Measurement of the Primary Beam of the Tianlai Cylindrical Antenna Using an Unmanned Aerial Vehicle

Technical Summary: Measurement of the Primary Beam of the Tianlai Cylindrical Antenna Using an Unmanned Aerial Vehicle

Problem Statement
The Tianlai Cylinder Pathfinder Array (TCPA) is a radio interferometer designed for 21 cm intensity mapping, consisting of three fixed parabolic cylindrical reflectors oriented along the North-South (N-S) axis. A critical challenge in calibrating such fixed-azimuth antennas is determining the primary beam pattern. While the East-West (E-W) beam profile can be measured via the transit of bright astronomical radio sources, the N-S profile remains difficult to characterize due to the scarcity of suitable point sources at varying declinations and the inability to place the large structure in an anechoic chamber. Previous reliance on analytical models fitted to simulations lacked empirical validation, particularly regarding the N-S direction and potential asymmetries caused by the local environment.

Methodology
The authors present a preliminary measurement of the TCPA beam profile in the 700–800 MHz frequency range using an Unmanned Aerial Vehicle (UAV) as a mobile calibration source. The methodology involves the following steps:

1. Experimental Setup: A DJI M300 RTK drone carries a calibrated noise source emitter (a broadband noise generator with bandpass filtering and amplification) and a dipole antenna. The drone operates in the far-field zone of the antenna array, defined as $d = 2D^2/\lambda$. For the TCPA's 15 m E-W aperture, this requires a distance of approximately 1050–1200 m; the drone flew at a height of 1220 m.
2. Flight Plan: The drone executed circular flight paths centered on a specific feed with a radius of 1220 m. Two distinct flight modes were employed:
   • N-S Flight: The drone traversed zenith angles ($\theta_{NS}$) from $-70^\circ$ to $+70^\circ$ in steps ranging from $5^\circ$ to $15^\circ$.
   • E-W Flight: The drone traversed zenith angles ($\theta_{EW}$) from $-3^\circ$ to $+3^\circ$ in $0.3^\circ$ steps to resolve the narrow E-W beam.
   • Flights were conducted at night to minimize solar interference and ensure system gain stability.
3. Data Processing: The TCPA correlator recorded auto-correlation signals. To isolate the drone signal ($V_{dns}$) from the sky background ($V_0$), the authors used data from an adjacent day (without the drone) as a baseline. A linear time-dependent gain model was applied to correct for receiver drift between the baseline and measurement days.
4. Drone Emitter Calibration: A crucial step involved characterizing the beam pattern of the drone-mounted dipole ($B_{dns}$), which is distorted by the drone's airframe. This was achieved by flying the drone in an arc over a ground-based dipole antenna. The ground dipole's beam ($B_{ground}$) was simulated using FEKO electromagnetic software with measured soil parameters. The actual drone beam was derived by deconvolving the ground dipole's known pattern from the received signal.
5. Beam Reconstruction: The final cylinder beam ($B_{cyl}$) was calculated by dividing the measured visibility (after sky subtraction) by the calibrated drone beam pattern: $B_{cyl} \propto \hat{V}_{dns} / B_{dns}$.

Key Results

• N-S Beam Profile: The measured N-S beam profile exhibits a peak at $\theta_{NS} = 0^\circ$ with a distinct "shoulder" structure around $\pm 30^\circ$, followed by a steep decline near $\pm 60^\circ$. The profile is slightly asymmetric, with the shoulder more pronounced on the northern side ($\theta_{NS} < 0$). This asymmetry contrasts with electromagnetic simulations, which show a symmetric, monotonic decline. The authors attribute this discrepancy likely to ground reflections from nearby hills, which were not included in the simulation.
• E-W Beam Profile: The E-W measurements align generally with simulations and bright source transit measurements (e.g., Cyg A). However, the measured beams are slightly broader and exhibit higher side lobes than simulations. The drone measurements show slightly better agreement with simulations than the transit measurements, likely due to the higher signal-to-noise ratio of the active source reducing noise-floor artifacts.
• Consistency: Measurements across different feeds (e.g., A18, A22, A24, A25) and repeated flights (separated by up to 24 hours) demonstrate robust consistency, with variations between flights comparable to variations between feeds.
• Polarization: Results for both XX (N-S) and YY (E-W) polarizations were obtained. The YY polarization showed a small dip near the center, possibly due to cross-coupling effects.

Significance and Claims
The paper claims that UAV-based far-field measurement is a feasible and efficient technique for characterizing the beam patterns of large, fixed radio telescope arrays, specifically addressing the long-standing difficulty of measuring the N-S profile. The study validates the UAV method by cross-referencing E-W results with astronomical transit data and simulations.

The authors emphasize that while the measured profiles are generally similar to electromagnetic simulations, discrepancies exist in the "shoulder" regions, side lobes, and beam widths. They conclude that these differences likely arise from simplifying assumptions in simulations, such as the neglect of local terrain reflections, surface imperfections, and cross-coupling noise. The paper posits that this UAV approach provides a necessary empirical correction to simulation models, thereby improving the calibration accuracy required for 21 cm intensity mapping and dark energy equation of state measurements.