Measurement of the LOFAR-HBA beam patterns using an unmanned aerial vehicle in the near field

Abstract. An unmanned aerial vehicle (UAV) is exploited to characterize in situ the high-band antennas (HBAs) of the low-frequency array (LOFAR) CS302 station located in Exloo, The Netherlands. The size of an HBA array is about 30 m. The Fraunhofer distance (a few kilometers) is not reachable in the frequency band (120 to 240 MHz) within the flight regulation limits. Therefore, far-field patterns cannot be directly measured. The UAV, equipped with an radio frequency synthesizer and a dipole antenna, flies in the near-field region of the considered array. Measurement of three different frequencies (124, 150, and 180 MHz) is efficiently made during the same UAV flight. The near-field focusing method is exploited to validate the far-field pattern of the array under test within an angular range around the beam axis. Such a technique avoids both the time consuming λ  /  2 sampling of the aperture field and the further application of computationally heavy near-field to far-field transformations. The array beam is well reconstructed in the main lobe and first sidelobes within a 2D scan plane sampled with a radial raster. A further postprocessing technique is proposed and validated on a subarray of HBAs. It suggests efficient ways for the future characterization of regular aperture arrays for SKA-MID Phase 2.


Introduction
The low-frequency array (LOFAR) 1 is a radio telescope composed of 52 stations located in Europe. Each station is composed of two subarrays, one with low-band antennas (LBAs) and one with high-band antennas (HBAs). Their operating frequency ranges are 10 to 90 MHz and 120 to 240 MHz, respectively. LBAs are arranged in a random configuration, whereas HBAs are placed in a regular lattice.
LOFAR is a pathfinder for the international square kilometer array (SKA). The SKA will become the biggest and most sensitive radio telescope in the world. Aperture arrays are envisioned for both SKA1-LOW (50 to 350 MHz, random configuration) 2,3 and possibly SKA1-Mid phase 2 (400 to 1.45 GHz, regular configuration). [4][5][6] Dishes will be adopted for higher frequencies up to 14 GHz.
All these powerful radio telescopes need to be validated and accurately calibrated. Of course, testing these large arrays is not an easy task due to their large size and the low operating frequencies. A few approaches have been proposed exploiting measured data in far or quasi-far-field condition. For example, a holographic technique has been applied to the engineering development array 2 of SKA1-LOW 7 and LOFAR 8 to retrieve aperture fields. Other tests on LOFAR have *Address all correspondence to Lorenzo Ciorba, lorenzo.ciorba@ieiit.cnr.it been performed using astronomical calibration sources 9 and radio frequency (RF) sources mounted on cranes. 10 More recently, thanks to the technological development of unmanned aerial vehicles (UAVs), flying test sources have been developed to test aperture arrays even at the element level [11][12][13][14][15][16] with a high signal-to-noise ratio and a huge scan flexibility. Due to the large electrical size of the aperture arrays, the Fraunhofer distance cannot always be reached. Therefore, validation of LOFAR LBA array has been performed comparing measurement and simulation in the near field. 17,18 All previous papers featured sparse arrays with particular emphasis on the random configuration. 19 In this work, the UAV-based measurement strategy is extended to the LOFAR HBA (Fig. 1), which is a large regular array. Near-field focusing 20,21 is adopted and its validity is assessed by comparison to the far-field simulated data (Sec. 2). This procedure has been applied on a two-dimensional scan path to provide a more complete characterization (Sec. 3). A first attempt to develop a far-field reconstruction strategy (to overcome the artifacts of the near-field focusing) and the corresponding definition of efficient near-field scan strategies for regular arrays such as the aperture arrays for SKA-MID Phase 2 is presented in Sec. 4.
To summarize, the novelty aspects of this paper are as follows: (1) The verification of all tiles within a single flight over a LOFAR-HBA substation.
(2) The application of near-field focusing to an array of tiles pointed in the same far-field direction to provide an end-to-end verification of the system from the antennas to the digitized data. (3) The usage of radial raster scans to represent the beam pattern in the u − v plane with a limited set of linear scans, which is an efficient choice in view of the limited UAV flight duration compared to Cartesian rasters. 11 (4) The definition of a far-field reconstruction strategy to partially overcome the artifacts of the near-field focusing and its validation on a subarray of the HBA substation.

UAV-Mounted Test Source and the HBA
The UAV is visible in Fig. 1. It is equipped with a differential global navigation satellite system (GNSS) receiver for accurate positioning within a few centimeters, a dipole antenna, and an RF synthesizer. 13 Three higher-order harmonics of the RF synthesizer (i.e., it was operating as a comb generator) have been used during the same flight. In this way, three different frequencies (i.e., 124, 150, and 180 MHz) have been measured simultaneously. This procedure is applicable when the receiver acquisition system can simultaneously record many frequency channels to drastically reduce the flight time of the UAV. Figure 1 also shows the Eastern HBA array of the CS302 LOFAR station located in Exloo. The detailed geometry of this LOFAR HBA subarray is shown in Fig. 2. It is composed of 24 square tiles (red numbers from 0 to 23) with a size of about 5 × 5 m 2 . Each tile is composed of a regular distribution of 4 × 4 dual-polarized elements, i.e., thin crossed-bowtie dipoles suspended over a ground plane by means of a polystyrene support structure. The dipole length is about 0.7 m. Within each tile, the element spacing is 1.25 m. 1 The distance between tile centers is Fig. 1 The UAV after take-off is reaching the first waypoint to perform the required scan path over the LOFAR Eastern HBA array of the CS302 station. The array dimension is about 30 m. 5.15 m, therefore, the spacing between elements of adjacent tiles is slightly larger (1.4 m) than within the tile. Nevertheless, the overall distribution can be considered as very close to a uniform regular array. Through the analog beam forming, each tile can be pointed within a field of view of 60 deg around zenith. Furthermore, signals from all tiles can be summed together by digital beam forming.
The two element polarizations are oriented along the north-west and north-east directions. For the considered CS302 station, the orientation of the regular array distribution is 48 deg from north (see Fig. 2). Hence, there is a 3-deg rotation between element polarization directions and array lattice principal directions. Nevertheless, the labels north-west and north-east will be still adopted in this paper for both polarization and array principal (periodicity) directions for the sake of simplicity.

Beam Patterns Using Near-Field Focusing
Several flights with linear trajectories and constant height have been performed. A sketch of a UAV path projected to the ground and oriented north-west is shown in Fig. 2 with the blackdashed line. This section presents the results obtained for a flight where both the UAV speed vector and the onboard dipole are oriented north-west. This corresponds to an E-plane scan of the array elements oriented north-west. The UAV flight duration to perform this single linear path was ∼1 min (flight speed was about 3 m∕s), whereas 2 to 3 min are necessary for take-off and landing. The flight height has been maintained at 140 m due to regulation limitations. This already satisfies the far-field condition for each tile (Fraunhofer distance is 60 m at 180 MHz) but is not enough for the full array (about 1.1 km at 180 MHz). This fact is confirmed in Fig. 3, where the measured tile beams (E-plane, 124 MHz) are shown for the tiles closest to the projection of the UAV path (dashed black line in Fig. 2), i.e., tiles 6-11 and 12-17. The effect of UAV pattern and path loss has been removed as in Ref. 22. All beams are reported with respect to the curvilinear abscissa on the UAV path. The origin of the curvilinear abscissa is set where the UAV path projection is closest to the center of the HBA array. The analog beam formers were programmed to point the tile beams at zenith. However, because of the low altitude of the UAV, the maxima of the tile beams occur at different values of the curvilinear abscissa. In particular, the maxima of tiles 11 and 17 occur at about −13 m, whereas the maxima of tiles 6 and 12 occur at þ13 m. This is consistent with the distance between tile centers of about 26 m. The successful comparison with simulations at tile level was already reported in Ref. 23. In this work, the tile beams are instead used to estimate the full array pattern by means of a near-field focusing method. 20 However, it should be mentioned that, differently from Ref. 17, the presence of analog beam-formers at the tile level prevents the application of the required parabolic phase shifts across the array aperture, i.e., to each array element. Such near-field focusing can only be applied on the tile signals. In other words, the tile beams are pointed to zenith (far field), whereas the array of tiles will be focused in near field. All the tile beams in Fig. 3 are normalized in magnitude and phase at the origin of the curvilinear abscissa to produce the near-field focusing for the array of tiles. The parabolic phase shifts for the various tiles are automatically produced by the different electrical distances with respect to the UAV-mounted source placed in the near field.
Normalization constants in magnitude are shown in Fig. 4. It is apparent that tile number 10 requires a larger normalization constant with respect to the other tiles to achieve proper equalization. From Fig. 3, it can be also noted that its signal is noisier and the sidelobes are  The equalized (magnitude and phase) signals from the two tile rows 6-11 and 12-17 have been summed together to obtain the radiation patterns at 124 MHz that are shown in Fig. 5 (blue line) as a function of the zenith angle. The zenith angle has been computed using the curvilinear abscissa and the UAV height. A far-field simulation obtained using a combination of WIPL-D and array factor is also shown in Fig. 5 (black solid line with circular markers). WIPL-D has been used on a subarray of 3 × 3 tiles, i.e., 12 × 12 dipoles. This configuration requires neither significant computational effort nor specific acceleration methods. However, it allows one to estimate the effect of mutual coupling on the tile beam. Differences between the nine simulated tile beams in the 3 × 3 tile array have been found to be negligible with respect to the measured discrepancies. 23 For this reason, an array factor approach has been adopted using the simulated tile beam (central tile within the 3 × 3 array) as element pattern. The agreement is satisfactory within AE15 deg from zenith. This is consistent with the near-field focusing method, which guarantees a good agreement between far-field and near-field focused beams only in the proximity of the beam axis. 20 The level of first sidelobes (−13 dB) is consistent with the uniform amplitude excitation. The pattern of the array of tiles 6-11 shows larger discrepancies with respect to simulation because of the faulty tile 10. Almost the same level of agreement has been obtained at 150 and 180 MHz (see Fig. 6, only the array of tiles 12-17 has been reported for brevity). As expected, the angular region with good agreement becomes narrower at higher frequencies (AE10 deg from zenith) because the Fraunhofer condition increases with frequency and all frequencies were measured during the same flight and, hence, at the same height.  The same near-field focusing procedure has been applied to the full HBA array in Fig. 2. No further faulty tile has been found besides number 10. (It should be noted that all the tiles in Fig. 2 have been verified in such a single flight.) Figures 7-9 show the measured (near-field focused) and the simulated (far field) radiation patterns at 124, 150, and 180 MHz. The angular region showing good agreement is again ranging from AE15 deg to AE10 deg at lower and higher frequencies, respectively.
The full-half power beamwidths are 5.2 deg, 3.9 deg, and 3.4 deg at 124, 150, and 180 MHz, respectively. The low level of the first sidelobes is due to the array geometry. It should be noted that all the tiles in Fig. 2 contribute to the array pattern. The number of tiles along the direction that is orthogonal to the UAV scan, i.e., the number of tiles along north-east direction is six in the array center and two at its edges. As far as the north-west cut reported in Figs. 7-9 is concerned, this is equivalent (in the far field) to a linear array with edge tapering, which in turn explains the low sidelobes. This fact can be easily demonstrated by computing the array factor along the north-west cut.

Radial Rasters as an Efficient Scan Strategy
The results in Sec. 2 concern a single-linear scan performed along the north-west direction. Additional linear scans were performed with an angular offset of 22.5 deg to achieve a more complete coverage of the u − v plane (directional cosines). All angular steps were performed with two orientations of the UAV-mounted dipole, i.e., parallel and orthogonal to the speed vector to sample both the θ and φ components of the radiation patterns. Each raster has been split as two flights for each field component, i.e., a total of four flights. The duration of each flight has been ∼10 min. The full flight duration capability of the UAV has not been exploited due to the severe wind condition observed during the campaign. A larger margin on the battery charge has been maintained for safety reasons. Longer flight durations up to 40 min are now available with modern UAVs operating in calm wind condition. The measured results for the north-west polarized elements of tile number 9 (see Fig. 2) are shown in Fig. 10.
The north-west radiation pattern cut (þ135 deg from u axis) for the (radial) θ component [ Fig. 10(a)] corresponds to the E-plane co-polar pattern for the tile elements polarized along the north-west direction (same cut that is discussed in both Sec. 2 and Ref. 23), where both main lobe and sidelobes are visible. The cut oriented north-east [θ component, Fig. 10(a)] instead represents a cross-polar H-plane pattern, which is quite low in magnitude as expected. The H-plane co-polar pattern is visible in Fig. 10(b) where the (azimuthal) φ component is shown.  The north-east cut shows again both main lobe and first sidelobes. This is consistent with the square geometry of the tiles.
The power pattern, i.e., the combination of the two orthogonal pattern components in Fig. 10, is shown in Fig. 11(a). Both E-plane and H-plane are now visible on the same plot as north-west and north-east paths, respectively. The symmetry of the beam, which is due to the square geometry of the tiles is clearly visible. The overall pattern is very consistent to the simulated data in Fig. 11(b). The main difference is the depth of the nulls, which is mainly related to source orientation errors, modeling errors, and of course manufacturing and position uncertainties of the real tile. Manufacturing tolerances are neither calibrated nor corrected for in the analog beamformer.
The near-field focusing method described in Sec. 2 has been applied to the full HBA shown in Fig. 2. The result is shown in Fig. 12(a) and is in good agreement with the simulation (b). The beam symmetry and width are consistent. Artifacts are still visible in both the north-west and north-east paths. Nevertheless, these results provide a good in situ validation of the HBA substation.
For brevity, we have only presented results for the HBA elements polarized along the northwest direction. However, similar results have been achieved for the north-east ones.

Far-Field Reconstruction
This section presents an alternative strategy to partially overcome the artifacts due to near-field focusing method already discussed in Sec. 2. It is based on the consideration that the performed UAV flights satisfy the far-field condition for the tiles but not for the array of tiles. For the tiles, both amplitude and phase of the acquired signals are available (complex voltages). The amplitude patterns can be easily obtained by geometrical considerations, i.e., the amplitude data for each tile (after removal of UAV pattern and path loss, see for example Fig. 3) are expressed as a function of a local reference system centered on the tile itself, instead of the center of the full array. The resulting patterns for tiles 12-17 are shown in Fig. 13. The frequency of 180 MHz has been selected for this example because it represents a worst case for the near-field focusing artifacts.
As far as far-field phase patterns are concerned, their determination is less straightforward because the UAV-mounted RF source is not phase-locked to the on-ground acquisition system of the telescope. In other words, the relative phase between transmitter and receivers is drifting during the flight in an uncontrolled way. For this reason, only differential phase data can be used. 24 In Ref. 25, a reference antenna with known phase pattern was placed in the proximity of the SKA-LOW array prototype to reconstruct a near-field phase pattern. In this campaign, no reference antenna was available. Therefore, one of the central tiles (i.e., tile number 15) is used as reference. This, of course, relies on the knowledge of its phase pattern by simulations [see Fig. 13(b), violet curve]. Under this hypothesis, the phase patterns of all other tiles ∅ j can be computed as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 2 1 3 where the time/position dependence of all the terms has been understood, ∅ i is the phase pattern of the reference tile (i ¼ 15 in our case), φ j and φ i are the phase of the acquired complex voltages, k is the wave number, and r j , r i are the distances between the UAV-mounted source and the centers of tiles j and i, respectively. It should be mentioned that in Eq. (1), the direction dependence of the source pattern has been neglected (it is in the order of a few degrees). Moreover, only the co-polar component is considered (transmitter and receiver are matched in polarization). The relative distances r j and r i are computed exploiting the UAV position data measured by GNSS and the knowledge of the tile center positions. (Nominal data have been used, however, an accurate measurement with ground-based instruments such as total station or GNSS is viable.) The resulting reconstructed far-field phase patterns for tiles 12-14 and 16-17 are shown in Fig. 13(b). They are quite similar to each other because local reference systems (centered on each tile) have been adopted. Each of them shows narrow anomalies where the phase rotates of 360 deg around the zenith angle AE20 deg. These anomalies are due to the two nulls on the pattern of the reference tile. At the nulls, the phase exhibits abrupt variations of 180 deg. In these regions, the accuracy of the models is generally lower and therefore, a perfect cancellation between the terms ∅ i and φ i does not occur in Eq. (1). A reference antenna with a smoother behavior would be desirable to avoid such anomalies (this can be implemented by either activating only one dipole within a tile that will be hence used as reference only or exploiting an additional external reference antenna in the proximity of the HBA). Nevertheless, after summation of the tile patterns in Fig. 13, the resulting beam in Fig. 14 (red curve) is more consistent to the far-field simulation (black curve) than the previous near-field focusing data (blue curve). It should be mentioned that, before summation, the tile phase patterns in Fig. 13 have been both converted to the same reference system by exploiting again the knowledge of the tile center positions and equalized at zenith (array calibration). The angular regions where the discrepancies occur are consistent with the position of the reconstructed far-field phase pattern anomalies in Fig. 13. A better agreement has been also achieved at 124 MHz (see Fig. 15) using the same reconstruction method.  The overall improvement has been quantified computing the average (along zenith angle) of the weighted logarithmic difference Δ w;log in Ref. 26 with β ¼ 0.5 between measurements and simulation. For the near-field focusing (blue curve), the quantity Δ w;log is 0.89 and 1.15 dB at 124 and 180 MHz, respectively. A smaller Δ w;log of 0.68 dB has been achieved for the reconstructed far-field case (red curve) at both frequencies.
The method presented in this section has only been applied to the linear array of tiles 12-17, which is close to the north-west scan path performed by the UAV (see Fig. 2). The array of tiles 6-11 has not been considered because of the faulty tile. The best condition for the presented farfield reconstruction is a scan path that intersects the maxima of the tile beams, whose pointing is set before the flight. Otherwise, the information of the principal cut of the tile radiation pattern is not available. A linear flight parallel to the array lattice direction (almost north-west in this case) will intersect the maximum number of tile beam maxima. According to these considerations, a Cartesian raster with 6 × 6 orthogonal linear scans and a spacing of 5.15 m (distance between tile centers) would have allowed the measurements of all the tile patterns in their principal planes and the subsequent reconstruction of the full array far-field pattern along the north-west and northeast planes using the method presented in this section. It should be noted that a raster that is suitable for a near-field to far-field transformation would have required a spacing of <λ∕2, i.e., 0.8 m at 180 MHz, with a strong impact on the UAV flight time requirement. Moreover, a computationally heavy inversion algorithm must be applied 27 to transform the scan paths performed by UAV in the near field. The presented solution, together with the exploitation of a smoother and well-known reference antenna could be considered for the characterization of the regular arrays of SKA-MID.

Conclusion and Future Developments
The application of near-field focusing to an array of LOFAR-HBA tiles pointed in the same farfield direction demonstrated that a useful end-to-end system validation can be performed even considering only a limited angular range around the beam axis. Simulated and measured results are in good agreement as far as beamwidth and first sidelobes are concerned. The method also pointed out the presence of a faulty tile in the Eastern HBA subarray of the CS302 station.
The combination of a few linear scans with different orientations has been performed to achieve a radial raster. This procedure confirmed the agreement between measurements and simulations on the full u − v plane, although with limited coverage. The angular step of 22.5 deg could be reduced at the expense of a longer flight/scan duration.
A far-field reconstruction method has been proposed and validated on a linear subarray of the HBA substation. It allows one to partially overcome the artifacts of the near-field focusing strategy exploiting the usage of a known reference antenna and the knowledge of the tile positions. This suggests a validation procedure for regular aperture arrays such as SKA-MID that is based on a Cartesian raster in the near field with a spacing that is equal to the tile spacing, which is several times larger than λ∕2. This efficient scan strategy will provide far-field pattern information on the principal planes only, which could already be satisfactory as far as validating stations in situ is concerned.