11institutetext:  Space Sciences Laboratory, University of California,
Berkeley, CA 94720, USA
11email<EMAIL_ADDRESS>22institutetext: School of Earth and Space
Exploration, Arizona State University, Tempe, AZ 85287, USA 33institutetext:
Departamento de Ingeniería Eléctrica, Universidad Católica de la Santísima
Concepción, Alonso de Ribera 2850, Concepción, Chile 44institutetext:
Department of Physics and Trottier Space Institute, McGill University,
Montréal, QC H3A 2T8, Canada 55institutetext: Department of Astronomy,
University of California, Berkeley, CA 94720, USA 66institutetext: School of
Mathematics, Statistics, & Computer Science, University of KwaZulu-Natal,
Durban, South Africa 77institutetext: David A. Dunlap Department of Astronomy
& Astrophysics, University of Toronto, Toronto, ON M5S 3H4, Canada
88institutetext: Departamento de Ingeniería Eléctrica, Universidad de Chile,
Santiago, Chile 99institutetext: CryoElec LLC, Chandler, AZ 85225, USA
1010institutetext: National Radio Astronomy Observatory, Charlottesville, VA
22903, USA 1111institutetext: Facultad de Ingeniería, Universidad ECCI,
Bogotá, 111311, Colombia 1212institutetext: School of Chemistry and Physics,
University of KwaZulu-Natal, Durban, South Africa 1313institutetext:
Commonwealth Scientific and Industrial Research Organisation (CSIRO), Space &
Astronomy, P. O. Box 1130, Bentley, WA 6102, Australia

# Mapper of the IGM Spin Temperature (MIST): Instrument Overview

R. A. Monsalve 112233 C. Altamirano 33 V. Bidula 44 R. Bustos 33 C. H. Bye 55
H. C. Chiang 4466 M. Díaz Sadly, Mauricio Díaz passed away before the
publication of this article.33 B. Fernández 33 X. Guo 11 I. Hendricksen 44 E.
Hornecker 77 F. Lucero 88 H. Mani 99 F. McGee 44 F. P. Mena 1010 M. Pessôa 44
G. Prabhakar 11 O. Restrepo 881111 J. L. Sievers 441212 N. Thyagarajan 1313

(Received XXXX; accepted XXXX)

###### Abstract

Context. The observation of the global $21$ cm signal produced by neutral
hydrogen gas in the intergalactic medium (IGM) during the Dark Ages, Cosmic
Dawn, and Epoch of Reionization requires measurements with extremely well-
calibrated wideband radiometers.

Aims. We describe the design and characterization of the Mapper of the IGM
Spin Temperature (MIST), which is a new ground-based, single-antenna, global
$21$ cm experiment.

Methods. The design of MIST was guided by the objectives of avoiding
systematics from an antenna ground plane and cables around the antenna, as
well as maximizing the instrument’s on-sky efficiency and portability for
operations at remote sites.

Results. We have built two MIST instruments, which observe in the range
$25$–$105$ MHz. For the $21$ cm signal, this frequency range approximately
corresponds to redshifts $55.5>z>12.5$, encompassing the Dark Ages and Cosmic
Dawn. The MIST antenna is a horizontal blade dipole of $2.42$ m in length,
$60$ cm in width, and $52$ cm in height above the ground. This antenna
operates without a metal ground plane. The instruments run on $12$ V batteries
and have a maximum power consumption of $17$ W. The batteries and electronics
are contained in a single receiver box located under the antenna. We present
the characterization of the instruments using electromagnetic simulations and
lab measurements. We also show sample sky measurements from recent
observations at remote sites in California, Nevada, and the Canadian High
Arctic. These measurements indicate that the instruments perform as expected.
Detailed analyses of the sky measurements are left for future work.

###### Key Words.:

methods: observational – galaxy: general – instrumentation: miscellaneous –
Astronomical instrumentation, methods and techniques – Cosmology:
observations, dark ages, reionization, first stars

##  1 Introduction

The measurement of the $21$ cm line from neutral hydrogen gas in the
intergalactic medium (IGM) has been recognized as a promising way to map the
evolution of the Universe during its first billion years and as the only way
to observe the Dark Ages (Hogan & Rees, 1979; Madau et al., 1997; Shaver et
al., 1999; Rees, 2000; Tozzi et al., 2000; Barkana & Loeb, 2001; Loeb &
Zaldarriaga, 2004; Furlanetto et al., 2006).

The observation frequency of the $21$ cm signal from redshift $z$ is given by
$\nu=1420\;\mathrm{MHz}\times(1+z)^{-1}$. Therefore, measurements of neutral
hydrogen before the end of the epoch of reionization (EoR) have to be
conducted at $\nu<220$ MHz111The EoR is currently estimated to have ended by
$z\approx 5.5$ (Kulkarni et al., 2019; Nasir & D’Aloisio, 2020; Raste et al.,
2021; Cain et al., 2021; Qin et al., 2021),. Several radio experiments are
trying to detect this cosmological signal. They can be classified into those
targetting the sky-averaged or global component, and antenna arrays focussing
on spatial anisotropies. Ground-based global $21$ cm experiments include
ASSASSIN (McKinley et al., 2020), CTP (Nhan et al., 2019), EDGES (Monsalve et
al., 2017b; Bowman et al., 2018), LEDA (Bernardi et al., 2016; Price et al.,
2018), LWA-SV (Dilullo et al., 2020), PRIZM (Philip et al., 2019), REACH (de
Lera Acedo et al., 2022; Razavi-Ghods et al., 2023), SARAS (Singh et al.,
2017, 2022), and SITARA (Thekkeppattu et al., 2022). Space-based global signal
missions and concepts include DAPPER (Burns, 2021), DSL/Hongmeng (Shi et al.,
2022b), LuSEE Night (Bale et al., 2023), and PRATUSH
222https://wwws.rri.res.in/DISTORTION/pratush.html. Arrays targeting the $21$
cm spatial anisotropies from the ground include HERA (DeBoer et al., 2017),
LOFAR (van Haarlem et al., 2013), MWA (Tingay et al., 2013), NenuFAR (Zarka et
al., 2020), OVRO-LWA (Garsden et al., 2021), and SKA-Low (Koopmans et al.,
2015). Space-based array concepts include CoDEX (Koopmans et al., 2021), the
DSL/Hongmeng array (Chen et al., 2021; Shi et al., 2022a), FARSIDE (Burns,
2021), and OLFAR (Bentum et al., 2020).

In this paper, we introduce the Mapper of the IGM Spin Temperature
(MIST)333www.physics.mcgill.ca/mist, which is a new ground-based experiment
trying to detect the global $21$ cm signal. The brightness temperature of this
signal is given by (Furlanetto et al., 2006)

$T_{b}(z)\approx
9x_{H}(z)\left[1-\frac{T_{cmb}(z)}{T_{spin}(z)}\right]\sqrt{1+z}\;\;\;\mathrm{mK},$
(1)

where $x_{H}$ is the mean hydrogen neutral fraction, $T_{cmb}$ is the
temperature of the cosmic microwave background, and $T_{spin}$ is the $21$ cm
spin temperature. $T_{b}$ can be represented as a frequency spectrum using the
redshift-to-frequency mapping for the $21$ cm line. Two absorption features
are expected in this spectrum: one from the Dark Ages and the other from the
Cosmic Dawn. The Dark Ages feature has a center at $\approx 17$ MHz ($z\approx
80$), an amplitude of $\approx 40$ mK, and a full width at half maximum (FWHM)
of $\approx 25$ MHz (Furlanetto et al., 2006; Pritchard & Loeb, 2008; Mondal &
Barkana, 2023). The absorption feature from the Cosmic Dawn is centered
somewhere in the range $\approx 45$–$130$ MHz ($30\gtrsim z\gtrsim 10$) and
has an amplitude of up to $\approx 250$ mK. The exact shape of the Cosmic Dawn
feature depends on the astrophysical characteristics of the first stars,
galaxies, and black holes (Tozzi et al., 2000; Furlanetto, 2006; Pritchard &
Loeb, 2010; Cohen et al., 2017; Mirocha et al., 2018).

One of the main challenges in the global $21$ cm measurement is the presence
of diffuse foreground contamination. This contamination is at least four
orders of magnitude stronger than the signal, and dominated by Galactic and
extragalactic synchrotron radiation (e.g., Voytek et al., 2014; Bernardi et
al., 2016). Radio point sources that also affect this measurement include Cas
A, Cyg A, Tau A, and Vir A (Helmboldt & Kassim, 2009; de Gasperin et al.,
2020), while Jupiter and the Sun can have a significant transient contribution
below $\approx 40$ MHz (e.g., Panchenko et al., 2013; Sasikumar Raja et al.,
2022). Other serious challenges to this measurement include very stringent
instrument calibration requirements (Monsalve et al., 2017a), human-made
radio-frequency interference (RFI) (Offringa et al., 2015; Dyson et al.,
2021), and absorption, emission, and refraction from the Earth’s ionosphere
(Vedantham et al., 2014; Rogers et al., 2015; Sokolowski et al., 2015; Datta
et al., 2016; Shen et al., 2021).

In Bowman et al. (2018), the EDGES global $21$ cm experiment made the only
detection claim of the Cosmic Dawn absorption feature to date. The reported
signal has a flattened Gaussian shape, an amplitude of $0.5_{-0.2}^{+0.5}$ K,
a center at $78\pm 1$ MHz, and a FWHM of $19_{-2}^{+4}$ MHz. The ranges in
each parameter represent $\pm 3$-sigma uncertainty, which is mainly
systematic. The reported best-fit amplitude is at least twice as large as
expected in standard models, which has motivated theorists to propose physical
scenarios for the early Universe not typically considered before the EDGES
result (e.g., Muñoz & Loeb, 2018; Fialkov & Barkana, 2019; Mirocha &
Furlanetto, 2019). However, the large absorption and unexpected flattened
Gaussian shape have also produced skepticism about the cosmological
interpretation of the feature (Hills et al., 2018; Singh & Subrahmanyan, 2019;
Sims & Pober, 2020). Alternative explanations that have been suggested include
instrumental systematics, such as resonances in the metal ground plane under
the EDGES antenna (Bradley et al., 2019), and contributions from other sources
in the sky, such as polarized Galactic emission (Spinelli et al., 2019). The
SARAS3 experiment recently reported a non-detection of the EDGES signal using
measurements with a vertical monopole antenna floating in a lake (Singh et
al., 2022). This null result has a significance of $<2$-sigma when considering
both the uncertainty of SARAS3 as well as the uncertainty of the reported
EDGES signal, but it nonetheless increases the pressure to determine the
origin of the EDGES feature. Whether or not the EDGES signal is cosmological,
detecting and validating the global $21$ cm signal from the Dark Ages and
Cosmic Dawn will require measurements from different experiments.

The MIST instrument is a single-antenna, single-polarization, total-power
radiometer that observes the sky at $25$–$105$ MHz, which for the $21$ cm
signal corresponds to redshifts $55.5>z>12.5$. This range represents a large
fraction of the range where the Dark Ages and Cosmic Dawn absorption features
are expected to be found. The instrument has been designed to achieve the
performance required for detection while remaining highly portable for
transportation to remote radio-quiet sites. A significant difference between
MIST and other wideband-dipole, total-power radiometers, such as EDGES, LEDA,
PRIZM, and REACH, is its operation without a metal ground plane over the soil.
This choice eliminates systematic effects associated with finite ground planes
and their physical limitations, with the tradeoff of folding soil properties
into MIST’s electromagnetic performance. The unique instrumental approach,
combined with observations from multiple locations and terrestrial latitudes,
will enable MIST to significantly contribute to the detection of the global
$21$ cm signal through independent measurements subject to different
experimental factors.

We have built two copies of the MIST instrument, which we deployed in the
field for the first time in 2022. Specifically, we conducted observations from
Deep Springs Valley in California, Death Valley in Nevada, and the McGill
Arctic Research Station (MARS) in the Canadian High Arctic.

This paper is organized as follows. Section 2 provides a general description
of the MIST instruments. Section 3 describes the calibration formalism for the
sky measurements. In Section 4 we show the characteristics of the MIST antenna
and discuss its sensitivity to the electrical properties of the soil. In
Section 5 we provide details about the balun, which acts as an interface
between the antenna and the receiver. Section 6 describes the receiver
electronics and laboratory calibration. In Section 7 we present sample field
measurements that provide an initial view of the instrument’s performance. We
summarise this paper in Section 8.

Figure 1: One of the two MIST instruments during sky observations in Death
Valley, Nevada, in May 2022.

##  2 General description

The MIST instrument444In this paper we refer to the two MIST instruments as
“instrument” because their design is nominally identical. is a single-antenna,
single-polarization, total power radiometer. The design of the instrument is
motivated by the following objectives:

  1. (a)

Have an antenna beam pattern above the soil that peaks at the zenith and
decreases toward the horizon. This pattern would maximize the sensitivity of
the instrument to the sky signal, and minimize the sensitivity to features of
the terrain and sky blockage by mountains (Bassett et al., 2021).

  2. (b)

Avoid using a metal ground plane. In addition to reducing the probability of
instrumental resonances (Bradley et al., 2019), this choice would eliminate
the possibility of signal reflections produced by the electrical discontinuity
between the edges of the ground plane and the soil (Mahesh et al., 2021;
Spinelli et al., 2022; Rogers et al., 2022). Operating without a ground plane
increases the ground loss. However, the ground loss can in principle be
estimated using electromagnetic simulations and then removed during data
analysis. Observations from different sites could be leveraged to test for
systematic effects related to ground loss.

  3. (c)

Keep the instrument small and of low power consumption. These characteristics
would enable the operation of the instrument with small batteries and
facilitate its transportation to remote sites. In a small instrument, the
radio-frequency (RF) paths would be short, increasing the accuracy with which
key calibration parameters, in particular of the receiver, could be measured.

  4. (d)

Avoid using cables outside of the receiver box. By avoiding cables we would
eliminate their potential impact on the antenna performance, reduce emission
of self-generated RFI, and simplify the design for electromagnetic
simulations.

From the guidelines above, we arrived at a design based on a horizontal $2.42$
m tip-to-tip blade dipole antenna made of solid aluminum panels. The antenna
operates $52$ cm above the soil and without a metal ground plane. The
instrument is powered by four $12$ V, $18$ Ah batteries, and has a maximum
power consumption of $17$ W. Except for a small balun, all the electronics of
the instrument, including the batteries, are contained in a single aluminum
receiver box of size $40.5$ cm $\times$ $33.5$ cm $\times$ $26$ cm located
under the antenna. The antenna and receiver box are supported by a frame made
of fiberglass tubes and angles, acrylonitrile butadiene styrene (ABS) plastic
elbows, and nylon rods, screws, and nuts. The full frequency range of the
radiometer is $0$–$125$ MHz but the sky observations are limited to the range
$25$–$105$ MHz. The high-frequency end of this range is imposed by the reduced
performance of the analog-to-digital converter (ADC) above $105$ MHz. The low-
frequency end of the range is imposed by the reduced efficiency of the antenna
combined with a significant increase in the shortwave RFI below $25$ MHz at
most locations. The average FWHM of the antenna beam directivity across
$25$–$105$ MHz is $\approx 85^{\circ}$.

Figure 1 shows a picture of one of the instruments deployed in Death Valley in
May 2022. Figure 2 shows a schematic of the instrument and Table 1 lists the
instrument’s dimensions.

Figure 2: Schematic of the MIST instrument (not to scale). The dimensions are
listed in Table 1.

##  3 Calibration formalism

Before describing the instrument in detail, here we summarize the mathematical
model used by MIST for the sky measurements.

###  3.1 Sky contribution to the antenna temperature

The contribution from the sky to the antenna temperature is given by

$\displaystyle
T_{S}(\nu)=\frac{\int_{0}^{2\pi}\int_{0}^{\pi/2}T_{sky}(\theta,\phi,\nu)D(\theta,\phi,\nu)\sin\theta
d\theta d\phi}{\int_{0}^{2\pi}\int_{0}^{\pi/2}D(\theta,\phi,\nu)\sin\theta
d\theta d\phi},$ (2)

where $T_{sky}$ is the sky brightness temperature spatial distribution; $D$ is
the antenna beam directivity; $\theta$ and $\phi$ are the antenna zenith and
azimuth angles, respectively; and $\nu$ is frequency.

The antenna temperature measured at the input of the calibrated receiver is
modeled as

$\displaystyle
T_{A}(\nu)=\eta(\nu)T_{S}(\nu)+\left[1-\eta(\nu)\right]T_{phys},$ (3)

where $\eta$ is the efficiency in the measurement of $T_{S}$ accounting for
passive sources of loss, and $T_{phys}$ is the physical temperature associated
with the passive sources of loss. MIST’s on-sky efficiency corresponds to the
multiplication of three factors: (1) the radiation efficiency, $\eta_{rad}$,
which accounts for resistive loss due to finite electrical conductivity in and
around the antenna; (2) the beam efficiency, $\eta_{beam}$, which corresponds
to the fraction of the beam solid angle toward the sky relative to the total;
and (3) the balun efficiency, $\eta_{balun}$, representing the efficiency of
the signal transmission through the balun used between the antenna excitation
port and the receiver input. Assuming the same physical temperature for the
three passive sources of loss, which typically corresponds to the ambient
temperature, Equation 3 can be solved for the sky contribution to obtain

$\displaystyle
T_{S}=\frac{T_{A}-\left[1-\eta_{rad}\eta_{beam}\eta_{balun}\right]T_{phys}}{\eta_{rad}\eta_{beam}\eta_{balun}}.$
(4)

###  3.2 Receiver calibration

The antenna temperature calibrated at the receiver input is related to the
power spectral density (PSD) measured by the receiver, $P_{A}$, by

$T_{A}(\nu)=\frac{P_{A}(\nu)}{g_{R}(\nu)}-T_{R}(\nu),$ (5)

where $g_{R}$ is the receiver gain and $T_{R}$ is the receiver temperature. We
determine $g_{R}$ and $T_{R}$ with the method developed in Rogers & Bowman
(2012) and Monsalve et al. (2017a). In this method, the receiver input is
continuously switched in the field between three positions: (1) the antenna,
(2) an internal ambient load, and (3) the internal ambient load in series with
an active noise source. In addition, external calibration standards of
different noise temperatures and reflection coefficients are measured in the
lab. These external standards provide the absolute calibration to the
receiver. With some rearrangement of the PSD equations for the three receiver
input positions presented in Monsalve et al. (2017a), $g_{R}$ and $T_{R}$ can
be written as (dropping the frequency dependences of all the quantities for
brevity)

$\displaystyle g_{R}$
$\displaystyle=\left(\frac{1}{K_{0}}\right)\left[\frac{P_{L+NS}-P_{L}}{C_{1}\left(T^{a}_{L+NS}-T^{a}_{L}\right)}\right],$
(6)

$\displaystyle T_{R}=$ $\displaystyle
K_{0}\Biggl{\\{}P_{L}\left[\frac{C_{1}\left(T^{a}_{L+NS}-T^{a}_{L}\right)}{P_{L+NS}-P_{L}}\right]-(T^{a}_{L}-C_{2})\Biggl{\\}}$
$\displaystyle+K_{U}T_{U}+K_{C}T_{C}+K_{S}T_{S}.$ (7)

Here, $P_{L}$ and $P_{L+NS}$ are the PSDs from the internal ambient load and
ambient plus noise source, respectively; $T^{a}_{L}$ and $T^{a}_{L+NS}$ are
assumed values for the noise temperatures of the internal ambient load and
ambient plus noise source, respectively; $C_{1}$ is an absolute multiplicative
correction to the difference $T^{a}_{L+NS}-T^{a}_{L}$; $C_{2}$ is an absolute
additive correction to $T^{a}_{L}$; and $T_{U}$, $T_{C}$, and $T_{S}$ are the
noise wave parameters of the receiver front-end in the formalism of Meys
(1978). $C_{1}$, $C_{2}$, $T_{U}$, $T_{C}$, and $T_{S}$ are referred to as the
absolute receiver calibration parameters, which we determine using the
measurements from the external calibration standards (Monsalve et al., 2017a).
The $K$ parameters in Equations 6 and 7 capture the impedance mismatch between
the antenna and the receiver input, and are given by:

$\displaystyle K_{0}$
$\displaystyle=\frac{1-|\Gamma_{R}|^{2}}{\left(1-|\Gamma_{A}|^{2}\right)|F|^{2}},$
(8) $\displaystyle K_{U}$
$\displaystyle=\frac{|\Gamma_{A}|^{2}}{1-|\Gamma_{A}|^{2}},$ (9)
$\displaystyle K_{C}$
$\displaystyle=\frac{|\Gamma_{A}|}{\left(1-|\Gamma_{A}|^{2}\right)|F|}\cos\alpha,$
(10) $\displaystyle K_{S}$
$\displaystyle=\frac{|\Gamma_{A}|}{\left(1-|\Gamma_{A}|^{2}\right)|F|}\sin\alpha,$
(11) $\displaystyle F$
$\displaystyle=\frac{\sqrt{1-|\Gamma_{R}|^{2}}}{1-\Gamma_{A}\Gamma_{R}},$ (12)
$\displaystyle\alpha$ $\displaystyle=\mathrm{arg}(\Gamma_{A}F),$ (13)

where $\Gamma_{A}$ is the reflection coefficient of the antenna, including the
effect of the balun, and $\Gamma_{R}$ is the reflection coefficient looking
into the receiver input.

##  4 Antenna

Similarly to other experiments (e.g., Cummer et al., 2022; Anstey et al.,
2022), in MIST we explored a variety of antenna types. In addition to having a
zenith-pointing beam (Section 2), the antenna must produce a good impedance
match with the receiver (Section 3.2) and have a geometry that is easy to
simulate electromagnetically. After considering the tradeoffs between these
criteria, we selected a horizontal blade dipole antenna for MIST.

The blade dipole antenna was introduced for global $21$ cm measurements by
EDGES-2 in Mozdzen et al. (2016)555In its first iteration, EDGES used a
fourpoint antenna.. However, in MIST we use this antenna without a ground
plane, which represents a significant difference. Moreover, in MIST all the
dimensions of the antenna and instrument (Table 1) are different from those in
EDGES. These differences offer a valuable opportunity for the cross-checking
of systematics between MIST and EDGES. The differences between MIST and other
current experiments are even more substantial. In particular, SARAS uses a
vertical monopole over water (Singh et al., 2022) and REACH uses two antenna
types: a hexagonal dipole and a conical log-spiral, both above a $20$ m
$\times$ $20$ m metal ground plane that is suspended above the soil (de Lera
Acedo et al., 2022). With its unique characteristics, the MIST antenna
represents a significant contribution to the experimental parameter space of
global $21$ cm instruments.

Table 1: Dimensions of the MIST instrument. The parameters correspond to those in the schematic of Figure 2. Dimension | Parameter | Value [m]
---|---|---
antenna panel length | al | $1.2$
antenna panel width | aw | $0.6$
antenna panel thickness | at | $0.003$
antenna panel separation | as | $0.02$
antenna panel height | ah | $0.52$
receiver length | rl | $0.405$
receiver width | rw | $0.26$
receiver depth | rd | $0.335$
receiver height | rh | $0.02$
balun length | bl | $0.05$
balun width | bw | $0.03$
balun depth | bd | $0.037$
balun height | bh | $0.022$
Figure 3: Screenshot of the FEKO electromagnetic simulations.

###  4.1 Electromagnetic simulations

We use electromagnetic simulations with the FEKO
software666https://www.altair.com/feko to predict the parameters of the MIST
antenna necessary for the calibration of the sky measurements —radiation
efficiency, beam directivity, beam efficiency, and reflection coefficient
(Section 3). In FEKO, we use the method of moments solver, which is the most
suited for radiation problems involving electrically large structures.

####  4.1.1 Simulation geometry

The simulation geometry includes the antenna panels, balun, and receiver box,
following the schematic of Figure 2 and dimensions of Table 1. The geometry
also includes soil, which extends to infinity in the horizontal direction and
depth777The effect of the soil is computed analytically using Sommerfeld
integrals as Green’s functions for solving the boundary conditions (Davidson,
2011; Mosig & Michalski, 2021).. Figure 3 shows a screenshot of the
simulations. The antenna panels are modeled as $3$ mm thick aluminum sheets.
Each panel includes the holes illustrated in Figure 2: six of these holes
connect to the support frame, and the four holes near the edge are used to
fine-tune the panel-to-panel separation distance. The excitation port is
simulated as a voltage source in the middle of a wire connecting the two
antenna panels. The diameter of the wire is $1$ mm, which matches the diameter
of the real wires that connect the antenna to the balun (Section 5). The
simulated wire is modeled as a perfect electric conductor because the effect
of the finite conductivity of the real wires is included in the S-parameters
of the balun. The balun and receiver box are modeled as hollow boxes with
$1.6$ mm thick aluminum walls, matching the real instrument. We use an
electrical conductivity of $3.816\times 10^{7}$ Sm-1 for aluminum (Gardiol,
1984). The antenna support frame (made out of fiberglass, nylon, and ABS
plastic) does not have a significant effect on the antenna response and is not
included in the simulations.

####  4.1.2 Soil models

The performance of the antenna depends very strongly on the electrical
parameters of the soil: specifically, the conductivity ($\sigma$) and relative
permittivity ($\epsilon_{r}$). In real soils, $\sigma$ and $\epsilon_{r}$ are
spatially inhomogeneous. However, in FEKO it is only possible to design
infinite soil models with variations as a function of depth. These variations
are implemented using horizontal layers of different $\sigma$ and
$\epsilon_{r}$ (Spinelli et al., 2022). To simplify the modeling and work
within the capabilities of FEKO, for MIST we must choose observation sites
where the soil is very close to flat and any variations primarily occur as a
function of depth.

To explore the effect of soil on the MIST antenna performance, we run FEKO
simulations with nine models for the soil. The characteristics of the models
are listed in Table 2. Five of these models, labeled “nominal” and `1L_xx`,
are single-layer models. These models intend to mimic the optimistic scenario
in which, from the point of view of the antenna, the soil can be well
described as effectively uniform. The nominal model, which in this paper is
used as a reference, has values $\sigma_{1}=0.01$ Sm-1 and $\epsilon_{r1}=6$.
In the `1L_xx` models, the value of one of the parameters is changed relative
to the nominal model, with the `xx` part of the label being used to identify
the change. Specifically, `c+` (`c-`) corresponds to an increase (decrease) in
conductivity to $0.1$ ($0.001$) Sm-1, and `p+` (`p-`) represents an increase
(decrease) in relative permittivity to $10$ ($2$). The values we use for
$\sigma$ and $\epsilon_{r}$ fall within the ranges reported for several
geological materials that we could encounter at our observation sites. For
instance, snow and freshwater ice typically have $0\lesssim\sigma\lesssim
0.01$ Sm-1 and $2\lesssim\epsilon_{r}\lesssim 6$. For sand, silt, and clay,
$\sigma$ and $\epsilon_{r}$ strongly depend on moisture level and span the
wide ranges $10^{-7}$–$10^{0}$ Sm-1 and $2$–$40$, respectively (Reynolds,
2011). Our choices for the parameter values, in particular, closely match the
values reported by Sutinjo et al. (2015) for the soil at the Inyarrimanha
Ilgari Bundara, the CSIRO Murchison Radio-astronomy Observatory, with
different moisture levels. Our values are also consistent with the soil
measurements done by Spinelli et al. (2022) at the Owens Valley Radio
Observatory for dry and wet conditions.

As shown in Table 2, our last four soil models, labeled `2L_xx`, are two-layer
models. The purpose of these models is to represent the more realistic
situation in which there is a change in the soil parameters at some depth from
the surface. In these models, the top layer has a thickness $L=1$ m and the
same conductivity and permittivity as the nominal case, while the bottom layer
extends to infinite depth and has a different value of either conductivity or
permittivity. In each case, the parameter change made to the bottom layer is
indicated in the model name, similarly to the single-layer models.
Furthermore, the conductivity and relative permittivity values assigned to the
bottom layer in the `c+`, `c-`, `p+`, and `p-` cases are the same as for the
single-layer models. As an example, one observation site where the soil could
be well represented by a two-layer model is MARS during the summer. At that
site, the soil in the summer consists of an unfrozen top layer and a
permanently frozen, or “permafrost”, bottom layer (e.g., Pollard et al., 2009;
Wilhelm et al., 2011). We leave for future work the exploration of a wider
range of soil models, including models with more than two layers (which were
studied in Spinelli et al. (2022) for the LEDA experiment), and models that
account for the fact that in real soils the conductivity and permittivity vary
as a function of frequency (e.g., Revil, 2013).

####  4.1.3 Simulation settings

The simulations are conducted in the range $25$–$125$ MHz with a resolution of
$1$ MHz. Although the sky measurements are currently analyzed up to $105$ MHz,
the simulations extend up to $125$ MHz anticipating a future increase in the
bandwidth of MIST. In FEKO, we use the `fine` mesh size setting and double-
precision calculations. Using the $64$ cores of an AMD Ryzen Threadripper PRO
5995WX processor, each simulation takes $\approx 60$ minutes.

Next, we describe the results of the FEKO simulations for the radiation
efficiency, beam directivity, beam efficiency, and reflection coefficient at
the dipole excitation port.

Table 2: Soil models used in the FEKO simulations of MIST. Five of these models are single-layer models (“nominal” and 1L_xx) and four are two-layer models (2L_xx). The layers are characterized in terms of their electrical conductivity ($\sigma$) and relative permittivity ($\epsilon_{r}$). In the two-layer models, the thickness of the top layer is $L=1$ m. Model | # layers |  $\sigma_{1}$ [Sm-1] | $\epsilon_{r1}$ |  $\sigma_{2}$ [Sm-1] | $\epsilon_{r2}$
---|---|---|---|---|---
nominal | 1 | $0.01$ | $6$ |  |
`1L_c+` | 1 | $0.1$ | $6$ |  |
`1L_c-` | 1 | $0.001$ | $6$ |  |
`1L_p+` | 1 | $0.01$ | $10$ |  |
`1L_p-` | 1 | $0.01$ | $2$ |  |
`2L_c+` | 2 | $0.01$ | $6$ | $0.1$ | $6$
`2L_c-` | 2 | $0.01$ | $6$ | $0.001$ | $6$
`2L_p+` | 2 | $0.01$ | $6$ | $0.01$ | $10$
`2L_p-` | 2 | $0.01$ | $6$ | $0.01$ | $2$
Figure 4: (a) Radiation efficiency for the nominal soil model. (b) and (c)
Differences in radiation efficiency between the alternative soil models and
the nominal model. For example, for model 1L_c+,
$\Delta\eta_{rad}=\eta_{rad,\;\texttt{1L\\_c+}}-\eta_{rad,\;nominal}$. In
panels (b) and (c), the zero-points for the differences are the labeled
horizontal grid lines.

###  4.2 Radiation efficiency

The radiation efficiency of the antenna, $\eta_{rad}$, is defined as the ratio
of radiated power to input power. $\eta_{rad}$ relates the beam gain, $G$, to
the beam directivity by

$\displaystyle G(\theta,\phi,\nu)=\eta_{rad}(\nu)D(\theta,\phi,\nu).$ (14)

In this definition, the efficiency only considers resistive, or “ohmic”, loss
in the antenna and conductive regions visible to the antenna, and not
impedance mismatch or external losses, such as ground loss (Stutzman & Thiele,
1998). In our FEKO simulations, we assign the finite conductivity of aluminum
to the antenna panels, balun, and receiver box, and the conductivities of
Table 2 to the soil. This information enables FEKO to calculate and directly
provide $\eta_{rad}$ and $G$. The beam directivity is a derived quantity and
obtained from $\eta_{rad}$ and $G$ (Section 4.3).

Figure 4 shows the radiation efficiency for the nine FEKO simulations. Panel
(a) shows that for the nominal soil model, the efficiency is in the range
$99.93\%$–$99.99\%$ and has a smooth frequency dependence. This high
efficiency is expected for the high conductivity of the instrument’s aluminum
surfaces. Panels (b) and (c) show the difference in the radiation efficiency
for the alternative soil models relative to the nominal model. The main
takeaway of these panels is the confirmation that the radiation efficiency is
sensitive to the characteristics of the soil, in addition to those of the
instrument’s surfaces. For our single-layer (two-layer) models, the largest
change is $\approx 0.08\%$ ($\approx 0.007\%$). Although small compared to the
total efficiency, these changes are comparable to, or larger than, the ratio
between the global $21$ cm signal and the diffuse astrophysical foreground,
which is $\approx 0.01\%$ for the Cosmic Dawn and smaller for the Dark Ages.
This comparison highlights the need to accurately determine and account for
the radiation efficiency in order to minimize biases in the $21$ cm signal
estimation.

Figure 5: Antenna beam directivity for the nominal soil model in the E- and H-
planes at six frequencies.

###  4.3 Beam directivity

We compute the beam directivity as $D=\eta_{rad}^{-1}$G using the gain and
radiation efficiency provided by FEKO. The directivity is only computed for
the top hemisphere because FEKO cannot provide the gain in the soil when the
soil has non-zero electrical conductivity. In MIST, the effect of the
directivity in the soil is accounted for through the beam efficiency, which is
calculated using the top-hemisphere directivity (Section 4.4).

Figure 5 shows slices of the directivity every $20$ MHz for the nominal soil
model. The slices are shown for the E- and H- planes, which are parallel and
perpendicular to the antenna excitation axis (i.e., the antenna’s length),
respectively. The directivity peaks at the zenith and is minimized at the
horizon, satisfying one of the main design objectives for the antenna (Section
2). The peak directivity increases monotonically from $\approx 0.6$ to
$\approx 5.1$ between $25$ and $125$ MHz, and the directivity pattern is wider
in the H-plane at all frequencies.

Figure 6: Antenna beam directivity for all the soil models at three reference
puncture points: (top row) zenith; (middle row) E-plane at
$\theta=45^{\circ}$; and (bottom row) H-plane at $\theta=45^{\circ}$. Figure
7: FWHM of the antenna beam directivity in the E- and H-planes for all the
soil models.

Figure 6 shows the directivity for the nine soil models at three reference
puncture points: (1) the zenith, (2) the E-plane at $\theta=45^{\circ}$, and
(3) the H-plane at $\theta=45^{\circ}$. In this figure, we identify the
following important points:

  1. (a)

The directivity is very sensitive to the properties of the soil. As expected,
the effects are larger when the changes in the soil extend all the way to the
surface, which occurs in the single-layer models. For these models, the
directivity increases with conductivity across most of the frequency range. In
particular, the directivity for model `1L_c+` is $>20\%$, and at some
frequencies $>50\%$, higher than the nominal. Changes in permittivity also
produce significant changes in the directivity, but the sign of the changes
evolves with frequency.

  2. (b)

The uniformity of the single-layer soil models results in a directivity that
is relatively smooth across frequency. For two-layer models, changes in the
bottom layer introduce ripples which, for the $1$ m thickness of the top
layer, have a period of $\approx 50$ MHz.

  3. (c)

At the zenith and the H-plane puncture point, the directivity increases with
frequency for all soil models to values that, at the highest frequencies, are
$>3$. At the E-plane puncture point, the directivity is always $<1$ and peaks
at $\approx 55$–$75$ MHz. The directivities at the E- and H-plane puncture
points indicate that the beam is wider in the H-plane for all the soil models.

As a direct quantification of the beam width, Figure 7 shows the FWHM of the
directivity pattern in the E- and H-planes for the nine soil models. For all
the models, the FWHM is larger in the H-plane than in the E-plane. Moreover,
in the H-plane the FHWM increases with frequency while in the E-plane it
decreases. For our soil models, the H-plane FWHM is in the range
$85^{\circ}$–$107^{\circ}$ at $25$ MHz, increasing to
$113^{\circ}$–$135^{\circ}$ at $125$ MHz. In the E-plane, the FWHM is in the
range $74^{\circ}$–$101^{\circ}$ at $25$ MHz, decreasing to
$39^{\circ}$–$43^{\circ}$ at $125$ MHz. In both planes, the FWHM increases
with decreasing permittivity at the soil surface, as seen when comparing
single-layer cases `1L_p+` and `1L_p-` with the nominal. Similarly to the
directivity (Figure 6), the frequency evolution of the FWHM for the single-
layer models is relatively smooth. For the two-layer models, the FWHM shows
ripples with a period of $\approx 50$ MHz and a peak amplitude of up to
$\approx 8^{\circ}$ with respect to the nominal model. The amplitude of the
ripples is larger in the H-plane than in the E-plane.

The beam directivity of a global $21$ cm instrument has a very strong impact
on the accuracy of the signal recovery (e.g., Mahesh et al., 2021; Anstey et
al., 2022; Cummer et al., 2022; Spinelli et al., 2022). In a future paper
(Monsalve et al., in prep.), we will discuss the $21$ cm signal extraction
accuracy expected for the MIST beam directivity and different soil
characteristics.

Figure 8: Beam efficiency for all the soil models.

###  4.4 Beam efficiency

We define the beam efficiency, $\eta_{beam}$, as the solid angle of the beam
directivity in the top hemisphere divided by the solid angle over the full
sphere, i.e.,

$\displaystyle\eta_{beam}(\nu)=\frac{1}{4\pi}\int_{0}^{2\pi}\int_{0}^{\pi/2}D(\theta,\phi,\nu)\sin\theta
d\theta d\phi.$ (15)

This efficiency is equivalent to one minus the ground loss fraction. Figure 8
shows the beam efficiency for the nine soil models. The main trend observed
across models is an increase of the efficiency with frequency. The efficiency
is in the range $9\%$–$15\%$ at $25$ MHz, increasing to $54\%$–$74\%$ at $125$
MHz. The efficiency also increases with the conductivity at the soil surface,
as seen when comparing single-layer cases `1L_c+` and `1L_c-` with the
nominal. This dependence is consistent with intuition: the efficiency would be
$100\%$ if the soil surface had infinite conductivity, or if an infinitely
large and infinitely conducting ground plane were used. As expected from the
directivity and FWHM plots (Figures 6 and 7), the beam efficiency has a
relatively smooth frequency evolution for single-layer models, while for two-
layer models it contains ripple-like structure. This structure has a period of
$\approx 50$ MHz and a peak amplitude of up to $\approx 5\%$ with respect to
the nominal model.

Figure 9: Reflection coefficient at the dipole excitation port for all the
soil models.

###  4.5 Reflection coefficient at dipole excitation port

Our FEKO simulations provide the reflection coefficient of the antenna at the
dipole excitation port, $\Gamma_{Ad}$. The reflection coefficient at the balun
output, $\Gamma_{A}$, which is the quantity required for receiver calibration
(Section 3.2), is described in Section 5.2.

Figure 9 shows $\Gamma_{Ad}$. At the excitation port, the main characteristic
of the reflection magnitude (top row) is a resonant feature at $\approx 52$
MHz, where the magnitude reaches a minimum. From this resonance, the magnitude
increases monotonically toward lower frequencies until it reaches $\approx 0$
dB at $25$ MHz. The magnitude also increases toward higher frequencies and has
a peak of $\approx-4$ dB at $90$–$95$ MHz. For single-layer models, the
reflection magnitude shows a strong dependence on soil parameters. The largest
effect is at the resonance, where the magnitude varies from $\approx-15$ to
$-45$ dB across our models. The soil parameters also affect the resonance
frequency. Specifically, this frequency decreases with conductivity and
increases with permittivity. For our models, these changes are within a few
MHz. For two-layer models, changes in the bottom layer produce changes in
reflection magnitude that are typically within $2$ dB, except at the
resonance.

The bottom row of Figure 9 shows the reflection phase. The phase has a
predominantly descending slope and a relatively fast $\approx 180^{\circ}$
transition at the resonance. Changes in the soil impact the phase primarily
around the resonance. For most of our models, when going through the resonance
from lower to higher frequencies the phase increases. However, for some models
the phase decreases, leading to a $\approx 360^{\circ}$ difference across
models above the resonance. The negative slope of the phase corresponds to the
antenna delay. Except around the resonance, the delay is similar across our
models. Specifically, the phase change between $25$ and $45$ MHz (below the
resonance) is $\approx 60^{\circ}$, corresponding to a delay of
$\approx(60^{\circ}/360^{\circ})\times(20\;\mathrm{MHz})^{-1}\approx
8\;\mathrm{ns}$. Between $55$ and $125$ MHz (above the resonance) the phase
change is $\approx 150^{\circ}$ and the delay is $\approx 6$ ns.

###  4.6 Variation of top layer thickness

Figure 10: Ripples in the antenna beam directivity at the zenith for the 2L_c+
two-layer soil model. The only parameter being varied is the thickness of the
top layer, $L$. The directivity for the nominal single-layer model is also
shown for reference. Relative to the nominal directivity, as $L$ increases,
both the amplitude and period of the ripples decrease. The directivity for
$L=4$ m (green line) is not visible because it is almost perfectly overlapped
by the nominal directivity. The dependence of the ripples on $L$ observed in
this example is, qualitatively, representative of the other antenna parameters
discussed in Section 4.

So far, the results we have shown for two-layer soil models correspond to
cases in which the thickness of the top layer is $L=1$ m. Here, we present one
example of how the ripples produced by two-layer models change when the top
layer thickness is varied in the range $0.25$–$4$ m. For this example, we use
the `2L_c+` model because it is the one that, among our two-layer models with
$L=1$ m, produces the largest ripples, making the results easier to see and
interpret. In this example, we only show the beam directivity at the zenith,
which qualitatively represents the behavior of the ripples in the other
antenna parameters. The results are shown in Figure 10. As the top layer
thickness increases, the period of the ripples in the directivity decreases.
This occurs because of the increased delay of the signal reflected back to the
antenna from the interface between the two layers. As $L$ increases, the
amplitude of the ripples also decreases. This is due to the increased
attenuation suffered by the reflected signal as it travels a larger round-trip
distance through the lossy top layer.

##  5 Balun

###  5.1 Description

Figure 11: Side view schematic of the balun (not to scale). The core
components are a 1:1 $50$ $\Omega$ transformer and a $3$ dB attenuator, which
are housed inside the aluminum box.

We use a passive balun to convert the balanced signal produced at the
excitation port of the dipole antenna to unbalanced, or ground-referenced,
which is how the signal is expected at the receiver input. Figure 11 shows a
schematic of the balun. The balun primarily consists of a Mini-Circuits TX1-1+
1:1 $50$ $\Omega$ transformer in series with a $\approx 3$ dB attenuator on
the unbalanced side. The transformer provides DC isolation and magnetic
coupling between the balanced and unbalanced sides. The attenuator reduces the
magnitude of the antenna reflection coefficient seen by the receiver input,
which makes the calibrated sky measurements less sensitive to errors in
reflection coefficient measurements (Monsalve et al., 2017a). The improved
impedance matching from the attenuator comes at a cost of increased signal
loss. However, this loss can be accurately measured in the laboratory and
subsequently corrected in the sky measurements. To minimize the sensitivity of
the balun to temperature fluctuations, the attenuator is constructed with
resistors that are temperature-stable to better than $10$ ppm ∘C-1. On the
balanced side of the balun, i.e., the balun input, the antenna panels are
connected to the transformer through two $1$ cm long wires of $1$ mm diameter
in series with male and female SMA connectors. The unbalanced side of the
balun, i.e., the balun output, connects to the receiver input through a male
SMA connector.

To characterize the balun, we measured its S-parameters in the lab. The
measurements, which include the effect of the wires connecting the antenna
panels to the transformer, are shown in Figure 12. These measurements were
calibrated using a Keysight 85033E $3.5$ mm calibration
kit888https://www.keysight.com/us/en/product/85033E/standard-mechanical-
calibration-kit-dc-9-ghz-3-5-mm.html. To increase the accuracy of this
calibration, instead of using the nominal value of $50$ $\Omega$ for the
impedance of the calibration load, we used the DC resistance of the load
measured with a $5.5$-digit multimeter. Also, instead of assuming zero delay
for the load’s transmission line, we used the delay estimated in Monsalve et
al. (2016).

Figure 12: S-parameters of the MIST baluns measured in the lab. Here, port $1$
is the unbalanced port facing the receiver input (balun output) and port $2$
is the balanced port facing the antenna excitation port (balun input). Figure
13: Reflection coefficient of the antenna at the balun output for all the soil
models. Here, the plots show the simulated reflection coefficients from Figure
9 after embedding the measured balun S-parameters from instrument $1$ (Figure
12). Figure 14: (a) Balun efficiency for the two MIST instruments computed
with the antenna reflection coefficient for the nominal soil model. (b) and
(c) Differences in balun efficiency for instrument $1$ between the alternative
soil models and the nominal model. For example, for model 1L_c+,
$\Delta\eta_{balun}=\eta_{balun,\;\texttt{1L\\_c+}}-\eta_{balun,\;nominal}$.
In panels (b) and (c), the zero-points for the differences are the labeled
horizontal grid lines.

###  5.2 Antenna reflection coefficient at balun output

The antenna reflection coefficient at the balun output, $\Gamma_{A}$, is
computed from the $\Gamma_{Ad}$ provided by FEKO (Section 4.5) using

$\Gamma_{A}=S^{b}_{11}+\frac{S^{b}_{12}S^{b}_{21}\Gamma_{Ad}}{1-S^{b}_{22}\Gamma_{Ad}}.$
(16)

In this equation, $S^{b}_{11}$, $S^{b}_{21}$, $S^{b}_{12}$, and $S^{b}_{22}$
are the S-parameters of the balun, with port 1 (2) being the balun output
(input). The process represented by Equation 16 is referred to as “embedding”
of S-parameters999Embedding corresponds to the inclusion of the electrical
effects that an intervening network has on the measurement of a device under
test. De-embedding, on the contrary, is the removal of such effects. When the
intervening network is described in terms of S-parameters, as in this paper,
the embedding equation is Equation 16.

Figure 13 shows $\Gamma_{A}$ computed for the nine soil models and the balun
S-parameters from instrument $1$. The top row of the figure shows that the
balun reduces the reflection magnitude relative to $|\Gamma_{Ad}|$ in Figure 9
across most of the frequency range, except for the resonance at $\approx
50$–$60$ MHz. As Equation 16 indicates, when $S^{b}_{11}$ and $S^{b}_{22}$ are
low, the decrease in the magnitude is mainly driven by
$|S^{b}_{12}S^{b}_{21}|$, which is $\approx-7$ to $-9$ dB (Figure 12). The
soil differences between our single-layer models produce magnitude variations
in the range $\approx-14$ to $-24$ dB at the $\approx 50$ MHz dip. For these
models, the reflection magnitude increases with both conductivity and
permittivity. For our two-layer models, soil changes below the surface lead to
changes in reflection magnitude $\lesssim 2$ dB.

The bottom row of Figure 13 shows that the reflection phase at the balun
output decreases monotonically across $25$–$125$ MHz. The transition at
$\approx 50$ MHz is smoother than for $\angle\Gamma_{Ad}$ and there are no
$360^{\circ}$ jumps. The phase variations across our single-layer (two-layer)
models are $\lesssim 40^{\circ}$ ($\lesssim 10^{\circ}$). The delay of the
antenna plus balun across $25$–$125$ MHz is
$\approx(630^{\circ}/360^{\circ})\times(100\;\mathrm{MHz})^{-1}\approx
18\;\mathrm{ns}$. For comparison, the delay of the EDGES low-band antenna
including the Roberts balun is $\approx 28$ ns (Bowman et al., 2018). A lower
delay is preferred because it makes the calibrated sky measurements less
sensitive to errors in reflection measurements (Monsalve et al., 2017a).

###  5.3 Balun efficiency

The balun efficiency is computed as (Monsalve et al., 2017a)

$\eta_{balun}=\frac{|S^{b}_{12}|^{2}\left(1-|\Gamma_{Ad}|^{2}\right)}{|1-S^{b}_{22}\Gamma_{Ad}|^{2}\left(1-|\Gamma_{A}|^{2}\right)}.$
(17)

Figure 14 shows the balun efficiency. Panel (a) shows the efficiency for both
MIST instruments and the nominal soil model. For this model, the lowest
efficiency is $\approx 5\%$ at $25$ MHz and the highest is $\approx 45\%$ at
$50$ MHz. The shape of these curves strongly follows the magnitude of the
reflection coefficient at the balun output (Figure 13), with higher efficiency
occurring for lower reflection magnitude. Because the antenna reflection
coefficient depends on the soil properties, so does the balun efficiency.
Panels (b) and (c) of Figure 14 show the differences in efficiency for the
alternative soil models relative to the nominal model with the balun of
instrument $1$. The largest differences occur for the single-layer models and
are of up to $\approx 8\%$. For the two-layer models, changes in the bottom
layer produce efficiency changes of up to $\approx 0.8\%$. These differences
are significantly larger than the $\lesssim 0.01\%$ ratio between global $21$
cm signal and astrophysical foreground, and have a spectral structure that
could bias the $21$ cm signal extraction if not accounted for. It is thus
necessary to compute the balun efficiency using high-accuracy in-situ
measurements of the antenna reflection coefficient.

##  6 Receiver

Figure 15: Block diagram of the MIST receiver. Figure 16: One of the MIST
receivers: (a) front-end box; (b) back-end box; (c) power box; and (d)
receiver box. The picture of the receiver box was taken during construction
and assembly, and not all the features are shown. Three specific things not
shown are: (1) the SMA input connector at the top of the box; (2) the plastic
sleeves that protect the batteries; and (3) the power box, which sits above
the batteries.

In this section, we describe the hardware and operation of the MIST receiver.

###  6.1 Overview

Figure 15 shows a block diagram of the receiver. Inside the receiver box, the
electronics are housed in three boxes: the front-end box, the back-end box,
and the power box. Figure 16 shows pictures of these boxes.

After leaving the balun, the antenna signal enters the front-end box. Here,
the first subsystem encountered is the calibration network. This network
contains calibration standards necessary for the implementation of our
receiver calibration formalism (Section 3.2). The calibration network has two
outputs; one to measure the antenna PSD, and the other to measure the
reflection coefficient of the antenna and the reflection coefficient looking
into the receiver input. From the PSD output101010Although when leaving the
calibration network the signal is an analog RF signal, for practicality we
call this output the “PSD output” because it provides the signal from which we
compute the PSD in the back-end box., the signal goes through an amplification
chain and is then routed to the back-end box. From the reflection output, the
signal is routed directly to the back-end box. A calibration control board in
the front-end box is used to provide the control signals required by the
calibration network.

In the back-end box, the analog signal from the PSD output is digitized by an
ADC and transformed to the frequency domain by a field-programmable gate array
(FPGA). A single ADC-FPGA board performs both functions. The signal from the
reflection output is measured by a vector network analyzer (VNA). A power
control board is used to independently turn on and off the ADC-FPGA and VNA. A
single-board computer (SBC) coordinates the PSD and reflection measurements,
and also stores the data. To coordinate the measurements, the SBC controls the
power control board in the back-end box and the calibration control board in
the front-end box. An ethernet connection is used to communicate with the SBC
from outside the back-end box.

The instrument is powered by four $12$ V, $18$ Ah batteries. Inside the power
box, two DC/DC converters stabilize the fluctuating battery voltage to $15$ V
and $12$ V. These voltages are used to power the front-end and back-end boxes,
respectively. The power box also contains a low voltage disconnect (LVD)
circuit to prevent the discharging of the batteries below safe levels.

Figure 17: Diagram of the calibration network. The network is composed of
calibration standards for PSD and reflection measurements, latching RF
switches, and two thermistors.

###  6.2 Front-end box

####  6.2.1 Calibration network

Figure 17 shows the components of the calibration network. The network
contains an ambient load and an active noise source for the calibration of PSD
measurements (Section 3.2). The ambient load is implemented as two SMA
attenuators ($20$ and $6$ dB) connected in series for a total attenuation of
$26$ dB. These attenuators provide a noise temperature equivalent to their
physical temperature (typically $\approx 300$ K). The noise source is built
around a noise diode with an excess noise ratio of $\approx 35$ dB. When
combined, the ambient load plus noise source provide a nominal noise
temperature of $\approx$2,500 K, which is higher than the expected antenna
temperature from sky measurements affected by losses (Equation 3). The noise
temperature of the ambient load plus noise source was tuned to optimize the
dynamic range of the ADC. The noise source is powered with $12$ V and only
during the measurement of its PSD. The calibration network also contains open,
short, and $50$ $\Omega$ load (OSL) standards for the calibration of
reflection coefficient measurements. For the open and short we use
commercially available SMA caps. The load is implemented using a $50$ $\Omega$
resistor that is temperature-stable to better than $10$ ppm ∘C-1. We use
thermistors to measure the temperatures of the $20$+$6$ dB attenuators and the
$50$ $\Omega$ resistor.

The network contains seven radio frequency (RF) switches (SW1 through SW7) to
route the signals in the required directions. The RF switches are
electromechanical, single-pole-double-throw, latching switches with SMA
connectors. Switch SW1 selects between the receiver input (to which we connect
the antenna plus balun or an external calibration device), and the internal
ambient load and noise source. SW2 routes the output of SW1 either toward the
PSD output or the reflection output. SW3 is used to switch the input of the
amplification chain between two modes: PSD measurements through SW1 and SW2,
and the measurement of the reflection coefficient looking into the
amplification chain through SW4. Switch SW4 is also used to measure the
reflection coefficient of the antenna, internal ambient, and ambient plus
noise source, through SW1 and SW2. Switches SW5, SW6, and SW7 are used to
measure the reflection coefficient of the OSL standards.

Figure 18: Custom LNA used by MIST.

####  6.2.2 Amplification chain

In PSD measurement mode, after leaving the calibration network, the signal
from the receiver input (or internal ambient and noise source) reaches the
amplification chain. The first elements in the chain are a $3$ dB attenuator
and an LNA. The attenuator is used to improve the impedance match between the
LNA and the antenna. The increased noise temperature due to this attenuator is
small compared to the temperature from the astrophysical foregrounds which,
aside from RFI, is the largest contributor to the system temperature when the
receiver input is in the antenna position. Figure 18 shows a picture of the
LNA. The LNA is a custom-made, silicon-germanium, heterojunction bipolar
transistor design optimized for low reflections at the input and output
($|S_{11}|$ and $|S_{22}|<-35$ dB), as well as for low reverse transmission
($|S_{12}|<-40$ dB). The gain of the LNA is $\approx 28$ dB and its noise
temperature is $\approx 150$ K. We measure the physical temperature of the LNA
using a thermistor.

A $10$ dB attenuator is connected to the output of the LNA to improve the
match between the LNA and the next components, as well as to regulate the
total receiver gain. After the $10$ dB attenuator, a $48$ MHz high-pass filter
is used to reduce incoming power from strong shortwave RFI. This filter is
followed by two $\approx 20$ dB amplifiers, another $48$ MHz high-pass filter,
and a $120$ MHz low-pass filter used to suppress RFI above the band, such as
from ORBCOMM satellites, and contamination from aliased signals. We have not
encountered the need to inject noise to the signal chain below the observation
band (i.e., $<25$ MHz) for conditioning purposes, as performed by EDGES
(Rogers & Bowman, 2012; Monsalve et al., 2017a; Bowman et al., 2018). The
total nominal gain of the amplification chain is $\approx 55$ dB. The power
consumption of the amplification chain is $2.5$ W.

####  6.2.3 Calibration control board

The calibration control board is used to generate the pulses that control the
latching RF switches in the calibration network. These pulses have a voltage
of $12$ V, a duration of one second, and are produced using MOSFET relays. The
calibration control board also regulates and filters the $15$ V coming from
the power box to produce the $12$ V used for the pulses. These $12$ V are also
used to power the amplification chain and the noise diode. The calibration
control board includes low-speed ADCs, which connect to the thermistors that
measure the physical temperatures of the LNA, the internal calibration loads,
and the external calibration devices.

###  6.3 Back-end box

####  6.3.1 ADC-FPGA

The ADC-FPGA used by MIST is a Koheron
ALPHA250111111https://www.koheron.com/fpga/alpha250-signal-acquisition-
generation, which is powered with $12$ V and has a consumption of $10$ W. The
board is built around a Zynq 7020 system-on-a-chip, which integrates an ARM
Cortex-A9 processor and a Xilinx 7-series FPGA. The board has two RF ADCs and
two RF digital-to-analog converters. MIST uses only one RF ADC. The analog
signal coming out of the amplification chain is sampled by this ADC at a rate
of $250\times 10^{6}$ samples per second and with an amplitude resolution of
$14$ bits. The FPGA converts this digital signal to the frequency domain using
an FFT algorithm with a Blackman-Harris window function. Each FFT computation
uses 8,192 time samples and produces a PSD in the range $0$–$125$ MHz with a
resolution of $30.518$ kHz.

####  6.3.2 Vector network analyzer

The VNA used by MIST is a Copper Mountain Technologies
R60121212https://coppermountaintech.com/vna/r60-1-port/, which is powered
through its USB connection and has a consumption of $3$ W. The reflection
measurements with this VNA are done over the range $1$–$125$ MHz, with a
resolution of $250$ kHz, and an intermediate frequency bandwidth of $100$ Hz.
These settings produce low measurement noise and a sweep time of six seconds.

####  6.3.3 Power control board

The power control board is used to turn on and off the ADC-FPGA and VNA. This
switching is done using MOSFET relays. A thermistor and low-speed ADC are
included in this board to monitor the air temperature in the back-end box.

####  6.3.4 Single-board computer

The SBC used by MIST is a Radxa ROCK Pi X131313https://wiki.radxa.com/RockpiX,
which is powered with $12$ V and has a consumption of $4.5$ W. In the
receiver, the SBC communicates with the ADC-FPGA using ethernet; with the VNA
using USB; and with the power control board and calibration control board
using I2C. The communication with an external laptop, to start and stop
observations as well as to retrieve data, is done through another ethernet
connection.

###  6.4 Power

The power consumption of the receiver during PSD (VNA) measurements is $17$ W
($10$ W). This low consumption enables the instrument to operate for
significant periods of time with small batteries. We use four $12$ V, $18$ Ah
batteries connected in parallel, which provide enough capacity to conduct
continuous autonomous operations for $48$ h (without fully discharging the
batteries for their protection). The size of each battery is $10$ cm $\times$
$10$ cm $\times$ $15$ cm. The weight of each battery is $2$ kg. The batteries
are sufficiently small that they can be housed in the receiver box directly
underneath the antenna (Figure 16), thus increasing instrument portability.
The internally housed batteries also eliminate potential systematic effects
associated with long cables connecting the instrument to an external power
source.

###  6.5 Receiver box and suppression of self-RFI

Because the receiver box is in close proximity to the antenna, multiple layers
of self-RFI suppression are required. The receiver box consists of walls made
of aluminum sheet attached with stainless steel screws to a frame made of
aluminum bars. The screws are placed every three centimeters along the
perimeter of the walls. Inside the box, copper tape is used along the edges to
maximize the electrical contact between the walls and the frame. The receiver
input connector is located at the top of the box and consists of a female-
female flange mount SMA adapter. On the outside of the box, this adapter
connects directly to the balun. A ferrite bead is used on this SMA connection
to suppress common-mode currents. The box does not have any other pass-through
connection. To communicate with the instrument, as well as to replace the
batteries, the front wall of the box has to be unscrewed and removed.

The front-end, back-end, and power boxes, including their lids, are made of
aluminum. The lids of the front- and back-end boxes are secured with stainless
steel screws, which are also placed every three centimeters along the
perimeter. Braided metal gasket and copper tape are also used along the
perimeter of the lids to ensure full electrical contact with the boxes. Inside
the front-end box, the calibration control board is housed in its own aluminum
box for suppression of potential RFI from the I2C bus and peripherals. An RJ45
feedthrough connector on the back-end box enables the ethernet communication
between the SBC and an external laptop. This connector has a metal cap on the
outside, which is bolted on during measurements.

Ferrite beads and capacitive filters are used on select connections inside the
front-end, back-end, and power boxes. Ferrite beads are also used on the
connections between the three boxes, as well as between the power box and the
batteries. All the contents of the receiver box are wrapped with aluminum foil
for additional RFI suppression.

Table 3: Structure of the MIST measurement blocks. The duration of the
measurements reported here includes buffer time needed to switch between
positions. The total duration for the $160$ PSD cycles (cycle # $3$ through
$162$) is $160\times 41$ s $=109$ min. The total duration of the measurement
blocks is $111$ min.

cycle # | Measurement type | Device | Duration
---|---|---|---
$1$ | Reflection $0$ dBm |  | 56 s
|  | thermistorsaa$a$For the thermistors we measure their voltage, instead of reflection coefficient or PSD.
| 4 s
|  | O | 8 s
|  | S | 8 s
|  | L | 8 s
|  | antenna | 8 s
|  | ambient | 8 s
|  | amb+ns | 12 s
$2$ | Reflection $-40$ dBm |  | 51 s
|  | thermistorsaa$a$For the thermistors we measure their voltage, instead of reflection coefficient or PSD.
| 4 s
|  | O | 8 s
|  | S | 8 s
|  | L | 8 s
|  | receiver input | 23 sbb$b$This duration includes $15$ s in which, after measuring the reflection looking into the receiver input, the VNA is turned off, the ADC-FPGA is turned on, and the instrument waits until the ADC-FPGA is ready to take data.
$3$–$162$ | PSD |  | 41 s
|  | thermistorsaa$a$For the thermistors we measure their voltage, instead of reflection coefficient or PSD.
| 4 s
|  | antenna | 12 s
|  | ambient | 12 s
|  | amb+ns | 13 s
141414

###  6.6 Measurement sequence

The MIST instrument takes measurements of the sky and internal calibration
standards in blocks of $111$ minutes. The structure of these blocks is shown
in Table 3. Each block is organized into $162$ cycles. In cycle # $1$, the
instrument measures the reflection coefficient of six devices with a VNA power
of $0$ dBm for a total of $56$ seconds. Here, the main measurement is of the
antenna or external device connected to the receiver input. We also measure
the internal ambient load and ambient plus noise source to verify the correct
functioning of the instrument. The internal OSL standards are measured to
calibrate the other three measurements. In cycle # $2$, which lasts $51$
seconds, the instrument measures the reflection coefficient of four devices at
$-40$ dBm. Here, the main measurement is the reflection looking into the
receiver input, which has to be done at a lower power to avoid saturating the
LNA. The internal OSL standards are also measured at this lower power for
consistency of the calibration. Starting with cycle # $3$, the instrument
carries out $160$ cycles of PSD measurements for a total of $109$ minutes.
Three measurements are done in each PSD cycle: (1) the antenna, (2) internal
ambient load, and (3) ambient plus noise source. Each of these measurements
corresponds to a $10$-second integration. At the beginning of each reflection
and PSD cycle, the instrument measures the physical temperatures of all the
thermistors. After a $111$-minute block finishes, a new one automatically
starts. This process continues until a stop command is sent to the instrument
from the external laptop, or the battery voltage decreases below the LVD
threshold.

Data are saved as binary files on the flash memory of the SBC. We save one
file per measurement block. This file is continuously updated as new
measurements are captured. The file size for a full block is $16.2$ MB,
yielding a daily data rate of $210$ MB.

Figure 19: Diagram of the calibration network highlighting the paths that
shift the internal reflection reference plane to the receiver input. Figure
20: S-parameters of path A in the calibration network. Port $1$ corresponds to
the internal reflection reference plane and port $2$ to the receiver input.

###  6.7 Reflection coefficient calibration

The reflection measurements described in Section 6.6 are done using the
calibration network and VNA incorporated into the receiver. Our receiver
calibration formalism (Section 3.2) requires these reflection measurements
themselves to be calibrated at the receiver input. Furthermore, and as
discussed in Monsalve et al. (2017a, b), the detection of the global $21$ cm
signal requires an accuracy in reflection coefficient measurements of
$\mathcal{O}(10^{-4})$. To calibrate the reflection measurements at the
receiver input and with the required accuracy, MIST conducts the two-step
process used by EDGES (Monsalve et al., 2017a; Bowman et al., 2018). First, a
relative calibration is done using the measurements of the internal OSL
standards. This step de-embeds a large fraction of the unwanted S-parameters
introduced by the calibration network, the cable to the VNA, and the VNA
itself. Calibrating using the internal OSL standards defines the reference
plane within the calibration network. Second, the reference plane is shifted
from the calibration network to the receiver input by applying S-parameter
corrections determined in the lab. These corrections account for the short
paths between the internal reference plane and the receiver input.

Three paths have to be accounted for and characterized. The paths, labeled A,
B, and C, are shown in Figure 19. The measurements of external devices (such
as the antenna) are calibrated at the receiver input by: (1) doing a relative
calibration using the internal OSL standards, and (2) de-embedding the
S-parameters of path A. The measurement of reflection coefficient looking into
the receiver input is calibrated by: (1) doing a relative calibration using
the internal OSL standards; (2) de-embedding the S-parameters of path B, which
shifts the calibration plane to the PSD output; and then (3) embedding the
S-parameters of path C, which shifts the calibration plane to the receiver
input.

Figure 20 shows the S-parameters for path A. The parameters for paths B and C
are similar and not shown for brevity. These parameters were measured in the
lab and calibrated in the same way as the S-parameters of the balun (Section
5.1).

Figure 21: Sample PSDs from the internal and external calibrators measured in
the lab with instrument 1. PSDs from instrument 2 are similar. Each PSD
corresponds to a $10$-second integration. Figure 22: Absolute receiver
calibration parameters and reflection coefficient looking into the receiver
input for the two instruments.

###  6.8 Receiver calibration

We determine the five absolute receiver calibration parameters, $C_{1}$,
$C_{2}$, $T_{U}$, $T_{C}$, and $T_{S}$ (see Section 3.2), from lab
measurements of four external calibration devices: (1) an ambient load, (2) a
hot load ($50$ $\Omega$ resistor heated up to $\approx 400$ K), (3) a $10$ m
open-ended low-loss cable, and (4) the same cable after being short-circuited
at its far end. For each of these devices, we measure the reflection
coefficient, PSD, and physical temperature following the same procedure as for
the antenna in the field (Section 6.6). Figure 21 shows sample PSDs from the
internal and external calibrators measured during this process. With these
measurements at hand, the five receiver parameters are computed using the
iterative method of Monsalve et al. (2017a). In the computation, we use $300$
K and 2,300 K as the assumptions for the noise temperature of the internal
ambient load ($T^{a}_{L}$) and ambient load plus noise source
($T^{a}_{L+NS}$), respectively. Figure 22 shows the five parameters, as well
as the reflection coefficient looking into the receiver input, for the two
receivers.

Figure 23: Sample measurements from MIST taken at the three observation sites.
These measurements preliminarily show that MIST is performing as expected. The
columns correspond to data from: (left) Deep Springs Valley taken with
instrument $1$; (middle) Death Valley taken with instrument $2$; and (right)
MARS taken with instrument $2$. (Top row) PSDs from the antenna and internal
calibrators corresponding to $10$-second integrations taken at an LST=$15$ h.
RFI has not been excised from the antenna measurements, which highlights the
excellent radio-quiet conditions at MARS. (Second row) Antenna reflection
coefficient at the balun output. (Third row) Receiver gain and temperature.
(Bottom row) $41$-second antenna temperature spectra after (1) receiver
calibration, and (2) receiver calibration plus radiation and balun efficiency
corrections. Figure 24: Sample $41$-second spectra from Deep Springs Valley,
Death Valley, and MARS, before and after beam efficiency correction. RFI has
not been excised from these measurements, which highlights the excellent
radio-quiet conditions at MARS. In panel (c), the upper limit of the $y$ axis
was reduced to 40,000 K to show the data from MARS in more detail. The beam
efficiency used here corresponds to the nominal soil model (Table 2). This
beam efficiency is used only as an example. In the future, we will refine the
soil model based on in-situ measurements of the antenna reflection
coefficient. The spectra without correction (green lines) are reproduced from
Figure 23, panels (j), (k), and (l). Figure 25: View of the sky at LST=$15$ h
and $25$ MHz from: (a) Deep Springs Valley and Death Valley, both of which are
at a latitude of $\approx 37.3^{\circ}$ N; and (b) MARS, at a latitude of
$\approx 79.38^{\circ}$ N. For this figure, we used the Global Sky Model (de
Oliveira-Costa et al., 2008; Price, 2016). The dashed lines represent the
$-10$ dB contours of the beam directivity at $25$ MHz for the nominal soil
model, shown as reference.

##  7 Field measurements

Between May and July 2022, we conducted sky measurements with MIST in Deep
Springs Valley in California ($37.34583^{\circ}$ N, $118.02555^{\circ}$ W),
Death Valley in Nevada ($37.21333^{\circ}$ N, $117.09111^{\circ}$ W), and MARS
in the Canadian High Arctic ($79.37980^{\circ}$ N, $90.99885^{\circ}$ W). The
Deep Springs Valley and Death Valley sites were used for observations because
they offer a relatively low-RFI environment (Monsalve & Mozdzen, 2014;
Anderson & Eastwood, 2016) and flat soil while remaining close to urban areas.
These sites are, respectively, $\approx$20 km and $\approx$100 km east of the
Owens Valley Radio Observatory (OVRO) (D’addario & Hodges, 2019). MARS is
located $>$1,800 km away from cities and possesses an extremely low-RFI
environment (Dyson et al., 2021).

Figures 23 and 24 show short sample measurements from the three sites. These
data preliminarily indicate that MIST is performing as expected. A more in-
depth discussion of instrument performance, observing sites, and analysis of
the full data sets will be presented in future papers.

###  7.1 Power spectral densities

Each column of Figure 23 corresponds to one of the three sites. Instrument $1$
was used at Deep Springs, and instrument $2$ was used at Death Valley and
MARS. The top row of the figure shows raw, unprocessed PSDs from the antenna,
the internal ambient load, and the ambient load plus noise source. Each of the
PSDs is a $10$-second integration. In each panel, the internal measurements
belong to the same PSD cycle as the antenna measurement, which was taken
around 15:00 local sidereal time (LST). The data shown from Deep Springs and
Death Valley were taken at night, while those from MARS are from the
continuous daytime of the Arctic summer. We have not excised RFI from these
measurements.

###  7.2 Reflection coefficient at balun output

The second row in Figure 23 shows the calibrated reflection coefficient of the
antenna at the balun output. This quantity was measured at the beginning of
the same $111$-minute measurement block as the PSDs. We see that the magnitude
and phase have the same general shape as those shown in Figure 13, which were
obtained from electromagnetic simulations propagated through the balun
S-parameters. One feature that differentiates the three sites is the magnitude
dip at $\approx 50$ MHz. This dip reaches $\approx-25$, $-16$, and $-20$ dB,
at Deep Springs Valley, Death Valley, and MARS, respectively. The reflection
coefficient is sensitive to the soil parameters, as discussed in Sections 4.5
and 5.2. Taking advantage of this sensitivity, the soil properties at the
different observing sites can be estimated by fitting electromagnetic
simulations to the measured reflection. This analysis will be presented in
future work.

###  7.3 Receiver gain and temperature

The third row in Figure 23 shows the receiver gain and temperature for the
three observations. The receiver gain and temperature were computed using
Equations 6 and 7, respectively, and the PSDs from the internal calibrators
shown in the first row. The gain (temperature) is relatively stable across the
frequency range but quickly decreases (increases) toward lower frequencies
below $\approx 45$ MHz due to the two $48$ MHz high-pass filters used in the
amplification chain to suppress shortwave RFI. The gain and temperature are
similar between the two instruments and three observations, with differences
$<10\%$.

###  7.4 Receiver calibration, and radiation and balun efficiency correction

The bottom row of Figure 23 shows the antenna temperature spectrum obtained
from the PSD after applying: (1) receiver calibration, and (2) receiver
calibration plus radiation and balun efficiency corrections. Applying the
receiver calibration consists of applying to the antenna PSD the receiver gain
and temperature shown in the third row of the figure following Equation 5. The
receiver gain and temperature are computed using the measurements of the
internal calibrators from the same PSD cycle. Because the PSD cycles have a
duration of $41$ seconds (Table 3), we refer to the antenna temperature
spectra as $41$-second integrations.

The antenna temperature with only receiver calibration and still affected by
all the losses is significantly lower than expected from the astrophysical
foreground in the northern hemisphere (Bernardi et al., 2016; Dowell et al.,
2017; Dowell & Taylor, 2018; Spinelli et al., 2021). Furthermore, the antenna
temperature has a peak at $\approx 45$–$50$ MHz and a decrease toward lower
frequencies, departing from the power law that characterizes the foreground.
This departure is mainly caused by the balun efficiency which, as Figure 14
shows, decreases quickly toward lower frequencies.

After applying the radiation and balun efficiency corrections the antenna
temperature increases significantly, especially at low frequencies, and its
shape becomes closer to the expected power law. Since the radiation efficiency
is $>99.9\%$ (Figure 4) while the balun efficiency peaks at $\approx 45\%$
(Figure 14), the balun efficiency correction dominates the combined
correction.

###  7.5 Beam efficiency correction

Figure 24 shows an example of the beam efficiency correction. For this example
we use the nominal beam efficiency, i.e., the beam efficiency produced by the
FEKO simulation that uses the nominal single-layer soil model. As Figure 8
shows, the nominal beam efficiency ranges between $11\%$ at $25$ MHz and
$56\%$ at $105$ MHz. This curve is not expected to represent well the soil
properties at our observation sites. Measuring soil electrical properties to
inform more accurate, site-specific beam efficiency corrections is work in
progress and will be discussed in future papers.

Figure 24 shows that, after beam efficiency correction, the antenna
temperature from the three sites increases significantly and its shape becomes
closer to the power law expectation. The sites in Deep Springs Valley and
Death Valley are at a similar latitude ($\approx 37.3^{\circ}$ N). Therefore,
at the same LST these sites have a similar visible sky and sky-averaged
contribution to the antenna temperature. The difference seen in Figure 24
between the corrected spectra from these two sites is mainly due to different
beam efficiencies in the observations resulting from different soil
characteristics. The spectrum from Deep Springs Valley, in particular, still
shows structure that deviates from a power law. This structure is an
indication that the soil at this site departs in important ways from the
nominal soil model used for the figure.

The MARS spectrum differs from the others because of the site’s contrasting
soil characteristics and significantly higher latitude ($\approx
79.38^{\circ}$ N). Figure 25 shows a view of the sky at $25$ MHz and LST=$15$
h from both latitudes. The fraction of the Galactic plane that is visible from
Deep Springs Valley and Death Valley is larger than from MARS.

###  7.6 Preliminary spectral index

As a preliminary characterization of the calibrated and efficiency corrected
spectra presented in Section 7.5, here we compute their spectral index. Since
the beam efficiency correction applied as an example in Section 7.5
corresponds to the nominal soil model, the accuracy of the spectral indices is
not expected to be high. Furthermore, we have not removed from the data the
effect produced by the frequency dependence of the beam directivity, i.e., the
“beam chromaticity”. The beam chromaticity changes the spatial weighting of
the sky brightness temperature as a function of frequency and, thus, can have
a significant impact on the spectral index (e.g., Mozdzen et al., 2017, 2019;
Spinelli et al., 2021). As discussed in Section 4.3, the beam directivity is
very sensitive to the properties of the soil, highlighting again that soil
characterization a critical task for MIST. We will address this aspect in
future analyses.

Instead of fitting functions to the data, we take a simpler approach and
compute the spectral index across our frequency range as

$\beta=\frac{\log\left(\frac{T_{S}(105\;\mathrm{MHz})}{T_{S}(25\;\mathrm{MHz})}\right)}{\log\left(\frac{105\;\mathrm{MHz}}{25\;\mathrm{MHz}}\right)},$
(18)

Table 4: Spectral index for the sample spectra from the three observation
sites. Beam efficiency correction has been applied but assuming the nominal
soil model. Beam chromaticity correction has not been applied.

Site | $T_{S}(25\leavevmode\nobreak\ \mathrm{MHz})$ | $T_{S}(105\leavevmode\nobreak\ \mathrm{MHz})$ | $\beta$
---|---|---|---
Deep Springs Valley | 60,000 K | 1,100 K | $-2.79$
Death Valley | 90,000 K | 1,150 K | $-3.04$
MARS | 35,000 K | 950 K | $-2.51$
151515The antenna temperatures shown and used for the computation of $\beta$
are representative values within the measurement noise of the $41$-second
integrated spectra at $25$ and $125$ MHz.

where $T_{S}$ is the calibrated and efficiency corrected sky spectrum.

Table 4 shows the antenna temperatures and spectral index for the three sites.
For Deep Springs Valley, Death Valley, and MARS, the spectral indices are
$-2.79$, $-3.04$, and $-2.51$, respectively. These values are in broad
agreement with previous results for the northern hemisphere (e.g., Dowell &
Taylor, 2018; Spinelli et al., 2021). This agreement is a good indication for
MIST, and future refinements of the beam efficiency, as well as beam
chromaticity correction, should improve the results.

##  8 Summary and conclusions

In this paper, we have provided an overview of the two instruments built so
far as part of the MIST global $21$ cm ground-based experiment. The
instruments are single-antenna, single-polarization, total-power radiometers
measuring the sky in the range $25$–$105$ MHz. For the $21$ cm signal, this
range corresponds to redshifts $55.5>z>12.5$, which encompasses the Dark Ages
and Cosmic Dawn.

Distinctive characteristics of MIST compared with the existing instruments
are:

  1. (a)

MIST operates above the soil but without a metal ground plane. This choice was
made to avoid systematic effects from the ground plane and its interaction
with the antenna. Not using a ground plane results in a higher ground loss and
overall dependence of the antenna performance on the soil’s electrical
characteristics. However, this choice defines an instrumental parameter space
that interacts with the $21$ cm signal differently from current experiments.

  2. (b)

The instruments have been designed with high portability and compactness in
mind in order to conduct measurements from remote sites. Before assembly, the
largest parts of the instrument are the $3$ mm thick, $1.2$ m $\times$ $0.6$ m
antenna panels. The instruments are battery-powered and have a maximum power
consumption of only $17$ W. The batteries and all the electronics apart from
the balun are contained in a single metal receiver box located under the
antenna. This compactness eliminates systematics related to cables near the
antenna and is a unique aspect of MIST, contrasting with other experiments
where the back-end or auxiliary electronics are kept at a secondary location.

  3. (c)

The MIST observation procedure includes measurements of the antenna reflection
coefficient and the reflection coefficient looking into the receiver input.
These reflection measurements are done every $111$ minutes with a VNA
integrated into the instrument. The antenna reflection measurements, in
addition to being used for receiver calibration, will be used to precisely
determine the electrical parameters of the soil. This represents another
unique aspect of MIST.

  4. (d)

Thanks to its portability and low power consumption, MIST has already
conducted observations from Deep Springs Valley in California and Death Valley
in Nevada, as well as from the McGill Arctic Research Station at a latitude of
$\approx 79.38^{\circ}$ N. MARS, in particular, offers excellent radio-quiet
conditions and a view of the sky that differs from, and thus complements,
observations from lower latitudes by MIST and other experiments.

We quantified the performance of the MIST antenna using electromagnetic
simulations and showed results for the beam directivity, radiation efficiency,
beam efficiency, and reflection coefficient. Through examples, we have
described how these parameters depend on the soil characteristics. As
expected, the parameters are more sensitive to soil changes that occur closer
to the surface, but changes below the surface are also significant and produce
spectral ripples in the parameters. In a future paper (Monsalve et al., in
prep.), we will discuss the impact of the MIST beam directivity on the global
$21$ cm signal extraction for different soil characteristics.

We have shown sample sky measurements taken in 2022 with the two MIST
instruments from Deep Springs Valley, Death Valley, and MARS. These
measurements are short integrations with different levels of calibration,
including a preliminary correction for beam efficiency that should improve in
the future after an accurate determination of the soil electrical parameters.
The measurements preliminarily show that the instruments have the expected
performance in the field. We computed initial estimates for the sky spectral
index and they were found in the range $\approx-2.5$ to $\approx-3$,
consistent with previous measurements (Dowell & Taylor, 2018; Spinelli et al.,
2021). These values will be refined after improving the beam efficiency
correction and applying beam chromaticity correction. We leave for future work
the detailed analysis of the data taken in 2022.

Taking advantage of MIST’s portability, we plan to carry out joint analyses
leveraging observations from different latitudes over different soils to help
separate the $21$ cm signal from other spectral contributions. This strategy
is conceptually similar to some suggested in previous works where, for
instance, data from more than one antenna, sidereal time, or Stokes
polarization component, are used to improve the signal separation (Nhan et
al., 2019; Tauscher et al., 2020; de Lera Acedo et al., 2022; Saxena et al.,
2022; Anstey et al., 2023).

###### Acknowledgements.

We are grateful to Stuart Bale, Judd Bowman, Nivedita Mahesh, Steven Murray,
Alan Rogers, Kaja Rotermund, Benjamin Saliwanchik, Peter Sims, Anže Slosar,
and Aritoki Suzuki for useful discussions on instrumentation for $21$ cm
cosmology. We are grateful to Matt Dobbs for lending us equipment from his
Cosmology Instrumentation Laboratory at McGill University. We are grateful to
Brian Hill, Sue Darlington, and Emily Rivera for welcoming us at the Deep
Springs College and providing logistical support during the measurements at
Deep Springs Valley. We are grateful to Laura Thomson and Christopher Omelon
for welcoming us and providing logistical support at the McGill Arctic
Research Station. We are also grateful to Joëlle Begin, Cherie Day, Eamon
Egan, Larry Herman, Marc-Olivier Lalonde, and Tristan Ménard for their support
with operations in the Arctic. We also acknowledge the Polar Continental Shelf
Program for providing funding and logistical support for our research program,
and we extend our sincere gratitude to the Resolute staff for their generous
assistance and bottomless cookie jars. We acknowledge support from ANID Chile
Fondo 2018 QUIMAL/180003, Fondo 2020 ALMA/ASTRO20-0075, Fondo 2021
QUIMAL/ASTRO21-0053. We acknowledge support from Universidad Católica de la
Santísima Concepción Fondo UCSC BIP-106. We acknowledge the support of the
Natural Sciences and Engineering Research Council of Canada (NSERC),
RGPIN-2019-04506, RGPNS 534549-19. We acknowledge the support of the Canadian
Space Agency (CSA) [21FAMCGB15]. This research was undertaken, in part, thanks
to funding from the Canada 150 Research Chairs Program. This research was
enabled in part by support provided by SciNet and the Digital Research
Alliance of Canada.

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