††thanks: ORCID: https://orcid.org/0000-0002-3004-0930††thanks: ORCID:
http://orcid.org/0000-0001-8837-4127††thanks: ORCID:
http://orcid.org/0000-0001-9888-0971

# The Cherenkov Telescope Array Will Test Whether Pulsars Generate the
Galactic Center Gamma-Ray Excess

Celeste Keitha,b Dan Hoopera,b,c Tim Lindend aUniversity of Chicago, Kavli
Institute for Cosmological Physics, Chicago IL, USA  bUniversity of Chicago,
Department of Astronomy and Astrophysics, Chicago IL, USA  cFermi National
Accelerator Laboratory, Theoretical Astrophysics Group, Batavia, IL, USA
dStockholm University and The Oskar Klein Centre for Cosmoparticle Physics,
AlbaNova, 10691 Stockholm, Sweden

###### Abstract

The GeV-scale gamma-ray excess observed from the region surrounding the
Galactic Center has been interpreted as either the products of annihilating
dark matter particles, or as the emission from a large population of faint and
centrally-located millisecond pulsars. If pulsars are responsible for this
signal, they should also produce detectable levels of TeV-scale emission. In
this study, we employ a template-based analysis of simulated data in an effort
to assess the ability of the Cherenkov Telescope Array (CTA) to detect or
constrain the presence of this emission, providing a new and powerful means of
testing whether millisecond pulsars are responsible for the observed excess.
We find that after even a relatively brief observation of the Inner Galaxy,
CTA will be able to definitively detect this TeV-scale emission, or rule out
pulsars as the source of the Galactic Center Gamma-Ray Excess.

††preprint: FERMILAB-PUB-22-923-T

##  I Introduction

An excess of GeV-scale gamma rays from the region surrounding the Galactic
Center has been identified in the publicly available data collected by the
Fermi Gamma-Ray Space Telescope Goodenough and Hooper (2009); Hooper and
Goodenough (2011); Hooper and Linden (2011). The spectral shape, morphology,
and intensity of this emission are each consistent with arising from the
annihilation of dark matter particles. More specifically, the characteristics
of this signal match those predicted from a $m_{X}\sim 50\,{\rm GeV}$ dark
matter particle with an annihilation cross section of $\sigma v\sim(1-2)\times
10^{-26}\,{\rm cm}^{3}/{\rm s}$, and that is distributed slightly more steeply
around the Galactic Center than described by the canonical Navarro-Frenk-White
profile, $\rho\propto r^{-1.2}$ Daylan  _et al._ (2016); Calore  _et al._
(2015a, b); Ackermann  _et al._ (2017); Di Mauro (2021); Cholis  _et al._
(2022). The possibility that Fermi could be detecting dark matter annihilation
products has generated a great deal of interest (see, for example, Refs.
Berlin  _et al._ (2014a); Izaguirre  _et al._ (2014); Ipek  _et al._ (2014);
Agrawal  _et al._ (2014); Berlin  _et al._ (2014b); Abdullah  _et al._ (2014);
Martin  _et al._ (2014); Alves  _et al._ (2014); Boehm  _et al._ (2014);
Berlin  _et al._ (2015); Karwin  _et al._ (2017)).

The leading alternative explanation for this excess is that it is instead
generated by a large population of unresolved millisecond pulsars Hooper and
Goodenough (2011); Abazajian (2011); Hooper  _et al._ (2013); Gordon and
Macias (2013); Cholis  _et al._ (2015); Hooper  _et al._ (2013); Petrović  _et
al._ (2015); Brandt and Kocsis (2015); Hooper and Mohlabeng (2016); Hooper and
Linden (2016). This possibility is motivated in large part by the fact that
pulsars are the only known class of astrophysical objects that produce a
gamma-ray spectrum with a shape that is similar to that of the Galactic Center
Gamma-Ray Excess. As the stellar population of the Galactic Bulge consists
predominantly of old stars, we expect relatively few young or middle-aged
pulsars to be found in the Inner Galaxy. In contract, pulsars with
millisecond-scale periods (known as millisecond pulsars, or recycled pulsars)
can remain bright for billions of years, and could plausibly be more abundant
in this region of the Galaxy.

The hypothesis that millisecond pulsars produce the observed gamma-ray excess
was elevated substantially in 2015, when two independent groups claimed to
have identified evidence that the photons constituting this excess are
spatially clustered Lee  _et al._ (2016); Bartels  _et al._ (2016).
Furthermore, it was claimed in Refs. Bartels  _et al._ (2018a); Macias  _et
al._ (2018, 2019); Pohl  _et al._ (2022) that this excess is not distributed
with spherical symmetry around the Galactic Center (as would be expected from
dark matter), but is instead correlated with the distribution of stars that
make up the Galactic Bulge and Bar. If true, these results would have
significantly favored the conclusion that the excess originates from a
population of near-threshold astrophysical point-sources, rather than from
annihilating dark matter.

The conclusions described in the previous paragraph have been strongly
challenged in recent years (for a summary, see Ref. Hooper (2022)). In
particular, the small scale power identified in Ref. Lee  _et al._ (2016) was
shown in Refs. Leane and Slatyer (2019, 2020a, 2020b) to be an artifact of
insufficiently understood backgrounds, causing smooth signals to be
mischaracterized as clumpy. Furthermore, the evidence for unresolved point
sources claimed in Ref. Bartels  _et al._ (2016) was found to disappear when
the point source catalog was updated Zhong  _et al._ (2020). Even more
recently, it was shown in Refs. Di Mauro (2021) and Cholis  _et al._ (2022)
that the angular distribution of the excess emission is best fit by a
spherical and dark matter-like morphology, and does not significantly
correlate with any known stellar populations; the Fermi data prefers the
excess to have a bulge-like morphology only when the background model provides
a poor fit to the overall dataset McDermott  _et al._ (2022). To the best of
our ability to measure, the gamma-ray excess appears to be both smooth, and
distributed with spherical symmetry around the Galactic Center. Furthermore,
Fermi data has been used to place strong constraints on the luminosity
function of any point source population that might be responsible for this
signal Bartels  _et al._ (2018b); Zhong  _et al._ (2020); Dinsmore and Slatyer
(2022), posing a significant challenge for millisecond pulsar interpretations
of the gamma-ray excess.

None of the results described above preclude the possibility that the gamma-
ray excess could be produced by a large population of very faint millisecond
pulsars, distributed with approximate spherical symmetry around the Galactic
Center. If this is the case, however, there are accompanying signals that
should be present in the GeV Bartels  _et al._ (2018b); Dinsmore and Slatyer
(2022), radio Calore  _et al._ (2016), and X-ray Haggard  _et al._ (2017)
bands. Such signals could be used to potentially constrain or confirm the
hypothesis that millisecond pulsars generate the gamma-ray excess.
Furthermore, observations by the High Altitude Water Cherenkov (HAWC)
Observatory and the Large High Altitude Air Shower Observatory (LHAASO) have
shown that young and middle-aged pulsars are typically surrounded by bright,
spatially-extended, multi-TeV emitting regions known as “TeV halos” Hooper
_et al._ (2017); Linden  _et al._ (2017); Albert  _et al._ (2021); Abeysekara
_et al._ (2020). Even more recently, it has been shown (at the 99% C.L.) that
millisecond pulsars also generate TeV halos Hooper and Linden (2022). If this
result is robustly confirmed, it will be possible to use ground-based gamma-
ray telescopes, such as the Cherenkov Telescope Array (CTA), to search for the
TeV-scale emission from any millisecond pulsars that might be present near the
Galactic Center. Such a measurement would provide an independent – and
potentially definitive – measurement of our Inner Galaxy’s millisecond pulsar
population Hooper and Linden (2018).

In this paper, we perform a template-based analysis of simulated data to
assess the ability of the Cherenkov Telescope Array (CTA) to identify and
measure the very high-energy gamma-ray emission from a population of
millisecond pulsars that are located in the region surrounding the Galactic
Center. When the intensity of this emission is normalized to the measurements
of other pulsars by HAWC and LHAASO, we find that if the Galactic Center
Gamma-Ray Excess originates from pulsars, this source population should
produce the dominant contribution to the TeV-scale emission from the Inner
Galaxy. Such a signal would be easily detectable by CTA, even after a
relatively short observation of this region. We conclude that CTA will either
be able to clearly identify the TeV halo emission associated with such a
pulsar population, or rule out the hypothesis that the Galactic Center Gamma-
Ray Excess originates from millisecond pulsars.

##  II Gamma-Ray Emission From TeV Halos Around Millisecond Pulsars

In 2017, observations by the HAWC Observatory identified bright, multi-TeV
emission from the regions surrounding the nearby Geminga and Monogem pulsars
Albert  _et al._ (2020); Abeysekara  _et al._ (2017a, b) (for earlier
observations by Milagro, see Ref. Abdo  _et al._ (2009)). It has since been
found that similar TeV halos are present around most, if not all, young and
middle-aged pulsars Linden  _et al._ (2017); Albert  _et al._ (2021); Sudoh
_et al._ (2021). This emission is produced through the inverse Compton
scattering of very high-energy electrons and positrons, and the intensity of
the observed emission implies that $\mathcal{O}(10\%)$ of the pulsars’ total
energy budget (i.e., spindown power) goes into the acceleration of such
particles Hooper  _et al._ (2017); Sudoh  _et al._ (2021). Applying these
characteristics to the larger population of pulsars, one expects TeV halos to
dominate the Milky Way’s diffuse gamma-ray emission at TeV-scale energies
Linden and Buckman (2018), and to contribute significantly to the isotropic
gamma ray background Xu and Hooper (2022).

Until recently, it was not clear whether or not pulsars with millisecond-scale
periods are also surrounded by TeV halos. Based on theoretical considerations,
it was generally expected that millisecond pulsars should produce TeV-scale
emission in their magnetospheres, at a level similar to that which takes place
among young and middle-aged pulsars Venter  _et al._ (2015); Bednarek  _et
al._ (2016); Venter  _et al._ (2016). On the other hand, young and middle-aged
pulsars are thought to accelerate TeV-scale electrons as they reach the
termination shock, and it is not clear to what extent this might occur within
millisecond pulsars Sironi and Spitkovsky (2011); Gaensler and Slane (2006).
Some light was shed on these questions recently, when an analysis of publicly
available HAWC data demonstrated that millisecond pulsars also generate TeV
emission, with an efficiency similar to that of young and middle-aged pulsars
Hooper and Linden (2022) (see also, Ref. Hooper and Linden (2018)). More
specifically, that study considered 37 nearby and high-spindown power
millisecond pulsars, finding (at the 99% confidence level) that these sources
produce TeV-scale emission with a luminosity proportional to their spindown
power. Furthermore, the efficiency of this emission was constrained to lie
between 39-108% of that measured for the TeV halo associated with the middle-
aged pulsar, Geminga. Future observations by telescopes including HAWC,
LHAASO, and CTA should be able to confirm and further refine this conclusion,
potentially confirming that millisecond pulsars have TeV halos, and also
measuring the spectra, intensity, and morphology of these sources.

In calculating the gamma-ray emission from TeV halos, we adopt the following
parameterization for the spectrum of the injected electrons and positrons:

$\displaystyle\\!\begin{aligned}
\frac{dN_{e}}{dE_{e}}=E^{-\alpha}_{e}e^{-E_{e}/E_{\mathrm{cut}}},\end{aligned}$
(1)

where observations indicate that $\alpha\sim 1.5-1.9$ and
$E_{\mathrm{cut}}\sim 30-100\,{\rm TeV}$ for typical TeV halos. These
particles lose energy through both inverse Compton scattering and synchrotron
processes, producing emission in the gamma-ray and radio bands, respectively
BLUMENTHAL and GOULD (1970). These processes lead to the following energy loss
rate:

$\displaystyle\begin{aligned}
-\frac{dE_{e}}{dt}&=\sum_{i}\frac{4}{3}\sigma_{T}u_{i}S_{i}(E_{e})\bigg{(}\frac{E_{e}}{m_{e}}\bigg{)}^{2}+\frac{4}{3}\sigma_{T}u_{\textrm{mag}}\bigg{(}\frac{E_{e}}{m_{e}}\bigg{)}^{2}\\\
&\equiv b(E_{e})\,\bigg{(}\frac{E_{e}}{{\rm TeV}}\bigg{)}^{2},\end{aligned}$

where $\sigma_{T}$ is the Thomson cross section and

$\displaystyle\begin{aligned} b&\approx 1.02\times 10^{-13}\,\mathrm{TeV/s}\\\
&\times\bigg{(}\sum_{i}\frac{u_{i}}{\mathrm{eV/cm^{3}}}S_{i}(E_{e})+\frac{u_{\mathrm{mag}}}{\mathrm{eV/cm^{3}}}\bigg{)}.\end{aligned}$
(2)

The sum in these expressions is carried out over the relevant components of
the radiation field. In our analysis, we adopt a three component radiation
model, consisting of the cosmic microwave background (CMB), infrared emission,
and starlight. We treat the spectra of these radiation components as
blackbodies with temperatures given by TCMB = 2.7 K, TIR = 20 K, and Tstar =
5000 K. In normalizing the infrared and starlight components, we adopt two
models, with energy densities equal to $\rho_{\rm IR}=\rho_{\rm star}=3\,{\rm
eV/cm}^{3}\,({\rm``max"})$ and $\rho_{\rm IR}=\rho_{\rm star}=0.6\,{\rm
eV/cm}^{3}\,({\rm``min"})$. For the energy density of the magnetic field, we
adopt $u_{\mathrm{mag}}=0.224\,{\rm eV/cm}^{3}$ (corresponding to
$B=3\,\mu{\rm G})$ and $u_{\mathrm{mag}}=2.5\,{\rm eV/cm}^{3}(B=10\,\mu{\rm
G})$ in the max and min models, respectively.111Note that our “max” and “min”
models for the radiation and magnetic fields are defined such that they
maximize or minimize the resulting gamma-ray emission, respectively.

At very high energies, inverse Compton scattering takes places in the Klein-
Nishina regime, leading to approximately the following degree of suppression
Schlickeiser and Ruppel (2010):

$\displaystyle\begin{aligned}
S_{i}(E_{e})\approx\frac{45m^{2}_{e}/64\pi^{2}T^{2}_{i}}{(45m^{2}_{e}/64\pi^{2}T^{2}_{i})+(E_{e}^{2}/m^{2}_{e})}.\end{aligned}$
(3)

The instantaneous spectrum of inverse Compton emission from an electron of
energy, $E_{e}$, is given by

$\displaystyle\begin{aligned}
\frac{dN_{\gamma}}{dE_{\gamma}}(E_{\gamma},E_{e})\propto\int\frac{dn}{d\epsilon}(\epsilon)\frac{d\sigma_{ICS}}{dE_{\gamma}}(\epsilon,E_{\gamma},E_{e})d\epsilon,\end{aligned}$
(4)

where $dn/d\epsilon$ is the spectrum of the target radiation, and the
differential cross section is given by Aharonian and Atoyan (1981)

$\displaystyle\frac{d\sigma_{ICS}}{dE_{\gamma}}(\epsilon,E_{\gamma},E_{e})$
$\displaystyle=$ $\displaystyle\frac{3\sigma_{T}m_{e}^{2}}{4\epsilon
E_{e}^{2}}\,\bigg{[}1+\bigg{(}\frac{z^{2}}{2(1-z)}\bigg{)}$ (5)
$\displaystyle+\bigg{(}\frac{z}{\beta(1-z)}\bigg{)}$ $\displaystyle-$
$\displaystyle\bigg{(}\frac{2z^{2}}{\beta^{2}(1-z)}\bigg{)}-\bigg{(}\frac{z^{3}}{2\beta(1-z)^{2}}\bigg{)}$
$\displaystyle-$
$\displaystyle\bigg{(}\frac{2z}{\beta(1-z)}\bigg{)}\ln\bigg{(}\frac{\beta(1-z)}{z}\bigg{)}\bigg{]},$

where $z\equiv E_{\gamma}/E_{e}$ and $\beta\equiv 4\epsilon E_{e}/m_{e}^{2}$.

Figure 1: The fraction of the instantaneous electron energy loss rate that
goes into inverse Compton scattering (as opposed to synchrotron) in our “max”
and “min” models for the Inner Galaxy’s radiation and magnetic fields.

Since we are interested in the steady state inverse Compton emission produced
from the Inner Galaxy’s millisecond pulsar population, we can integrate the
spectrum described by Eq. 4 over the lifetime of an electron to obtain the
total emission from a single injected electron. In performing this
calculation, we take into account the energy that is lost to synchrotron, as
shown in Fig. 1. We then integrate this result over the spectrum of injected
electrons, as parameterized in Eq. 1, to obtain the spectrum of inverse
Compton emission that is generated per unit energy injected from millisecond
pulsars in the form of very high-energy electrons and positrons.

From this spectrum of the inverse Compton emission per unit of leptonic power,
$dN_{\gamma}/dE_{\gamma}dL_{e}$, we can calculate the spectrum and angular
distribution of the gamma-ray emission from the Inner Galaxy’s millisecond
pulsar population:

$\displaystyle\frac{dN_{\gamma}}{dE_{\gamma}}(E_{\gamma},\Delta\Omega)$
$\displaystyle=\frac{1}{4\pi}\int_{\Delta\Omega}\int_{los}\frac{dN_{\gamma}}{dE_{\gamma}dL_{e}}\,\eta\dot{E}\,n_{\rm
MSP}(r)\,dl\,d\Omega.$ (6)

The integrals in this expression are performed over a given angular bin,
$\Delta\Omega$, and over the line-of-sight, $los$. The quantity, $\dot{E}$, is
the average spindown power per millisecond pulsar, and $\eta$ is the average
fraction of the spindown power that goes into the production of electrons and
positrons with $E_{e}>100\,{\rm GeV}$. For the spatial distribution of
millisecond pulsars, we adopt $n_{\rm MSP}\propto r^{-2.4}$, where $r$ is the
distance from the Galactic Center. This profile was selected because it
provides provides a good fit to the observed morphology of the Galactic Center
Gamma-Ray Excess Daylan  _et al._ (2016); Calore  _et al._ (2015a, b);
Ackermann  _et al._ (2017); Di Mauro (2021); Cholis  _et al._ (2022).

Figure 2: The spatial templates used in our analysis, as evaluated at 0.1 TeV.
In the top row, these templates correspond (from left-to-right) to the
emission from pion production, inverse Compton scattering, and bremsstrahlung,
as generated using the publicly available code GALPROP Vladimirov  _et al._
(2011); Górski  _et al._ (2005). In the bottom row, we show the templates
associated with the Fermi bubbles Ackermann  _et al._ (2014), the point
sources described by the Fermi 4FGL-DR2 catalog Abdollahi  _et al._ (2020),
and for the emission from the TeV halos associated with millisecond pulsars.
The scale is logarithmic, and the brightest point in each frame is normalized
to unity. Note that the region-of-interest used in our analysis is a
$3^{\circ}$ radius circle centered at the location of the Galactic Center.

The gamma-ray and radio emission from millisecond pulsars is powered by the
loss of rotational kinetic energy, and thus the energy budget of such an
object is set by its spindown power, $\dot{E}=4\pi^{2}I(dP/dt)/P^{3}$, where
$I$ and $P$ are the pulsar’s moment of inertia and period. In Ref. Hooper and
Linden (2018), the contents of the Fermi pulsar catalog Abdo  _et al._ (2013)
were used to estimate the efficiency at which millisecond pulsars produce GeV-
scale emission, finding that such objects produce an average luminosity in the
GeV-band (i.e., integrated above 0.1 GeV) equal to $\langle\eta_{\rm
GeV}\rangle\approx 0.12$ times their spindown power. This quantity, however,
does not take into account the fact that some pulsars have beams which are not
aligned in our direction. Combining these factors, the luminosity of the GeV-
scale emission from the Inner Galaxy’s millisecond pulsar population can be
expressed as follows:

$\displaystyle L_{\mathrm{GeV}}=\langle\eta_{\rm
GeV}\rangle\,f_{\mathrm{beam}}\dot{E}_{\mathrm{tot}},$ (7)

where $f_{\rm beam}$ is the fraction of millisecond pulsars whose gamma-ray
beam is pointed in the direction of Earth, and $\dot{E}_{\rm tot}$ is the sum
of the spindown power of all of the millisecond pulsars in a given region of
the Inner Galaxy. Comparing this to the intensity of the Galactic Center
Gamma-Ray Excess observed within a $0.5^{\circ}$ radius around the Galactic
Center, $L_{\rm GCE}\approx 2\times 10^{36}\,{\rm erg/s}$ ($>0.1\,{\rm GeV}$),
we can determine the total spindown power of the pulsar population required to
accommodate $L_{\rm GeV}=L_{\rm GCE}$, as a function of $\langle\eta_{\rm
GeV}\rangle$ and $f_{\rm beam}$. From this total spindown power and the TeV
halo efficiency, $\eta$, the intensity of the TeV halo emission from the Inner
Galaxy’s millisecond pulsar population will be equal to

$\displaystyle L_{\rm TeV}$ $\displaystyle=\dot{E}_{\rm
tot}\,\eta=\frac{L_{\rm GeV}\,\eta}{\langle\eta_{\rm GeV}\rangle f_{\rm
beam}}$ $\displaystyle=f_{\rm GCE}\,\frac{L_{\rm GCE}\,\eta}{\langle\eta_{\rm
GeV}\rangle f_{\rm beam}},$ (8)

where $f_{\rm GCE}\equiv L_{\rm GeV}/L_{\rm GCE}$ is the fraction of the
Galactic Center Gamma-Ray Excess that is generated by millisecond pulsars.

Figure 3: The gamma-ray spectra of the various components of our background
model, and from the TeV halos associated with millisecond pulsars in the Inner
Galaxy, averaged over a $3^{\circ}$ (left) or $0.5^{\circ}$ (right) radius
circle centered around the Galactic Center. For each of the three components
of the Galactic diffuse emission (pion decay, inverse Compton scattering, and
bremsstrahlung), we adopt the default GALPROP parameters as described in the
text. In calculating the emission associated with TeV halos, we have assumed
that the entire Galactic Center Gamma-Ray Excess is generated by millisecond
pulsars, and have adopted $\alpha=1.5$, $E_{\rm cut}=30\,{\rm TeV}$,
$\eta=0.1$, $\langle\eta_{\rm GeV}\rangle=0.12$, $f_{\rm beam}=0.5$, and the
“min” model for the radiation and magnetic fields. For comparison, we also
show the spectra associated with the Fermi Bubbles Ackermann  _et al._ (2014),
the extragalactic gamma-ray background (EGB) Ackermann  _et al._ (2015), and
the point sources contained within the Fermi 4FGL-DR2 catalog Abdollahi  _et
al._ (2020). If the gamma-ray excess is generated by millisecond pulsars,
their TeV halos should dominate the TeV-scale emission from the Inner Galaxy.

Figure 4: The gamma-ray spectrum from the TeV halos associated with
millisecond pulsars in the Inner Galaxy, averaged over a $3^{\circ}$ (left) or
$0.5^{\circ}$ (right) radius circle centered around the Galactic Center, for
eight different combinations of parameters. We continue in this figure to
assume that the entire Galactic Center Gamma-Ray Excess is generated by
millisecond pulsars, but adopt either $\alpha=1.5$ (top frames) or
$\alpha=2.0$ (bottom frames). In each frame, we show results for $E_{\rm
cut}=30\,{\rm TeV}$ or $100\,{\rm TeV}$, and using our “min” or “max” model
for the radiation and magnetic fields. As before, we have adopted $\eta=0.1$,
$\langle\eta_{\rm GeV}\rangle=0.12$, $f_{\rm beam}=0.5$, and the spectra shown
are as averaged over a $3^{\circ}$ (left) or $0.5^{\circ}$ (right) radius
circle centered around the Galactic Center.

Figure 5: The 68% containment radius (left) and effective area (right) of CTA
as a function of gamma-ray energy Maier  _et al._ (2019).

##  III Observations With The Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA) is a next-generation ground-based gamma-
ray telescope, designed to be sensitive to photons in the energy range of 20
GeV to 300 TeV Maier (2019). Although CTA will occupy two sites, we will focus
here on the southern hemisphere array, located in Paranal, Chile. This
southern array will consist of 14 medium-sized and 37 small-sized telescopes,
covering an area of approximately 4 km2. This instrument is expected to have
angular resolution on the order of two arcminutes, and energy resolution
better than 10%.

To evaluate the sensitivity of CTA to a population of TeV halos associated
with millisecond pulsars in the Inner Galaxy, we have created a series of
simulated data sets based on the proposed design of CTA, and analyzed this
simulated data utilizing a set of spatial templates. Such template-based
analyses are extremely powerful in that they allow us to simultaneously
exploit both spectral and morphological distinctions between the signal being
searched for, and the various astrophysical backgrounds that are present. In
addition to the TeV halo template, our analysis includes spatial templates
associated with the processes of pion production, bremsstrahlung, and (non-TeV
halo) inverse Compton scattering, as well a template for the point sources
described by the Fermi 4FGL-DR2 catalog Abdollahi  _et al._ (2020), and a
template that is isotropic throughout our region-of-interest (a $3^{\circ}$
radius circle centered on the Galactic Center) which accounts for the emission
associated with the Fermi Bubbles Ackermann  _et al._ (2014) and the
extragalactic gamma-ray background Ackermann  _et al._ (2015), as well as
misidentified cosmic rays.222For the rate and spectrum of misidentified
cosmic-ray, we use the background rate given at https://www.cta-
observatory.org/science/ctao-performance/ for CTA’s Southern Array. Note that
this background significantly exceeds those associated with the Fermi Bubbles
and the extragalactic gamma-ray background. The templates associated with pion
production, bremsstrahlung, and inverse Compton scattering were each generated
using the publicly available code, GALPROP Vladimirov  _et al._ (2011); Górski
_et al._ (2005).333In using GALPROP, we have adopted the default parameters
from GALPROP WebRun, https://galprop.stanford.edu/webrun.php, which have been
selected to reproduce a wide variety of cosmic-ray and gamma-ray observations.
These templates are shown in Fig. 2, and the gamma-ray spectrum associated
with each of these components is shown in Fig. 3. In Fig. 4, we show the
spectrum associated with the TeV halo template for a selection of different
parameter choices. Note that in modeling the emission associated with the
Fermi bubbles, point sources, and the extragalactic gamma-ray background, we
are forced to extrapolate to energies well above those measured by Fermi, as
shown in Fig. 3.

To produce a simulated data set, we first convolve each of the templates by
the point spread function of CTA, which we treat as a gaussian with a 68%
containment radius as given in the left frame of Fig. 5 Maier  _et al._
(2019). Because of CTA’s very high angular resolution, this convolution has
very little effect on our results. We divide our region-of-interest (taken to
be a $3^{\circ}$ radius circle around the Galactic Center) into 0.2098 square
degree HEALPix bins, corresponding to $N_{\rm side}=128$. We also divide the
spectrum into 10 energy bins per decade, spanning 10 GeV to 100 TeV. Then,
after summing the templates described above, we calculate the mean number of
events in a given angular and energy bin. This is done by multiplying the flux
in that bin by the effective area of CTA (as given in the right frame of Fig.
5) Maier  _et al._ (2019), and by 20 hours of observation time. For each bin,
we then draw from a Poisson distribution using the mean number of events
predicted by our model to obtain the simulated number of events in that bin.
Using a simulated data set, we then calculate the likelihood as a function of
our model’s parameters. These parameters consist of the normalizations of each
of our templates, in each energy bin. This procedure allows us to place
constraints on the spectra of each of our background components, as well as on
the spectrum of the emission from TeV halos associated with millisecond
pulsars. In presenting our projected constraints, we show results as averaged
over five sets of simulated data, to reduce the presence of statistical
variation.444We use the publicly available MINUIT algorithm Dembinski and et
al. (2020) to perform our likelihood analysis. Given that MINUIT can
occasionally identify false minima of the likelihood landscape, we also
utilize the PyMultiNest package Buchner  _et al._ (2014) to test the
robustness of our results by searching for the global minimum in case it was
not encountered in our MINUIT scan.

##  IV Projected Sensitivity

Figure 6: The projected upper limit from CTA on the fraction of the Galactic
Center Gamma-Ray Excess that is generated by millisecond pulsars, $f_{\rm
GCE}$, under the assumption that no TeV halos are present in the Inner Galaxy.
This result corresponds to 20 hours of observation of a $3^{\circ}$ radius
circle around the Galactic Center, and we have adopted $\eta/(\langle\eta_{\rm
GeV}\rangle f_{\mathrm{beam}})=1.67$. If no TeV halo emission is present in
the Inner Galaxy, we expect CTA to be able to place extremely stringent
constraints on the fraction of the excess that is generated by millisecond
pulsars, at a level of approximately $f_{\rm GCE}\mathrel{\raise
1.29167pt\hbox{$<$\kern-7.5pt\lower 4.30554pt\hbox{$\sim$}}}(1-7)\%$.

Figure 7: The total gamma-ray emission predicted from our background model,
including misidentified cosmic-rays (left), and from the background model plus
the emission expected from TeV halos in the Inner Galaxy (right), assuming
either that the entire Galactic Center Gamma-Ray Excess, or 20% of it, is
generated by millisecond pulsars, $f_{\rm GCE}=1$, (top) or $f_{\rm GCE}=0.2$
(bottom). Here, we have adopted $\alpha=1.5$, $E_{\rm cut}=30\,{\rm TeV}$,
$\eta=0.1$, $\langle\eta_{\rm GeV}\rangle=0.12$, $f_{\rm beam}=0.5$, and our
“min” model for the radiation and magnetic fields. Each image represents the
value of $\int dE_{\gamma}E_{\gamma}dN_{\gamma}/dE_{\gamma}$, integrated above
1 TeV, and in units of $\log_{10}$(TeV/cm2/s/sr).

Figure 8: The ability of CTA, after 20 hours of observation, to measure the
spectrum of the gamma-ray emission from an Inner Galaxy population of TeV
halos, for values of $f_{\rm GCE}=1,0.2$, or 0.05, and in each case adopting
$\alpha=1.5$, $E_{\rm cut}=30\,{\rm TeV}$, $\eta=0.1$, $\langle\eta_{\rm
GeV}\rangle=0.12$, $f_{\rm beam}=0.5$, and our “min” model for the radiation
and magnetic fields. The gamma-ray emission from a centrally-located TeV halo
population would be clearly identified and measured by CTA, even if only a
relatively small fraction of the Galactic Center Gamma-Ray is generated by
millisecond pulsars.

We begin by generating a series of simulated data sets under the assumption
that no TeV halos are present in the Inner Galaxy. We then perform our
template analysis on this simulated data to place constraints on the TeV halo
population. More specifically, we place an upper limit on the quantity,
$\dot{E}_{\rm tot}\,\eta$, as a function of $\alpha$ and $E_{\rm cut}$.
Equivalently, we can use Eq. 8 to instead express this result as an upper
limit on the fraction of the Galactic Center Gamma-Ray Excess that is
generated by millisecond pulsars, $f_{\rm GCE}$, for a given choice of
$\eta/(\langle\eta_{\rm GeV}\rangle f_{\mathrm{beam}})$.

The main result from this first analysis is shown in Fig. 6, where we plot the
upper limit on $f_{\rm GCE}$, for the case of $\eta/(\langle\eta_{\rm
GeV}\rangle f_{\mathrm{beam}})=0.1/(0.12\times 0.5)=1.67$. From this figure,
we conclude that if no TeV halo emission is present in the Inner Galaxy, we
can expect CTA to place an extremely stringent constraint on the fraction of
the Galactic Center Gamma-Ray Excess that is generated by millisecond pulsars,
at a level of approximately $f_{\rm GCE}\mathrel{\raise
1.29167pt\hbox{$<$\kern-7.5pt\lower 4.30554pt\hbox{$\sim$}}}(1-7)\%$. This
projected limit is able to be so restrictive simply because the emission from
the TeV halo population is incredibly bright in this case. This is illustrated
in the spectra shown in Figs. 3 and 4, as well as in Fig. 7, where we show a
sky map of the gamma-ray intensity in the Inner Galaxy above 0.1 TeV for the
case of our background model, and for our background model plus the TeV halo
emission, normalized to $f_{\rm GCE}=1$ or 0.2 for $\eta/(\langle\eta_{\rm
GeV}\rangle f_{\mathrm{beam}})=1.67$. The presence of TeV halos in the Inner
Galaxy dramatically changes the morphology and spectrum of the very high-
energy gamma-ray emission from this region, and should be easily detectable
after even a brief observation by CTA.

For our second analysis, we have generated a series of simulated data sets
assuming that TeV halos are present in the Inner Galaxy. The ability of CTA to
measure the spectrum of the gamma-ray emission from these Inner Galaxy TeV
halos is shown in Fig. 8, for values of $f_{\rm GCE}=1,0.2$, or 0.05 (and in
each case adopting $\alpha=1.5$, $E_{\rm cut}=30\,{\rm TeV}$, $\eta=0.1$,
$\langle\eta_{\rm GeV}\rangle=0.12$, $f_{\rm beam}=0.5$, and our “min” model
for the radiation and magnetic fields). Note that these figures depict the
results of an individual simulated data set, explaining the bin-to-bin
variations seen in the projected error bars. These results demonstrate that
CTA should be able to clearly identify and measure the gamma-ray emission from
a centrally-located TeV halo population, even if only a relatively small
fraction of the Galactic Center Gamma-Ray is generated by millisecond pulsars.

##  V Discussion

Measurements of the very high-energy gamma-ray emission from the Inner Galaxy
have already been reported by the HESS Collaboration Abramowski  _et al._
(2016). That study, however, produced spectra only from the innermost
$0.5^{\circ}$ around the Galactic Center. In that region, the observed
emission is approximately equal to that expected from TeV halos in a scenario
in which the entire Galactic Center Gamma-Ray Excess originates from
millisecond pulsars Hooper and Linden (2018) (see also, Ref. Hooper  _et al._
(2018)). This information allows us to place an upper limit of roughly $f_{\rm
GCE}\,\eta/(\langle\eta_{\rm GeV}\rangle f_{\mathrm{beam}})\mathrel{\raise
1.29167pt\hbox{$<$\kern-7.5pt\lower 4.30554pt\hbox{$\sim$}}}\mathcal{O}(1-3)$
on our TeV halo/MSP parameters. Furthermore, it has been argued by the HESS
Collaboration that this emission is correlated with the observed distribution
of molecular gas, suggesting a hadronic origin Abramowski  _et al._ (2016),
and thereby further limiting how much of this emission could originate from
TeV halos. With CTA’s greater sensitivity and larger field-of-view, it should
be possible to rigorously test this interpretation, in particular by measuring
the spectrum and intensity of the gamma-ray emission from the regions several
degrees north or south of the Galactic Center.

A number of assumptions have gone into our analysis which could potentially
impact our conclusions. First, we have assumed that the emission from TeV
halos has the same angular distribution as that from the GeV-scale emission
from MSPs (and thus traces the morphology of the Galactic Center Gamma-Ray
Excess). The transport of electrons and positrons could, however, broaden the
TeV halo signal, at least in principle. The TeV halos observed by HAWC are
extended on scales of roughly $\sim$20-30 pc, corresponding to an angular
extent of $\sim 0.14^{\circ}-0.21^{\circ}$ for sources located near the
Galactic Center. This has motivated our choice for the size of the angular
bins used in our study, 0.2098 square degrees, which is slightly larger than
the size of a typical TeV halo, limiting the impact of particle transport on
our signal. At this time, however, it has not yet been established whether
diffusion is inhibited within the volumes surrounding MSPs, as it is observed
to be around young and middle-aged pulsars Evoli  _et al._ (2018); Fang  _et
al._ (2019). If diffusion is more efficient around MSPs, the signal of these
TeV halos could be broadened by up to $\sim\mathcal{O}(1^{\circ})$, while
still leaving the total flux of gamma-ray emission from these sources
approximately unchanged. Future measurements of the TeV halos surrounding
nearby MSPs will inform the shape of our TeV halo template.

Second, if the magnetic fields are very large in the Inner Galaxy, most of the
energy injected into very high-energy electron-positron pairs could emitted as
synchrotron emission, rather than as inverse Compton, suppressing the signal
at TeV-scale energies. While this is unlikely to be an important factor over
most of our region-of-interest, it could be significant in the innermost
volume around the Galactic Center, where magnetic fields could potentially be
quite large. This scenario, however, is limited by radio observations of the
Inner Galaxy Crocker  _et al._ (2010). If millisecond pulsars generate all or
most of the Galactic Center Gamma-Ray Excess, their TeV halos will produce
electrons and positrons which lose most of the energy to inverse Compton
scattering Hooper and Linden (2018).

Third, throughout this study, we have scaled our results to
$\eta/(\langle\eta_{\rm GeV}\rangle f_{\mathrm{beam}})=0.1/(0.12\times
0.5)=1.67$. As the predicted intensity of the TeV halo emission scales with
this combination of parameters, our constraints would be less stringent if the
true value of $\eta/(\langle\eta_{\rm GeV}\rangle f_{\mathrm{beam}})$ were
significantly smaller than our default value. Fortunately, CTA should be able
to measure the value (or distribution) of $\eta$ across a large number of
pulsars, including many with millisecond-scale periods, reducing this
uncertainty considerably. In light of this, we expect that the uncertainty on
$\langle\eta_{\rm GeV}\rangle f_{\mathrm{beam}}$ will not qualitatively impact
our conclusions.

Lastly, while the conclusions reached in this study are in broad agreement
with those presented in Ref. Macias  _et al._ (2021), that paper’s projections
for CTA’s sensitivity to a centrally-located TeV halo population are somewhat
more modest than those reported here. While the precise origin of this
difference is not entirely clear, we note that the authors of Ref. Macias  _et
al._ (2021) have adopted a model for the gamma-ray emission associated with
the Fermi Bubbles that significantly increases in brightness at low galactic
latitudes. In contrast, we have used the fact that the brightness of the
Bubbles is approximately uniform between $10^{\circ}<|b|<50^{\circ}$ Ackermann
_et al._ (2014) to motivate the assumption that this emission is comparably
bright at $|b|<10^{\circ}$. Regardless of this distinction, both groups reach
the same conclusion that CTA should be able to clearly identify the emission
associated from TeV halos if the Galactic Center Gamma-Ray Excess originates
from millisecond pulsars.

##  VI Summary and Conclusions

The Galactic Center Gamma-Ray Excess, as observed by Fermi, has a spectrum,
angular distribution, and overall intensity that is in good agreement with
that expected to be produced by annihilating dark matter particles. The
leading alternative to this interpretation is that this signal is instead
generated by a large number of unresolved millisecond pulsars. If millisecond
pulsars are responsible for this signal, however, they should also produce
detectable levels of TeV-scale emission, as recent observations indicate that
pulsars appear to be universally surrounded by bright, spatially-extended,
multi-TeV emitting regions known as “TeV halos”.

In this study, we have performed a template-based analysis of simulated data
to assess the ability of the Cherenkov Telescope Array (CTA) to identify and
measure the very high-energy gamma-ray emission from a population of
millisecond pulsars surrounding the Galactic Center. When the intensity of
this emission is normalized to the measurements of other pulsars by HAWC and
LHAASO, we find that if the Galactic Center Gamma-Ray Excess originates from
pulsars, this source population should produce a very bright flux of gamma
rays, dominating the total TeV-scale emission from the direction of the Inner
Galaxy. Such a signal would be easily detectable by CTA, even after a
relatively brief period of observation. If such a pulsar population is present
in the Inner Galaxy, we conclude that CTA should be able to clearly identify
the TeV halo emission associated with these sources. If this emission is not
observed by CTA, this would strongly rule out the hypothesis that the Galactic
Center Gamma-Ray Excess originates from millisecond pulsars.

###### Acknowledgements.

CK is supported by the National Science Foundation Graduate Research
Fellowship Program under grant No. DGE-1746045, and by the U.S. Department of
Energy Office of Science Graduate Student Research (SCGSR) program under
contract number DE‐SC0014664. DH is supported by the Fermi Research Alliance,
LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy,
Office of Science, Office of High Energy Physics. TL is partially supported by
the Swedish Research Council under contract 2019-05135, the Swedish National
Space Agency under contract 117/19 and the European Research Council under
grant 742104. CK would like to thank Elyssa Cotter for helpful conversations.

## References

  * Goodenough and Hooper (2009) L. Goodenough and D. Hooper, (2009), arXiv:0910.2998 [hep-ph] .
  * Hooper and Goodenough (2011) D. Hooper and L. Goodenough, Phys. Lett. B 697, 412 (2011), arXiv:1010.2752 [hep-ph] .
  * Hooper and Linden (2011) D. Hooper and T. Linden, Phys. Rev. D 84, 123005 (2011), arXiv:1110.0006 [astro-ph.HE] .
  * Daylan  _et al._ (2016) T. Daylan, D. P. Finkbeiner, D. Hooper, T. Linden, S. K. N. Portillo, N. L. Rodd, and T. R. Slatyer, Phys. Dark Univ. 12, 1 (2016), arXiv:1402.6703 [astro-ph.HE] .
  * Calore  _et al._ (2015a) F. Calore, I. Cholis, and C. Weniger, JCAP 03, 038 (2015a), arXiv:1409.0042 [astro-ph.CO] .
  * Calore  _et al._ (2015b) F. Calore, I. Cholis, C. McCabe, and C. Weniger, Phys. Rev. D 91, 063003 (2015b), arXiv:1411.4647 [hep-ph] .
  * Ackermann  _et al._ (2017) M. Ackermann _et al._ (Fermi-LAT), Astrophys. J. 840, 43 (2017), arXiv:1704.03910 [astro-ph.HE] .
  * Di Mauro (2021) M. Di Mauro, Phys. Rev. D 103, 063029 (2021), arXiv:2101.04694 [astro-ph.HE] .
  * Cholis  _et al._ (2022) I. Cholis, Y.-M. Zhong, S. D. McDermott, and J. P. Surdutovich, Phys. Rev. D 105, 103023 (2022), arXiv:2112.09706 [astro-ph.HE] .
  * Berlin  _et al._ (2014a) A. Berlin, D. Hooper, and S. D. McDermott, Phys. Rev. D 89, 115022 (2014a), arXiv:1404.0022 [hep-ph] .
  * Izaguirre  _et al._ (2014) E. Izaguirre, G. Krnjaic, and B. Shuve, Phys. Rev. D 90, 055002 (2014), arXiv:1404.2018 [hep-ph] .
  * Ipek  _et al._ (2014) S. Ipek, D. McKeen, and A. E. Nelson, Phys. Rev. D 90, 055021 (2014), arXiv:1404.3716 [hep-ph] .
  * Agrawal  _et al._ (2014) P. Agrawal, B. Batell, D. Hooper, and T. Lin, Phys. Rev. D 90, 063512 (2014), arXiv:1404.1373 [hep-ph] .
  * Berlin  _et al._ (2014b) A. Berlin, P. Gratia, D. Hooper, and S. D. McDermott, Phys. Rev. D 90, 015032 (2014b), arXiv:1405.5204 [hep-ph] .
  * Abdullah  _et al._ (2014) M. Abdullah, A. DiFranzo, A. Rajaraman, T. M. P. Tait, P. Tanedo, and A. M. Wijangco, Phys. Rev. D 90, 035004 (2014), arXiv:1404.6528 [hep-ph] .
  * Martin  _et al._ (2014) A. Martin, J. Shelton, and J. Unwin, Phys. Rev. D 90, 103513 (2014), arXiv:1405.0272 [hep-ph] .
  * Alves  _et al._ (2014) A. Alves, S. Profumo, F. S. Queiroz, and W. Shepherd, Phys. Rev. D 90, 115003 (2014), arXiv:1403.5027 [hep-ph] .
  * Boehm  _et al._ (2014) C. Boehm, M. J. Dolan, C. McCabe, M. Spannowsky, and C. J. Wallace, JCAP 05, 009 (2014), arXiv:1401.6458 [hep-ph] .
  * Berlin  _et al._ (2015) A. Berlin, S. Gori, T. Lin, and L.-T. Wang, Phys. Rev. D 92, 015005 (2015), arXiv:1502.06000 [hep-ph] .
  * Karwin  _et al._ (2017) C. Karwin, S. Murgia, T. M. P. Tait, T. A. Porter, and P. Tanedo, Phys. Rev. D 95, 103005 (2017), arXiv:1612.05687 [hep-ph] .
  * Abazajian (2011) K. N. Abazajian, JCAP 03, 010 (2011), arXiv:1011.4275 [astro-ph.HE] .
  * Hooper  _et al._ (2013) D. Hooper, I. Cholis, T. Linden, J. Siegal-Gaskins, and T. Slatyer, Phys. Rev. D 88, 083009 (2013), arXiv:1305.0830 [astro-ph.HE] .
  * Gordon and Macias (2013) C. Gordon and O. Macias, Phys. Rev. D 88, 083521 (2013), [Erratum: Phys.Rev.D 89, 049901 (2014)], arXiv:1306.5725 [astro-ph.HE] .
  * Cholis  _et al._ (2015) I. Cholis, D. Hooper, and T. Linden, JCAP 06, 043 (2015), arXiv:1407.5625 [astro-ph.HE] .
  * Petrović  _et al._ (2015) J. Petrović, P. D. Serpico, and G. Zaharijas, JCAP 02, 023 (2015), arXiv:1411.2980 [astro-ph.HE] .
  * Brandt and Kocsis (2015) T. D. Brandt and B. Kocsis, Astrophys. J. 812, 15 (2015), arXiv:1507.05616 [astro-ph.HE] .
  * Hooper and Mohlabeng (2016) D. Hooper and G. Mohlabeng, JCAP 03, 049 (2016), arXiv:1512.04966 [astro-ph.HE] .
  * Hooper and Linden (2016) D. Hooper and T. Linden, JCAP 08, 018 (2016), arXiv:1606.09250 [astro-ph.HE] .
  * Lee  _et al._ (2016) S. K. Lee, M. Lisanti, B. R. Safdi, T. R. Slatyer, and W. Xue, Phys. Rev. Lett. 116, 051103 (2016), arXiv:1506.05124 [astro-ph.HE] .
  * Bartels  _et al._ (2016) R. Bartels, S. Krishnamurthy, and C. Weniger, Phys. Rev. Lett. 116, 051102 (2016), arXiv:1506.05104 [astro-ph.HE] .
  * Bartels  _et al._ (2018a) R. Bartels, E. Storm, C. Weniger, and F. Calore, Nature Astron. 2, 819 (2018a), arXiv:1711.04778 [astro-ph.HE] .
  * Macias  _et al._ (2018) O. Macias, C. Gordon, R. M. Crocker, B. Coleman, D. Paterson, S. Horiuchi, and M. Pohl, Nature Astron. 2, 387 (2018), arXiv:1611.06644 [astro-ph.HE] .
  * Macias  _et al._ (2019) O. Macias, S. Horiuchi, M. Kaplinghat, C. Gordon, R. M. Crocker, and D. M. Nataf, JCAP 09, 042 (2019), arXiv:1901.03822 [astro-ph.HE] .
  * Pohl  _et al._ (2022) M. Pohl, O. Macias, P. Coleman, and C. Gordon, Astrophys. J. 929, 136 (2022), arXiv:2203.11626 [astro-ph.HE] .
  * Hooper (2022) D. Hooper, in  _14th International Workshop on the Identification of Dark Matter 2022_ (2022) arXiv:2209.14370 [astro-ph.HE] .
  * Leane and Slatyer (2019) R. K. Leane and T. R. Slatyer, Phys. Rev. Lett. 123, 241101 (2019), arXiv:1904.08430 [astro-ph.HE] .
  * Leane and Slatyer (2020a) R. K. Leane and T. R. Slatyer, Phys. Rev. D 102, 063019 (2020a), arXiv:2002.12371 [astro-ph.HE] .
  * Leane and Slatyer (2020b) R. K. Leane and T. R. Slatyer, Phys. Rev. Lett. 125, 121105 (2020b), arXiv:2002.12370 [astro-ph.HE] .
  * Zhong  _et al._ (2020) Y.-M. Zhong, S. D. McDermott, I. Cholis, and P. J. Fox, Phys. Rev. Lett. 124, 231103 (2020), arXiv:1911.12369 [astro-ph.HE] .
  * McDermott  _et al._ (2022) S. D. McDermott, Y.-M. Zhong, and I. Cholis, (2022), arXiv:2209.00006 [astro-ph.HE] .
  * Bartels  _et al._ (2018b) R. Bartels, D. Hooper, T. Linden, S. Mishra-Sharma, N. L. Rodd, B. R. Safdi, and T. R. Slatyer, Phys. Dark Univ. 20, 88 (2018b), arXiv:1710.10266 [astro-ph.HE] .
  * Dinsmore and Slatyer (2022) J. T. Dinsmore and T. R. Slatyer, JCAP 06, 025 (2022), arXiv:2112.09699 [astro-ph.HE] .
  * Calore  _et al._ (2016) F. Calore, M. Di Mauro, F. Donato, J. W. T. Hessels, and C. Weniger, Astrophys. J. 827, 143 (2016), arXiv:1512.06825 [astro-ph.HE] .
  * Haggard  _et al._ (2017) D. Haggard, C. Heinke, D. Hooper, and T. Linden, JCAP 05, 056 (2017), arXiv:1701.02726 [astro-ph.HE] .
  * Hooper  _et al._ (2017) D. Hooper, I. Cholis, T. Linden, and K. Fang, Phys. Rev. D 96, 103013 (2017), arXiv:1702.08436 [astro-ph.HE] .
  * Linden  _et al._ (2017) T. Linden, K. Auchettl, J. Bramante, I. Cholis, K. Fang, D. Hooper, T. Karwal, and S. W. Li, Phys. Rev. D 96, 103016 (2017), arXiv:1703.09704 [astro-ph.HE] .
  * Albert  _et al._ (2021) A. Albert _et al._ (HAWC), Astrophys. J. Lett. 911, L27 (2021), arXiv:2101.07895 [astro-ph.HE] .
  * Abeysekara  _et al._ (2020) A. U. Abeysekara _et al._ (HAWC), Phys. Rev. Lett. 124, 021102 (2020), arXiv:1909.08609 [astro-ph.HE] .
  * Hooper and Linden (2022) D. Hooper and T. Linden, Phys. Rev. D 105, 103013 (2022), arXiv:2104.00014 [astro-ph.HE] .
  * Hooper and Linden (2018) D. Hooper and T. Linden, Phys. Rev. D 98, 043005 (2018), arXiv:1803.08046 [astro-ph.HE] .
  * Albert  _et al._ (2020) A. Albert _et al._ (HAWC), Astrophys. J. 905, 76 (2020), arXiv:2007.08582 [astro-ph.HE] .
  * Abeysekara  _et al._ (2017a) A. U. Abeysekara _et al._ , Astrophys. J. 843, 40 (2017a), arXiv:1702.02992 [astro-ph.HE] .
  * Abeysekara  _et al._ (2017b) A. U. Abeysekara _et al._ (HAWC), Science 358, 911 (2017b), arXiv:1711.06223 [astro-ph.HE] .
  * Abdo  _et al._ (2009) A. A. Abdo _et al._ , Astrophys. J. Lett. 700, L127 (2009), [Erratum: Astrophys.J.Lett. 703, L185 (2009), Erratum: Astrophys.J. 703, L185 (2009)], arXiv:0904.1018 [astro-ph.HE] .
  * Sudoh  _et al._ (2021) T. Sudoh, T. Linden, and D. Hooper, JCAP 08, 010 (2021), arXiv:2101.11026 [astro-ph.HE] .
  * Linden and Buckman (2018) T. Linden and B. J. Buckman, Phys. Rev. Lett. 120, 121101 (2018), arXiv:1707.01905 [astro-ph.HE] .
  * Xu and Hooper (2022) F. Xu and D. Hooper, Phys. Rev. D 106, 023005 (2022), arXiv:2111.03646 [astro-ph.HE] .
  * Venter  _et al._ (2015) C. Venter, A. Kopp, A. K. Harding, P. L. Gonthier, and I. Büsching, Astrophys. J. 807, 130 (2015), arXiv:1506.01211 [astro-ph.HE] .
  * Bednarek  _et al._ (2016) W. Bednarek, J. Sitarek, and T. Sobczak, Mon. Not. Roy. Astron. Soc. 458, 1083 (2016), arXiv:1602.03629 [astro-ph.HE] .
  * Venter  _et al._ (2016) C. Venter, A. Kopp, A. K. Harding, P. L. Gonthier, and I. Büsching, PoS ICRC2015, 462 (2016), arXiv:1508.04676 [astro-ph.HE] .
  * Sironi and Spitkovsky (2011) L. Sironi and A. Spitkovsky, Astrophys. J. 741, 39 (2011), arXiv:1107.0977 [astro-ph.HE] .
  * Gaensler and Slane (2006) B. M. Gaensler and P. O. Slane, Ann. Rev. Astron. Astrophys. 44, 17 (2006), arXiv:astro-ph/0601081 .
  * BLUMENTHAL and GOULD (1970) G. R. BLUMENTHAL and R. J. GOULD, Rev. Mod. Phys. 42, 237 (1970).
  * Schlickeiser and Ruppel (2010) R. Schlickeiser and J. Ruppel, New Journal of Physics 12, 033044 (2010), arXiv:0908.2183 [astro-ph.HE] .
  * Aharonian and Atoyan (1981) F. A. Aharonian and A. M. Atoyan, Phys. Lett. B 99, 301 (1981).
  * Vladimirov  _et al._ (2011) A. E. Vladimirov, S. W. Digel, G. Jóhannesson, P. F. Michelson, I. V. Moskalenko, P. L. Nolan, E. Orlando, T. A. Porter, and A. W. Strong, Computer Physics Communications 182, 1156 (2011), arXiv:1008.3642 [astro-ph.HE] .
  * Górski  _et al._ (2005) K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelmann, Astrophys. J. 622, 759 (2005), arXiv:astro-ph/0409513 [astro-ph] .
  * Ackermann  _et al._ (2014) M. Ackermann _et al._ (Fermi-LAT), Astrophys. J. 793, 64 (2014), arXiv:1407.7905 [astro-ph.HE] .
  * Abdollahi  _et al._ (2020) S. Abdollahi _et al._ (Fermi-LAT), Astrophys. J. Suppl. 247, 33 (2020), arXiv:1902.10045 [astro-ph.HE] .
  * Abdo  _et al._ (2013) A. A. Abdo _et al._ (Fermi-LAT), Astrophys. J. Suppl. 208, 17 (2013), arXiv:1305.4385 [astro-ph.HE] .
  * Ackermann  _et al._ (2015) M. Ackermann _et al._ (Fermi-LAT), Astrophys. J. 799, 86 (2015), arXiv:1410.3696 [astro-ph.HE] .
  * Maier  _et al._ (2019) G. Maier, L. Arrabito, K. Bernlöhr, J. Bregeon, P. Cumani, T. Hassan, J. Hinton, and A. Moralejo, “Performance of the cherenkov telescope array,”  (2019).
  * Maier (2019) G. Maier, in  _36th International Cosmic Ray Conference (ICRC2019)_ , International Cosmic Ray Conference, Vol. 36 (2019) p. 733, arXiv:1907.08171 [astro-ph.IM] .
  * Dembinski and et al. (2020) H. Dembinski and P. O. et al.,  (2020), 10.5281/zenodo.3949207.
  * Buchner  _et al._ (2014) J. Buchner, A. Georgakakis, K. Nandra, L. Hsu, C. Rangel, M. Brightman, A. Merloni, M. Salvato, J. Donley, and D. Kocevski, Astron. Astrophys. 564, A125 (2014), arXiv:1402.0004 [astro-ph.HE] .
  * Abramowski  _et al._ (2016) A. Abramowski _et al._ (H.E.S.S.), Nature 531, 476 (2016), arXiv:1603.07730 [astro-ph.HE] .
  * Hooper  _et al._ (2018) D. Hooper, I. Cholis, and T. Linden, Phys. Dark Univ. 21, 40 (2018), arXiv:1705.09293 [astro-ph.HE] .
  * Evoli  _et al._ (2018) C. Evoli, T. Linden, and G. Morlino, Phys. Rev. D 98, 063017 (2018), arXiv:1807.09263 [astro-ph.HE] .
  * Fang  _et al._ (2019) K. Fang, X.-J. Bi, and P.-F. Yin, Mon. Not. Roy. Astron. Soc. 488, 4074 (2019), arXiv:1903.06421 [astro-ph.HE] .
  * Crocker  _et al._ (2010) R. M. Crocker, D. Jones, F. Melia, J. Ott, and R. J. Protheroe, Nature 468, 65 (2010), arXiv:1001.1275 [astro-ph.GA] .
  * Macias  _et al._ (2021) O. Macias, H. van Leijen, D. Song, S. Ando, S. Horiuchi, and R. M. Crocker, Mon. Not. Roy. Astron. Soc. 506, 1741 (2021), arXiv:2102.05648 [astro-ph.HE] .


# Generative AI for RF Sensing in IoT systems††thanks: This work has been
submitted to the IEEE for possible publication. Copyright may be transferred
without notice, after which this version may no longer be accessible.

Li Wang, Chao Zhang, Qiyang Zhao, Hang Zou,
Samson Lasaulce, Giuseppe Valenzise, Zhuo He, and Merouane Debbah

###### Abstract

The development of wireless sensing technologies, using signals such as Wi-Fi,
infrared, and RF to gather environmental data, has significantly advanced
within Internet of Things (IoT) systems. Among these, Radio Frequency (RF)
sensing stands out for its cost-effective and non-intrusive monitoring of
human activities and environmental changes. However, traditional RF sensing
methods face significant challenges, including noise, interference, incomplete
data, and high deployment costs, which limit their effectiveness and
scalability. This paper investigates the potential of Generative AI (GenAI) to
overcome these limitations within the IoT ecosystem. We provide a
comprehensive review of state-of-the-art GenAI techniques, focusing on their
application to RF sensing problems. By generating high-quality synthetic data,
enhancing signal quality, and integrating multi-modal data, GenAI offers
robust solutions for RF environment reconstruction, localization, and imaging.
Additionally, GenAI’s ability to generalize enables IoT devices to adapt to
new environments and unseen tasks, improving their efficiency and performance.
The main contributions of this article include a detailed analysis of the
challenges in RF sensing, the presentation of innovative GenAI-based
solutions, and the proposal of a unified framework for diverse RF sensing
tasks. Through case studies, we demonstrate the effectiveness of integrating
GenAI models, leading to advanced, scalable, and intelligent IoT systems.

###### Index Terms:

Generative AI, RF sensing, cross-modal estimation, multi-modal fusion, large
language models.

##  I Introduction

With the development of the Internet of Things (IoT), many kinds of wireless
sensing signals (e.g., Wi-Fi, Infrared images, visible images, Radio Frequency
(RF) signal) are filling our living and working spaces nowadays. Recently,
researchers have also utilized RF signals to capture events in the IoT
environment (i.e., RF sensing). While RF signals are transmitted, reflected,
blocked, and scattered by objects like walls, furniture, vehicles, and human
bodies, it is possible to extract useful information, such as position,
movement direction, speed, and vital signs of a human subject, from received
RF signals. Unlike traditional hardware sensors, RF sensing provides users
with low-cost and unobtrusive services. Furthermore, due to the broadcast
nature of RF signals, RF sensing can be used not only to monitor multiple
subjects, but also to capture changes in the environment over a large area
[1].

Traditional RF sensing methods face several limitations in IoT systems,
including noise and interference, which degrade signal quality and lead to
inaccurate data interpretation. The presence of other electronic devices and
RF sources causes further data loss or corruption. Incomplete data is common
in scenarios with limited sensor deployment, and the high costs of deploying
and maintaining extensive sensor networks make large-scale implementations
expensive. Additionally, unstable environments cause signal weakening and
multipath propagation, reducing reliability. These challenges necessitate
advanced solutions like Generative AI (GenAI) to enhance the robustness,
efficiency, and scalability of IoT systems.

GenAI refer to neural network models designed to generate new data similar to
a given dataset, including Generative Adversarial Networks (GANs), Variational
Autoencoders (VAEs), Autoregressive Models, flow-Based Models, Diffusion
Models (DMs), and Transformer-based Large Language Models (LLMs). These
techniques offer significant advantages in data-intensive applications by
creating high-quality synthetic data, improving data quality through
denoising, and filling in missing values. Generative AI is particularly
effective in both cross-modal and multi-modal applications: integrating
diverse data types into unified representations for better decision-making and
translating information between modalities to enhance robustness. This
capability supports innovative IoT applications, smart cities, healthcare, and
autonomous systems, showcasing generative AI’s transformative potential.

Figure 1: This figure demonstrates an application scenario of RF sensing in
IoT systems, highlighting the enhancements provided by generative AI
techniques. These enhancements include RF data augmentation to complete
missing observations and augment limited real-world data, cross-modality
generation to infer missing data from available modalities, and multi-modal
fusion to combine information from different data types with RF signals. The
figure showcases the use of GANs, VAEs, DMs, and LLMs to address these
challenges and improve the overall effectiveness of RF sensing in IoT
applications.

GenAI’s ability to enhance data quality and integrate various data types makes
it ideal for IoT applications, which require universality. With the advent of
smarter devices, advanced sensors, and enhanced connectivity technologies like
5G and 6G, IoT systems can greatly benefit from GenAI. It extends conventional
deep learning to manage diverse and unforeseen tasks with limited data and
resources. GenAI’s generalization capability is crucial for IoT devices to
adapt to new environments and tasks. Additionally, GenAI’s natural language
processing enhances multi-modal sensing by integrating text, audio, and visual
data, creating more comprehensive and intelligent IoT systems.

As shown in Fig. 1, we discuss the main challenges in RF sensing applications
and explore how GenAI can address these issues using unimodal and multi-modal
datasets, including reviewing the most relevant works and proposing feasible
solutions for the potential use of GenAI. The main contributions of this
article can be summarized as follows:

  * •

We provide a comprehensive review of state-of-the-art GenAI techniques in RF
sensing, covering both uni-modal and multi-modal challenges. We highlight how
GenAI models address key RF sensing issues, leveraging their statistical
characteristics to model complex data distributions, handle missing data, and
enhance signal processing.

  * •

We discuss the challenges in IoT systems posed by vast data volumes, numerous
smart devices, task complexity, and the need for high generalization,
particularly in RF sensing. We propose addressing these challenges using
GenAI, including LLMs.

  * •

We propose a unified RF sensing framework for individual, multiple, and
general tasks, and illustrate the effectiveness of integrating GenAI models
with a case study.

##  II A short review of GenAI techniques

In this section, a short review of GenAI and their potential in RF sensing
applications are provided (see Table II). GenAI is defined as AI models which
are capable of generating new contents, data, or information from the learned
distribution of the trained data. We provide a brief introduction to popular
GenAI models and review their application to RF sensing, respectively.

GANs [2] generally consist of two neural networks interacting in the form of a
zero-sum game, in which the generator $G$ aims to generate new data with the
same statistics as the training dataset while the discriminator $D$ focuses on
the identification of the true and fake data samples. In RF sensing
applications, GANs offer the potential to generate realistic synthetic RF
data, enhance signal quality, and enable robust anomaly detection. Their
ability to model complex signal environments and facilitate data augmentation
paves the way for more resilient and adaptive RF sensing systems.

VAEs learn an encoder and a decoder to embed data into a continuous latent
space, where the decoder uses a parameterized likelihood function [3]. This
approach reduces overfitting, making VAEs ideal for large datasets like radio
map construction. In RF sensing, VAEs significantly enhance performance by
denoising data and reconstructing incomplete information. By understanding the
structure and distribution of RF signals, VAEs filter out noise and infer
missing parts, creating comprehensive datasets even with partial sensor
coverage or data loss. These capabilities make RF sensing systems more robust,
adaptable, and effective, improving their performance and reliability in
various IoT applications.

DMs use a Markov chain to add random noise to data (forward diffusion) and
then denoise it to generate desired samples (reverse diffusion) [4]. The
forward process transforms the data distribution into a simple prior (e.g.,
Gaussian noise), and new data is generated by denoising samples from this
prior. Diffusion models enhance RF sensing in IoT by iteratively generating
and denoising data, producing high-quality synthetic RF data and improving
signal clarity. They effectively detect anomalies and capture fine variations
in RF environments, and robustly reconstruct incomplete RF data, ensuring
comprehensive datasets despite partial sensor coverage. These capabilities
improve the precision, reliability, and robustness of RF sensing in IoT
applications.

LLMs [5] are pre-trained on massive text datasets to learn contextual
dependencies, and have achieved remarkable success in various applications,
including question answering, language comprehension, reading comprehension,
code creation, and both mathematical and common sense reasoning. In IoT
systems, LLMs enhance RF sensing by incorporating natural language processing,
enabling sensors to interpret and generate human language for smarter device
communication. By involving the natural language modality, LLMs facilitate
sophisticated multi-modal data analysis, combining RF data with textual and
audio inputs for comprehensive insights. This capability improves anomaly
detection, contextual understanding, and decision-making processes, making IoT
systems more intelligent and adaptive.

TABLE I: The outline of issues encountered in RF sensing for IoT applications,
the limitations of traditional AI techniques in addressing these challenges,
and the potential of generative AI to enhance performance and efficiency in
these contexts.

Principal issues | Limitation of traditional deep learning techniques | Potential of Generative AI
---|---|---
$\cdot$ Incomplete RF data; |  |
$\cdot$ Limited training data in new environments. |  $\cdot$ Dependency on large and clean datasets; |
$\cdot$ Lack of Built-in Mechanisms for Missing Data. |  $\cdot$ Data augmentation and synthesis; |
$\cdot$ Learning data distributions; |  |
$\cdot$ Generated plausible values from learned data distribution. |  |
$\cdot$ Strong noise; |  |
$\cdot$ Interference. |  $\cdot$ Trained on data with specific noise characteristics; |
$\cdot$ Limited robustness to varying conditions; |  |
$\cdot$ Tendency to overfit to noise. |  $\cdot$ Learn the underlying distribution of both signal and noise; |
$\cdot$ Generalize to different noise conditions; |  |
$\cdot$ Synthesizing training data with various noise and interference scenarios. |  |
$\cdot$ Missing modalities; |  |
$\cdot$ Unstable acquisition during test. |  $\cdot$ Require complete datasets for training and inference; |
$\cdot$ Missing data result in degraded performance. |  $\cdot$ Integrate information from multiple modalities; |
$\cdot$ Compensate for missing data in one modality using the available data from others. |  |
$\cdot$ Fuse information in different modality; |  |
$\cdot$ Low communication efficiency among Internet of Sensors |  $\cdot$ Static network structures; |
$\cdot$ Difficult to exchange information among sensors; |  |
$\cdot$ Difficult to adapt to different tasks and dynamic environment. |  $\cdot$ Provide potential for communication among sensors and intelligent edges; |
$\cdot$ Provide convenience for dynamical environment adaptation. |  |

##  III GenAI empowered uni-modal wireless sensing in IoT

The field of RF sensing involves utilizing radio frequency signals to detect
and interpret physical phenomena, offering critical capabilities for
applications such as environmental monitoring, health diagnostics, and
security systems. Both traditional and modern RF sensing techniques face
inherent challenges during the data acquisition and transmission stages. Among
these challenges, high costs for data collection, significant interference
during data acquisition, and bandwidth limitations for the data transmission
are particularly prominent. Additionally, although RF signals are considered
crucial information source in many IoT applications, they are extremely sparse
due to the difficulty and high costs associated with setting up extensive
observation points. To address these issues, we explore the emerging
application of GenAI techniques to uni-modality RF sensing, building on their
success in the computer vision domain, and provide visions for future
directions.

Moreover, despite the advantages of using RF signals in IoT systems,
challenges arise due to the rapid increase in IoT devices, which complicates
efficient signal acquisition and data collection. Precise synchronization,
robust interference handling, and managing large data volumes are particularly
challenging. Consequently, RF signals often suffer from missed observations
and exhibit a sparse structure, creating obstacles for effective downstream
tasks. Generative AI addresses these challenges by using models like GANs,
VAEs, and DMs to reconstruct missing data, infer information for localization,
and generate representative samples for downstream tasks (see Fig. 2). The
advantages of GenAI in the unimodal case can be discussed in three main
aspects.

###  III-A Data imputation

A specific issue within RF sensing is the handling of missing Received Signal
Strength (RSS) readings, which can lead to low accuracy and reliability in
various applications, such as localization and environment monitoring. In
these cases, the missing data needs to be filled in based on the observed data
to minimize the impact. In the context of filling missing data, the
correlation between the missing data and observed data is crucial. However,
this correlation varies and traditional neural networks face challenges in
handling this variability, as they often assume fixed spatial relationships or
rely on predefined spatial structures. To address this issue, GenAI models,
such as Transformers, have a great potential in learning complex dependencies
and varying impacts of different observations, in which attention mechanisms
can explicitly model the varying impact of each observation. Additionally,
GenAI can create embeddings that capture broader context and relationships
within the data, which can generate more accurate missing data. For instance,
Wang et al.[6] leverages the Bidirectional Encoder Representations from
Transformers (BERT) model, known for its strong representation learning
ability and generalization capability in natural language processing, to input
collected RSS data and predict missing signals in the radio map. In the case
of RF sensing, BERT can be adapted to understand the contextual relationships
within RSS data, much like it understands word relationships in a sentence.
This capability allows BERT to model complex dependencies and patterns in the
RSS data, making it highly effective at inferring missing values. By
accurately predicting these missing signals, BERT helps to reduce the workload
of collecting RSS in the offline phase and provides accurate positioning
results in the online phase. This ultimately improves the efficiency,
accuracy, and cost-effectiveness of radio map construction.

###  III-B Super-resolution

While these advancements are promising, there are still significant challenges
to address in RF sensing. In particular, in many IoT deployments, the number
of sensors is limited due to cost constraints, power requirements, or physical
space limitations. This can result in large areas with minimal sensor
coverage, leading to extremely sparse data. When there are large missing
regions (e.g., 90% missing), GenAI models are more effective due to their
ability to generate data that is not directly present in the input, enabling
to infer missing data under large missing rates and complicated loss patterns
[7]. Among them, DMs show its biggest potential for super-resolution data
generation from extremely sparse latent spaces. DMs generate images through a
process of gradually reducing noise, modeling the distribution of possible
images at each step. This makes them effective at dealing with incomplete
input. Despite the efficiency of DMs, they still bring the problem of low
authenticity. This problem could be addressed by the idea of guided diffusion
models, which utilize additional information, such as labels, text
descriptions, or other types of metadata to guide the model for a more
expected output. Building on this concept, LLMs can be employed to create
customized guidance for a wide range of sensing tasks, such as tailoring the
guiding prompts for radio map or any other patterns.

###  III-C Synthetic data generation

In IoT scenarios, data collection is challenging due to logistical, financial,
and privacy constraints, as well as the variability and complexity of real-
world environments. By leveraging AI models to generate high-fidelity
synthetic data, it is possible to augment limited real-world data, enhancing
the training and performance of RF signal processing algorithms. GenAI can
improve model robustness by generating synthetic data from learned
distributions, introducing controlled variability, and helping models
generalize to unseen conditions. Specifically, GenAI can create data tailored
to specific scenarios, such as varying environmental conditions, interference
patterns, and device configurations, simulating diverse settings like urban
environments, indoor spaces, and rural areas. In [8], a generative adversarial
networks for RSS data augmentation is proposed to generate synthetic RSS data
based on a small set of real collected labeled data, which achieved to
efficiency improving localization accuracy. The inherent statistical character
and use case examples in various domains illustrate that GenAI play a crucial
role in addressing the data collection issues by generating synthetic data
that enhances the training and performance of RF sensing models in IoT
scenarios.

Figure 2: Illustration of GenAI techniques addressing challenges in uni-modal
RF sensing for IoT systems through three key examples: completing missing RF
sensor data, reconstructing radio maps from extremely sparse observations, and
generating synthetic data to enhance model robustness and generalization
across diverse environmental conditions.

##  IV GenAI empowered multi-modality RF sensing in IoT

In this section, we introduce the multi-modality RF sensing techniques in two
parts, namely cross-modality RF sensing and multi-modality fusion for RF
sensing (see Fig. 3). This division is motivated by the capabilities of GenAI
to enhance RF sensing performance through distinct approaches. Cross-modality
RF sensing leverages GenAI to correlate RF signals with another modality, such
as images, to mitigate challenges like sparsity, interference and missing
data. Meanwhile, multi-modality fusion combines data from multiple modalities
using GenAI to create a comprehensive representation, overcoming the
limitations of individual modalities and improving overall sensing
performance.

To better highlight the potential of GenAI in each category of techniques, we
provide the following definitions:

###### Definition 1

Cross-Modality RF sensing focuses on learning and utilizing the relationships
between different modalities to infer one modality from another. It aims to
handle scenarios where one modality may be missing or incomplete, by
leveraging information from another modality.

###### Definition 2

Multi-modality fusion for RF sensing involves the simultaneous integration of
multiple data modalities (e.g., visible images, LiDAR, audios), with RF
signals, to create a unified representation that leverages the strengths of
each modality and improve overall sensing accuracy and effectiveness. In this
approach, it is assumed that multiple modalities are available, and it focuses
on combining them to improve performance.

###  IV-A Cross-modal RF sensing with GenAI

In RF sensing scenarios, during the training phase, models may be trained
using simulated RF data or data collected under controlled conditions where
signals are easy to observe and interference are controlled. However, in real-
world deployment, the actual RF signals might be sparse, noisy, or even
unavailable due to environmental constraints or hardware limitations. GenAI-
empowered cross-modal RF sensing techniques address the problems in various
methodologies.

LLMs provide great potential for cross-modal learning with their strong
capacity to enhance the generalizability of multimodal systems. A first
strategy is to train universal models on vast datasets across numerous
modalities, to encode these modalities into embeddings. More specifically,
multi-modal LLMs can help to generate embeddings that effectively represent
the underlying information from different modalities, therefor helping to
enhance the generalizability of the universal models. The second direction,
From a more precise perspective with LLM models, is to convert every modality
into text modality and build the model based on text prompts. It has the
potential to provide robust system for cross-modal sensing when one of the
modalities is missing, as text can serve as a unified semantic space,
leveraging the extensive zero-shot prediction capabilities of LLMs. For
instance, [9] leverages LLMs and foundational models to create a unified
semantic space using text. This approach shows the capacity of LLMs to enhance
the generalizability of multimodal systems, allowing them to perform zero-shot
predictions across different modality combinations during testing.

Figure 3: This figure illustrates the scenario of Generative AI-empowered
multi-modal RF sensing applications. Three parts of different techniques are
presented, namely the cross-modal generation, multi-modal fusion and LLM-
enhanced interaction among sensors. The utilization of GenAI for multi-modal
sensing makes the Internet of Sensors system more adaptive to dynamic
environments and significantly improving overall efficiency.

VAEs provide great potential to learn to encode RF signals into a latent space
and decode them into another modality. More specifically, based on the
probabilistic nature of VAEs, they have the capacity to adopts a hierarchical
approach to encode data into a distribution over latent variables, and
generate diverse outputs in cross-modal tasks. VAEs can learn both joint and
modality-specific distributions for different data types (e.g., RF signals and
images), enabling effective cross-modality inference. This allows the model to
leverage the strengths of each modality and make accurate predictions even
when some data is missing or incomplete, by inferring the missing parts from
the shared latent space. For instance, [10] introduced a Multimodal
Hierarchical Variational Auto-encoder (MHVAE), where the single modality
nature of VAEs is extended to a multimodal hierarchical setting, enabling the
learning of modality-specific distributions and a joint-modality distribution
for cross-modality inference. It showcasts the effectiveness of VAEs in
learning rich multimodal representation and cross-modal generation.

DMs also offers a effective solution for synthesizing cross-modality data by
leveraging existing datasets. Based on hierarchical statistical structure and
iterative denoising process, DMs show its capacity for tasks requiring high-
quality and detailed cross-modal outputs, such as text-to-image generation.
What’s more, DMs can effectively capture and model complex relationships
between different modalities, making them suitable for sophisticated cross-
modal tasks, such as text-to-image generation. For instance, in [11], an
effective method for synthesizing RF sensing data using cross-modal diffusion
models to enhance the generalization capability of millimeter-wave (mmWave)
sensing systems is proposed, demonstrating a remarkable enhancement in sensing
and generalization capabilities across two distinct sensing tasks.

Besides, GenAI has the potential to revolutionize RF sensing by enabling
personalized and context-aware applications that enhance user experiences and
improve the efficiency of various systems. For instance, conditional GenAI
techniques can be trained to generate data conditioned on specific inputs,
such as text descriptions and contextual data like location or user
preferences, therefor integrating contextual information to generate relevant
and personalized outputs.

###  IV-B Multi-modal fusion with GenAI

The growing demand for real-world applications highlights the limitations of
uni-modal sensing, especially for comprehensive environmental understanding.
Integrating multi-modal sensing techniques can address this challenge by
combining different data types (radio, optical, audio, thermal) with RF
signals. This integration provides complementary information, enhancing the
accuracy and robustness of sensing tasks. The redundancy from different
sensors also improves the reliability and fault tolerance of wireless systems.
For instance, in wireless localization, multi-modal techniques enhance
positioning accuracy by providing redundant and complementary data, such as
visible images, thermal images, and audio, which support and improve
conventional uni-modal fingerprinting methods.

The advantages of multi-modal sensing come with new challenges, particularly
the unique data patterns of each modality, making it hard to adapt models
across modalities. Multi-modal fusion techniques, such as the Meta-Transformer
[12], address this issue. A Meta-Transformer uses a data-to-sequence tokenizer
to project data into a shared embedding space, a modality-agnostic encoder to
process these embeddings, and task-specific heads for downstream predictions.
This approach consolidates latent patterns for tasks like wireless
positioning, autonomous driving, smart home technologies, and industrial
automation.

Integrating GenAI, particularly LLMs, into multi-modality fusion offers
transformative potential for RF sensing tasks. GenAI models are highly
effective in understanding, generating, and translating complex data across
various modalities. LLMs, with their advanced natural language processing, can
integrate language as a supplementary modality alongside RF signals, images,
and audio. This is particularly useful when sensor data is incomplete or
sparse. For example, supplementary sensors can capture and transmit textual
descriptions of the environment, such as object locations or specific
conditions, with minimal data overhead, reducing costs. LLMs can then fuse
this language data with RF signals and other modalities, enriching contextual
understanding and filling gaps left by incomplete RF data, thereby enhancing
overall sensing capabilities.

Figure 4: Illustration of the RF-to-image Generative AI model utilizing a
text-prompt conditioned Transformer, and the reconstructed building obstacles
image from real measurement. Initially, a Convolutional Neural Network (CNN)
generates rough images from extremely sparse receive power samples of RF
signals, which are blurred and noisy. These blurred images are then refined by
GPT4o with a text prompt, enhancing image quality by removing noise and
sharpening details. The figure highlights the significant improvements
achieved through generative AI, demonstrating its capability to generate
images with low distortion and high perceptual quality, thereby showcasing its
advantages in RF sensing applications.

Enhancing RF Sensing with Language Descriptions: 1) Consider a scenario where
a network of sensors is deployed in an environment for monitoring purposes.
While the primary RF sensors capture signals that provide spatial and movement
RF data, supplementary sensors record descriptive information about the
environment. These descriptions might include details such as ”three people
standing near the entrance,” ”a moving vehicle is approaching from the west,”
or ”there is an obstruction in the path.” Transmitting these descriptions
instead of raw data minimizes the bandwidth requirements and simplifies data
collection. 2) Using LLMs, these language descriptions can be fused with the
RF signal data to enhance downstream tasks such as localization, object
detection, and activity recognition. LLMs can process and integrate the
descriptive information, correlating it with the RF data to create a more
complete and accurate representation of the monitored environment. Moreover,
the flexibility of LLMs allows them to interpret the descriptive data, making
them adapted to scenarios where traditional sensing methods might struggle.
For instance, in dynamic environments where RF signals might be highly
variable, the additional context provided by language descriptions can
significantly improve the reliability and accuracy of the sensing system. A
hybrid End-to-End learning framework for autonomous driving by combining basic
driving imitation learning with LLMs based on multi-modality prompt tokens is
proposed in [13], where end-to-end integration of visual and LiDAR sensory are
input into learnable multi-modality tokens, and a hybrid setting is explored
which use LLMs to help the driving model correct mistakes and complicated
scenarios.

###  IV-C Case study: GenAI models for RF imaging

GenAI models have been widely used to generate data cross different
modalities. For example, DALLE-2 uses diffusion model or auto-regressive model
to generate image embedding from text embedding, plus contrastive learning to
align the embeddings on pair-wise data. Moreover, causal transformer and U-Net
are shown as effective architecture to implement the diffusion prior and
diffusion generator. Inspired by this, we propose a RF to image GenAI model
based text-prompt conditioned Transformer model. As illustrated in 4, the
figure depicts the structure of our proposed method. Initially, a
Convolutional Neural Network (CNN) is trained to generate images from
extremely sparse receive power samples of RF signals, producing a rough
representation often characterized by blur and noise. These blurred images are
then fed into a Transformer model conditioned by a text prompt, which further
enhances the image quality by leveraging its learned data distribution to
remove noise and sharpen details. The comparison between the intermediate
blurred images and the final output highlights the significant improvements
achieved through generative AI. While traditional neural networks struggle to
generate clear images from sparse data due to their limited capacity to learn
exact data distributions, the Transformer model outperforms by providing high-
quality reconstructions. This case study can show the capability of GenAI to
generate images with both low distortion and high perceptual quality,
highlighting its significant advantage in RF sensing applications.

##  V A foundation model for RF sensing and communication

Figure 5: GenAI model for multi-task wireless sensing. A unified GenAI model
trained on generating visual or radio images is proposed and shown to
integrate an LLM fine-tuned for downstream sensing and communication tasks.

While we have discussed the potential of GenAI models to enhance wireless
sensing, an additional research question arises: can we pretrain a foundation
GenAI model on sensory data that can be used for different sensing tasks and
scenarios?

Inspired by the Meta-Transformer [12], a task-agnostic model trained for
generating visual data, e.g., 3D environment image, can be used for computer
vision tasks such as object detection, visualization and tracking. Similarly,
a model trained for generating RF signals, e.g., 4D radio map, can support
various wireless communication tasks, such as beam selection, mobility and
spectrum management (Fig. 5), via task-specific fine-tuning. Specifically,
cross-modality encoders can be trained to encode the raw data on a common
latent space. This can be achieved by contrastive learning, following the CLIP
[14] method to maximize cross-modality similarity between environment image
and RF signal. Thereafter, a unified GenAI model is trained on the data
embedding to generate the visual or radio environment representation, which
can be realized by AR or DM trained on self-supervised learning (i.e. masked
or next image/RF token prediction). Finally, the generated visual or RF
embedding can be used by a multi-modal LLM to perform multiple downstream
tasks in wireless sensing and communications. For example, a visual language
model such as [15] can produce location of a targeted user from the
constructed environment image, to complete the localization task. Similarly, a
RF-language model can generate policies of optimal beams for tracking a user,
to perform the beam management task. After pre-training on large wireless
sensing datasets, we anticipate LLMs with embedded visual and radio data can
perform multiple tasks in sensing and communications based on the user’s
prompts. In doing so, we can build a unified model framework for sensing which
does not require task specific retraining or fine-tuning, as shown by Fig. 5.

##  VI Challenges

In this section, we elaborate on several challenges of using generative AI
encountered in RF sensing applications within IoT systems.

###  VI-A Prior information combination

One critical challenge lies in the effective utilization of prior information
to enhance the accuracy of generated samples from sparse observations. In RF
sensing, additional prior information, such as spatial configurations,
historical signal patterns, and environmental characteristics, is often
available and can significantly improve reconstruction accuracy by providing
context and reducing ambiguity in the generated data. To leverage this, it is
essential to integrate the prior information seamlessly with the architecture
design in generative models, such as GANs or diffusion models, possibly by
conditioning the generative model based on the prior information.

###  VI-B Distortion-perception tradeoff

GenAI techniques are highly effective in tasks requiring human or machine
perception but encounter challenges when distortion is more critical, such as
in radio map reconstruction. Therefore one challenge is to develop models that
optimize both distortion and perception. One possible way to address this
challenge is to integrate traditional neural networks, trained to minimize
distortion, with GenAI models when dealing with problems that involve both
distortion and perception.

###  VI-C Implementation of large models

Another challenge is the storage and computing of large GenAI models,
particularly LLMs. These models enable intelligent edges in IoT systems but
present storage and computing challenges on user equipment or edge devices.
Efficient model compression techniques, such as pruning, quantization, or more
developed techniques such as goal-oriented compression, are essential to
deploy large models in resource-constrained equipment. Overcoming this
challenge is essential for the practical deployment of GenAI-empowered RF
sensing techniques.

###  VI-D Balancing synthetic and real data

While GenAI offers significant potential to enhance the training of neural
networks by generating large amounts of synthetic data, it is crucial to
carefully consider the balance between synthetic and real-world data. A major
concern in the context of data augmentation with GenAI is determining the
optimal amount of synthetic data to use in training a neural network. An
insufficient amount of synthetic data can lead to inadequate training and poor
generalization, while an excessive amount of synthetic data may introduce
biases and reduce the model’s performance on real-world data.

##  VII Conclusions

In this paper, we explore the potential of GenAI for RF sensing to address
data acquisition and transmission resource scarcity driven by the increasing
demand for IoT systems. Our approach utilizes GenAI for efficient RF signal
processing, incorporating uni-modal processing, cross-modal generation, and
multi-modal fusion to effectively perform tasks such as radio map
reconstruction and localization. We not only present these visions but also
demonstrate them through practical case studies, discussing the challenges and
opportunities, and proposing GenAI-based solutions as promising avenues for
future developments in RF sensing. We foresee GenAI significantly benefiting
various IoT applications: enhancing smart city operations by accurately
predicting vehicle movements and reducing congestion through real-time data
analysis; improving wearable IoT devices for better patient outcomes and
reduced healthcare costs; and advancing predictive maintenance in industrial
IoT by analyzing sensor data to predict equipment failures. GenAI has the
potential to revolutionize our interactions with interconnected systems,
leading to smarter, more efficient, and responsive IoT environments.

## References

  * [1] RF datasets, www.rfdatafactory.com
  * [2] I. Goodfellow et al., “Generative adversarial nets,” in Proc. Adv. Neural Inf. Process. Syst., vol. 27, 2014, pp. 53–65.
  * [3] D. P. Kingma, and M. Welling. ”Auto-encoding variational bayes.” arXiv preprint arXiv:1312.6114 (2013).
  * [4] J. Ho, A. Jain, and P. Abbeel, “Denoising diffusion probabilistic models,” in Proc. Int. Conf. Neural Inf. Process. Syst., 2020, pp. 6840–6851.
  * [5] G. Yenduri, M. Ramalingam, G. C. Selvi, Y. Supriya, G. Srivastava, P. K. R. Maddikunta, G. D. Raj, R. H. Jhaveri, B. Prabadevi, W. Wang, A. V. Vasilakos, and T. R. Gadekallu, “Generative pre-trained transformer: A comprehensive review on enabling technologies, potential applications, emerging challenges, and future directions,” 2023, arXiv:2305.10435.
  * [6] Z. Wang, Q. Kong, B. Wei, L. Zhang, and A. Tian, “Radio map con- struction based on BERT for fingerprint-based indoor positioning system,” EURASIP J. Wireless Commun. Netw., vol. 2023, no. 39, 2023.
  * [7] A. Zhang, K. Zhu, R. Wang, and C. Yi, “Missing data inference for crowdsourced radio map construction: An adversarial auto-encoder method,” in IEEE Wireless Communications and Networking Conference, WCNC, 2021, vol. 2021-March.
  * [8] W. Njima, M. Chafii, A. Chorti, R.M. Shubair, and H.V. Poor, “Indoor localization using data augmentation via selective generative adversarial networks,” in IEEE access, 9, pp.98337-98347, 2021.
  * [9] Y.D. Tsai, T.Y. Yen, P.F. Guo, Z.Y. Li, and S.D. Lin, “Text-centric Alignment for Multi-Modality Learning,” 2024, arXiv preprint arXiv:2402.08086.
  * [10] M. Vasco, F.S. Melo, and A. Paiva, “MHVAE: a human-inspired deep hierarchical generative model for multimodal representation learning,” 2020, arXiv preprint arXiv:2006.02991.
  * [11] X. Chen, and X. Zhang, “RF Genesis: Zero-shot generalization of mmwave sensing through simulation-based data synthesis and generative diffusion models,” In Proceedings of the 21st ACM Conference on Embedded Networked Sensor Systems (pp. 28-42), 2023, November.
  * [12] Y. Zhang, K. Gong, K. Zhang, H. Li, Y. Qiao, W. Ouyang, and X. Yue, “Meta-transformer: A unified framework for multimodal learning,” 2023, arXiv:2307.10802.
  * [13] Y. Duan, Q. Zhang, and R. Xu, “Prompting Multi-Modal Tokens to Enhance End-to-End Autonomous Driving Imitation Learning with LLMs,” 2024, arXiv preprint arXiv:2404.04869.
  * [14] A. Radford, J.W. Kim, C. Hallacy, A. Ramesh, G. Goh, S. Agarwal, G. Sastry, A. Askell, P. Mishkin, J. Clark, and G. Krueger, “Learning transferable visual models from natural language supervision,” in Proc. 38th Int. Conf. Mach. Learn., 2021, pp. 8748–8763.
  * [15] J.B. Alayrac, J. Donahue, P. Luc, A. Miech, I. Barr, Y. Hasson, K. Lenc, A. Mensch, K. Millican, M. Reynolds, and R. Ring, “Flamingo: A visual language model for few-shot learning,” in Proc. Int. Conf. Neural Inf. Process. Syst., 2022, pp. 23716–23736.

##  VIII Biography Section

Li Wang<EMAIL_ADDRESS>is an Assistant Professor at Central South
University, China.

Chao Zhang<EMAIL_ADDRESS>is an Assistant Professor at Central South
University, China.

Qiyang Zhao<EMAIL_ADDRESS>is a Principal Researcher at Technology
Innovation Institute, UAE.

Hang Zou<EMAIL_ADDRESS>is a Researcher at Technology Innovation Institute,
UAE.

Samson Lasaulce<EMAIL_ADDRESS>is a CNRS Director of
Research with CRAN at Nancy, France.

Giuseppe Valenzise<EMAIL_ADDRESS>is a CNRS
researcher with L2S, CentraleSupelec, France.

Zhuo He<EMAIL_ADDRESS>is a Researcher at Michigan Technological University,
USA.

Mérouane Debbah<EMAIL_ADDRESS>is a Professor at Khalifa
University, UAE.