IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 2, APRIL 2009 229

Improvement of a Doppler-RadiometerUsing a Sparse Array

Hyuk Park, Student Member, IEEE, and Yong-Hoon Kim, Member, IEEE

Abstract—A 2-D Doppler-radiometer has been proposed toimprove the poor angular resolution of microwave radiometers,using aperture synthesis on a moving platform. In this letter,we investigate drawbacks of the Doppler-radiometer, which havenot been discussed previously in detail. The imaging method isrevised to be suitable for imaging of distributed sources, whichis the more common situation than a point source, and then thespecklelike sidelobes in the point source response are discussed. Indistributed source imaging, the specklelike sidelobes in the pointsource response of the Doppler-radiometer severely degrade theimaging performance, so it is necessary to reduce them. The causeof specklelike sidelobes is discussed, and a sparse array is proposedto improve the imaging performance of the Doppler-radiometer.The improvement is demonstrated by simulation of the pointsource response, showing reduced speckle.

Index Terms—Interferometry, radiometry, sparse arrays,synthetic aperture imaging.

I. INTRODUCTION

A PERTURE synthesis has been used to improve the an-gular resolution achievable by microwave radiometers.

A large aperture is synthesized by using interferometric tech-niques with an antenna array composed of many elementaryantennas. It has been reported that high-resolution imaging canbe achieved with a much smaller number of antennas (only twoor three) by using platform motion. There have been severalstudies of aperture synthesis with platform motion, includingthe supersynthesis radiometer [1]–[8] and the RADSAR [9],[10]. The most recent and detailed study presented a Doppler-radiometer using 2-D imaging with an analysis of point sourceresponse and spatial resolution [11], [12].

This letter focuses on a problem of the Doppler-radiometer,which has not been discussed in detail to date. The problem isa kind of speckle (or specklelike artifacts) of the point sourceresponse, shown in Fig. 4(a) in [11]. Although the artifacts canbe removed by median filtering, as shown in Fig. 4(b) in [11],they severely degrade the imaging performance of the Doppler-radiometer, particularly in case of distributed source imaging.In other words, median filtering may be effective for pointsource imaging, but it does not work for imaging of distributedsources that is the more common case for remote sensing.

Manuscript received July 18, 2008; revised September 5, 2008 andOctober 15, 2008. First published January 20, 2009; current version publishedApril 17, 2009. This work was supported in part by KICOS through a Grantprovided by the Korean Ministry of Education, Science and Technology inK20701010357-07B0100-10710 and in part by the Brain Korea Program(BK21) at the Gwangju Institute of Science and Technology, Korea.

The authors are with the Department of Mechatronics, Gwangju Institute ofScience and Technology, Gwangju 500-712, Korea (e-mail: yhkim@gist.ac.kr).

Digital Object Identifier 10.1109/LGRS.2008.2010630

Fig. 1. Observation scenario of the Doppler-radiometer. The size of anelementary antenna footprint is 2Lx by 2Ly ; y denotes the center point of afootprint along the y-axis.

It is, therefore, required to reduce the specklelike artifacts ofDoppler-radiometer imaging.

This letter investigates a problem of the Doppler-radiometerand discusses a method to improve it. First, the observationand imaging are modeled for a distributed source, which is notdescribed in [11]. The models show some differences betweena point source and distributed sources. The cause of speckleis then investigated based on spatial frequency coverage ofthe Doppler-radiometer. Finally, a sparse array is proposed toimprove the imaging performance. The improvement is demon-strated by simulating its point source response, as comparedwith that of a three-antenna Doppler-radiometer.

II. IMAGING OF THE DOPPLER-RADIOMETER

A. Observation/Imaging Model

The observation scenario is shown in Fig. 1. The antennasare mounted on a platform at a height z = H0 that moves alongthe x-axis at a constant speed va. Moving along the x-axis, theantennas observe a brightness source at (xo, yo) from positionsranging from x = −xi, at time t = −ti, to x = xi, at time t =ti, with an antenna tilt angle in the cross-track direction of θ.

The image is formed by matched filtering the signals receivedby antennas with proper delay lines to compensate for thepropagation delay, focusing the source during the observation.

1545-598X/$25.00 © 2009 IEEE

230 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 2, APRIL 2009

For a point source, the response of the baseline k − l (with thekth and the lth antenna) is presented in [11, Eq. (A1.1)]. Fordistributed sources, it is given by

Vkl(xo, yo) =C

2ti

ti∫−ti

y+Ly∫y−Ly

vat+Lx∫vat−Lx

T (x, y) |Fn(t;x, y)|2

×r(Δτ)ej2πf0Δτdxdydt (1)

where f0 is the center frequency of the radiometer; T (x, y) de-notes the modified brightness temperature given by [TB(x, y) −Tph]/ cos θi(x, y; t), where TB(x, y) is the brightness tempera-ture of the source at (x, y), and Tph is the physical temperatureof the receivers (the so-called “Corbella term”). The obliquityfactor is given by cos θi(x, y; t), where θi(x, y; t) is the sourceincidence angle. The obliquity factor is approximately constantwhen the incidence angle does not vary significantly duringthe observation, which is the case for the Doppler-radiometerobservation. The constant C is equal to kBΩpix/Ωant, where kis Boltzmann’s constant, B is the receiver noise bandwidth, andΩpix/Ωant is the beam filling factor.

The antenna beam pattern and fringe-washing function aremodeled as the same as in [11], i.e., Fn(t;x, y) = exp{−(y −y)2/2L2

y} exp{−(x − vat)2/2L2x}, and r(t) = exp(−πB2t2),

respectively. The delay error Δτ is given by

Δτ(t;x, y;xo, yo) = {rk(t;x, y) − rk(t;xo, yo)−rl(t;x, y) + rl(t;xo, yo)} /c (2)

where c is the speed of light, rk(t;x, y) is distance be-tween the source at (x, y) and the kth antenna at time t.

The delays τk(t;xo, yo)Δ= rk(t;xo, yo)/c and τl(t;xo, yo)

Δ=rl(t;xo, yo)/c are adjusted so that the baseline k − l measure-ment is focused on the source at (xo, yo), and the signals col-

lected by antennas with the propagation delays of τk(t;x, y) Δ=rk(t;x, y)/c and τl(t;x, y) Δ= rl(t;x, y)/c have the delay errorof Δτ , except the focused pixel at (xo, yo) that has Δτ = 0during the observation. Note that the model of the baselineresponse in (1) is not the same as that in [11, Eq. (A1.1)],because (1) is modeled for distributed sources.

After some mathematical manipulation, we can express (1)similar to an equivalent array factor (AF) representation

Vkl(xo, yo)=

y+Ly∫y−Ly

vati+Lx∫−vati−Lx

T (x, y)AFkl(xo−x, yo−y)dxdy

(3)where

AFkl(xo − x, yo − y) =C

2tie− (y−y)2

L2y

×ti∫

−ti

e− (x−vat)2

L2x e−πB2Δτ2

ej2πf0Δτdt. (4)

In (4), AFkl cannot be called yet the equivalent AF becauseit is a model of a single baseline. After assembling all of thebaseline responses, it can be called the equivalent AF.

Note the similarity between (4) and the baseline response[11, Eq. (A1.1)]. The equivalent AF in synthetic aperture ra-diometers represents the system’s point source response, andthe baseline response [11, Eq. (A1.1)] is modeled for thepoint source condition. The two equations, therefore, becomeidentical when TB0 = 1 in [11, Eq. (A1.1)].

Now, we discuss the method of brightness estimation, orhow to assemble each of the baseline responses, which changesfor the imaging model of distributed sources. In [11], thegeometric mean of the two baseline responses was proposedfor the brightness estimation, i.e., the brightness estimation in[11] can be expressed using the definitions in this letter as (5),shown at the bottom of the page. However, the geometric meancan be used only for the case of point source imaging. Forthe distributed source model, the geometric mean of the twobaseline responses is

√Vkl(xo, yo)Vkm(xo, yo)

=

⎡⎢⎣⎧⎪⎨⎪⎩

y+Ly∫y−Ly

vati+Lx∫−vati−Lx

T (x, y)AFkl(xo−x, yo−y)dxdy

⎫⎪⎬⎪⎭

×

⎧⎪⎨⎪⎩

y+Ly∫y−Ly

vati+Lx∫−vati−Lx

T (x, y)AFkm(xo−x, yo−y)dxdy

⎫⎪⎬⎪⎭

⎤⎥⎦

12

�= T (xo, yo)√

AFkl(0, 0)AFkm(0, 0). (6)

In (6), the last inequality changes to an equality only if theobserved brightness image T (x, y) is a point source, i.e.,

T (x, y) ={

T (xo, yo), if (x, y) = (xo, yo)0, otherwise.

Consequently, a different method of brightness estimation isrequired for the imaging of distributed sources.

The baseline response (3) is not the same as the visibility.Although it is the result of a cross correlation, the Doppler-radiometer compensates the propagation delay by insertingadjustable delay lines before the cross correlation. The baselineresponse (3), therefore, is equivalent to a weighted average ofthe brightness temperatures of the focused pixel observed usinga single baseline, i.e.,

Tkl(xo, yo)Δ= Vkl(xo, yo) (7)

where Tkl(xo, yo) means the estimation of the brightness tem-perature of the source at (xo, yo) using a baseline k − l. Then,the brightness can be estimated (or the baseline responses can

T (xo, yo)Δ=

√Vkl(xo, yo)Vkm(xo, yo) = T (xo, yo)

√AFkl(xo − x, yo − y)AFkm(xo − x, yo − y) (5)

PARK AND KIM: IMPROVEMENT OF A DOPPLER-RADIOMETER USING A SPARSE ARRAY 231

be assembled) using a weighted sum of all of the baselineresponses

T (xo, yo)Δ=

∑i

Wi · Ti(xo, yo) (8)

where Wi denotes the weight of the response of the ith baseline(often it is a window), and i is the index of each baseline. Theresulting equivalent AF AFeq is then obtained by inserting (3)into (8)

T (xo, yo)

=∑

i

Wi ·y+Ly∫

y−Ly

vati+Lx∫−vati−Lx

T (x, y)AFi(xo − x, yo − y)dxdy

=

y+Ly∫y−Ly

vati+Lx∫−vati−Lx

T (x, y)∑

i

Wi ·AFi(xo − x, yo − y)dxdy

=

y+Ly∫y−Ly

vati+Lx∫−vati−Lx

T (x, y)AFeq(xo − x, yo − y)dxdy (9)

where

AFeq(xo − x, yo − y) =∑

i

Wi · AFi(xo − x, yo − y).

(10)

B. Spatial Frequency Coverage of the Doppler-radiometer

In the previous section, the observation and imaging weremodeled for distributed sources, but the specklelike artifactshave not been discussed. We will now examine them basedon an analysis of spatial frequency coverage (often referredto as the (u, v) coverage in the literature on synthetic apertureradiometry) because the (u, v) coverage determines the imag-ing performance. The spatial frequencies u and v are given bythe baseline antenna spacing divided by the wavelength whenthe platform motion is not considered. However, u and v aredifferent for the Doppler-radiometer because the phase term inthe baseline response depends on time t and the position of thesource (xo, yo) as well as the antenna spacing Dkl. For aperturesynthesis with motion, the instantaneous spatial frequency attime t is given by [1]

ukl(t;xo, yo)

=

√x2

o + y2o + H2

0

λ

∂ {rk(t;xo, yo) − rl(t;xo, yo)}∂xo

=

√y2

o + H20

λ

{vatyoDy,kl −

(y2

o + H20

)Dx,kl

}(v2

at2 + y2o + H2

0 )3/2(11)

vkl(t;xo, yo)

=

√x2

o + y2o + H2

0

λ

∂ {rk(t;xo, yo) − rl(t;xo, yo)}∂yo

=

√y2

o + H20

λ

{−vatyoDx,kl −

(v2

at2 + H20

)Dy,kl

}(v2

at2 + y2o + H2

0 )3/2

(12)

Fig. 2. Spatial frequency coverage of a three-antenna Doppler-radiometer.

where Dx,kl = Dkl cos α and Dy,kl = Dkl sinα denote theantenna spacing between the kth and the lth antennas alongthe x-axis and the y-axis, respectively, and the baseline angleα denotes the angle between the baseline and the x-axis; thesecond equalities in (11) and (12) hold for xo = 0.

Fig. 2 shows instantaneous spatial frequency coverage of athree-antenna Doppler-radiometer under the following observa-tion scenario: platform height H0 = 800 km, antenna tilt anglein the cross-track direction θ = 45◦, antenna spacing D12 =D13 = 20λ, baseline angle α = ±45◦, elementary antennahalf-power beamwidth BWx = 20◦ along-track and BWy =30◦ cross-track, corresponding footprint 2Lx = 960 kmand swath width 2Ly = 1000 km, receiver center fre-quency f0 = 1.4 GHz, and noise bandwidth B = 20 MHz.Therefore, the platform observes the brightness source at(xo, yo) = (0, 800) km from −xi = −480 km(= −Lx) to+xi = +480 km(= +Lx).

As shown in Fig. 2, a baseline with large spacing coversonly the outer range (high spatial frequency region) of the(u, v) plane, not sampling the low spatial frequency region.This causes the specklelike artifacts in the point source re-sponse of the Doppler-radiometer. These artifacts are a kindof sidelobes induced by spatial undersampling. In the three-antenna Doppler-radiometer in [11], since the baseline lengthis very large (339 λ), it can cover only a very high-frequencyregion of the (u, v) plane. As a result, sidelobes of the pointsource response arise as a very sharp beam, and they appearas a specklelike artifacts. The high sidelobes of the Doppler-radiometer are well revealed in the resulting equivalent AF,shown in Fig. 3. These sidelobes degrade the imaging perfor-mance severely, and therefore, a modified scheme is requiredfor the Doppler-radiometer.

III. DOPPLER-RADIOMETER WITH A SPARSE ARRAY

Since the specklelike sidelobes of the Doppler-radiometer re-sponse are caused by undersampling, it is required to cover thespatial frequency plane sufficiently in order to reduce them. Thesimplest scheme is to use a uniform antenna array satisfying theNyquist criterion, i.e., antenna spacing smaller than half of awavelength. However, this scheme gives up the main advantage

232 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 2, APRIL 2009

Fig. 3. Simulation result of the equivalent AF of the three-antenna Doppler-radiometer under the same observation scenario as for Fig. 2.

of the Doppler-radiometer, which is that reduces the number ofantennas.

Instead of the uniform array, aperture synthesis with plat-form motion, including the Doppler-radiometer, can employ thesparse array configuration because the (u, v) coverage is nota point, but a curve. As the platform moves, the visibility issampled not at individual points alone, but along a curve, thelength of which increases with antenna spacing, as shown inFig. 2. The number of antennas, therefore, can be reduced byincreasing the antenna spacing to achieve the required lengthof the (u, v) curve. This is the main advantage of aperturesynthesis using platform motion.

For a sparse array configuration, some array types canbe considered, including a rectangular, a triangular, and aY-shaped. Among them, we have studied a T-shaped array inorder to improve the imaging performance of the Doppler-radiometer. The sparse T-shaped array studied is shown inFig. 4, which is configured so that the maximum antennaspacing is 20 times the wavelength (20 λ) in order to becompared with the configuration simulated in Figs. 2 and 3. Theset of values for diagonal baseline are the following: Dn = λ ×{1, 2, 3.54, 4.96, 7.09, 9.92, 14.18, 20}, and the diagonal base-line angle is α = ±55◦. Correspondingly, the antenna positionsalong the x-axis and y-axis are determined by AXn = Dn cos αand AUn = Dn sin α, respectively.

Although this array design is not ideal, it covers the (u, v)plane efficiently to some extent. The (u, v) coverage of theproposed array is shown in Fig. 5, which is obtained underthe same observation scenario as in Fig. 2. The set of Dn andα values was determined to make the (u, v) coverage by adiagonal baseline approximately a continuous line. Under theseconditions, the length of diagonal baselines is determined by

Dn−1 ≈Dn/1.41 if n ≥ 4

D1 =λ, D2 = 2λ. (13)

Fig. 4. Configuration of the sparse T-shaped array; AXn, AUn, and ALn

denote the positions of elementary antennas along the x-axis, the positivey-axis, and the negative y-axis, respectively; Dn denotes the antenna spacingbetween AXn and AUn (or ALn).

Fig. 5. Spatial frequency coverage of the sparse T-shaped array. Each curveof (u, v) coverage becomes longer with antenna spacing.

As shown in Fig. 5, the (u, v) coverage by the diagonalbaselines is nearly continuous, and the proposed array coversthe (u, v) plane much better than the three-antenna Doppler-radiometer. This improved (u, v) coverage results in the im-provement of the point source response. As shown in Fig. 6,the specklelike sidelobes are reduced substantially. The pixelsize at −3 dB is 81 km along the x-axis and 115 km along they-axis. The beam efficiency is calculated to be 26.8% at −3 dBand 74.6% at −10 dB.

PARK AND KIM: IMPROVEMENT OF A DOPPLER-RADIOMETER USING A SPARSE ARRAY 233

Fig. 6. Simulation result of the equivalent AF of the sparse T-shaped array.Contour levels are at −3, −6, and −10 dB.

IV. DISCUSSION

A. Drawbacks of the Doppler-radiometer

Previous realizations of the Doppler-radiometer imaginghave some drawbacks; they are effective only for point sourceimaging, and specklelike sidelobes degrade the imaging per-formance. In this letter, it has been shown that the previousimaging method, the geometric mean, has difficulty in imagingdistributed sources, and the weighted sum was proposed asan alternative. With respect to the specklelike sidelobes, theDoppler-radiometer had been demonstrated using only two orthree antennas with very large antenna spacing as was com-monly used in previous studies on aperture synthesis with mo-tion, for example, 1000 λ for the supersynthesis [1] and 339 λfor the Doppler-radiometer [11]. For these configurations, it isvery difficult to achieve an acceptable image since a baselinewith large spacing covers only high spatial frequencies inthe (u, v) plane. This means that the low spatial frequencyregion cannot be sampled by using only two or three antennaswith large spacing, and the high sidelobes are induced as aconsequence.

In summary, previous aperture synthesis using platform mo-tion is not capable of covering the (u, v) plane appropriately,and therefore, the image is degraded seriously. On the otherhand, the sparse T-shaped array introduced in this letter is ca-pable of covering the (u, v) plane better than previous systems,and consequently, the specklelike sidelobes in the point sourceresponse are reduced, as shown in Fig. 6.

B. Future Work

Several considerations are discussed in [11] regarding thepractical implementation and limitations of the Doppler-radiometer system. Additionally, the following topics are to bestudied further.

1) Array design: It is required to design an optimal ar-ray configuration for the Doppler-radiometer observa-tion scenario; it should cover the (u, v) plane widely,

homogeneously, and efficiently with as few antennas aspossible. In addition to the T-shaped array, various arrayconfigurations should be studied in a systematic way suchas a rectangular, a triangular, and a Y-shaped array.

2) Windowing method: Although covering the plane to someextent, it is inevitable for the Doppler-radiometer tosample sparsely. As shown in Fig. 5, the proposed arraycannot yet cover the (u, v) plane perfectly, and this causessidelobes and reduced beam efficiency. In the simulationresult shown in Fig. 6, the beam efficiency of the sparseT-shaped array is still not large enough to meet the high-performance requirements in remote sensing, althoughit is an improvement upon previous realizations of theDoppler-radiometer. A weighting (windowing) has theapparent effect of reducing the sidelobes, and thereforea method of widowing should be studied for the Doppler-radiometer, including the selection of an appropriatewindow.

V. CONCLUSION

This letter has presented drawbacks of the Doppler-radiometer and proposed a method to improve them. The imag-ing method was modified to be suitable for distributed sources,and the cause of the specklelike sidelobes was identified basedon the analysis of spatial frequency coverage. Through thisletter, it was shown that the three-antenna Doppler-radiometerwith long baselines provides only poor sampling of the spatialfrequency domain and, consequently, the high sidelobes arise.An improved sparse array was presented, showing simulationresults of the improved point source response.

REFERENCES

[1] K. Komiyama, “High resolution imaging by supersynthesis radiometers(SSR) for the passive microwave remote sensing of the Earth,” Electron.Lett., vol. 27, no. 4, pp. 389–390, Feb. 1991.

[2] K. Komiyama, “Supersynthesis radiometer for passive microwave imag-ing,” in Proc. IGARSS, 1992, vol. 2, pp. 1417–1419.

[3] K. Komiyama, Y. Kato, and T. Iwasaki, “Indoor experiment oftwo-dimensional supersynthesis radiometer,” in Proc. IGARSS,Aug. 1994, vol. 3, pp. 1329–1331.

[4] K. Komiyama and Y. Kato, “Characteristics of the baseline off-nadirangle of supersynthesis radiometer,” in Proc. IGARSS, May 1996, vol. 2,pp. 875–877.

[5] K. Komiyama, Y. Kato, and K. Furuya, “Interpretation of brightness tem-perature retrieved by supersynthesis radiometer,” in Proc. IGARSS, 1997,vol. 1, pp. 481–483.

[6] K. Komiyama, “Preliminary experiment of one-dimensional imaging bymicrowave supersynthesis radiometer,” in Proc. IGARSS, 1998, vol. 3,pp. 1708–1710.

[7] K. Komiyama, “Field imaging experiments by a prototype super-synthesisradiometer,” in Proc. IGARSS, 2000, vol. 7, pp. 2991–2993.

[8] K. Komiyama, R. Shioya, T. Morioka, Y. Kakimi, and T. Nukariya, “Aprototype of super-synthesis radiometer for field imaging experiments,”in Proc. IGARSS, 2000, vol. 2, pp. 871–873.

[9] C. Edelsohn, “Synthetic array radiometry,” in Proc. IGARSS, 1992, vol. 2,pp. 1429–1431.

[10] C. Edelsohn, “Applications of synthetic aperture radiometry,” in Proc.IGARSS, Aug. 1994, vol. 3, pp. 1326–1328.

[11] A. J. Camps and C. T. Swift, “A two-dimensional Doppler-radiometer forEarth observation,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 7,pp. 1566–1572, Jul. 2001.

[12] H. Park, Y.-H. Kim, and A. Camps, “Correction to ‘a two-dimensionalDoppler radiometer for Earth observation’,” IEEE Trans. Geosci. RemoteSens., vol. 45, no. 12, p. 4194, Dec. 2007.