RFSoC receiver calibration system for 21-cm global spectrum experiments from space: The CosmoCube case

TL;DR

CosmoCube targets a space-based global 21-cm spectrum measurement in the 10–100 MHz band from the lunar far side to bypass ionospheric and terrestrial interference. The authors develop an RFSoC-based receiver calibration system comprising a VNA sub-system and a source switching sub-system, and they systematically evaluate quantization, leakage, and measurement errors through simulation and laboratory tests. A noise-wave parameter–driven calibration framework, multi-port mock-data modeling, and S-parameter/temperature corrections enable sky temperature recovery and foreground subtraction, achieving residuals within about ±20 mK in the 50–90 MHz band under realistic error budgets. The work demonstrates the feasibility of compact, low-power calibration-enabled receivers for future lunar-orbit global 21-cm experiments, and it identifies practical paths to further improve calibration accuracy in resonance regions and isolation schemes.

Abstract

The CosmoCube project plans to deploy a global 21-cm spectrometer with 10-100 MHz observation band in a lunar orbit. The farside part of such an orbit, i.e. the part of orbit behind the Moon, offers an ideal site for accurately measuring the 21-cm signal from the Dark Ages, Cosmic Dawn and Epoch of Reionization, as the effects of the Earth's ionosphere, artificial radio frequency interference (RFI), and complex terrain and soil are all avoided. Given the limitations of a satellite platform, we propose a receiver calibration system design based on a Radio Frequency system-on-chip, consisting of a Vector Network Analyzer (VNA) sub-system, and a source switching sub-system. We introduce the measurement principle of the VNA, and discuss the effect of quantization error. The accuracy, stability and trajectory noise of the VNA are tested in laboratory experiments. We also present the design of the source-switching sub-system, generating mock datasets, showing that the imperfect return loss, insertion loss, and isolation of surface-mounted microwave switches have a minimal effect on the sky foreground fitting residuals, which are within $\pm10$ mK under optimal fitting condition. When all possible measurement errors in reflection coefficients and physical temperatures are taken into account, the foreground fitting residuals for the 50-90 MHz part of the spectrum remain around $\pm20$ mK.

Figures (20)

• Figure 1: The block diagram of the analog receiver. The part framed by dashed blue line is the VNA sub-system. 'DC1' and 'DC2' are two directional couplers that constitute the VNA-subsystem. 'SP6T' is the 6-way microwave switch. 'SPDT' is the 2-way microwave switch. 'DPDT' is the double pole double throw switch. $\Gamma_{\text{source}}$ represents the reflection coefficient of the antenna or calibrators, $\Gamma_{\text{rec}}$ is the reflection coefficient of the receiver. A microwave switch is used in the dashed red box to enhance isolation and reduce antenna signal leakage. The part framed by dashed orange line is considered as a multi-port microwave network in the mock datasets generation process. The solid red and blue lines represent the signal paths for the different states of the DPDT switch. When the DPDT switch is in state 1, the VNA measures $S_{\text{11}}$ of the antenna, calibrators and the LNA. When the DPDT switch is in state 2, the RFSoC measures the spectrum of antenna and calibrators
• Figure 2: The internal computation process of the RFSoC FPGA.
• Figure 3: Measurement errors in VNA simulation when calibrating with a -5 dBm power level and measuring with different power levels: The first column corresponds to source 1 with $\Gamma_1 = 0.5\exp{(-i\times0.01f)}$, and the second column to source 2 with $\Gamma_2 = 0.02\exp{(-i\times0.01f)}$. The first row represents the magnitude errors in dB, and the second row represents the phase errors in degrees. Different colored lines represent different power levels. The root mean squares (RMS) of the measurement errors are labelled in the legend.
• Figure 4: Measurement errors in VNA simulation when calibrating and measuring with the same power level. The first column corresponds to source 1 and the second column to source 2. Different colored lines represent different power levels. The RMS of the measurement errors are labelled in the legend.
• Figure 5: Top panel shows the magnitude of raw measurement $S_{\text{11}}$. Bottom panel shows the magnitude difference between the raw $S_{\text{11}}$ obtained from the low-power measurements and the -5 dBm measurement. Left: Load Calibration Standards. Right: Source 2.