetarget; some details of precession are provided in [19]. A metalcone target is designed to conduct precession, with length of1.4 m and bottom diameter of 0.37 m, as shown in Fig. 5.There are three engines for driving the cone in precessionwith the variable parameters, namely, the angle of precessionα, the cycle of precession T , and the angle θ between theline of radar sight and the precession axis. Radar works withsweep frequency mode operating at X-band (9.5–10.5 GHz,the bandwidth is 1 GHz, and the frequency step is 10 MHz)and K-band (14.5–16 GHz, the bandwidth is 1.5 GHz, and thefrequency step is 15 MHz). The pulsewidth is 100 ms, and thepulse repetition time is 200 ms.

The time–frequency representations of the K-band (14.5–16 GHz) radar returns from the precession cone are shown inFig. 6, with the parameters of α = 2◦, T = 10 s, and θ = 25◦.The results indicate that it is hard to extract the parameters ofmicromotions from the time–frequency representations of radarreturns when the cone conducts small-amplitude micromotionsdue to the low effect of Doppler frequency, interaction ofmultiple signal components induced by multiscatters in thetarget, and limitation of time–frequency resolution.

In order to acquire the characteristic of micromotions, withthe diagram of the proposed method in Fig. 4, the first step isto resolve the different scatters in the target by the sequences of1-D HRRP (K-band with bandwidth of 1.5 GHz), as shown inFig. 7, resolving the head and bottom of the cone. The secondstep is to extract the Doppler phase from peaks in HRRPs,and the final step is to determine the relative radial range

Fig. 7. HRRP sequences (K-band with bandwidth of 1.5 GHz) of cone.

Fig. 8. Relative radial range of corresponding parts of the cone.

of corresponding parts of the cone based on phase resolutionwith the scatter associations, as shown in Fig. 8, where theinitial value of every scatter radial range is zero, indicating thatthe position of the scatter at the instance of the first pulse isconsidered as reference zero position.

The results have demonstrated that the proposed methodcan provide the relative radial range with high precision atthe level of subwavelength, which can estimate the cycles, theamplitudes, and the relative directions of scatters, providing thegreat potential for analyzing the characteristic of micromotions.These experiment results have shown the feasibility of Dopplerphase extraction from wideband radar returns and the validationof ambiguous Doppler phase resolution, and the next experi-ment is conducted to validate the performance of ambiguousDoppler phase resolution under different conditions.

B. Performance Validation of Ambiguous DopplerPhase Resolution

There are two factors that affect the performance of ambigu-ous phase resolution: One is the relative micromotion amplitudeto the wavelength, and the other is the measurement error (i.e.,the effect of SNR).

Let the precession cone (with the parameters of α = 5◦, T =10 s, and θ = 25◦) be measured at X-band with a bandwidthof 1 GHz and K-band with a bandwidth of 1.5 GHz. Thecorresponding radial range curves of every scatter are givenin Fig. 9.

The results have shown that a more stable estimation canbe obtained at X-band than at K-band, which means thatthe proper wavelength (ensures that the radial amplitude of


Fig. 9. Comparison of relative radial range estimation between X- andK-band.

Fig. 10. RMS of the radial range measurement errors of the head underdifferent SNRs.

micromotions is less than the wavelength) rather than shorterwavelength can be considered as candidate. The phase shiftsmore rapidly at high band, and the phase measurement preci-sion will be reduced; therefore, the higher phase measurementerror will eventually cause the instability of the ambiguousphase resolution.

Considering the effect of noise to the proposed method, theX-band radar experiments of the precession cone under SNRvarying from −10 to 40 dB with a step of 0.1 dB are conducted,calculating 100 times at every SNR condition. The RMS ofthe relative radial range estimation errors for the head of thecone is provided in Fig. 10. The experimental result showsthat the conditions of SNR for radar operation should belarger than 17.5 dB to get the expected highly precise relativeradial measurement (i.e., the RMS level of half wavelengthλ/2(0.015 m)). Substituting the parameters of the experimentinto (36), we can get the CRLB of the SNR for ambigu-ous phase resolution SNR > 18/π2 + 9T 2

r /(2Nπ2τ2s rms) =5.62 dB. This means that there is about 12-dB loss in thereceiver and signal processing unit in the radar system, and thisresult can provide the reference for radar system design andexperimental parameter evaluation when measuring the preciseradial range based on wideband radar phase.

C. Ambiguous Phase Resolution Considering the Influencesof Micro-Doppler Frequency

This section is intended to verify the influence of micro-motion on ambiguous phase resolution, particularly when the

Fig. 11. HRRP (X-band with bandwidth of 1 GHz) of cone.

Fig. 12. Relative radial range estimation of cone at X-band.

Fig. 13. Micro-Doppler frequency of cone in the 58th range bin.

amplitude of micromotion is too large to consider as a measure-ment error. Let the cone with vibration (with the parameters ofT = 2.5 s and amplitude of vibration A = 0.1 m) be measuredby the X-band wideband radar (the bandwidth is 1 GHz withLFM, the pulsewidth is 50 μs, and the pulse repetition time is8 ms), and the sequence of the 1-D HRRP is shown in Fig. 11,which indicates that the strong scatter corresponding to thehead of cone lies around the 58th range bin and the scattercorresponding to the bottom of the cone is hidden because ofthe line of radar sight in the experiments. The relative radialrange estimation of the head is shown in Fig. 12. The cycleestimation fits the scenario well, and the amplitude estimationhas a fair error.

By applying time–frequency representations to the 58thrange bin in the HRRP sequences, the time-varying micro-Doppler frequency of the cone can be obtained, as shownin Fig. 13, and the micro-Doppler frequency can be esti-mated as fd = 20 sin(0.8πt+ 2π/3) by fitting the curve on thetime–frequency plane. Using the ambiguous phase resolutionmethodology considering micromotion effects in (33), i.e., withthe compensation of the phase delta induced by micromotion,the revised relative radial range estimation can be obtained as


Fig. 14. Relative radial range of the cone with the compensation of the micro-Doppler frequency.

shown in Fig. 14, and the cycle and amplitude estimation fitthe scenario well. Comparing the results in Fig. 14 to those inFig. 12, there are obvious differences not only in the amplitudebut also in the shape of the envelope, which means the influenceof the micromotion cannot be ignored.

VI. CONCLUSION

A novel method of precise radial range measurement basedon wideband radar phase has been presented in this paper.This method has the advantage of high precision with rmserror values at subwavelength levels, which could provide thegreat potential to acquire micromotion characteristics. The twotechnical challenges in the method were emphasized, includingthe extraction phase from the wideband radar echoes and theresolution of the ambiguous phase. A comprehensive technicaldiagram was presented for micromotion characteristic synthesisbased on wideband radar phase. The experiments have shownthe capability of high precision measurement and the restraintof some factors, such as the choice of radar wavelength,precision of phase measurement, and SNR. The experimentshave also shown that the extraction phase from the widebandradar needs a relatively simple structure of scatters and theambiguous phase resolution needs a relatively high SNR. Theselimitations are the points that need improvement in our study.

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Yongxiang Liu (M’13) received the B.S. and Ph.D.degrees from the National University of DefenseTechnology (NUDT), Changsha, China, in 1999 and2004, respectively.

He has been with NUDT since 2004 and is cur-rently a Professor with the College of ElectricalScience and Engineering, conducting research onradar target recognition, time–frequency analysis,and micromotions. He was with Imperial CollegeLondon as an Academic Visitor in 2008.

Dekang Zhu received the B.S. degree in communi-cations engineering from Wuhan University, Wuhan,China, in 2009, and the M.S. degree from the Na-tional University of Defense Technology, Changsha,China, in 2011, where he is currently working towardthe Ph.D. degree in electrical engineering.

His research interests lie in the area of radar targetrecognition.

Xiang Li (M’09) received the B.S. degree fromXidian University, Xi’an, China, in 1989, and theM.S. and Ph.D. degrees from the National Universityof Defense Technology (NUDT), Changsha, China,in 1995 and 1998, respectively.

He is currently a Professor with NUDT, wherehe researches on automatic target recognition, signaldetection, and nonlinear signal processing.

Zhaowen Zhuang received the B.S. and M.S. de-grees from the National University of Defense Tech-nology (NUDT), Changsha, China, in 1981 and1984, and the Ph.D. degree from Beijing Institute ofTechnology, Beijing, China, in 1989.

He is currently a Professor and the Deputy Headof NUDT. His research interests lie in the area ofartificial intelligence and target recognition.

micromotion characteristic acquisition based on wideband radar phase

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