interferometric microwave radiometers for high-resolution imaging of the atmosphere brightness...

INTERFEROMETRIC MICROWAVE RADIOMETERS FORHIGH-RESOLUTION IMAGING OF THE ATMOSPHERE BRIGHTNESS

TEMPERATURE BASED ON THE ADAPTIVE CAPON SIGNALPROCESSING ALGORITHM

HYUK PARK, JUNHO CHOI, VLADIMIR KATKOVNIK and YONGHOON KIM∗Sensor System Laboratory, Department of Mechatronics, Kwangju Institute of Science and

Technology, 1 Oryong-dong, Buk-gu, Gwangju, Korea(∗ author for correspondence, e-mail: [email protected], [email protected])

Abstract. Passive microwave remote sensing from satellites and ground stations has contributeduniquely, and substantially, to the study of atmospheric chemistry, meteorology, and environmentalmonitoring. As user requirements are raised, in terms of the accuracy and the spatial resolution, amechanically scanning radiometer, with a real aperture, becomes impractical due to the requirementfor a very large antenna size. However, an aperture synthesis interferometric radiometer presents avaluable alternative. The work presented in this paper was devoted to high spatial resolution imaging,using the 37 GHz band interferometric radiometer, developed by ourselves. The spatially adaptiveCapon beamforming method was exploited for the imaging, which outperformed the conventionalFourier Transform method. We concluded that the high spatial resolution imaging of the brightnesstemperature of the atmosphere could be accomplished with an interferometric radiometer equippedwith the developed Capon beamforming imaging algorithm.

Keywords: brightness temperature, Capon beamforming, interferometric radiometer

1. Introduction

Passive microwave remote sensing is a technique that provides information aboutan observed field of view (FOV) based on its microwave band radiation. All matterradiates electromagnetic energy, and microwave radiometers are able to measurethese low levels of radiation in the microwave region (Ulaby, 1981, p. 12). Theintensity of radiation emitted by objects in a scene is characterized as the bright-ness temperature. From brightness temperature measurements, a scene image canbe reconstructed due to the different brightness temperatures of different objects.Therefore, it is possible to establish useful relationships between the power re-ceived by the radiometer and the specific terrestrial or atmospheric parameters ofinterest. Due to this useful property, radiometers have been used for the followingvarious applications (Chang, 2000, p. 320):

Environmental Monitoring and Assessment 92: 59–72, 2004.© 2004 Kluwer Academic Publishers. Printed in the Netherlands.

60 HYUK PARK ET AL.

1. Monitoring earth environments: ocean, land surface, water, clouds, wind,weather, forest, vegetation, soil moisture, desert, flood, precipitation, snow,iceberg, pollution, and ozone etc.

2. Exploring resources: water, agriculture, fisheries, forestry, and mining etc.3. Transportation application: mapping road networks, land and aviation scen-

arios, analyzing urban growth, and improving aviation and marine servicesetc.

4. Military application: surveillance, mapping, weather, and target detection andrecognition etc.

With air environmental monitoring especially, it is essential to gather data, suchas temperature, pressure, wind speed, the distribution of water vapor, clouds, andother active constituents. Such data enable to test the existing models of the atmo-sphere’s energy balance, the depletion of the ozone layer, the hydrological cycle,climate trends, and other aspects of the atmospheric system. Furthermore, they arealso indispensable for formulating new and better models in the future (Janssen,1993). Microwave radiometry is central to this effort because it is one of the mostefficient ways of obtaining the full spatial and temporal perspective needed to un-derstand atmospheric processes. Various atmospheric data are measured efficientlyin all-weather conditions using microwave radiometers.

As the applications of radiometers increases, the user requirements, in termsof the accuracy and the spatial resolution, are raised. These requirements are ex-tremely difficult to achieve, especially with respect to the high spatial resolutionbecause these measurements are constrained by the antenna size. Consequently, itis almost impossible to meet the resolution requirements of modern user using asingle antenna radiometer system.

However an aperture synthesis interferometric radiometer presents a valuablealternative, in terms of the high spatial resolution to fulfill the user requirements.An interferometric radiometer uses a receiver, consisting of a number of antennaswith a wide beam; and indirectly generates an image by measuring the cross-correlation of the radio frequency (RF) signals received by pairs of spatially sep-arated antennas with overlapping FOV (Ruf et al., 1998). The cross-correlationmeasurements, which are referred to by radio astronomers as the visibility function,are interpreted as the Fourier transform of the brightness temperature distributionover the FOV.

The work in this paper was devoted to the high-resolution imaging of the atmo-spheric brightness temperature using an interferometric radiometer. In Section 2,the hardware design of a 37 GHz band radiometer for monitoring of the atmo-spheric environment is discussed. The observation equation of the interferometricradiometer is derived in Section 3, with the array beamforming scheme employedfor imaging. The spatially adaptive Capon method was developed to estimate thebrightness temperature. The imaging performance of this method was evaluatedand compared with the conventional inverse Fourier Transform method.

HIGH-RESOLUTION IMAGING OF THE ATMOSPHERE BRIGHTNESS TEMPERATURE 61

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2. Radiometer System

The developed experimental radiometer employs single-sideband dual intermediatefrequency (IF) superheterodyne receivers, which were used in order to obtain thehigh image selectivity, sensitivity and stability of the system. The receiver wascomposed of an RF front-end, IF and low frequency (LF) units, two local oscillators(LO), a calibration unit, an A/D converter and software based I/Q demodulator, anda complex correlator. The RF center and IF were equal to 37 and 1.95 GHz, respect-ively. The LF frequency and equivalent noise bandwidth were 80 and 96.65 MHz,respectively. The RF center frequency of 37 GHz is one of the window bandsappropriate for the measurement of the water vapor and temperature profile of theatmosphere. The receiver had less than 4.2 dB noise figure, which was calculatedby the Y-factor method, and the receiver’s gain could be adjusted from 60 to 80 dB.Overall, the receiver was designed to achieve low noise figure, high stability and agood gain-phase balance of the two channels. The system block diagram is shownin Figure 1.

2.1. RF FRONT-END

The RF front-end consisted of two stage low noise amplifiers; the coupled lineimage rejection filter, the isolator and the single balanced mixer (see Figure 1).The coupled line image rejection filter was designed to have an image selectivitygreater than 15 dB in the image band. A 20 dB isolator was inserted between thecoupled line image rejection filter and the mixer. This isolator minimizes the offsetsgenerated by the correlation of the receiver noises, and improved the voltage stand-ing wave ratio (VSWR). The receiver noises were radiated and coupled throughthe antennas. The isolator at the local port was inserted to provide a high isolationbetween the two channels to reduce the channel interference (Camps et al., 2000).

2.2. IF AND LF UNIT

The IF and LF unit consisted of Low Noise Amplifiers (LNA), band-pass filters, amixer, two low-pass filters and an attenuator to adjust the gain and provide a lowVSWR (see Figure 1). Five stages of IF LNAs provide a suitable gain to the A/Dconverter. The two band-pass filters with center frequencies of 1.95 and 79.6 MHznoise bandwidths were inserted for channel selection, with an image frequencyrejection above 40 dB in the image band. An LF frequency of 80 MHz was selectedto satisfy the sampling frequency (f < 250 MHz) of the A/D converter.

2.3. LO UNIT

A coherent signal generator was used to provide the LO signal in this system. Thepower divider was designed accurately in order to provide an in-phase local signalbetween the two channels. The in-phase and equal gain injection was required to


Figure 2. Block diagram of the software based I/Q.

remove the gain and phase errors generated by the local input (Torres et al., 1997).A high isolation was also required in order to reduce the channel interference andresidual offset error generated by the local oscillator (Camps et al., 2000; Toress etal., 1997).

2.4. I/Q DEMODULATOR AND COMPLEX CORRELATORS

The software based I/Q demodulator and complex correlator were developed fora 37 GHz demonstration model. The diagram of the algorithm used for the I/Qdemodulation and correlation is shown in Figure 2. The I/Q demodulator couldbe used together with various A/D sampling frequencies. It was also possible tochange the integration time of the correlator.

64 HYUK PARK ET AL.

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3. Image Reconstruction

3.1. ARRAY OBSERVATION MODEL FOR THE INTERFEROMETRIC

RADIOMETER

This work started from the observation equation for a two-dimensional planararray. The wave propagation scenario is illustrated in Figure 3. The m antennaswere distributed on the sensor plane, with the positions [(λu1, λv1) (λu2, λv2) . . .

(λum, λvm), where λ denotes the wavelength of the incident radiation. The directionof arrival (DOA) of a signal, sk(t), were defined as θk (elevation angle) and ϕk

(azimuth angle). If the first antenna located at (λu1, λv1) is selected as a referencepoint, the model of the two-dimensional array antenna output, under the far-fieldand narrowband assumptions, has the following form (Stoica et al., 1997; Johnsonet al., 1993; Naidu, 2001):

y(t) =n∑

k=1

a(θk, ϕk)sk(t) + e(t)

a(θk, ϕk) = [1 au2v2(θk, ϕk). . .aumvm

(θk, ϕk)]T

aucvc(θk, ϕk) = exp[j2π(uc cos ϕk + vc sin ϕk) sin θk] for c = 1, 2, . . ., m

(1)

where y(t) is the antenna output vector, e(t) the additive noise vector, the super-script ‘T ’ denotes the transpose of the vector, and n is the total number of signalsources. (uc, vc) denotes the coordinates of the c-th antenna position, given inwavelengths, λ, relative to the position of a reference antenna (u1, v1). a(θk, ϕk)is the steering vector, which gives the phase of each antenna’s outputs relative tothe phase of the signal at the reference antenna.

3.2. ARRAY POWER MODEL OF THE INTERFEROMETRIC RADIOMETER

Generally, the measurements of an interferometric radiometer are modeled by thefollowing formula (Camps, 1996; Ruf et al., 1998):

V (�u,�v) =∫ ∫

ξ+η2≤1T (ξ, η) exp[j2π(�uξ + �vη)]dξdη , (2)

where (�u,�v) = (up − uq, vp − vq ) is the spacing between two antennas, inwavelengths, ξ and η are the direction angles linked with the angles θ and ϕ,according to the equations ξ = cos ϕ sin θ and η = sin ϕ sin θ . T (ξ, η) denotesthe brightness temperature, and V (�u,�v) the visibility function. This termino-logy originates from radio astronomy. Equation (2) shows that the interferometricradiometer generates an image by measuring the visibility function, V (�u,�v),

66 HYUK PARK ET AL.

which is the cross-correlation of the signals received by the two spatially separatedantennas.

In this section, the basic measurement for Equation (2) was derived using thearray observation model (1). Assuming the input signals, sk(t), are incoherent,narrowband, and random spatially independent:

E{sk(t)} = 0, E{sk(t)s∗l (t)} = 0, if k �= l

E{|sk(t)|2} = σ 2(θk, ϕk)

(3)

where ‘∗’ denotes the complex conjugate, and E{·} the mathematical expectation.The correlation between the outputs of any pair of antennas, without the noise, isgiven as

Ry(up − uq, vp − vq) = E{yt(up, vp)y∗t (uq, vq)}

=n∑

k=1

exp[j2π{(up − uq) cos ϕk + (vp − vq) sin ϕk} sin θk]σ 2(θk, ϕk)

=n∑

k=1

exp[j2π(�uξk + �vηk)]σ 2(ξk, ηk).

(4)

The correlation in Equation (4), can be interpreted as the two-dimensional FTof the distribution of the signal power, σ 2(ξk, ηk), where �u,�v are the spatialfrequencies. Furthermore, assuming that the numbers of signal sources are denselyincreased in the FOV, the integral form of the power model of the interferometricradiometer can be achieved:

R(�u,�v) =∫ ∫

ξ2+η2≤1σ 2(ξ, η) exp[j2π(�uξ + �vη)]dξdη . (5)

Comparing Equations (2) and (5), they can be seen to be identical since the sig-nal power distribution, σ 2(ξ, η), in Equation (5) has the same meaning as thebrightness temperature, T (ξ, η), in Equation (2), and the correlation, R(�u,�v),in Equation (5) has the same meaning as the visibility function, V (�u,�v), inEquation (2).

3.3. IMAGE RECONSTRUCTION

The observed visibility function, V (�u,�v), in Equation (2) is the FT of thebrightness temperature, T (ξ, η), so the brightness temperature is estimated by the


inverse FT of the visibility function (Camps, 1996). The discrete form of imagereconstruction by this FT method is:

T̂ (ξ, η) =1

K

∑p

∑q

W(�up, �vq)V (�up,�vq) exp{−j2π(�upξ + �vqη)} ,(6)

where K is a proper constant, and W(�up,�vq ) the weight function used todecrease the sidelobes (Camps, 1996). In Equation (6), the point spread function(PSF) is defined by (Camps, 1996):

PSFFT (ξ, η) = 1

K

∑p

∑q

W(�up,�vq) exp{−j2π(�upξ + �vqη)} . (7)

This PSF is the system’s impulse response, that is, the response of the system to atemperature distribution given as a delta function. It is also called the array factor(AF).

The Capon method proposed in this paper was derived from the array obser-vation model (1). In order to estimate the brightness temperature distribution, thebeamforming (spatial filtering) scheme was exploited. After measuring the signalin the array, the spatial filter, h(ξ, η), was applied to the antenna output, y(t), inorder to form a beam:

yF =m∑

k=1

h∗kyk(t) = h∗y(t) (8)

where yF is a filter output and ‘∗’ for the vectors indicates the Hermitian transpose.For the Capon beamforming method, the filter weights, h, are obtained from the

following optimization problem (Stoica et al., 1997):

minh

h∗Rh subjected to h∗a(ξo, ηo) = 1 (9)

where R = E{y(t)y∗(t)} is the covariance matrix of the antenna output, and denotesthe desired DOA. This technique minimizes the contribution of the undesired inter-ferences, by minimizing the output power, while maintaining a constant gain alongthe desired DOA. The solution of Equation (9) gives:

h(ξo, ηo) = R−1a(ξo, ηo)

a∗(ξo, ηo)R−1a(ξo, ηo)

, (10)

with the estimation of the signal power, σ̂ 2(ξo, ηo), as:

σ̂ 2(ξo, ηo) = E{|yF |2} = E{∣∣h∗y∣∣2} = h∗Rh = 1

a∗(ξo, ηo)R−1a(ξo, ηo)(11)

68 HYUK PARK ET AL.

Thus, according to Equation (11), the brightness temperature, T̂ (ξo, ηo) =σ̂ 2(ξo, ηo), is reconstructed by the Capon method. In the actual imaging, the covari-ance matrix R is replaced by some estimate, such as R̂ = 1/

N∑N

t=1 yk(t)y∗k (t) =

h∗y(t), where N denotes the number of observations (Stoica et al., 1997). It isemphasized that the Capon filter weight, h(ξo, ηo), contains the data dependentterm R−1. This is the reason the Capon method is referred as an adaptive method.

3.4. PERFORMANCE ANALYSIS BASED ON THE POINT SPREAD FUNCTION

(PSF)

The imaging performance of the interferometric radiometer is greatly related tothe PSF. The PSF of a narrow main beam and low sidelobes shows higher res-olution and better image quality than the PSF of a wide main beam and highsidelobes. Therefore, the imaging performances of the FT and Capon methods canbe analyzed using their PSFs.

In contrast to the FT method, the PSFs of the Capon method are very difficult toobtain in an analytical form because the filter weight, h(ξo, ηo), contains the datadependent term R−1. Some results, however, can be derived for the simple caseof a single point-wise signal source of the power σ 2(ξk, ηk). Assuming the noise,e(t), to be spatially white, with the same power, σ 2

noise, for all the antennas, thecovariance matrix, R, of the antenna outputs can be expressed as follows:

R = E{y(t)y∗(t)}

= a(θk, ϕk)a∗(θk, ϕk)σ2(θk, ϕk) + σ 2

noiseI

= σ 2(θk, ϕk)

(a(θk, ϕk)a∗(θk, ϕk) + σ 2

noise

σ 2(θk, ϕk)I)

= σ 2(θk, ϕk)R̃

R̃ =(

a(θk, ϕk)a∗(θk, ϕk) + σ 2noise

σ 2(θk, ϕk)I)

(12)

where I denotes the identity matrix. The inverse of R is:

R−1 = 1

σ 2(θk, ϕk)R̃−1 . (13)

Then the power given by the Capon method, Equation (11), can be rewritten as:

σ̂ 2(ξo, ηo) = 1

a∗(ξo, ηo)R̃−1a(ξo, ηo)σ 2(ξk, ηk) . (14)


Figure 4. Performance comparison between the FT method and Capon method (SNR = 5).

From Equation (14), the PSF of the Capon method, for a single point-wise source,can be defined as:

PSFcapon(ξo, ηo, SNRk) = 1

a∗(ξo, ηo)R̃−1a(ξo, ηo)

R̃−1 = (a(ξk, ηk)a∗(ξk, η+ 1SNRk

I)−1

(15)

where SNRk = σ 2(θk, ϕk)/σ 2

noise denotes the signal to noise ratio. The perform-ance comparison between the FT and Capon methods can now be achieved by theanalysis of this PSF.

The PSF of the interferometric radiometer depends on the array type, the num-ber of antennas, and the antenna spacing etc. It is known that the Y-shaped arrayshows higher spatial resolution than the rectangular type of array for the FT method(Camps, 1996). In this paper, the analysis for this Y-shaped array was performedwith 37 antennas and a 0.5λ spacing between consecutive antennas. The 0.5λ spa-cing was employed in order to avoid the alias effect in the reconstructed images.The calculated results are illustrated in Figure 4. The antenna plane of the Y-shaped

70 HYUK PARK ET AL.

Figure 5. Cross section of PSF of FT method and Capon method (SNR = 0.5).

array is given in Figure 4a. Figures 4c and d are the contour plots of the PSFs for theFT and Capon methods, respectively. These contour lines are plotted from –20 dBto 0 dB with a 2 dB spacing. Figure 4b shows the cross section of the PSF for thetwo methods. The PSF of the Capon method was calculated for an SNRk = 5.As shown in Figure 4b, the adaptive Capon method shows a significantly narrowermain beam than the FT method. Moreover, the sidelobes of the Capon method aremuch lower than the sidelobes of FT method. Therefore, the Capon method has abetter imaging ability when a signal is radiated from a single point-wise source.

The Capon method is an adaptive, data-dependent method, so the imaging per-formance varies with the value of SNRk. In particular, the performance of theCapon method becomes worse as the SNRk changes from 5 to 0.5. In Figure 5, thecross section of the PSF, which was calculated for an SNRk = 0.5, is illustrated.As compared with Figure 4b, the main beam of the Capon PSF was wider and thesidelobes higher. This reveals that the imaging performance of the Capon methoddegrades as the SNRk decreases.

However, even when degraded, the main beam for the Capon method, SNRk =0.5, was still narrower than that of the FT method. The imaging simulation resultsare shown in Figure 6. Compared with the FT imaging, Figure 6b, the Capon


Figure 6. Imaging simulation of the FT and the Capon algorithm (with 37 antenna Y-shaped array).

imaging, Figures 6c and d, resolves the target squares better. The result of theimaging simulation is in agreement with the PSF comparisons in Figures 4 and 5.

4. Conclusions

The aperture synthesis interferometric radiometer allows us to obtain high-spatialresolution imaging of an observed brightness temperature distribution. This pa-per has presented the hardware design and image reconstruction algorithm for aninterferometric radiometer at the 37 GHz frequency band for atmospheric applic-ations. The design of the test model under development has been presented. Asthe image reconstruction method, an adaptive Capon beamforming algorithm wasdeveloped. The study shows that the Capon method demonstrates a better perform-ance, in terms of the quality of the PSF, as well as for point-wise objects, than theconventional Fourier Transform method. We conclude that high spatial resolutionimaging of the atmosphere brightness temperature could be accomplished with theinterferometric radiometer when coupled with the developed Capon beamformingimaging method.

72 HYUK PARK ET AL.

Acknowledgement

This work was supported, in part, by the Korea Science and Engineering Founda-tion (KOSEF), through the Advanced Environmental Monitoring Research Centerat Kwangju Institute of Science and Technology (K-JIST) and the InternationalCollaboration Program with the Center for Space Science and Applied Research(CSSAR), funded by MOST.

References

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Camps, A., Corbella, I., Torres, F., Bara’, J. and Capdevila, J.: 2000, ‘RF interference analysis inaperture synthesis interferometric radiometers: Application to L-band MIRAS instrument’, IEEETrans. Geosci. 38, 942–950.

Chang, K.: 2000, RF and Microwave Wireless System, John Wiley & Sons, pp. 320.Janssen, M. A.: 1993, Atmospheric Remote Sensing by Microwave Radiometry, John Wiley & Sons.Johnson, D. H. and Dudgeon, D. E.: 1993, Array Signal Processing: Concepts and Techniques,

Prentice Hall.Naidu, P. S.: 2001, Sensor Array Signal Processing, CRC Press.Ruf, C. S., Swift, C. T., Tanner, A. B. and Le Vine, D. M.: 1998, ‘Interfermetric synthetic aperture

microwave radiometry for the remote sensing of the earth’, IEEE Trans. Geosci. 26, 597–611.Stoica, P. and Moses, R. L.: 1997, Introduction to Spectral Analysis, Prentice Hall, pp. 230.Torres, F., Camps, A., Bara’, J. and Corbella, I.: 1997, ‘Impact of receiver errors on the radiometric

resolution of large two-dimensional aperture synthesis radiometers,’ Radio Sci. 32, 629–647.Ulaby, F. T., Moore, R. K. and Fung, A. K.: 1981, Microwave Remote Sensing, Vol. I, Artech House,

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