EMAG II

Analysis of a Distributed Array System for Satellite Acquisition

ALBERTO ANTÓN ISABEL GARCÍA-ROJO ALEJANDRO GIRÓN EVA MORALES Ingenierı́a de Sistemas para la Defensa de España (ISDEFE), Madrid, Spain

RAMÓN MARTÍNEZ ETSIT-UPM, Madrid, Spain

Orbiting satellites and other spatial vehicles have complex trajec- tories that can usually be precisely approximated with analytical or numerical trajectory estimation algorithms. However, some scenarios, such as Launch and Early Orbit Phase (LEOP) or critical maneuvers, present greater angular uncertainty. During these, large dish antennas used for telemetry, tracking, & command (TT&C) may have too nar- row a beamwidth to perform a reliable and fast acquisition. A novel acquisition aid system based on distributed array elements placed on the rim of the main antenna’s reflector has been implemented and successfully tested with real satellite signals. This paper presents an analysis of the proposed solution, from a system engineering per- spective, exposes several simulations carried out in MATLAB, which motivated some of the design criteria, and compares them with the ac- tual results obtained in field campaigns, thus deriving the final figures of merit (FoM) of the system.

Manuscript received March 13, 2015; revised July 22, 2016; released for publication November 23, 2016. Date of publication February 14, 2017; date of current version June 7, 2017.

DOI. No. 10.1109/TAES.2017.2667898

Refereeing of this contribution was handled by M. Jah.

This work was supported by the European Space Agency (ESA) through General Support Technical Programme A (GSTP-A) and by Ingenierı́a de Sistemas para la Defensa de España (ISDEFE).

Authors’ addresses: A. Antón, I. Garcı́a-Rojo López, A. Girón, and E. Morales are with Ingenierı́a de Sistemas para la Defensa de España (ISDEFE), Madrid 28040, Spain, E-mail: ([email protected]; [email protected]; [email protected]; [email protected]); R. M. Rodrı́guez-Osorio is with ETSIT-UPM, Madrid 28040, Spain, E- mail: ([email protected]).

0018-9251/16 C© 2017 IEEE

I. INTRODUCTION

Ground stations aimed to receive or transmit data from/to orbiting satellites and other spatial vehicles need to know their angular location with great precision and ac- curacy. Indeed, large antennas in the ground segment are characterized for having a narrow beam, and thus a high gain. Such narrow beams become a problem in the initial phases of satellite acquisition, especially when dealing with Launch and Early Orbit Phase (LEOP). As the angular un- certainty window during this phase is wide it can take a long time before the ground station acquires the satellite, caus- ing data losses and obviously potential inability to operate the spacecraft.

In many situations, the problem can be solved through complex mathematical models of the vehicle trajectory. In particular, for satellites, orbital propagators are com- monly used for calculating expected positions. However, those techniques are generally designed for stable or- bits, with decreasing precision in critical scenarios where too much inherent uncertainty makes the estimation less reliable.

When the trajectory data of the satellite to be tracked is not precise enough, Program Track modes solely based on the ephemerides cannot be used. Ground station an- tennas include an additional feature, known as Autotrack, which is typically based on monopulse techniques [1], [2]. Monopulse has good tracking performance and does not need pointing predictions, but the initial acquisition is lim- ited by the −3 dB beamwidth of the antenna.

An alternative, originally proposed in [3], is to add a circular motion to the tracking antenna, which cause sinu- soidal variations in the power of the received signal. These variations in turn can be used to interpolate the true space- craft position. The technique is known as Conical Scan (CONSCAN).

In [4], two variants of CONSCAN are proposed, where the circular motion is replaced by Lissajous and Rosette curves. However, as stated in the reference, the performance between the three of them in the estimation of the position of a spacecraft is similar, so that CONSCAN is favored due to its simplicity. The main drawback of CONSCAN, though, is that, since it relies on a mechanical movement, it takes a long time to converge. In fact, it has been widely used for deep space applications, where spacecraft angular speeds are reduced, but for launchers in LEOP or low earth orbit (LEO) satellites, faster estimation techniques should be considered.

CONSCAN belongs to a class of techniques known as Sequential Amplitude Sensing. Another popular method in this class is the Step-Track one. Step-Track, also known as Hill-Climbing, is a very simple technique, which seeks the maximum of the received signal power in successive small movements, alternating between two orthogonal axes [5]. The main disadvantages of the technique are its lower noise robustness when compared to monopulse (it is better to track using a sharp null than a beam maximum), slow convergence as was the case with CONSCAN, and a per- manent lag between spacecraft and antenna position [6].

Another technique presented in the same reference is the Electronic Beam Squinting, which is closer to array solutions and relies on electronic steering of the beam.

1158 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 53, NO. 3 JUNE 2017

The performance is similar to, but does not surpass that of monopulse.

In 2009, Astrium proposed an innovative solution to this conundrum in X-band. The new system, known as X-band Acquisition Aid (XAA), cf. [7], consists of an auxiliary an- tenna, attached to the reflector of the main one. While the larger reflector antenna performs tracking and has full trans- mission and reception functionalities, the XAA is charged with the initial acquisition and the correction of the error offsets of the main antenna at the start of the pass. Both antennas share the same coordinate system, reducing the effect of parallax errors.

The smaller antenna has a diameter of 1.3 m, and a gain over noise temperature (G/T) greater than 14.5 dB/K. Its broader beam permits to increase the acquisition range of the overall system, beyond 2° in elevation and cross- elevation offsets. A monopulse tracking system is used for the estimation of the direction of arrival (DoA) of the satel- lite to be tracked.

While XAA fully covers the uncertainty range of LEOP, the use of a smaller antenna increases its sensitivity to ther- mal noise. On the other hand, this additional dish can have a nonnegligible impact on the mechanical performance of the main antenna, especially taking into account the current trend to reduce the overall diameter for cost savings. These limitations, thermal noise robustness and mechanical im- pact, are complementary, and a trade-off between the two of them must be established, with no evident solutions in some scenarios.

It is thus in this context that an innovative array-based solution, termed Spanish acronym for Fast Acquisition of Satellites System (SARAS), is proposed [8] (Fig. 1). The use of a distributed array of antennas, attached to the rim of the main reflector, clearly reduces the mechanical impact when compared to the single dish-based XAA solution. On the other hand, thermal noise robustness is guaranteed thanks digital array processing, while the resolution of the system is greatly improved thanks to the large separation among array elements [9]. Finally, hardware implementa- tions in field-programmable gate array (FPGA) or Graphics Processing Units (GPUs) guarantee a fast convergence of the estimation algorithms, which do not rely on a mechan- ical scanning but on an electronic one.

Arrays for increased acquisition ranges have also been proposed in [10], for NASA Deep Space Network. In this case, though, the system relies on multiple feed arrays and neural networks. The idea of extending this to distributed arrays, thus increasing the resolution, is a novel aspect of SARAS, as well as its application in launcher acquisition.

The concept of the system, with a uniform distribution of array elements, is shown later.

In sum, the proposed system has the following key char- acteristics [11]:

1) High white noise robustness: The system can operate at very negative signal-to-noise ratio (SNR), which is essential, taking into account the reduced G/T of the in- dividual radiating elements. This robustness is achieved through dual super-resolution space-frequency estima- tors.

2) Fast acquisition: Through an electronically steered ar- ray.

Fig. 1. SARAS prototype installed in Vil-1 Antenna, ESAC, Madrid.

3) Tracking and prediction: Features using Spacecraft Tra- jectory Data Message (STDM) files and an extended Kalman filter (EKF).

4) Interferer discrimination: Capabilities, both in space and frequency.

With the successful acquisition of real satellite signals, a technology readiness level (TRL) of 6 has been achieved with the current prototype. As will be analyzed, the in- novative array-based solution couples DoA estimation and calibration algorithms to obtain a fast, reliable, and high- precision acquisition aid system with negligible mechanical impact on the main antenna.

The present paper will present a system analysis of SARAS in Section II. This analysis will be further de- composed into the main statistical processing algorithms in Section III. In Section IV, simulations carried out in the de- sign stage will be shown with the theoretical lower bounds of the estimators, combined with results obtained from test campaigns with real satellite signals. Finally, conclusions will be drawn accordingly in Section V.

II. SYSTEM ANALYSIS

A. System-Level Requirements

Taking into account the state-of-the-art as explored in Section I, the European Space Agency (ESA) formulated high-level requirements for an innovative solution to the problem of acquiring spacecraft in LEOP and similar criti- cal phases, which can be summarized as follows:

1) The new solution shall be an array-based acquisition aid system and make use of digital processing techniques and algorithms.

2) The new solution shall be tested with S-band sig- nals from at least one of the following target mission satellites: Cryosat-2, GOCE, XMM-Newton and/or IN- TEGRAL. Other missions, such as CALIPSO, Pleiades or MetOp-A, were also added during test campaigns, though. An S-band implementation has been considered as a first step in the overall viability analysis, with a fu- ture X-band migration in mind. The S-band bandwidth is limited to 2.2−2.3 GHz.

3) It shall minimize or completely eliminate the mechanical impact on the main antenna charged with the actual tracking of the spacecraft. In particular, such mechanical impact shall be lower than the one caused by the XAA

ANTÓN ET AL.: ANALYSIS OF A DISTRIBUTED ARRAY SYSTEM FOR SATELLITE ACQUISITION 1159

system, using lighter components. Total weight of the system shall be below 50 kg, to be evenly distributed between array elements.

4) The solution shall be able to acquire signals with +/− 1° of uncertainty regarding their location in elevation and cross-elevation offsets with respect to the broad- side direction of the main antenna. Such uncertainty can be expected in LEOP and other critical phases of the satellite mission.

5) The accuracy and precision of the improved DoA es- timates shall be such that the main antenna is able to continue with the tracking, i.e., residual errors shall be within the −3 dB beamwidth of this antenna. In the frame of the project Vil-1 antenna from the European Space Astronomy Center (ESAC) station in Madrid was considered. This antenna has a diameter of 15 m, and a corresponding S-band −3 dB beamwidth of approxi- mately 0.56° (+/− 0.28°).

6) The system shall be able to acquire spacecraft with el- evations equal to or higher than 5° and with arbitrary azimuth.

7) The time to compute one DoA estimate, from the mo- ment the order is given to the system, must be below 10 s. The requirement imposes an improvement when considering conical scan solutions, which take around 1 min to converge.

The precision and accuracy requirements were adapted to the 15 m Vil-1 antenna, where SARAS system has been implemented, with a possible application in the acquisition of S-band signals from launchers. However, as mentioned, an improvement of the system has been envisaged to con- sider acquisition of X-band signals, following the trend to migrate telemetry, tracking, & command (TT&C) commu- nications to that frequency band. Moreover, as there are also economic considerations which seek to decrease the diameter of the tracking antennas, the use of a lightweight array-based solution would be clearly advantageous.

The logical decomposition of these high-level require- ments gave rise to the functional blocks that will be de- scribed in the next section.

B. System Functional Breakdown

SARAS is composed of the following subsystems:

1) Antennas and associated radio frequency/intermediate frequency (RF/IF) receivers;

2) A digital processor, where the incoming signals are dig- itized and transformed into a DoA estimate;

3) A calibrator, where the array response to incoming sig- nals is characterized;

4) Frequency and time (F&T), which distributes a local oscillator (LO) signal, as well as timing references;

5) Monitoring and control (M&C) and graphical user in- terface (GUI).

The Fig. 2 summarizes the architecture of SARAS sys- tem, along with relevant internal and external interfaces.

In the Fig. 2 three antennas are considered for clarity reasons, although, in the actual implementation, eight have been used. Also, auxiliary subsystems such as power sup- ply or mechanical parts are not explicitly shown. Finally, as discussed afterwards, the Calibrator subsystem may in-

Fig. 2. SARAS architecture.

Fig. 3. Digital processor architecture.

terface directly with the antennas or the RF/IF chains by generating adequate reference or beacon signals.

The next two sections will analyze in more detail both the digital processor and the calibrator, which are the most application-specific subsystems of SARAS.

1) Digital Processor: The digital processor is the core of the processing algorithms and performs the specific task of estimating the DoA of desired signals based on digitized samples. The Fig. 3 later shows its representation for a three element array.

The first block is constituted by the analog-to-digital converters (ADCs), which sample the output from the RF/IF receivers. There are as many ADC as antennas. Once more, three channels are considered for simplicity’s sake. All the ADCs must be synchronized by the F&T subsystem, using a trigger signal to start the acquisition at the same time and a periodic clock to obtain successive samples in the same manner. The digitized signal can have a varying number of bits. More bits will increment the dynamic range of the ADC, at the expense of higher computing and memory requirements, so that the main advantage of reducing the number of bits is that higher sampling rates can be achieved.

After these comes the digital conditioner stage. This dig- ital conditioner can be implemented in a number of ways. Some tasks for it are the following: digital filtering, base- band downconversion, and decimation. One of the main advantages of this block is that, if implemented in generic

1160 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 53, NO. 3 JUNE 2017

Fig. 4. Calibrator architecture.

digital processing devices, such as FPGAs, flexibility in the whole system can be maintained while considering very specific conditioning of received signals. Indeed, the RF/IF receivers can be made more general, in terms of band- width, for example, while a more specific, user-selected filtering is performed in the digital realm. Thus, the config- uration of this stage can be specified in the M&C and GUI subsystem.

Once the signal has been properly conditioned, the sta- tistical processing is carried out. The output of this pro- cessing will be either calibration information or the DoA of the desired signal. It is a statistical processor because it estimates this information based on the statistics of the re- ceived digital signal samples. Thus, the statistical processor can operate in two modes. In normal acquisition mode, the digital signal samples are processed in order to obtain an im- proved DoA estimation of the desired signal. In calibration mode, the pertinent statistics of the signal samples are sent to the calibrator to obtain a parametric calibration model of the array or update the existing one. This information is later used in acquisition mode for proper estimation.

After the statistical processor comes the time stamping. The estimated DoA parameters are associated with an ab- solute time reference given by the F&T subsystem. This absolute time reference is also applied to the digital sig- nal samples. The timestamp is essential for the predicting functionalities of the system.

The last stage is the signal tracker and discriminator. This block operates if iterative estimations are carried out over time in the statistical processor, i.e., if instead of a set of DoA for desired signal and interferers, there is a set of DoA vectors, where estimations are carried out in different times, properly referenced in the time stamping block. This block seeks to filter the resulting trajectories from the spacecraft, discriminate desired signal from inter- ferers, and predict future values of the DoA of the desired signal.

The specific structure of the statistical processor and the signal tracker and discriminator will be covered in Section III.

2) Calibrator: The Fig. 4 summarizes the generic architecture of the calibrator subsystem.

The calibrator is divided into calibrating algorithms and the resulting calibration information. This last data are stored in the calibration data collector, which can adopt several forms, such as files in the processing computer, a

database, etc. From this block, the pertinent and updated information will be extracted to be used by the digital pro- cessor. Prior to this, though, the calibration data processor combines and adapts the calibration information obtained from various sources.

The M&C and GUI subsystem will give the indications to the calibration data collector so that it can obtain the required calibration data. Parameters that can change the calibration data to be used include the polarization, fre- quency, and a priori known DoA of the desired signal.

The geometrical calibrator seeks to estimate the posi- tions of the auxiliary antennas. These will be geometrical references, although, in truth, the interest resides in the phase centers of each radiating element. The phase center of an antenna is a reference point, which is the origin of the ideal equivalent spherical wave front of the radiated signal. Due to the duality properties of antennas, this also applies for reception. Since in practical implementations geomet- rical references and phase centers need not be the same, it is interesting to complement the geometrical calibrator with an antenna calibrator. This block will compute am- plitude and phase radiation patterns of antennas, typically in anechoic chambers. From these, the position of phase centers for differing DoA can be computed and, thus, some of the errors made in the geometrical calibrator corrected. The amplitude and phase radiation pattern response for var- ious DoA, frequencies, and polarizations will be sent to the calibration data collector.

These calibration methods may not be enough to guar- antee the estimation of an accurate parametric model. Dy- namical perturbations and the offsets generated by the RF/IF receivers, among other errors, require proper com- pensation. This is done by the statistical calibrator, which performs a calibration using the incoming signal samples’ statistics estimated in the statistical processor of the digi- tal processor subsystem. Combining these statistics with a priori calculated calibration models, the statistical calibra- tor computes an improved model. The parameters of the algorithms in this block are given by the M&C and GUI subsystem.

The signals samples used by the statistical calibrator can be of diverse origin. The simplest one is a test signal injected to couplers in the RF/IF receivers. In this case, the test signal is typically a tone with the same frequency as that of the desired one, specified by the end user and sent from the M&C and GUI subsystem. The signal is generated in the test signal generator. This calibration will compute the phase and amplitude offsets of the analogue components beyond the couplers. However, in this computation, two spurious offsets will be included: those of the cables that route the signal to the couplers, and those of the couplers themselves.

In order to compensate these, they must be previously calibrated in the component calibrator, using devices such as vector analyzers, and included in the calibration data collector. These parameters describe the electrical behavior of linear electrical components and networks and can be used to determine the phase and amplitude changes, which apply to an electrical steady-state stimulus as it traverses the corresponding component or network. The cables must also be phase stable with respect to differences of temperature and bending angles among them, if there are significantly different routing paths.

ANTÓN ET AL.: ANALYSIS OF A DISTRIBUTED ARRAY SYSTEM FOR SATELLITE ACQUISITION 1161

The test signal can also be sent to one or several test antennas, to be received by SARAS system as a beacon signal.

III. SARAS ALGORITHMS

A. DoA Estimation

After initial digital signal conditioning, DoA estima- tion is carried out in the statistical processor of Fig. 3. The first step, which is optional, is to compensate the Doppler frequency shift of the signal. The idea is that, if frequency estimation is to be performed prior to spatial processing, as will be described later, it is advisable to minimize the drift in the central frequency of the desired signal during the ac- quisition time of the signal samples. The Doppler rate can be estimated, even if roughly, provided some information of the spacecraft’s trajectory is available. The estimated fre- quency shift rate is obtained thus from the M&C subsystem, using ephemerides data from STDM files, and can be used to suitably modify the received samples (for more details, see [12] and [13]).

If the preceding operations are carried out, the next stage, also optional, is the frequency estimation process. It is useful when the desired signal has a nonuniform power distribution in the considered bandwidth. Indeed, for the DoA estimation algorithms, it is optimum to process only those frequency bins where the desired signal’s power is the highest. A typical application is the processing of the carrier of a signal, discarding the modulated part. In this context, a frequency bin is a frequency window given by the resolution of frequency processing algorithms.

The simplest way to carry out the frequency estima- tion is to perform a Fast Fourier Transform (FFT) of the input signal samples, take its absolute value, and locate the peaks where maximum power is present through a direct search algorithm. In order to improve the SNR, the maxi- mum search must be performed with the average of all the incoming digital channels.

More than one frequency can be estimated, thus taking into account the presence of interfering signals with nonuni- form power distribution. Each estimation must be treated in parallel, until the desired signal can be discriminated from interferers.

On the other hand, DoA estimation algorithms require as basic inputs the array autocorrelation matrix, and the size of the signal subspace. The former is obtained with the following equation:

Rxx = 1

K X X H . (1)

For an N -element array, X is an N × K complex ma- trix with either the baseband digital samples in the temporal domain, or the selected frequency bins after frequency fil- tering. K is thus the parameter controlling the block size to be considered for statistical estimation. Finally, X H is the hermitic transpose of matrix X .

As commented, the size of the signal subspace, i.e., the number of incoming signals, including interferers, must be estimated prior to performing DoA estimation. Two pop- ular likelihood estimators are Akaike Information Crite- rion (AIC) and minimum description length (MDL). AIC, though, tends to overestimate the number of signals, even at high SNR, whereas MDL tends to underestimate them, especially at low SNR [14]. To cope with this, a modified AIC algorithm has been considered, as specified in [15].

If only one signal is detected the DoA estimation can be directly carried out, optimizing a spectrum function, which is derived from the weighted subspace fitting (WSF) algorithm [16], Eqn. (2) shown at the bottom of this page.

I is the N × N identity matrix. v(θ, ϕ) is known as the SV (Steering Vector) of the array, obtained from the cali- bration process, which will be discussed in Section III-B. U s is the signal subspace, composed by the eigenvectors as- sociated to the dominant eigenvalues of the autocorrelation matrix. The trace{} operator sums the diagonal elements of the matrix argument. On the other hand W opt is an opti- mized weighting matrix. The desired DoA, θ0, ϕ0, will be calculated as

θ0, ϕ0 = argmax θ,ϕ

[� (θ, ϕ)] . (3)

The DoA of the desired signals is represented by the spherical angles θ and ϕ in the equations, although, in SARAS, elevation and cross-elevation offsets will be ap- plied [2], [17].

If the modified AIC algorithm determines that more than one signal is present, interferers must be sorted out from desired components. One obvious solution to the multisig- nal DoA estimation problem would be to take as many eigenvectors as the number of detected signals D and use them as a basis for the signal subspace U s . This will work as long as D < N . However, taking more eigenvectors adds noise to the estimation process, and this is unnecessary if the end user is only interested in the DoA of a single signal. In such cases, it is desirable to treat each signal separately, computing as many spatial spectrums as signals presents, and obtaining thus completely uncoupled DoA estimates. Due to its stability, the method presented by Weiss and Friedlander [18] has been selected for the uncoupling of signal subspaces.

The preceding processing scheme will produce two DoA estimates, but will not distinguish between desired sig- nal and interferers. This is performed in the signal tracker and discriminator from Fig. 3, which, in the current im- plementation of SARAS system, consists of an EKF, to take into account non-linearities of the equations involved. State equations use ECI (Earth Centerd Inertial) coordi- nates, while measurement variables, elevation and azimuth, are obtained from the ECI coordinates with non-linear equa- tions. Indeed, the transformation from state vector to mea- surement one undergoes the following stages [19]:

� (θ, ϕ) = 1 trace

{[ I − v (θ, ϕ)

( vH (θ, ϕ) v (θ, ϕ)

)−1 vH (θ, ϕ)

] U s W optU Hs

} . (2)

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1) Transformation from ECI to earth-centered earth-fixed (ECEF) coordinate frame.

2) Transformation from ECEF to topocentric geodetic co- ordinate frame. This produces a topocentric state vector Y , where the first three parameters are position coordi- nates.

3) Azimuth and elevation are obtained from this last vector

Az = tan−1 ( −Y1

−Y2

) + π (4)

El = sin−1 ⎛ ⎝ Y3√

Y 21 + Y 22 + Y 23

⎞ ⎠ . (5)

The EKF uses the Jacobian of these equations. Square root filtering was considered both for the filtering and the Riccati prediction estimation of the error correlation ma- trix. Namely, Bierman and Thornton algorithms were im- plemented, as suggested in [20].

EKF can be used to obtain filtered trajectories for space- craft tracking and interferer discrimination when taking ad- vantage of a priori data from STDM files. The filter can also be considered for DoA prediction.

B. Array Calibration

The estimation of the SV v(θ, ϕ) in (2) constitutes the array calibration problem. Two main procedures can be defined for this problem:

1) A nonparametric approach, which seeks to directly ob- tain the numerical values of the vector for a set of steer- ing directions of the array. This set can be made as exhaustive as required.

2) A parametric approach, where the array manifold is ex- pressed as an equation which depends on a given set of DoA-independent unknowns. If these are estimated, nu- merical values of v(θ, ϕ) can be obtained for any desired DoA.

This last approach has been considered in SARAS, mod- eling the nth component of the SV as follows:

v̂ (n) = ρ̂(n) exp

{ j

[ 2πf

c

( x̂

(n) sin θ cos ϕ + ŷ(n) sin θ sin ϕ

+ ẑ(n) cos θ )

+ φ̂(n) ]}

(6)

Here, x̂(n), ŷ(n), and ẑ(n) are the Cartesian coordinates indicating the position of the phase center of the nth antenna in the array. They are functions of DoA and can also change with the elevation of the main antenna due to gravitational deformations of the main dish.

On the other hand ρ̂(n) and φ̂(n) are, respectively, the amplitude and the phase offset in the nth branch. In the most general case, they may change with time, frequency, and DoA. This last case can be seen as an alternative repre- sentation of the variation of the position of the phase center.

It is clear that in solving the equation, taking into ac- count all the perturbations, several methods must be com- bined. The actual combination has been introduced in Sec- tion II-B.2) and discussed in more detail in [12] and will not be further explored in the present paper.

Fig. 5. Pointing error definition.

IV. SIGNAL PROCESSING RESULTS

Monte Carlo simulations, performed in a MATLAB en- vironment, have proven to be critical to assess the actual performance of the proposed solution, and to take early de- sign decisions. MATLAB generates a scenario with a given set of inputs, determined by the type of simulations, and generally produces an estimate of the elevation and cross- elevation offsets, obtained from WSF, of the signal under consideration with respect to the broadside direction of the array. Since the true direction of the signal is known, the total error, for each Monte Carlo iteration, can be computed as

ε = √(

êl − elT )2 + ( x̂el − xelT

)2 (7)

Here, êl and x̂el are the estimated values, and elT and xelT are the true ones. This error can be seen as the module of the difference vector between estimated and true steerings and is represented graphically later (Fig. 5).

Taking the definition of the total error, it is clear that it is the root squared quadratic sum of two random variables, the errors in elevation and cross-elevation, which can be ap- proximated by Gaussian density functions with zero mean and equal standard deviation σ . Thus, by definition, ε fol- lows a Chi distribution, with its mean and variance defined in terms of the Gamma function �() as [21]:

E (ε) = σ √

2 �

( 3

2

) (8)

Var (ε) = 2σ 2 [

1 − �2 (

3

2

)] . (9)

Results from simulations will be compared, in the next sections, with actual system performance using satellite signals and the prototype installed in Vil-1 antenna. Unless otherwise stated, scenarios will be set out for an eight- element array, operating in S-band, and 100 000 samples will be processed.

A. Gaussian White Noise and Lower Bounds

The simulated performance of the system in the pres- ence of Gaussian white noise was explored in [12], for dif- ferent SNR and number of processed samples. The analysis is expanded in the next figures, including several statisti- cal bounds: the CRLB (Cramér-Rao Lower Bound) [22], the second-order Bhattacharyya bound [23], [24], and the Barankin bound [25], with the Chapman-Robbins formula- tion [26], [27], as well as real measurements obtained from CALIPSO and Pleiades spacecraft (Fig. 6).

ANTÓN ET AL.: ANALYSIS OF A DISTRIBUTED ARRAY SYSTEM FOR SATELLITE ACQUISITION 1163

Fig. 6. WSF estimator standard deviation (std) in the presence of white noise.

The results were obtained with an acquisition window of +/− 0.9° in elevation and cross-elevation. There is a clear threshold at −24 dB of input SNR, with pronounced degradation of WSF simulated performance below it. This threshold effect is partly captured by the Barankin bound, with a 1 dB offset, due to the fact that the bound requires the definition of test points which do not fully contain all statistical information of extreme events. On the other hand, the Bhattacharyya bound is tighter than the CRLB above the threshold. It is also worth commenting that the simulated WSF std is upper bounded due to the a priori knowledge of the acquisition window. A mathematical basis for bounded CRLB can be found in [28].

Regarding real measurements, those corresponding to CALIPSO are close to the simulated results, especially for SNR above −22 dB. Pleiades, on the other hand, is slightly degraded. For CALIPSO, the signal was coming from the broadside direction, whereas in Pleiades an offset was in- troduced in the main antenna, which may account for the degradation.

It is important to mention that, while real measurements were obtained for a given SNR, extra results have been derived with artificially increased noise using MATLAB routines and Monte Carlo simulations.

B. Array Topology

During the design phase of SARAS, one of the critical decisions was whether to resort to a distributed topology, as is presently the case, or to a compact, making use of a single phased array. Next simulation shows the advantage of distributed topologies, as a function of the radius of the array, for an SNR of −23 dB (Fig. 7).

It is not surprising that the performance improves as the array radii increases, since so do the resolution capabilities of the WSF algorithm. However, increasing the size of the array comes at the expense of the presence of grating lobes, thus limiting the maximum acquisition range that can be achieved (Fig. 8).

Bias presents a similar behavior. It is clear that dis- tributed topologies are superior to compact ones, at least in some prescribed ranges. Of course, specific array radii val- ues are limited by physical restrictions, taking into account

Fig. 7. WSF performance for different array radii.

Fig. 8. WSF performance for different array radii.

that the array must be attached to an existing parabolic antenna of a prescribed size. Other reasons for choosing distributed topologies over compact ones were considered during the project that gave rise to the prototype, including economic ones. Indeed, the use of an independent compact array, for example, was deemed too expensive due to the price of electronic antenna positioners.

The final point in the analysis of array topologies is to consider the required number of array elements, suppos- ing that a distributed implementation has been chosen. Of course, a minimum value of 2 elements has to be imple- mented. More elements, on the other hand, imply not only more hardware and installation costs but also improved ac- quisition ranges.

The election of eight elements is justified by the Fig. 9, obtained for an SNR of −24 dB. It is clear that improve- ments beyond eight elements do not justify the extra hard- ware and installation costs.

C. Calibration Errors

As commented, SARAS is sensitive to calibration errors in the modeling of the SV, namely, to uncompensated phase offsets in the array branches and to errors in the determina- tion of the position of each radiating element’s phase center. Unbalances in amplitude response, on the other hand, do not affect performance, since it is the phase of the SV, which

1164 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 53, NO. 3 JUNE 2017

Fig. 9. WSF performance for different number of array elements.

Fig. 10. WSF performance with phase calibration errors.

contains the DoA information that needs to be extracted. This is not the case in more complex scenarios, such as in the presence of strong multipath, but, as verified during the test campaigns, multipath levels are low for elevations above 5°.

Figures 10 and 11 show the performance of WSF in the presence of calibration errors, both simulated and with real data from CALIPSO spacecraft, at an SNR of −22 dB. In both scenarios, calibration errors have been added to the models used for the SV.

While the threshold for the simulated performance is around 18°, it decreases to 10°−15° for CALIPSO. Simu- lated results are slightly below the lower bounds because they considered uniform random errors, whereas the bounds were specified for Gaussian ones (Fig. 11).

The Fig. 11 clearly underpins the importance of proper position calibration, as errors beyond 2 mm can cause se- vere degradation. In SARAS, position calibration has been solved using a combination of photogrammetry, which cre- ates a three-dimensional (3-D) model of the array from several pictures taken with different angles, and online cali- bration, i.e., using calibration signals while trying to acquire the desired spacecraft.

As already commented, more details are provided in [12].

Fig. 11. WSF performance with position calibration errors.

Fig. 12. WSF performance with FFT processing as a function of C/No.

D. Moving Signal and Frequency Processing

All the previous simulations and test results made use of the whole IF bandwidth. In the presence of signals with non-suppressed carrier, though, as already discussed, great improvements may be achieved with pre-FFT processing, as those frequency bins close to the carrier have higher signal power. The level of improvement depends on the carrier modulation index, which determines how the total power of the signal is shared among carrier and modula- tion part, and on the uncompensated frequency shifts af- fecting the received signal. Indeed, in this case, the power of the carrier is smeared across several frequency bins, decreasing the effective carrier over noise floor power ra- tio (C/No). The main cause of this shift arises from im- perfect knowledge of the signal trajectory and, thus, its Doppler rate, but other contributions, such as instabilities in the satellite phase-locked loop (PLL), may also have an impact.

The Fig. 12 shows the performance of the combined FFT and WSF processing, as a function of C/No, with simulated and real data from Cryosat-2 and INTEGRAL satellites. In all cases, frequency processing down to a band- width of 35 Hz has been performed, even if narrower pro- cessing may be optimum for perfect knowledge of Doppler shift.

The Fig. 12 shows the 3.3σ root-mean-square error (RMSE). A deviation of 3.3σ gives a confidence level

ANTÓN ET AL.: ANALYSIS OF A DISTRIBUTED ARRAY SYSTEM FOR SATELLITE ACQUISITION 1165

TABLE I SARAS FoM

FoM Simul. Value Real Value

Threshold SNR −24 dB Between −22 and −20 dB

Threshold C/No 13 dBHz Between 15 and 17 dBHz (for compensated

Doppler) Maximum acq. range <2° <2.2° Maximum uncompensated phase calibration error

<18° <15°

Maximum uncompensated position calibration error

<4 mm <2 mm

of 99.9% for Gaussian errors. For INTEGRAL, the com- pensation of the Doppler shift does not translate into a meaningful improvement. Indeed, the spacecraft presents a highly eccentric orbit, and during the acquisition, it had a very small angular speed. The effect of Doppler compensa- tion is more clearly seen for Cryosat-2. Of course, perfect compensation of Doppler shift is not achievable for space- craft with unstable orbits so that the final performance will be in an intermediate position. The differences between Cryosat-2 and INTEGRAL, with Doppler compensation, are due to some imprecisions in the estimation of the ac- tual C/No, taking into account the small number of samples processed.

E. Summary

Table I summarizes some of the FoM previously dis- cussed, both for simulated and real scenarios.

V. CONCLUSION

An S-band array-based acquisition system, SARAS, has been designed and implemented in the frame of a con- tract with the ESA. The system relies on a distributed topology, with radiating elements placed on the rim of a main reflector antenna for TT&C communications, with improved resolution capabilities. Electronic search, cou- pled with robustness against thermal noise, makes SARAS a solid alternative for state-of-the-art solutions in scenar- ios where low power level and fast-moving signals can be expected and where reliable acquisition is critical, such as LEOP.

This paper has expanded previously published informa- tion concerning SARAS. It has presented a system analysis of the solution, starting with high-level requirements from ESA. Emphasis has been laid on the DoA estimation pro- cessing algorithms. Some indications have also been given concerning the proper calibration of the array.

Finally, MATLAB simulations in complex scenarios have been presented, justifying some of the design criteria that were applied to the system, combined with theoretical statistical lower bounds and results from test campaigns with real satellites, and showing the final performance of SARAS, compared with the simulated scenarios.

ACKNOWLEDGMENT

The authors would like to thank P. M. Besso from ESA- ESOC for the original concept and constant support during the project, M. M. de Mendijur from ESA-ESOC for her very useful ideas and comments, and ESAC personnel for their indispensable help during the installation phase and test campaigns. Besides, the authors would like to acknowl- edge the Spanish Government, Ministry of Economy, Na- tional Program of Research, Development and Innovation for the support of the project ENABLING-5G "ENABLING INNOVATIVE RADIO TECHNOLOGIES FOR 5G NET- WORKS" (project number TEC2014-55735-C3-1-R).

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Alberto Antón received the M.Sc. degree in telecommunications engineering from the Polytechnic University of Madrid, Madrid, Spain, in 2008.

For more than four years, he was a Space System Engineer, involved in several projects in the area of antenna arrays, digital signal processing, satellite communications, and statistical analysis. He has acted as a Technical Leader in SARAS project. He currently manages the Antenna Array R&D Program in the Spanish company Ingenierı́a de Sistemas para la Defensa de España (ISDEFE), Madrid.

Isabel Garcı́a-Rojo López was born in Valdepeñas, Spain, on June 18, 1982. She received the M.Sc. degree in telecommunication engineering, specialized in communications, and the M.Sc. in space technology from the Polytechnic University of Madrid, Madrid, Spain, in 2007.

She is a Project Manager (PMP certified) of SARAS project as well as a Space System Engineer. She has been involved in Space R&D projects and in Communications and Ground Segment projects for eight years in ISDEFE (former INSA Company), Madrid.

ANTÓN ET AL.: ANALYSIS OF A DISTRIBUTED ARRAY SYSTEM FOR SATELLITE ACQUISITION 1167

Alejandro Girón received the M.Sc. degree in telecommunications engineering from the University of Alcalá, Madrid, Spain, in 2010.

From 2005 to 2007, he was a member of the Technical Staff with Motorola Inc. and France Telecom España. From 2007 to 2013, he was a Radar Engineer with the National Institute of Aerospace Technology (INTA). He is currently with Ingenierı́a de Sistemas para la Defensa de España (ISDEFE), Madrid. His current research interests include analysis and simulation of analog/digital RF systems, phased arrays, and deep space communications.

Eva Morales was born in Madrid, Spain, in 1982. She received the Graduate degree in computer engineering from the Universidad Politécnica Madrid, Madrid, Spain, in 2006, Master’s degree in graphic design from Aula Creactiva Madrid, Madrid, in 2010, and Master’s degree in marketing online from the Universidad Complutense Madrid, Madrid, in 2014.

She was involved in designing and developing desktop and web applications. She has been involved in SARAS project designing and developing the monitoring and control software application at Ingenierı́a de Sistemas para la Defensa de España (ISDEFE), Madrid.

Ramón Martı́nez was born in Madrid, Spain, in 1975. He received the Ingeniero de Telecomunicación and Doctor Ingeniero de Telecomunicación degrees from the Technical University of Madrid (UPM), Madrid, Spain, in 1999 and 2004.

In 1999, he joined ETSIT-UPM, Madrid, where he is currently an Associate Profes- sor. His current research interests include smart antennas arrays for mobile and satellite communication systems, in particular in the calibration, control, and antenna arraying procedures.

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