Soil Moisture (SM) and Sea Surface Salinity (SSS) may seem to be unconnected, but both variables are intrinsically linked to the Earth's water cycle and the climate system. Thanks to the technological advances, the interest of the scientific community in remotely measuring SSS and SM has increased in the last years, spending much effort in this direction. The three current and planned Earth observation missions focused in these variables are: the MIRAS instrument aboard the SMOS mission of the European Space Agency (ESA) launched on November 2, 2009 [1], the Aquarius radiometer from National Aeronautics and Space Administration (NASA) aboard the Satelite de Aplicaciones Cientificas (SAC-D) spacecraft of the Comisión Nacional de Actividades Espaciales (CONAE) [2] launched on June 10, 2011, and the Soil Moisture Active and Passive (SMAP) mission of NASA [3] to be launched in 2014. All three missions carry an L-band microwave radiometer as primary instrument. A microwave radiometer is an instrument that measures the spontaneous electromagnetic radiation emitted by all bodies at a physical temperature different from 0 Kelvin. Microwave radiometers were first used in radio-astronomy in the 1930s [4]. In [5] the Passive Advanced Unit for ocean monitoring (PAU) project was proposed aiming at demonstrate that collocated measurements of sea brightness temperature and reflected Global Navigation Satellite System Reflectrometry (GNSS-R) signals can result in a significant improvement of the retrieved SSS. Its scientific goals are to perform ocean monitoring by passive remote sensing to improve the knowledge of the relationship of the GNSS-R signal with the sea state, and to improve the knowledge of the relationship between the L-band brightness temperature and the sea state. To accomplish these goals, the PAU sensor consists of three instruments that operate in a synergetic way:

an L-band radiometer to measure the brightness temperature,

The PAU project is also a test-bed of new technological demonstrators such as real aperture radiometers with digital beamforming and polarization synthesis [7], fully-digital synthetic aperture radiometers, etc. To perform this, a ground-based instrument demonstrator PAU-SA has been designed, implemented, and tested to validate these possible improvements. This work is organized as follows: in order to understand better these improvements, some basic concepts on interferometric radiometry are reviewed in Section 2. The interested reader is referred to [8,9] for a detailed review. Section 3 provides an overview of the PAU-SA instrument, and describe in detail the instrument itself. Section 4 describes briefly the processing steps of the PAU-SA data. The interested reader is referred to [10] for more details. Section 5 presents an comparison between the PAU-SA and the MIRAS instruments to illustrate which improvements and new techniques have been implemented and tested, and their rationale. Finally, Section 6 presents some measurements performed, and Section 7 summarizes the main conclusions and the lessons learned.

The fundamental operation of a synthetic aperture radiometer is the complex cross-correlation of the signals collected by each pair of channels (antenna + receiver), or baseline as shown in Figure 1.

The variables in Figure 1 are: F m , n p , q ( ξ , η ) the normalized antenna patterns of channels m and n, at p and q polarizations, (ξ, η) = (sin θ cos φ, sin θ sin φ) are the direction cosines defined with respect to the X and Y axes, T_Am,_n is the antenna temperature, H_m,n(f) is the frequency response, G_m,n is the power gain of the channel, B_m,n is the equivalent noise bandwidth, b m , n p , q analytical signal collected by each channel, and 〈 〉 is the expectation operator implemented in practice as a time average. A synthetic aperture radiometer measures the cross-correlations between all pair of signals, collected by the antennas. The auto-correlation and the cross-correlation of the signals at each receiver output are defined as: (1) 1 2 〈 | b m , n p ( t ) | 2 〉 ≜ k B ⋅ B m , n ⋅ G m , n ⋅ ( T A m , n p , q + T REC m , n )and (2) 1 2 〈 b m p ( t ) b n q ∗ ( t ) 〉 ≜ k B ⋅ B m ⋅ B n ⋅ G m ⋅ G n ⋅ V m n p q ( u m n , v m n )where k_B is the Boltzmann constant, T_RECm,n is the equivalent receiver's noise temperature, and V m n p q is the visibility function defined in the spatial frequency (baseline) (u_mn, v_mn) ≜ (x_n − x_m, y_n − y_m)/λ₀ that depends on the difference of the antenna positions normalized to the wavelength, being λ₀ = c/f₀. According to Equation (2), the visibility function with units of Kelvin can be derived as a sample of the cross-correlation function: (3) V m n p q ( u m n , v m n ) = 1 k B B m ⋅ B n G m ⋅ G n 1 2 〈 b m ( t ) b n ∗ ( t ) 〉

Assuming that the collected signals are stationary random processes (thermal noise radiation) that fulfill the ergodicity property, narrow-band, spatially uncorrelated, and that the distance between antennas is much larger than the wavelength, Equation (3) can be computed in practice using the cross-correlation (time average) of the in-phase and quadrature components ( b m , n p , q = I m , n p , q ( t ) + j Q m , n p , q ( t ) ) : V m n p q ( u m n , v m n ) = < I m q I n p > + j < Q m q I n p >.

From the Van-Cittert Zernicke theorem [11], the visibility function can be related to the brightness temperature distribution [12] as: (4) V m n q p ( u m n , v m n ) = 1 Ω m Ω n ∫ ∫ ξ 2 + η 2 ≤ 1 T B q p ( ξ , η ) − T rec δ q p 1 − ξ 2 − η 2 F m q ( ξ , η ) F n p ∗ ( ξ , η ) ⋅ r ˜ m n ( − u m n ξ + v m n η f 0 ) e − j 2 π ( u m n ξ + v m n η ) d ξ d ηwhere

𝛀_m,n are the equivalent solid angles of the antennas,

In addition, Equation (4) is normalized by the term k B ⋅ B m B n ⋅ G m G n ⋅ Ω m Ω n to ensure that the visibility function has units of Kelvin.

The Digital Correlation Unit (DCU) computes all possible cross-correlations between antenna pairs at each polarization by counting the number of samples with the same sign (1 bit), obtaining the so-called correlation counts matrices (N_cm,n). Figure 11 shows a single polarization correlation counts matrix structure: the upper triangle part of the matrix contains the I/I correlations between pairs of signals (real part of the visibilities samples), while the lower triangular part contains the I/Q correlations (imaginary part of the visibilities samples). The diagonal contains the cross-correlations of the I and Q components of the signals from the same antenna. These cross-correlated are related in MIRAS to the quadrature errors, but in PAU-SA, since the I/Q demodulation is performed digitally, there are no quadrature errors, and the diagonal is always zero. This 25 × 25 matrix is then completed by adding a right column containing the cross-correlation between the in-phase component and 0's (I-‘0’), and the bottom row with the cross-correlation between the quadrature component and 0's (Q-‘0’) (both for calibration purposes). These values are used to compensate for threshold errors in the comparators. The total number of samples N_cmax is added at the right bottom element, which is used to normalize the whole N_cm,n matrix. It can be observed that the number of correlation counts is an integer, with respect the equation: 0 < N_cm,n < N_cmax. Recalling that the sampling frequency (F_S) is 5.745 MHz, and that the maximum integration time (T_int) is 1 s, then the maximum number of counts or samples (N_cmax) is: (26) N c max = F S ⋅ T int = 5.745 M Samples

Finally, these matrices, and the power measurements are sent to an external PC in real time, where the calibration and the image reconstruction algorithms are implemented to retrieve the brightness temperature image.

The first step consists of computing the cross-correlation (̿) by normalizing the correlation count matrix N_cm,n to the maximum number of possible samples (N_cmax), at each polarization (V, H and V/H): (27) c m , n = N c m , n N c maxwhere m and n indicate the corresponding receivers. Once c̿ is computed, it is necessary to compensate the offset introduced in the measurements by the up-counters and apply a scaling factor to obtain the digital correlation (Z and μ correspond to either the real or imaginary parts of the digital and the normalized cross-correlation, depending if the cross-correlation is performed between the in-phase components, or between the in-phase and quadrature components.) (Z): (28) Z m , n = A ( c m , n − offset m , n )

The digital correlation (Z) is a real number, for which it can be assumed that 0 < Z < 1. On one hand, when two signals are uncorrelated, the correlation c_m,n = 0.5 and Z_m,n = 0, and on the other hand, when two signals are correlated, the correlation c_m,n = 1 and Z_m,n = 1, therefore in the absence of hardware errors [33]

The normalized cross-correlation (μ) between two Gaussian signals sampled with 1 bit (2 levels) is related to the digital correlation by the following expression: (30) μ m , n = sin ( π 2 Z m , n )

However, this relationship is only valid for ADCs having a zero offset (ideal case). Taking into account the sample threshold error, to correct the correlation offset, the normalized correlation μ is calculated with a non-linear relationship (Equation (31)) using Equation (30) as initial solution, and using an iterative method (fixed point iteration or Newton-Raphson) [34,35] until the difference between two iterations is smaller than, for example, 10⁻⁶.

In Equation (31)X₀₁ is calculated in the last column of the matrix of correlators (26^th column) as the cross-correlator between the in-phase components (I) and a signal equal to all zeros. Similarly, Y₀₁ is computed in the last row (26^th row) as the cross-correlator between the quadrature components (Q) and the signal to all zeros. After the fixed-point iteration, the new normalized correlation matrices are reorganized to compute the 25 × 25 visibility matrices. The upper and bottom parts of the diagonal are combined to form the normalized complex cross-correlation.

(32) μ m , n = μ m , n i i − j ⋅ μ m , n i q = μ m , n i i + j ⋅ μ m , n q iwhere the subscripts stand for the correlation between two in-phase ii, and quadrature in-phase iq contributions. This relationship can be also be expressed as: (33) μ m , n = 1 T S Y S m T S Y S n ( ℜ e [ r ˜ m , n i i ( 0 ) V ^ m , n ] + j ⋅ ℑ m [ r ˜ m , n q i ( 0 ) V ^ m , n ] )where ℜe and jm are the real and imaginary part operators respectively, and r ˜ m , n i i ( 0 ) and r ˜ m , n q i are the Fringe-Wash Function (FWF) at the origin for the corresponding pair of receivers indicated by the sub-scripts, and the system temperatures of the denominator are given by: (34) T SYS ≜ T A ′ + T RECwhere T A ′ is the antenna temperature including the contribution from the ohmic losses η Ω ( T A ′ = η Ω T A + ( 1 − η Ω ) T p h ), and V̂_m,n represents the corrected visibility: the m and the n receiver assuming that both receivers are at the same physical temperature T_ph, which is given by: (35) V ^ m , n = ∫ ∫ ξ 2 ± η 2 ≤ 1 T B q p ( ξ , η ) 1 − ξ 2 − η 2 ⋅ F m ( ξ , η ) Ω m F n ( ξ , η ) Ω m ⋅ r ˜ ¯ m , n ( − u m , n ξ + v m , n η f 0 ) e − j 2 π ( u m , n ξ + v m , n η ) d ξ d ηwhere the overbar in the FWF means normalization at the origin, that is: (36) r ˜ ¯ m , n ( t ) = r ˜ m , n α β ( t ) r ˜ m , n α β ( 0 )

Once the normalized complex cross-correlations μ_m,n have been calculated for every combination of antenna polarizations, they are arranged as 25 × 25 visibilities matrices. Then, the normalized visibility function can be derived from Equation (37).

(37) V m , n = μ m , n ⋅ T S Y S m T S Y S n

Finally, the visibility samples must be corrected for phase and amplitude errors [10,36]. The main differences with the MIRAS instrument calibration are:

Since the I/Q demodulation is performed digitally, quadrature errors are zero and do not have to corrected.

(38) V ^ m , n = μ m , n ⋅ T S Y S m T S Y S n ︸ De − normalization 1 g m , n ︸ Amplitude calibration e j α m , n ︸ Phase calibration

Afterwards, these visibility samples must be re-ordered and assigned to the corresponding baseline ((u, v) point) before applying the image reconstruction algorithm. Since it has not been possible to measure the antenna patterns when mounted in the structure, antenna pattern mismatches are compensated for by using a sort of Flat Target Response as described in [10].

Table 1 shows an inter-comparison table between both instruments to show up the potential improvements over the current MIRAS design that have been implemented and tested.

One of the main differences between MIRAS and PAU-SA is the frequency of operation. L-band radiometer should operate in the 1,400–1,427 MHz “protected” band as MIRAS. However, PAU-SA is an instrument concept demonstrator, and to minimize the hardware requirements the GPS reflectometer and the L-band radiometer share the same front-end and frequency band. Although sharing the same front-end provides a significant hardware reduction, there are some drawbacks. The first one concerns to the possible interference that GPS signals can introduce in the radiometric measurements. This non-optimal operation frequency for the radiometer instrument has an impact on the radiometric measurements, introducing some errors. This issue is analyzed in Section 5.1. The second one concerns the bandwidth. In the case of MIRAS, the bandwidth is limited by the protected band with a maximum value of 27 MHz, and an effective noise bandwidth of ∼19 MHz. For the PAU-SA instrument the bandwidth is 2.2 MHz imposed by the IF frequency of the GP2015 chip from Zarlink being used, and by the SAW filters used for the implementation of the receiver chain. This reduction in the bandwidth has an impact on the radiometric sensitivity that can only be compensated by increasing the integration time, which is not critical in a ground-based instrument.

Each arm of the MIRAS instrument is approximately three times longer than the PAU-SA ones: ∼4 m with 23 elements in front of 1.3 m with just 8 elements. The total number of antennas in MIRAS is 69 and 25 in the case of PAU-SA. This decision was taken for two reasons: the first one is due to the use of fixed non-foldable arms in order to simplify the mechanical complexity, and the second one was pragmatic: to be able to take the instrument out of the laboratory, where it was assembled. Since the bandwidth of PAU-SA is narrower than that used in MIRAS and the arm length is smaller, spatial decorrelation effects modeled by the FWF are negligible. This factor is quantified in Section 5.2. One of the improvements of PAU-SA is the additional dummy antenna at the end of each arm to improve the antenna pattern similarity (Figure 2).

Concerning the antenna type and separation, they are quite similar in both instruments. For instance, both MIRAS and PAU-SA use patch antennas without dielectric substrate for the V- and H-polarizations. For hardware simplicity, MIRAS has sequential acquisitions since the receiver is shared for both polarizations. In the case of PAU-SA, each polarization has its own receiver channel. Therefore, continuous acquisitions at both polarizations can be obtained simultaneously, as well as mixing the polarizations.

In order to increase the AF-FOV, the minimum distance between element spacing is kept to the minimum, only limited by the receiver's size. MIRAS has an antenna spacing of 18.75 cm, corresponding to 0.875 λ at 1,400 MHz. In the case of PAU-SA the antenna spacing is reduced to 15.5 cm = 0.816 λ at 1,575.42 MHz, the GPS L1 signal.

Moreover, the distribution of the LO used in the down-converter is different in both instruments. In MIRAS the LO is fed to groups of 6 elements forming an arm section, whereas PAU-SA uses a centralized reference clock of 10 MHz, and the LO is generated by means of a PLL inside each receiver to minimize offsets coming from common LO noise leaking through the mixer.

MIRAS'quantification scheme uses 1 bit sampling at intermediate frequency IF [37] depending upon the noise uptake level inside the Light Cost Effective Front-end (LICEF). PAU-SA uses 8 bits ADC using IF sub-sampling techniques to down-convert and demodulate simultaneously. Using 8 bits, it is possible to filter, demodulate, and perform the power estimation, and finally use only 1 bit to obtain the three complex correlation matrices V, H, V/H.

Due to the large number of receivers in interferometric radiometers, it is advisable to obtain a quasiperfect matching of the frequency responses, mass reduction, and to eliminate temperature and frequency drifts as much as possible. For these reasons, the most important contributions in PAU-SA are focused on the replacement of analog by digital subsystems being the most important:

I/Q down-conversion to eliminate quadrature errors,

All these subsystems and the DCU that computes the full cross-correlation matrix (V, H and V/H) have been implemented in a Virtex 4 FPGA. In this case, since the clock frequency is much higher than the sampling frequency, hardware reuse techniques are used to compute the full-polarization matrices in each snapshot.

The imaging capabilities can be sequential dual-polarization or full-polarimetric in MIRAS, and non-sequential full-polarimetric in PAU-SA. The use of both polarizations simultaneously is also necessary to compose the reflected LHCP GPS signal.

The integration time is fixed for MIRAS with a value of 1.2 s, while PAU-SA has predefined 4 values: 10 ms, 100 ms, 0.5 s and 1 s for test purposes.

Finally, MIRAS uses a classical correlated noise injection method for calibration proposes. Due to the large number of receivers to feed, it is necessary to use several noise sources distributed along the instrument increasing the hardware complexity, and introducing additional noise. In addition, the distributed noise injection is not capable of calibrating all sorts of errors. To overcome this problem PRN signals can be used instead of a centralized noise source for calibration purposes. Moreover, since the PRN signals are deterministic and known, new calibration approaches are feasible through the correlation of the output signals with a local replica of the PRN signal, leading to the estimation of the receivers' frequency responses and the FWF [36]. PAU-SA has the possibility of using both the classical noise-injection method or this new technique with PRNs.

This section is divided into three parts. The first part presents the temperature characterization of the instrument, the second part is the characterization at baseline level in an anechoic chamber, and the last part is an outdoor experiment with the instrument.

This paper has described the PAU-SA instrument. It is a synthetic aperture radiometer that has been designed and tested to study potential improvements in SMOS follow-on or in other missions using synthetic aperture radiometers as GAS [44], PATH [45] or GIMS [46]. A comparison table between MIRAS and PAU-SA has been presented, describing the main novelties of the PAU-SA instrument design. These contributions have been focused on the replacement of analog by digital subsystems such as: I/Q down-conversion, digital filtering, full-correlation matrix (V, H and VH), power estimation implemented in an FPGA, and the use of both a centralized noise source, and PRN signals for calibration purposes. This last one has been one of the most remarkable contributions in the hardware design, since with this method it is possible to feed a large number of receivers using a centralized topology. Once the instrument has been assembled and calibrated, imaging results can be obtained. Instrument characterization has focused on the measurement of Allan's variance, the angular resolution, and the radiometric performance. Finally, imaging results recovery of point sources using PRN sequences and imaging real GPS satellites have been performed. However, the radiometric performances achieved so far are not good enough for the sea surface salinity retrievals originally foreseen.