waveform-diversity-based millimeter-wave uav sar remote sensing

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 47, NO. 3, MARCH 2009 691

Waveform-Diversity-Based Millimeter-WaveUAV SAR Remote Sensing

Wen-Qin Wang, Member, IEEE, Qicong Peng, and Jingye Cai

Abstract—To integrate a synthetic aperture radar (SAR) intoan operational unmanned airborne vehicle (UAV), it should beas small as possible to meet stringent limitations of size, weight,and power consumption. It appears that the novel combination ofmillimeter-wave frequency-modulated continuous-wave (FMCW)technology and SAR techniques can provide an optimal solution.However, some efficient techniques should be applied to resolverange/Doppler ambiguities in FMCW UAV SAR systems. As such,a technique of waveform-diversity-based millimeter-wave UAVSAR imaging is presented in this paper. Along with the describedsystem concept and signal model, the performance of the diversi-fied waveforms evaluated by their cross correlations is detailed.As the conventional stop-and-go approximation is not valid forFMCW SAR, a modified wavenumber-domain algorithm with aconsideration of continuous antenna motion during transmissionand reception is derived. This imaging algorithm is validated withcomputer simulations. Furthermore, one parallel direct-digital-synthesizer-driven phase-locked-loop synthesizer with adaptivenonlinearity compensation, which has been validated by the exper-imental results, is proposed to obtain a millimeter-wave FMCWsignal with fine frequency linearity.

Index Terms—Frequency-modulated continuous-wave(FMCW) radar, millimeter-wave synthetic aperture radar(SAR), unmanned airborne vehicle (UAV), waveform diversity.

I. INTRODUCTION

SYNTHETIC aperture radar (SAR) has been successfullyused in a variety of applications such as terrain mapping

[1], reconnaissance [2], [3], and environmental monitoring [4];however, the costs associated with existing SAR preclude theiruses in the applications requiring frequent revisits. Hence, thereis a special interest in lightweight, cost-effective, and high-resolution imaging sensors [5], [6]. To be successful, such sen-sors should consume little power and should be small enoughto be mounted on small airborne platforms. Moreover, costeffectiveness is also mandatory. It appears that unmanned air-borne vehicle (UAV) SAR can provide an optimal solution andcould play an essential role in small-scale Earth-observationapplications [7]–[10].

Manuscript received December 2, 2007; revised July 11, 2008 andSeptember 18, 2008. First published January 27, 2009; current version pub-lished February 19, 2009. This work was supported in part by the Open Fundsof the Key Laboratory of Ocean Circulation and Waves, Chinese Academyof Sciences, under Contract KLOCAW0809 and the in part by Beijing KeyLaboratory of Spatial Information Integration and 3S Application, PekingUniversity, under Contract SIIBKL08-1-04.

The authors are with the School of Communication and InformationEngineering, University of Electronic Science and Technology of China,Chengdu 610054, China (e-mail: [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.2008.2008720

However, to integrate a SAR into an operational UAV, strin-gent limitations of size, weight, and power consumption shouldbe satisfied. This is because a small UAV would typicallyhave wingspan length of about 2–4 m, takeoff weight of about30–300 kg, and operational flight altitude between 300 and2000 m [11]. Pulse SAR is not suitable for operation in UAVbecause it is complex and neither cost effective nor compact. Incontrast, frequency-modulated continuous-wave (FMCW) SARrequires only a much lower transmission power [12]. Thus,the combination of millimeter-wave FMCW technology andSAR processing technique can provide a small and lightweightimaging sensor [13].

To integrate FMCW SAR into UAV, another problem is rangeor azimuth ambiguity. Unlike pulse SAR, for FMCW SAR,ambiguous Doppler frequencies are not folded within the samerange resolution cell but is shifted to a nearby resolution cell.Azimuth ambiguities can be reduced by reducing waveformrepetition period but, consequently, creates range ambiguities.Alternatively, range ambiguities can be reduced by employinga waveform with adequate duration to detect the farthest echo,but the corresponding azimuth ambiguities will be introduced.Therefore, range- or azimuth-ambiguity suppression is requiredfor FMCW UAV SAR.

This paper proposes a waveform-diversity-based UAV SARimaging technique. By applying diversified waveform, rangeor azimuth ambiguity can be reduced. The system conceptand signal models are described, and an imaging algorithmis developed. The remaining sections of this paper are orga-nized as follows. Section II describes the proposed waveform-diversity-based FMCW UAV SAR. Along with the describedsystem configuration, the performance of the diversified wave-forms evaluated by their cross correlations is analyzed. Next, awavenumber-domain imaging algorithm that takes into accountthe special characteristics of UAV SAR is derived in Section III,and some computer simulations are performed. As frequencynonlinearities in the transmitted FMCW signal will deterio-rate the imaging performance, Section IV proposes one par-allel direct-digital-synthesizer (DDS)-driven phase-locked-loop(PLL) synthesizer with adaptive nonlinearity compensation toobtain the millimeter-wave FMCW signal with fine frequencylinearity. This paper is concluded in Section V.

II. WAVEFORM-DIVERSITY-BASED FMCW UAV SAR

A. Motivations

It appears that the novel combination of millimeter-waveFMCW technology and SAR technique can lead to a small

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692 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 47, NO. 3, MARCH 2009

Fig. 1. Simplified FMCW SAR block diagram.

sensor that can be integrated into an operational UAV platform[11]. The FMCW principle employed in SAR sensors is basedon the transmission of continuous frequency sweeps. It can bemonostatic, bistatic, or multistatic, depending upon the locationof the receiver in relation to the transmitter [14], [15]. Withoutloss of generality, one monostatic case, in which the transmitterand receiver are placed in the same UAV platform, is assumed inthis paper. As shown in Fig. 1, between transmission and recep-tion, the signal experiences a round-trip delay that is due to theobject distance. For a given target, there is a constant frequencydifference between the transmitted and received signals. Aftermultiplication and filtering, this frequency difference translatesinto a harmonic output signal (a sum for multitarget scenarios inactual FMCW SAR systems). In this way, UAV SAR achievesits high spatial resolution in range direction by utilizing thetransmitted wideband FMCW signals. Similarly, in azimuthdirection, high resolution is obtained by exploiting the relativemotion between the target and the sensor.

However, a fundamental restriction to UAV FMCW SARperformance improvement is the range/azimuth ambiguity. InSAR systems, unambiguous Doppler frequency shift is limitedto be ±1/(2Tp) Hz with Tp as the transmitted chirp duration.For pulse SAR systems, the Tp is usually on an order of 10−6 s;hence, there is no azimuth ambiguity for most airborne pulsedSAR systems. Moreover, range/azimuth ambiguity in pulsedSAR systems can be resolved by applying a staggered pulse-repetition frequency (PRF) [16]. However, for FMCW SARsystems, the Tp is usually on an order of 10−3 s; accordingly,the problem of range or azimuth ambiguity is severe. Therefore,FMCW SAR gives advantages of low-transmit power and highresolution at an expense of limited imaging range and swathcoverage.

B. Waveform Diversity For UAV SAR

To reduce possible range ambiguity for FMCW radar (notFMCW SAR), a three-cell-structure waveform was proposed in[17]. This waveform consists of a linear-frequency-modulation(LFM) section whose duration is chosen to avoid range ambi-guity, followed by a CW transmission that provides an indepen-dent measure of Doppler shift. The target’s range is determinedfrom the difference frequency between the modulated andthe CW sections. This waveform is useful for a point target.However, for distributed targets, it is difficult to identify thetarget corresponding to the measured Doppler shift during the

Fig. 2. Waveform diversity with different chirp waveforms.

second half. Notice that some methods that can be used to detectpoint targets may be useless for imaging radar. It is shown in[18] that there is no range ambiguity for extended targets forup- and down-chirp modulation signals. However, in SAR, anadditional requirement is that the transmitted waveforms shouldbe uncorrelated.

This paper uses diversified chirp waveforms with differentchirp rates, as shown in Fig. 2, to increase unambiguous rangecoverage without decreasing PRF. The chirp duration (in thispaper is same for each chirp) and chirp number are chosenadequately to resolve range ambiguities and maintain the re-quired Doppler resolution, respectively. This idea is to allowthe echoes received from subsequent echoes to fall within thesame range cell. In this way, the received raw data wouldcontain the energy from the whole chirp waveforms. For per-fectly uncorrelated waveforms, the ambiguous signals can besuccessfully suppressed. Once they are separated, successfulmatched filtering can be achieved.

It is well known that the limit of SAR pulse-repetitioninterval (PRI) is given by

PRI >2(Rfar − Rnear)

c0(1)

where c0 is the speed of light, the near and far slant rangesRnear and Rfar, respectively, are related to the swath width Wa

through the incidence angle θi

Wa =Rfar − Rnear

sin θi. (2)

Thus, if N -diversified chirp waveforms are used, the requiredPRI (i.e., chirp duration) for each chirp waveform can berelaxed to

PRI >2Wa sin θi

c0N. (3)

This means that either the PRI can be decreased by the factor Nto yield an increased azimuth resolution or the swath width Wa

increased by the factor N while keeping the PRI unchanged.

C. Correlation Analysis

Practically, a quantity of interest is in the relative levelbetween the correlation of identical (wanted) chirp waveforms

WANG et al.: WAVEFORM-DIVERSITY-BASED MILLIMETER-WAVE UAV SAR REMOTE SENSING 693

and the correlation of different (unwanted) chirp waveforms. Achirp waveform can be represented by the starting frequencyfs, the chirp rate k = Br/Tp (Br is the transmitted signalbandwidth), and the chirp duration Tp. Neglecting amplitude-and carrier-frequency terms, we have

s(t) = rect

(t

Tp

)exp

{jπ[2fst + kt2]

}(4)

with rect as a window function. The possibilities of processingmultiple-chirp waveforms can be investigated by analyzing thecorrelation performance. The correlation function between twosignals x(t) and y(t) is defined as [19]

Rxy(τ) =

+∞∫−∞

x∗(t)y(t + τ)dt. (5)

From (4), we have (where the subscripts i and j relate thequantities to one of two chirp waveforms)

Rsisj(τ)=

+∞∫−∞

s∗i (t)sj(t+τ)dt

=

t2∫t1

exp

[j

π√2

(fsj+kjτ − fsi√

kj−ki

+√

2(kj − ki)t

)2]dt

×exp

[j2πfsj +jπkjτ

2−jπ(fsj +kjτ−fsi)2

kj−ki

]

(6)

where t1 and t2 denote the integration limits.Denoting

γ(t) =fsj + kjτ − fsi√

kj − ki

+√

2(kj − ki)t (7)

there is

dγ =√

2(kj − ki)dt. (8)

Accordingly, (6) can be further simplified into

Rsisj(τ) =

exp[j2πfsj + jπkjτ

2 − jπ(fsj+kjτ−fsi)

2

kj−ki

]√

2(kj − ki)

×γ(t2)∫

γ(t1)

exp

(j

√2π

2γ2

)dγ (9)

with

γ(t2)∫γ(t1)

exp

(j

√2π

2γ2

)dγ =C (γ(t2)) + jS (γ(t2))

−C (γ(t1)) − jS (γ(t1)) (10)

where C(γ) and S(γ) denote the Fresnel integrals defined as

C(γ) + jS(γ) =

γ∫0

exp(+j

π

2γ2

)dγ. (11)

Equation (10) can then be used to determine the correlationperformance between any two chirp waveforms. Fig. 3 showsdifferent combinations of chirp rates and starting frequencies.The influence of different starting frequencies (fs1 = 0 Hz,fs2 = 0 Hz, fs3 = 250 MHz, fs4 = 500 MHz, fs5 = 1 GHz)and equivalent chirp rate (k1 = k2 = k3 = k4 = k5 =5 · 1011Hz/s) is shown in Fig. 3(a). It is obvious that R14(τ)shows the highest cross-correlational suppression, and R12

shows the lowest cross-correlational suppression. The influenceof different starting frequencies (fs1 = 0 Hz, fs2 = 0 Hz,fs3 = 250 MHz, fs4 = 500 MHz, fs1 = 1 GHz) and inversechirp rates (k1 = −k2 = −k3 = −k4 = −k5 = 5 · 1011Hz/s)is shown in Fig. 3(b). It is obvious that R14(τ) shows thehighest cross-correlational suppression, and R12 shows thelowest cross-correlational suppression, because in additionto a reduced maximum R14(τ), it falls off rapidly for τ �= 0.The influence of different chirp rates (k1 = 5 · 1011Hz/s,k2 = k1/2, k3 = −k1/2, k4 = k1/4, k5 = −k1/4) andequivalent starting frequencies (fs1 = fs2 = fs3 = fs4 =fs5 = 0 Hz) is shown in Fig. 3(c). R13(τ) gives the smallestmaximum but with the widest occupied time; R12(τ)gives the narrowest occupied time but with the biggestmaximum. The influence of different starting frequencies(fs1 = 0 Hz, fs2 = 0 Hz, fs3 = 250 MHz, fs4 = 500 MHz,fs5 = 500 MHz) and different chirp rates (k1 = 5 · 1011Hz/s,k2 = k1/2, k3 = k1/2, k4 = k1/2, k5 = −k1/2) is shown inFig. 3(d). It is obvious that both R14(τ) and R15(τ) give highercross-correlational suppression than R12(τ) and R13(τ). ForUAV SAR imaging, a quantity of importance is the relativelevel between the correlation of identical chirp waveformsand the correlation of different chirp waveforms. Hence, thechirp waveforms with high cross-correlational suppression aredesired.

From Fig. 3, it is deduced that the chirp waveforms withadjacent starting frequency and inverse chirp rate can provide agood cross-correlational suppression; hence, it is possible to usean arbitrary number of chirp waveforms that are having goodcross-correlational performance, provided that they occupy ad-jacent or nonoverlapping frequency bands. Note that, if theecho is Doppler shifted, this is also true because Doppler effectbrings an equivalent frequency shift. However, using an adja-cent starting frequency means wider total radio-frequency (RF)bandwidth and more complexity for the SAR hardware system.From a practical point of view, we consider that practical UAVSAR system should use the chirp waveforms with equal chirpduration and equal absolute of chirp rate |ki| = |kj | (i and j

denote any two chirp waveforms) so as to reduce the complexityof hardware system and make the imaging performance beingindependent of the chirp parameters used for the actual chirp.Therefore, three typical chirp waveforms, as shown in Fig. 4,are used in this paper. From (4) and (9), we can get

Rab(τ) =Rba(τ)

= rect

[|τ |Tp

]sin [π(fsb − fsa + kτ)Tp]

π(fsb − fsa + kτ)

× exp {jπ [(fsb−fsa)Tp+(fsb+fsa)τ +2kTpτ ]}(12)


Fig. 3. Correlation between different combinations of chirp rates and starting frequencies. (a) Different starting frequencies (fs1 = 0 Hz, fs2 = 0 Hz, fs3 =250 MHz, fs4 = 500 MHz, fs5 = 1 GHz) and equivalent chirp rate (k1 = k2 = k3 = k4 = k5 = 5 · 1011Hz/s). (b) Different starting frequencies (fs1 =0 Hz, fs2 = 0 Hz, fs3 = 250 MHz, fs4 = 500 MHz, fs1 = 1 GHz) and inverse chirp rates (k1 = −k2 = −k3 = −k4 = −k5 = 5 · 1011Hz/s). (c) Differentchirp rates (k1 = 5 · 1011Hz/s, k2 = k1/2, k3 = −k1/2, k4 = k1/4, k5 = −k1/4) and equivalent starting frequencies (fs1 = fs2 = fs3 = fs4 = fs5 =0 Hz). (d) Different starting frequencies (fs1 = 0 Hz, fs2 = 0 Hz, fs3 = 250 MHz, fs4 = 500 MHz, fs5 = 500 MHz) and different chirp rates (k1 =5 · 1011Hz/s, k2 = k1/2, k3 = k1/2, k4 = k1/2, k5 = −k1/2).

Rac(τ) =Rca(τ)

=exp

[j2πfsc + jπkτ2 − jπ (fsc−fsa+kτ)2

k

]2√

k× [C (γ(tj))+jS (γ(tj))−C (γ(ti))−jS (γ(ti))]

(13)Rbc(τ) =Rcb(τ)

=exp

[j2πfsc + jπkτ2 − jπ (fsc−fsb+kτ)2

k

]2√

k× [C (γ(tj))+jS (γ(tj))−C (γ(ti))−jS (γ(ti))]

(14)

Rbb(τ) = rect

[|τ |Tp

]sin [πkaτ(Tp − |τ |)]

πkaτ× exp [jπ(2fsa + kaTp)τ ] . (15)

As an example, assuming that the following parame-ters ka = kb = 5 · 1011Hz/s, kc = −5 · 1011Hz/s, Ba = Bb =

Bc = 500 MHz, fsa = −250 MHz, fsb = 0 Hz, and fsc =250 MHz, the corresponding cross correlation between anytwo chirp waveforms is shown in Fig. 5. It is obvious thatthe autocorrelation Raa shows a higher peak than the cross-correlational peaks. The results show that, if the chirp wave-forms with |ki| = |kj | and different starting frequencies areused, for UAV SAR, their echoes can be separated duringsubsequent signal processing. Thereafter, matched filtering canbe applied successfully. To describe this process, we suppose atransmitted down-chirp signal

sdw(t) = rect

[t

Tp

]exp[−jπkt2]. (16)

Matched filtering this down-chirp signal with its referencefunction

Gdw(f) = exp[−jπ

f2

k

](17)


Fig. 4. Example waveform diversity with different chirp waveforms.

yields

runamb(t) = exp(−jπ

4

)√kT 2

p sinc[πkTpt]. (18)

However, for the up-chirp signal

sdw(t) = rect

[t

Tp

]exp[−jπkt2] (19)

matched filtering it with the reference function Gdw(f) willyield

ramb(t) =12

rect

[t

2Tp

]exp

(−jπ

k

2t2

). (20)

Comparing (18) and (20), we can see that the diversifiedchirp waveforms can be separated with an appropriate filter.Therefore, although the total imaged scatterers contribute to thereceived signal in UAV SAR, the chirp signals can be separatedand fused with their different cross and autocorrelations. Thatis to say, the specific chirp signal can be extracted with itsautocorrelations. Next, the desired chirps can be fused with theextracted specific chirp signals. Hence, after chirp separationand data fusion, they can be coherently combined into the rawdata for the unambiguous region, which can then be processedwith one uniform-image-formation algorithm.

III. IMAGE-FORMATION ALGORITHM

In pulse SAR imaging algorithms, it is often assumed that theradar platform is stationary during transmission and receptionof a pulse. In contrast, in FMCW SAR system, the radar iscontinuously transmitting; consequently, the platform cannot beconsidered being stationary during transmission and reception;hence, range change during transmission and reception shouldbe accounted for. A modified range-Doppler algorithm hasbeen proposed for FMCW SAR imaging in [20], in whichthe continuous antenna motion is compensated by modifyingthe range-migration compensation. However, as commented in[21], one disadvantage is the need of interpolation in perform-ing additional range-cell-migration correlation. Another disad-vantage is the required secondary range compression, whichcannot be easily incorporated because of its azimuth-frequency

Fig. 5. Correlation results for different combination of chirp waveforms.

dependence. To get around these disadvantages, a wavenumber-domain algorithm that takes into account the special character-istics of continuous antenna motion is derived in this section.

A. Signal Models

Without loss of generality, starting with the up-chirp signal[the definitions are the same as in (4)]

si(t) = rect

[t

Tp

]exp

[jπ(2fsit + kt2)

](21)

where fsi denotes the starting frequency. The received signalis mixed with the transmitted signal, and the mixer outputfrequency is proportional to the echo delay time τi and, hence,to the target range, i.e.,

sir(t)= rect

[t−τi

Tp

]exp

[−jπ

(2fsiτi+2kτit − kτ2

i

)](22)

where the time delay τi is determined by τi = 2Ri(μ)/c0 withμ as the slow time in azimuth and Ri(μ) as the slant range.Hence, the phase term of (22) is represented by

φi(t, μ)=−4πfsi

c0Ri(μ) − 8πkt

c0Ri(μ) +

8πk

c20

R2i (μ) (23)

where the first term denotes the phase independent of thefast time t, the second term denotes the phase term contain-ing the scatterer’s position information, the last term denotesthe unwanted residue video phase (RVP) which should becompensated.

Substitute (23) into (22), Fourier transforming in t-directionyields

Sir(fir, μ) = Tpsinc

[Tp

(fir +

2kRi(μ)c0

)]exp

×[−j2π

(2fsi

c0Ri(μ)+

2k

c20

R2i (μ)+

4fir

c0Ri(μ)

)](24)


Fig. 6. Signal models with RVP removal and range-deskew operation.

where fir is directly related on a chirp-to-chirp basis to therange direction to the target. To remove the RVP, multiplying(24) with

(25)Sic(fir) = exp(−j

πf2ir

k

)(25)

and applying an inverse Fourier transform, we can get

Sird(t, μ)= rect

[t

Tp

]exp

[−j

4πk

c0

(t+

fsi

k

)Ri(μ)

]. (26)

This is known as RVP removal and range-deskew operation, asshown in Fig. 6 [22].

In a like manner, for the down-chirp waveform, we canobtain similar results. After signal separation and data fu-sion, they can be processed with one uniform-image-formationalgorithm.

B. Imaging Algorithm

To derive an imaging algorithm, we write the UAV SAR slantrange as

R(x) = R′(x) + Rd(x) (27)

where x is defined by x = vsμ, R(x) is the measured range tothe target, and R′(x) is the actual range to the target

R′(x) =√

R20 + (x − Xt)2 (28)

where R0 and Xt denote the range to the target at μ = 0and the target position in azimuth, respectively, and Rd is the

TABLE ISIMULATION PARAMETERS

range shift due to the Doppler frequency shift which can berepresented by [20]

Rd(fd) =Tp

B

c0

2fd =

c0fd

2k(29)

with fd as the Doppler frequency shift.Hence, from (27), we can represent the phase history by

ϕ(x) =4πk

c0

(t +

fs

k

)[R′(x) + Rd(x)] (30)

with fs as the start frequency.Let

kr =4πk

c0

(t +

fs

k

)(31)

from the principle of stationary phase, we can get

ϕ(kx, kr) = −kxXt −√

k2r − k2

xR0 − krRd. (32)

Applying a phase-compensation function

ϕcp(kx, kr) = krRd +√

k2r − k2

xRr (33)

with Rr as the reference range, we have

U(kx, kr) = exp{−j

[kxXt +

√k2

r − k2x(R0 − Rr)

]}.

(34)

Denote

ky = k2r − k2

x (35)Yt =R0 − Rr. (36)

Equation (34) can then be represented by

U(kx, ky) = exp [−j(kxXt + kyYt)] . (37)

Thereafter, the FMCW SAR images can be reconstructed byapplying a 2-D inverse Fourier transform to (37).

In summary, the focusing of FMCW UAV SAR proceeds asfollows [23]:

1) range compression;2) multiple-chirp waveforms separation and fusion with

their different cross and autocorrelations;3) RVP removal and range-deskew operation;4) Fourier transform in azimuth direction;5) phase compensation in wavenumber domain.6) interpolating;7) 2-D inverse Fourier transform;8) focused UAV SAR images.


Fig. 7. Comparative magnitudes of range slice of processed point-targetimage between without and with the consideration of continuous antennamotion.

C. Simulation Results

To evaluate the performance of the derived image-formationalgorithm, stripmap FMCW UAV SAR data from a point targetare simulated using the parameters listed in Table I, which aresimilar to the FMCW SAR demonstrator system designed in[20]. The FMCW SAR sensor is carried on an UAV movingat constant speed in a straight line. Continuous antenna motionwill bring additional range shift. This range shift can be seen asadditional range migration. To avoid distinct range and azimuthbroadening, this range migration should be kept lower thanhalf the range resolution. If not, the continuous antenna motionwill cause an additional quadratic phase error in the azimuthprocessing.

Fig. 7 shows the comparative magnitudes of the range re-sponse between without and with the consideration of con-tinuous antenna motion. Note that the comparative results areobtained by using the conventional frequency-scaling algorithm[24] without compensating continuous antenna motion and thewavenumber-domain algorithm described earlier. It validatesagain that the continuous antenna motion results in a smallrange shift. Fig. 8 shows the comparative magnitudes of theazimuth response between without and with the considerationof continuous antenna motion. We notice that the continuousantenna motion results in a small loss of peak power. Thepoint-target response quality can be evaluated by the peaksidelobe ratio (PSLR). An additional quality parameter is theintegrated SLR (ISLR). The processed PSLR and ISLR areshown in Table II. The results show that the effect of continuousantenna motion in this case is very small and negligible. Similarphenomenon has been stated in [20] and [25], which concludedthat the effect of continuous antenna motion is negligible forthe velocities lower than 120 m/s.

Generally speaking, the flying speed of UAV is lower than120 m/s. However, the compensation of the Doppler frequencyshift caused by continuous antenna motion may be necessaryfor some high-speed UAV SAR systems. For instance, near-space UAV SAR [26], the cruise speed of near-space UAV can

Fig. 8. Comparative magnitudes of range slice of processed point-targetimage between without and with the consideration of considering continuousantenna motion.

TABLE IIPSLR AND ISLR IN RANGE AND AZIMUTH: CASE A DENOTES THE

PROCESSING RESULTS WITHOUT THE CONSIDERATION OF CONTINUOUS

ANTENNA MOTION, CASE B DENOTES THE PROCESSING RESULTS

WITH THE CONSIDERATION OF CONTINUOUS ANTENNA MOTION

fly at a speed as high as 1000 m/s [27]. In this case, rangeresponse will migrate through several range cells due to therelative big additional Doppler frequency shift, and correspond-ing compensation processing is required. Moreover, it shouldbe aware that continuous antenna motion may bring seriouseffects for ultrahigh-resolution FMCW SAR imaging even if ata low velocity. As the range shift caused by continuous antennamotion can be seen as additional range migration, we cancompensate it like range-migration correction. An importantattribute of the wavenumber-domain algorithm for SAR imag-ing is its ability to completely compensate severe range migra-tion inherent in conventional imaging algorithms [28]. Fromthis point, it is anticipated that wavenumber-domain imagingalgorithm can successfully process the FMCW SAR carriedon high-speed UAV platform; however, for the conventionalimaging algorithms such as range-Doppler and frequency scal-ing, compensating continuous antenna motion requires someadditional processing steps.

IV. WAVEFORM GENERATION

To achieve high range resolution, FMCW UAV SAR needsmillimeter-wave FMCW signals with large bandwidth. If fre-quency nonlinearities are present, the cheap and simple dechirp-on-receive technique cannot be used successfully. Otherwise,frequency nonlinearities will deteriorate the range resolution.Consequently, the beat frequency corresponding to a giventarget is not constant, as shown in Fig. 9. Several poten-tial solutions have been proposed. The use of a predistorted


Fig. 9. Dechirp-on-receive FMCW SAR with frequency nonlinearities.

Fig. 10. Generation of FMCW signals with nonlinearity compensation.

voltage-controlled-oscillator (VCO) voltage to generate anLFM signal was investigated in [29], where a measurement ofthe VCO voltage-frequency characteristic is required. However,as VCO dynamic behavior, particularly in modulated frequency,typically differs from the static case, a sequence of static-frequency measurements is usually not sufficient. Practically,there is relative lack of practical nonlinearity-compensationtechnique for wideband LFM frequency synthesizers, particu-larly for millimeter-wave FMCW SAR applications, and somenew approaches should be developed.

We proposed a full-coherent configuration of parallel DDS-driven PLL synthesizer with the output frequency range from33.5 to 35.5 GHz, as shown in Fig. 10. As one DDS has limited-output bandwidth, parallel DDSs are used. By continuouslyincreasing the input DDS phase increment, a wideband LFMsignal with good frequency nonlinearity can be synthesizedfrom the parallel DDS-based synthesizer. Thereafter, it is fur-ther upconverted to millimeter wave by one triple-tuned PLLsynthesizer [30]. Practically, some other factors may result inunwanted frequency/phase nonlinearities. These system non-linearities will change during data collection. To resolve thisproblem, we apply an iterative algorithm to real-time compen-sate the possible system nonlinearities.

To describe this technique, we rewrite the frequency of LFMsignal as

F [u(t)] = F0 + Au(t) + E [u(t)] = fc + kt. (38)

It can be further changed into

u(t) = − 1A

E [u(t)] +1A

(fc + kt)

= − 1A

E [u(t)] + v0(t) (39)

with v0(t) = (fc + kt)/A. Denoting u0(t) = v0(t), we canrepresent (39) by{

u0(t) = v0(t)un(t) = −E[un−1(t)]

A + v0(t).(40)

As there is

limn→∞

un(t) = u(t) (41)

we then have

un(t) = − 1A

E[un−1] + v0(t) +1A

E [un−2(t)]

− 1A

E [un−2(t)]

=un−1(t) −1A

E [un−1(t) − un−2(t)]

=un−1(t) − Δun−1(t), n = 1, 2, 3, . . . (42)

with{Δun−1(t)=1

A{E[un−1(t)−un−2(t)]}=1A{Fn−1(t)−Fn−2(t)}

Δu0(t)=F0(t)−kt−fc.(43)

To obtain Δun(t), the output of the mixer D is convertedinto digital signal by an analog-to-digital converter, then theiterative algorithm described earlier is applied. Next, the es-timated tuning voltage is converted into analog signal by andigital-to-analog converter and used to tune the VCO outputfrequency. In this way, possible frequency nonlinearities canbe adaptively compensated by tuning the VCO voltage. Toevaluate this nonlinearity-suppression approach, we have madean experiment with our designed frequency synthesizer. Fig. 11shows the performance of output phase noise in the frequencyrange from 33.5 to 35.5 GHz. The results show that consistentperformance of low phase noise in wideband case is obtainedby applying this approach.

V. CONCLUSION

Millimeter-wave UAV SAR will play an important role infuture small and low-cost high-resolution remote-sensing appli-cations. This paper proposes one system model of waveform-diversity-based millimeter-wave FMCW UAV SAR imaging.Along with the described system concept and signal model,the diversified waveform is evaluated by their correlation per-formances, and a modified wavenumber-domain algorithm that


Fig. 11. Experimental results of the output performance of phase noise in thefrequency range from 33.5 to 35.5 GHz.

takes into account the special characteristics of UAV SARis described. Moreover, to obtain a millimeter-wave FMCWsignal with fine frequency linearity, a parallel DDS-drivenPLL synthesizer with adaptive nonlinearity compensation isdesigned. The originality of this paper lies in the combination ofwaveform-diversity technique and millimeter-wave technologyfor UAV SAR imaging including parallel DDS-driven wave-form generation. This approach is suitable for lightweight, cost-effective, and high-resolution imaging sensors. Note that it isequally relevant to other aircraft imaging sensors, e.g., near-space SAR, and not just UAV SAR.

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Wen-Qin Wang (M’08) received the B.S. degreein electrical engineering from Shandong University,Shandong, China, in 2002 and the M.S. degree inelectrical engineering from the University of Elec-tronic Science and Technology of China (UESTC),Chengdu, China, in 2005. From 2005 to 2007, heworked toward the Ph.D. degree in the NationalKey Laboratory of Microwave Imaging Technology,Chinese Academy of Sciences, Beijing, China.

Since September 2007, he has been with theSchool of Communication and Information Engi-

neering, UESTC. His current interests include bistatic SAR, microwave imag-ing and inversion, and nonlinear signal processing.


Qicong Peng received the B.S. degree fromTsinghua University, Beijing, China, and the M.E.degree from the University of Electronic Science andTechnology of China (UESTC), Chengdu, China.

He is currently a Full Professor with the Schoolof Communication and Information Engineering,UESTC. His research interests include real-time sig-nal processing, communication signal processing,and DSP technology.

Jingye Cai received the B.S. degree from SichuanUniversity, Sichuan, China, in 1983 and the M.E.degree from the University of Electronic Science andTechnology of China (UESTC), Chengdu, China,in 1990.

He is currently a Full Professor with the Schoolof Communication and Information Engineering,UESTC. His research interests include communica-tion and radar signal processing, frequency synthe-sis, RF and wireless systems, and spectra estimation.

waveform-diversity-based millimeter-wave uav sar remote sensing

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