On-Orbit Signal Processing Procedure for Determining Microwave Radiometer Non-Linearity

Zoubair Ghazi*, Student Member, IEEE, Sayak Biswas, Student Member, IEEE, Linwood Jones, Life Fellow, IEEE, Yazan Hejazin, Student Member, IEEE, and María Marta Jacob2.

Central Florida Remote Sensing Lab Department of EECS

University of Central Florida Orlando, FL 32816-2362

2CONAE – Comisión Nacional de Actividades Espaciales *zoubair@knights.ucf.edu

Abstract— This paper presents a novel signal processing approach used to diagnose non-linear (gain compression) operation of the MicroWave Radiometer (MWR) flown on the Aquarius/SAC-D satellite. This instrument was commissioned in September 2011, and on-orbit observations of blackbody earth emissions (brightness temperatures) have been evaluated over the past year. Results are presented, which suggest that the radiometer system is slightly non-linear, and the resulting receiver gain is a function of the observed radiometric brightness temperature.

Index Terms— receiver non-linearity, Dicke microwave radiometer, MWR, Aquarius.

I. INTRODUCTION The Aquarius/SAC-D satellite was launched on June 10th,

2011. The goal of this joint NASA/Argentine Space Agency (CONAE) science mission is to understand the interactions between ocean circulation and global water cycle by measuring the Sea Surface Salinity (SSS). The prime sensor is the Aquarius microwave radiometer/scatterometer that produces three elliptical antenna footprints on the ground in a cross-track direction (see Fig. 1).

This paper concerns the principal Argentinean remote sensor named MicroWave Radiometer (MWR) on-board the Aquarius/SAC-D satellite. The MWR consists of three separate radiometer receivers, one operating at 23.8 GHz (K-band) H-pol, and two operating at 36.5 GHz (Ka-band) H- & V-pol. Each MWR channel is a Dicke radiometer, which is used to sequentially measure the ocean blackbody noise emission from 8 antenna beams (arranged in two rows of four horns) as shown in Fig.1. For each radiometer a 1x8 antenna switch matrix is used to sample the eight feed horns and feed signals into a time-shared receiver.

II. DICKE MICROWAVE RADIOMETER A microwave radiometer is a very sensitive microwave

receiver with a square-law “power detector”. The desired signal is the average thermal “blackbody emission” (noise power) from the earth’s surface that is captured by the radiometer

antenna. The unit of measure is known as the brightness temperature (Tb), which is defined as:

Tb = <P>/kB (1)

where <P> is the average noise power collected by the antenna, k is Boltzmann’s constant and B is the receiver bandwidth.

The MWR is a 3-state Dicke radiometer [1, 2] and the simplified block diagram is shown in Fig. 2. An important feature of this radiometer is the radiometric calibration cycle, during which two known noise powers (blackbody sources) are input to the receiver and the output voltages are measured. Since the receivers and square-law detector are designed to be linear with input noise power, a two-point calibration is all that is required to define the radiometer linear transfer function that relates the radiometer output voltage to the antenna average input noise power (brightness temperature).

For the MWR the two noise references are: 1) a blackbody waveguide termination at ambient physical temperature and 2) a reverse-biased avalanche noise diode that produces an equivalent “hot” blackbody source. The radiometer uses a microwave (Dicke) switch to alternately sample the noise collected from the antenna, the antenna noise plus the noise diode turned-on, and the ambient reference waveguide termination. These are the 3 radiometer states and the output voltages for each are A/D converted into “rad_counts”.

Fig. 1. MWR and Aquarius measurement geometry.

978-1-4799-0053-4/13/$31.00 ©2013 IEEE

Fig.2 MWR radiometer with internal calibration.

Fig.3 Typical total power radiometer transfer function.

A typical total-power radiometer transfer function is illustrated in Fig.3. The slope of the linear regression line is the receiver power gain, and the offset is the intercept of the linear regression at Tant = 0 K.

For a typical radiometer, the radiative transfer function between the output (digital “rad_counts”) and the input (antenna brightness, Tant) is linear and defined as:

Radcounts = Gain * Tant + offset (2)

Gain= (Radcounts_hot – Radcounts_cold)/( Tbhot - Tbcold) (3)

If the MWR radiometer is linear, then the receiver gain is constant during the 3 Dicke radiometer states and the following equations apply:

Ca = Gain * Tant + offset (4) Cn = Gain * (Tant + Tn) + offset (5) Co = Gain * To + offset (6)

where Ca is the radiometer digital output “antenna counts”, Cn is the “antenna plus noise” counts, Co is the “reference load” counts Co, To is the physical temperature of the reference load, and Tn is the injected noise diode temperature (constant and known). Using equations (4) and (5), we can solve for the gain.

Gain = ( Cn - Ca)/ Tn (7)

Where Cn - Ca is known as the “Noise Diode Deflection” (deflection counts), which should be a constant that is independent of the received antenna noise power (Tant).

On-orbit, the physical temperature of the MWR changes, which causes the radiometer gain to change. Thus, by Eq. (7) the gain is measured using the deflection counts, and by subtracting Eqs (6) and (4), the antenna brightness temperature is

Tant = (Ca – Co)/gain + To

= [(Ca – Co)/( Cn – Ca)]* Tn + To (8)

III. MWR ON-ORBIT OBSERVATIONS Simulated Noise Deflections: For an ideal linear radiometer receiver with a constant gain, the noise diode deflection for both ascending and descending passes would be constant and independent of the radiometer input power (antenna scene Tb). This is illustrated in Fig. 4 as an earth located image of the noise deflection counts for 14 orbits in one day. Here each green line represents the MWR swath coverage (~390 km wide) for 8 antenna beams for one orbit.

Fig.4 Simulated image of noise deflection counts for a linear radiometer

with constant gain.

Under typical on-orbit conditions, the radiometer gain will NOT be fixed because the physical temperature of the receiver will vary cyclically over the orbit period. Since the receiver gain is proportional to 1/Tphys , this causes the noise deflection counts to be above (shown in warm colors) and below (cool colors) the mean value (green color) shown in Fig. 4. The resulting simulated noise deflection for a linear system with a variable gain is plotted in Fig. 5, for the same orbits shown in Fig. 4. Since each orbit undergoes an identical physical temperature cycle, the pattern of noise deflections are the same for each orbit.

Fig.5 Simulated image of an expected noise deflection counts for a linear

radiometer with sinusoidal physical temperature changes.

Observed Noise deflections: Because of the receiver physical temperature variations on-orbit, the observed MWR noise deflections were similar to Fig. 5. However, upon closer inspection, it was discovered that all three receivers exhibited an anomalous behavior that was correlated with the antenna scene Tb. This is illustrated in Fig. 6 for the 36.5 GHz H-pol channel [3], whereby the noise deflection counts decreases abruptly (indicated by cool colors) whenever the antenna temperature transitions from radiometrically cold oceans to hot land. Note for both ascending and descending revs, the noise deflection counts depends upon the instrument physical temperature orbital cycle (as expected) and upon the scene Tb (anomalous performance). Thus, the fact that the noise deflection changes with the scene Tb means that the system is non-linear.

Fig.6 Image of observed noise deflection (Cn - Ca) for 36.5GHz H-pol. Warm colors indicate higher than average noise deflection and cool colors indicate

less than average counts.

To characterize this radiometer non-linearity, we carefully removed the time variable gain (using the stable reference load). Since the reference load temperature was measured, we could normalize the receiver gain over an orbit to make the reference counts constant. Next we divided the noise deflection (Cn – Ca) by this normalized gain, which removed the time varying component of the noise deflection. Finally we cross-correlated the noise deflection counts with the radiometer input Tb in a scatter diagram (Fig. 7). Note that the x-axis is defined in Fig. 2 as the brightness temperature output from the Dicke switch (Tin). Also note that the color is the corresponding scene Tb. The linear regression fit with negative slope indicates that the receiver gain is compressed with increasing Tin.

IV. CHARACTERIZATION OF MWR GAIN NON-LINEARITY Based upon the on-orbit noise deflection described above,

the system gain compression is monotonic decreasing with increasing radiometer input brightness temperature Tin. We can model this receiver gain as

Grecv = Go*g(To)*h(Tin) (9)

Fig.7 Noise diode deflection for MWR 37H radiometer after removing the time-varying component of gain change due to physical temperature. Color is

the scene Tb. where Go is the mean “long term gain”, g(To) is the orbital gain change due to physical temperature (To), and h(Tin) is the gain compression due to variable scene brightness temperature.

As a result, the instantaneous gain for the three Dicke states are different, and become

Ca = Gainrad-ant * Tin-ant + offset (10) Cn = Gainrad-ant * Tin-N + offset (11) Co = Gainrad-ref * Tin-ref + offset (12)

where Gainrad-ant, Gainrad-N and Gainrad-ref are the gains corresponding to the antenna, antenna plus noise and reference states, and Tin-ant, Tin-N and Tin-ref are the receiver input temperatures, respectively. By subtracting equations (10) and (11), the noise diode deflection counts are defined as:

Cn – Ca = Gainrad-N * Tin-N – Gainrad-ant * Tin-ant (13)

Substituting (9) for Gain becomes

Gainrad-ant = Go * g(Tref) * h(Tin-ant) (14)

Gainrad-N = Go * g(Tref) * h(Tin-N) (15)

Gainrad-ref = Go * g(Tref) * h(Tin-ref) (16)

We define g(Tref) as the time-variable orbital gain change due to physical temperature, and a typical example is shown in Fig. 8.

Fig.8 Typical Orbital Gain Change, g(Tref)

After combining the data from the antenna, antenna+noise, and reference load counts, a quadratic regression was applied, to derive the following radiometer transfer function for one orbit:

Rad_counts = -0.000772 * Tin2 + 16.611 * Tin +3272.9 (17)

This is shown in Fig. 9, where the y-axis is the Rad_counts and the x-axis is the full dynamic range that includes Tin-ant and Tin-N . It can be noted from this quadratic regression that the receiver is not linear.

Fig.9 Radiometer Transfer Function for One Orbit

The first derivative of Eq. (17) is:

h(Tin) = -0.0015438 * Tin + 16.611 (18)

This equation represents the radiometer gain compression h(Tin), as shown in Fig. 10, where the x-axis is the full dynamic range of Tin. Note that the gain monotonically decreases (compression) with increasing brightness temperature.

Fig.10 Radiometer Gain Compression

By normalizing the radiometer gain compression to the

peak value, as illustrated in Fig. 11, it can be seen that the

MWR receiver gain is 96% linear, and only 4% is not linear.

Fig.11 Normalized Radiometer Gain Compression

In general, the radiometer gain compression for a single

orbit is defined as:

h(Tin) = ao * Tin + a1 (19)

where ao and a1 are the linear regression coefficients for a single orbit. The following figures show the results for seven MWR orbits.

Fig.12 Radiometer Transfer Function for Seven Orbits

Fig.13 Normalized Radiometer Gain Compression for Seven Orbits

V. CONCLUSION In this paper, an empirical approach is presented to

characterize the slightly non-linear operation of the MWR satellite microwave radiometer. A model of the MWR receiver gain is presented and is evaluated using on-orbit brightness temperature measurements over the Tb range from cold space (2.7 K) to earth surface ~ 300 K. Over this dynamic range of input, the MWR receiver gain compresses in a linear manner. This receiver model accurately captures the dynamic orbital gain changes due to physical temperature (To) and the gain saturation due to the input antenna brightness temperature Tin. Results indicate that at the highest input Tb the receiver gain is compressed by 4%. An investigation is in progress to understand the hardware cause of this problem and to implement a linearization correction at the counts level of the counts-to-Tb algorithm.

VI. REFERENCES [1] Fawwaz T. Ulaby, Richard K. Fung, and Adrian K. Fung; Microwave

remote sensing: active and passive.Volume I, Microwave Remote Sensing Fundamentals and Radiometry, pp. 358-368, Norwood, MA: Artech House, 1981.

[2] Biswas, Sayak K.; Jones, Linwood; Rocca, Daniel; Gallio, Juan-Cruz; , "Aquarius/SAC-D Microwave Radiometer (MWR): Instrument description & brightness temperature calibration," Proc. IEEE Geosci and Rem Sens Symp (IGARSS-2012), pp. 2956-2959, 22-27 July 2012, Munich, Germany.

[3] Biswas, Sayak K. "Brigthness temperature calibration of Aquarius/SAC-D microwave radiometer (MWR)", Dissertation for the degree of Doctor of Philosophy, Univ. Central FL, Spring 2011