Radiometer Calibration using Machine Learning

TL;DR

This work introduces a neural-network–based calibration framework for radiometers that directly infers Noise Parameters from internal reference measurements to achieve absolute, frequency-resolved calibration without relying on ideal impedance matching. Demonstrated on the REACH receiver, the method achieves sub-0.1 K residuals on internal loads and, in end-to-end simulations, recovers a sky-averaged 21-cm signal with tens-of-milliKelvin accuracy when integrated over 1-MHz channels. By modeling complex, non-linear receiver behavior and drift, the approach preserves spectral features and offsets, enabling robust 21-cm cosmology measurements. The framework, including temporal-variability capabilities and simulated end-to-end validation, points to scalable calibration for future high-sensitivity radiometers in ground, space, or lunar environments.

Abstract

Radiometers are crucial instruments in radio astronomy, forming the primary component of nearly all radio telescopes. They measure the intensity of electromagnetic radiation, converting this radiation into electrical signals. A radiometer's primary components are an antenna and a Low Noise Amplifier (LNA), which is the core of the ``receiver'' chain. Instrumental effects introduced by the receiver are typically corrected or removed during calibration. However, impedance mismatches between the antenna and receiver can introduce unwanted signal reflections and distortions. Traditional calibration methods, such as Dicke switching, alternate the receiver input between the antenna and a well-characterised reference source to mitigate errors by comparison. Recent advances in Machine Learning (ML) offer promising alternatives. Neural networks, which are trained using known signal sources, provide a powerful means to model and calibrate complex systems where traditional analytical approaches struggle. These methods are especially relevant for detecting the faint sky-averaged 21-cm signal from atomic hydrogen at high redshifts. This is one of the main challenges in observational Cosmology today. Here, for the first time, we introduce and test a machine learning-based calibration framework capable of achieving the precision required for radiometric experiments aiming to detect the 21-cm line.

Figures (8)

• Figure 1: A schematic overview explaining the core challenge in radiometer calibration. An impedance mismatch between the receiver and the source (usually a radio antenna) causes standing waves between the receiver and source. This adds power to the output signal and must be corrected for via calibration. $\Gamma_{A}$ and $\Gamma_{\text{rec}}$ represent the reflection coefficient of the antenna and the receiver and $P_{\text{src}}^{\text{out}}$ is the measured power. Throughout the paper, green and orange represent "inputs" and "outputs", which will be described in detail in Section \ref{['sec:radiometrcalibration']}.
• Figure 2: High-level overview of the machine learning-based calibration framework, applied to a 21-cm cosmology experiment. The 21-cm signal obscured by foregrounds pritchard201221 is received by the radio telescope as $T_{\text{sky}}$. The signal then passes through an amplifier and other components in the receiver chain. The effect of the receiver chain on the signal is "calibrated" by the neural network, which recovers the antenna signal where the 21-cm signal can be extracted. A detailed description of the calibration parameters is provided in Section \ref{['sec:radiometrcalibration']}.
• Figure 3: Temperature calibration using internal sources on the REACH receiver. The four panels in the bottom-left quadrant show the measured resistor temperatures (black lines) and the calibrated training solutions (coloured dots). The blue, green, red, and purple dots represent the training data. RMSE errors are shown in the titles. The four panels in the bottom-right quadrant show the predicted Noise Parameters for each source. The top-right two panels show the predicted gain $g$ (source-independent) and receiver temperature $T_{\text{rec}}$ (source-dependent) for each source, calculated from the predicted Noise Parameters. The two panels in the top-left quadrant show the predictions for the unseen source (a $69\,\Omega$ resistor on a 2-meter cable). The "relative residuals" represent the error when the data are centred on zero along the temperature axis. All other plots are "absolute" (i.e., no offset correction applied). The colours of the predicted resistor temperatures on the left correspond to the plots on the right.
• Figure 4: The top panel shows the predicted antenna temperature in orange, with the true temperature overlaid in black dashes. The true signal is the simulated signal, including the foregrounds, beam effects, and simulated 21-cm signal. The predicted temperature is that recovered by the machine learning calibration methodology after the simulated temperatures have passed through the receiver simulation pipeline. The bottom panel shows the relative calibration residuals when the predicted temperatures are subtracted from the true temperatures. The sky-averaged 21-cm signal injected into the simulated antenna temperature is shown in green for scale. The black crosses represent the orange points (originally at a resolution of 12 kHz) binned to 1-MHz channels. $\sigma$ and $\sigma_\text{1~MHz}$ are the RMSE errors when the orange points are subtracted from the true temperature at 12 kHz and 1 MHz, respectively.
• Figure 5: Inferred sky-averaged 21-cm signal from the calibrated antenna temperature shown in Figure \ref{['fig:image1']}. Left: The reconstructed sky-averaged 21-cm signal, showing the inferred signal's functional posterior in orange and the initially injected true signal in green. Right: Posterior distributions for the parameters of the recovered sky-averaged 21-cm signal, with the true values indicated in green.