AoA

    angle of arrival
AoD

    angle of departure
AWGN

    additive white Gaussian noise
BS

    base station
CP

    cyclic prefix
CRLB

    Cramér-Rao lower bound
FOV

    field of view
FIM

    Fisher information matrix
FFT

    fast Fourier transform
GML

    generalized maximum likelihood
ICI

    inter-carrier interference
ISAC

    integrated sensing and communication
ISI

    inter-symbol interference
LoS

    line of sight
MIMO

    multiple-input multiple-output
ML

    maximum likelihood
OFDM

    orthogonal frequency-division multiplexing
PEB

    position error bound
QPSK

    quadrature phase shift keying
Rx

    receiver
RCS

    radar cross section
RMSE

    root mean square error
SNR

    signal-to-noise ratio
THz

    terahertz
Tx

    transmitter
UE

    user equipment
ULA

    uniform linear array
6G

    sixth generation

# Bistatic Sensing at THz Frequencies via a Two-Stage Ultra-Wideband MIMO-OFDM
System ††thanks: This work was supported in part by the European Union under
the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU,
partnership on “Telecommunications of the Future” (PE00000001 - program
“RESTART”), and in part by the HORIZON-JU-SNS-2022 project TIMES (Grant
Agreement Number: 101096307).

Tommaso Bacchielli, Lorenzo Pucci, Davide Dardari, and Andrea Giorgetti
Wireless Communications Laboratory, CNIT, DEI, University of Bologna, Italy
Email: {tommaso.bacchielli2, lorenzo.pucci3, davide.dardari,
<EMAIL_ADDRESS>

###### Abstract

The availability of abundant bandwidth at terahertz (THz) frequencies holds
promise for significantly enhancing the sensing performance of integrated
sensing and communication (ISAC) systems in the next-generation wireless
systems, enabling high accuracy and resolution for precise target
localization. In orthogonal frequency-division multiplexing (OFDM) systems,
wide bandwidth can be achieved by increasing the subcarrier spacing rather
than the number of subcarriers, thereby keeping the complexity of the sensing
system low. However, this approach may lead to an ambiguity problem in target
range estimation. To address this issue, this work proposes a two-stage
maximum likelihood method for estimating target position in an ultra-wideband
bistatic multiple-antenna OFDM-based ISAC system operating at THz frequencies.
Numerical results show that the proposed estimation approach effectively
resolves the ambiguity problem while achieving high resolution and accuracy
target position estimation at a very low signal-to-noise ratio regime.

###### Index Terms:

THz ISAC, bistatic sensing, two-stage ML approach, MIMO-OFDM, ultra-wideband
systems.

##  I Introduction

ISAC at THz frequencies is a key promising enabler to meet requirements for
next-generation wireless systems, where the ubiquitous integration of sensing,
connectivity, and intelligence across various domains will be crucial [1]. For
an ISAC system, the vast bandwidth availability at THz ($0.1-10\,$THz) holds
the potential of exploiting ultra-wide bandwidth, leading to the simultaneous
transmission of a large amount of data with unprecedented data rates [2],
alongside very high range estimation accuracy and resolution [3].

Most of the studies regarding ISAC have focused on OFDM-based systems,
primarily at sub-6 GHz and millimeter wave frequencies, exploring both
monostatic and bistatic radar configurations [4, 5, 6, 7]. However, little
investigation has been conducted to exploit the potential of ISAC system
operating at THz frequencies. In [8], a novel ISAC technique with joint beam-
squint and beam-split for THz massive multiple-input multiple-output (MIMO)
system is presented. The authors show the advantage of the beam-squint to
simultaneously transmit towards various directions and the possibility of
beam-splitting to extend sensing range and enhance accuracy using only a few
subcarriers. In [9], the authors evaluate the range estimation performance of
a system at THz frequencies by analyzing different waveforms. This work
demonstrates that OFDM is still an excellent candidate for ISAC, also at THz,
but focuses on systems with limited bandwidth, in the order of MHz.

To the author’s knowledge, there remains a lack of research investigating the
potential advantages of utilizing OFDM-based ISAC systems at THz with ultra-
wide bandwidth. Since the coherence bandwidth of short-range THz channels is
hundreds of MHz, it is possible to achieve very high bandwidth by properly
setting the subcarrier spacing without a large amount of subcarriers. However,
while this solution ensures controlling the complexity, it may result in a low
maximum unambiguous range, which reduces the system’s operating range [5].

In this context, this work proposes to mitigate the range estimation ambiguity
problem inherent to large subcarrier spacings with a novel two-stage
transmission scheme followed by a two-stage maximum likelihood (ML) estimation
approach at the receiver. This approach first performs coarse target
estimation over a sub-band with a smaller subcarrier spacing to avoid the
ambiguity problem, followed by refined super-resolution estimation using the
whole system bandwidth. Numerical results demonstrate that the proposed system
can localize the target without ambiguity in a confined indoor area, ensuring
cm-level range resolution and mm-level accuracy.

In this paper, we adopt the following notation: capital boldface letters for
matrices, lowercase bold letters for vectors, $\operatorname{Tr}(\cdot)$ for
the trace of a matrix, $(\cdot)^{\ast}$, $(\cdot)^{\mathrm{T}}$ and
$(\cdot)^{\mathrm{H}}$ for conjugate, transpose and conjugate transpose of a
vector/matrix, respectively, and $|\cdot|$, $||\cdot||_{2}$ for the modulus
and Euclidean norm, respectively. Also, $\otimes$, $\mathbb{E}[\cdot]$,
$\mathrm{var}[\cdot]$ for Kronecker product, statistical mean value and
variance operator. $[\mathbf{X}]_{a:b,c:d}$ denotes a submatrix of
$\mathbf{X}$ composed of a subset $[a,b]$ of rows and $[c,d]$ of columns. A
zero-mean circularly symmetric complex Gaussian random vector with covariance
$\boldsymbol{\Sigma}$ is denoted by
$\mathbf{x}\thicksim\mathcal{CN}(\mathbf{0},\boldsymbol{\Sigma})$, while
$x\sim\mathcal{U}(a,b)$ represents a uniformly distributed random variable $x$
within the interval $(a,b)$.

The rest of the paper is organized as follows. In Section II and III, the
system model and the proposed two-stage ML estimation method are introduced.
Numerical results are presented in Section IV, while Section V concludes the
paper.

##  II System Model

This work considers a bistatic MIMO OFDM-based ISAC system operating at THz
frequencies. In particular, for what concerns sensing, such a system consists
of a transmitter (Tx) and a receiver (Rx) to form a bistatic pair. Both the Tx
and the Rx are base stations used to communicate with user equipments or
machinery while simultaneously localizing targets in the surrounding
environment by using downlink signals. Differently from an ISAC monostatic
system, in which a full-duplex architecture and self-interference cancellation
techniques are required [4], in the bistatic configuration these problems are
naturally solved as Tx and Rx are not co-located [7]. However, in this case,
the Tx and the Rx need to be synchronized to perform target localization,
e.g., by connecting them to a central unit that coordinates sensing
operations. This work assumes that Tx and Rx are synchronized.

Without loss of generality, both Tx and Rx are equipped with a uniform linear
array (ULA) composed of $N_{\mathrm{t}}$ and $N_{\mathrm{r}}$ antenna elements
half-wavelength spaced, respectively. To perform sensing tasks, an OFDM frame
consisting of $M$ OFDM symbols with $K$ active subcarriers is transmitted. The
$k$-th subcarrier has frequency $f_{k}=f_{\mathrm{c}}+k\Delta f$, with
$k=-K/2,\dots,K/2-1$, where $f_{\mathrm{c}}$ is the carrier frequency and
$\Delta f$ the subcarrier spacing. The total frame duration is equal to
$MT_{\mathrm{s}}$, being $T_{\mathrm{s}}\triangleq 1/\Delta f+T_{\mathrm{cp}}$
the total OFDM symbol duration including the cyclic prefix (CP); the total
bandwidth is therefore $B=K\Delta f$. Moreover, to exploit the ULA,
beamforming is performed at the Tx through a precoding vector, $\mathbf{w}$.

###  II-A Input-Output Relationship

The complex envelope of the continuous-time OFDM signal transmitted by the Tx
antenna array is defined as

$\mathbf{s}(t)=\sqrt{\frac{P_{\mathrm{t}}G_{\mathrm{t}}}{K}}\mathbf{w}\sum_{m=0}^{M-1}\left(\sum_{k=0}^{K-1}x[k,m]e^{j2\pi
k\Delta ft}\right)g(t-mT_{\mathrm{s}})$ (1)

where $P_{\mathrm{t}}$ is the total transmitted power, $G_{\mathrm{t}}$ is the
single antenna element gain at the Tx, and
$\mathbf{w}\in\mathbb{C}^{N_{\mathrm{t}}\times 1}$ represents a unit-norm
beamforming vector designed to illuminate with an almost constant gain a
relatively wide angular sector where a target $p$ is expected to be located.
Moreover, $x[k,m]$ denotes a generic complex modulation symbol transmitted at
time instant $m$ on subcarrier $k$, while $g(t)$ represents the modulating
pulse.

After the fast Fourier transform (FFT) block in the OFDM demodulator at the Rx
and taking into account negligible inter-carrier interference (ICI) and inter-
symbol interference (ISI), a received time-frequency grid of complex elements
$y[k,m]$ is obtained at each antenna element. By aggregating the symbols at
each antenna, a vector $\mathbf{y}[k,m]\in\mathbb{C}^{N_{\mathrm{r}}\times 1}$
of received complex modulation symbols is obtained, as follows

$\mathbf{y}[k,m]=\sqrt{\frac{P_{\mathrm{t}}G_{\mathrm{t}}G_{\mathrm{r}}}{K}}\mathbf{H}_{\mathrm{t},\mathrm{r}}[k,m]\mathbf{w}x[k,m]+\mathbf{\tilde{n}}[k,m]$
(2)

where $G_{\mathrm{r}}$ is the single antenna element gain at the Rx,
$\mathbf{H}_{\mathrm{t},\mathrm{r}}[k,m]\in\mathbb{C}^{N_{\mathrm{r}}\times
N_{\mathrm{t}}}$ is the MIMO channel matrix between the Tx and the Rx for the
subcarrier $k$ at time $m$, and
$\mathbf{\tilde{n}}\sim\mathcal{CN}(\mathbf{0},\sigma_{\tilde{n}}^{2}\mathbf{I}_{N_{\mathrm{r}}})$
represents the additive white Gaussian noise (AWGN), with
$\sigma_{\tilde{n}}^{2}=N_{0}\Delta f$. Here,
$N_{0}=k_{\mathrm{B}}290n_{\mathrm{F}}$ is the noise power spectral density,
with $k_{\mathrm{B}}$ the Boltzmann constant and $n_{\mathrm{F}}$ the receiver
noise figure.

###  II-B Channel Model

Without loss of generality, this work considers a single point-like target
scenario. Since a bistatic setting is considered, the channel matrix at
subcarrier $k$ and time $m$ can be obtained as the outer product of the
channel vector
$\mathbf{h}_{p,\mathrm{r}}[k,m]\in\mathbb{C}^{N_{\mathrm{r}}\times 1}$, which
represents the channel between the target $p$ and the Rx, with the vector
$\mathbf{h}_{\mathrm{t},p}[k,m]\in\mathbb{C}^{1\times N_{\mathrm{t}}}$
representing the channel between the Tx and the target $p$. These vectors are
given by

$\mathbf{h}_{p,\mathrm{r}}[k,m]=\beta_{p,\mathrm{r}}e^{j2\pi(mT_{\mathrm{s}}f_{\mathrm{D}_{p,\mathrm{r}}}-k\Delta
f\tau_{p,\mathrm{r}})}\mathbf{b}(\theta_{p,\mathrm{r}})$ (3)
$\mathbf{h}_{\mathrm{t},p}[k,m]=\alpha_{\mathrm{t},p}e^{j2\pi(mT_{\mathrm{s}}f_{\mathrm{D}_{\mathrm{t},p}}-k\Delta
f\tau_{\mathrm{t},p})}\mathbf{a}^{\mathrm{H}}(\phi_{\mathrm{t},p})$ (4)

respectively. In (4),
$\alpha_{\mathrm{t},p}=\sqrt{\xi_{\mathrm{t},p}}e^{-j(2\pi
f_{\mathrm{c}}\tau_{\mathrm{t},p}+\varphi_{0})}$ represents the complex
channel coefficient associated with target $p$, where $\xi_{\mathrm{t},p}$
denotes the channel gain, and $\varphi_{0}\in\mathcal{U}{[0,2\pi)}$ accounts
for the phase shift between Tx and Rx. Furthermore,
$\tau_{\mathrm{t},p}=r_{\mathrm{t},p}/c$ represents the propagation delay with
respect to target $p$, where $r_{\mathrm{t},p}$ is the distance between target
$p$ and Tx; $f_{\mathrm{D}_{\mathrm{t},p}}$ and $\phi_{\mathrm{t},p}$ denote
the Doppler shift and angle of departure (AoD) associated with target $p$,
respectively. The transmit array response, denoted by
$\mathbf{a}(\phi_{\mathrm{t},p})\in\mathbb{C}^{N_{\mathrm{t}}\times 1}$, is
defined considering far-field propagation conditions with the center of the
array as a reference, as follows

$\mathbf{a}(\phi_{\mathrm{t},p})=\left[e^{-j\frac{N_{\mathrm{t}}-1}{2}\pi\sin{(\phi_{\mathrm{t},p})}},\dots,e^{j\frac{N_{\mathrm{t}}-1}{2}\pi\sin{(\phi_{\mathrm{t},p})}}\right]^{\mathrm{T}}.$
(5)

When line of sight (LoS) propagation conditions are in place, the path loss
coefficient is given by $\xi_{\mathrm{t},p}=\frac{\sigma_{p}}{4\pi
r^{2}_{\mathrm{t},p}}$, where $\sigma_{p}$ is the radar cross section (RCS) of
target $p$.

Similarly, in (3), $\tau_{p,\mathrm{r}}=\gamma_{p,\mathrm{r}}/c$ is the
propagation delay from the target $p$ to the center of the Rx, with
$\gamma_{p,\mathrm{r}}$ the Euclidean distance between $p$ and the Rx.
Furthermore, $\beta_{p,\mathrm{r}}=\sqrt{\zeta_{p,\mathrm{r}}}e^{-j2\pi
f_{\mathrm{c}}\tau_{p,\mathrm{r}}}$ is the channel coefficient, and
$\mathbf{b}(\theta_{p,\mathrm{r}})\leavevmode\nobreak\ \in\leavevmode\nobreak\
\mathbb{C}^{N_{\mathrm{r}}\times 1}$ is the array response vector defined as
in (5), being $\theta_{p,\mathrm{r}}$ the angle of arrival (AoA) related to
the target $p$. Considering LoS propagation conditions and isotropic antenna
elements with effective area $A_{\mathrm{eff}}=c^{2}/(4\pi
f_{\mathrm{c}}^{2})$, the path loss factor is given by
$\zeta_{p,\mathrm{r}}=\frac{c^{2}}{(4\pi
f_{\mathrm{c}}\gamma_{p,\mathrm{r}})^{2}}$.

Starting from (3) and (4), the $N_{\mathrm{r}}\times N_{\mathrm{t}}$ channel
matrix in (2), which represents the channel between Tx and Rx for subcarrier
$k$ at time $m$, can be modeled as

$\mathbf{H}_{\mathrm{t},\mathrm{r}}[k,m]=\epsilon_{p}e^{j2\pi(mT_{\mathrm{s}}f_{\mathrm{D}_{p}}-k\Delta
f\tau_{p})}\mathbf{b}(\theta_{p,\mathrm{r}})\mathbf{a}^{\mathrm{H}}(\phi_{\mathrm{t},p})$
(6)

where $\epsilon_{p}=\alpha_{\mathrm{t},p}\beta_{p,\mathrm{r}}$ and
$\tau_{p}=\tau_{\mathrm{t},p}+\tau_{p,\mathrm{r}}$ are the bistatic complex
channel factor and bistatic propagation delay, respectively, associated with
the target $p$. The bistatic Doppler shift $f_{\mathrm{D}_{p}}$ is defined as
$f_{\mathrm{D}_{p}}=f_{\mathrm{D}_{\mathrm{t},p}}+f_{\mathrm{D}_{p,\mathrm{r}}}=\frac{2|\mathbf{v}_{p}|}{\lambda}\cos{(\delta)}\cos{(\beta/2)}$,
where $\mathbf{v}_{p}$ is the velocity of the target $p$, while $\beta$ and
$\delta$ are the bistatic angle and the angle between the velocity direction
and the bisector of the bistatic angle $\beta$, respectively [7].

###  II-C Received Signal and Signal-to-Noise Ratio

By replacing (6) in (2) and stacking the $K\times M$ transmitted symbol grid
into a $KM\times 1$ vector $\mathbf{\underline{x}}$, a more compact form of
the vector of received symbols
$\mathbf{\underline{y}}\in\mathbb{C}^{N_{\mathrm{r}}KM\times 1}$ can be
obtained as follows

$\mathbf{\underline{y}}=\sqrt{\frac{P_{\mathrm{t}}G_{\mathrm{t}}G_{\mathrm{r}}}{K}}\epsilon_{p}\mathbf{G}(f_{\mathrm{D}_{p}},\tau_{p},\theta_{p,\mathrm{r}},\phi_{\mathrm{t},p})\mathbf{\underline{x}}+\mathbf{\tilde{\underline{n}}}$
(7)

where $\mathbf{G}(\cdot)$ is the effective channel matrix of dimension
$N_{\mathrm{r}}KM\times KM$, defined for a generic target $p$, as

$\displaystyle\mathbf{G}(f_{\mathrm{D}_{p}},\tau_{p},\theta_{p,\mathrm{r}},\phi_{\mathrm{t},p})\triangleq\mathbf{T}(\tau_{p},f_{\mathrm{D}_{p}})\otimes\left(\mathbf{b}(\theta_{p,\mathrm{r}})\mathbf{a}^{\mathrm{H}}(\phi_{\mathrm{t},p})\mathbf{w}\right)$
(8)

with $\mathbf{T}(\tau_{p},f_{\mathrm{D}_{p}})\in\mathbb{C}^{KM\times KM}$
defined as

$\displaystyle\mathbf{T}(\tau_{p},f_{\mathrm{D}_{p}})\triangleq\mathrm{diag}\Bigl{(}[1,\dots,$
$\displaystyle
e^{j2\pi(M-1)T_{\mathrm{s}}f_{\mathrm{D}_{p}}}]^{\mathrm{T}}\otimes$ (9)
$\displaystyle\otimes[1,\dots,e^{-j2\pi(K-1)\Delta
f\tau_{p}}]^{\mathrm{T}}\Bigr{)}.$

Recalling the complex channel factor $\epsilon_{p}$ and the noise variance
$\sigma^{2}_{\tilde{n}}$ introduced in Section II-B, the signal-to-noise ratio
(SNR) of the bistatic radar system related to target $p$ can be defined as

$\displaystyle\mathrm{SNR}$
$\displaystyle=\frac{\mathbb{E}\bigl{\\{}\bigl{|}x[k,m]\bigr{|}^{2}\bigr{\\}}P_{\mathrm{t}}G^{a}_{\mathrm{t}}G_{\mathrm{r}}|\epsilon_{p}|^{2}}{K\sigma^{2}_{\tilde{n}}}$
(10)
$\displaystyle=\mathbb{E}\bigl{\\{}\bigl{|}x[k,m]\bigr{|}^{2}\bigr{\\}}\frac{P_{\mathrm{t}}G^{a}_{\mathrm{t}}G_{\mathrm{r}}\sigma_{p}c^{2}}{(4\pi)^{3}r^{2}_{\mathrm{t},p}\gamma^{2}_{p,\mathrm{r}}f^{2}_{\mathrm{c}}N_{0}K\Delta
f}.$

where $G^{a}_{\mathrm{t}}$ is the total Tx antenna array gain in the direction
of $p$, considering both $G_{\mathrm{t}}$ and beamforming gain. If convenient,
when performing numerical simulations varying the SNR, (10) can be recast as
$\text{SNR}=1/\sigma^{2}_{\tilde{n}}$, by normalizing the transmitted complex
symbols to average unit transmit power as
$\mathbb{E}\bigl{\\{}\bigl{|}x[k,m]\bigr{|}^{2}\bigr{\\}}=1$ and setting
$|\epsilon_{p}|^{2}=1$.

###  II-D Target Position Estimation

In this work, the bistatic propagation delay $\tau_{p}$, which is directly
related to the bistatic range $r_{p}=\tau_{p}c$, and the AoA $\theta_{p}$, are
estimated via a ML approach.

As already mentioned, at Tx we perform beamforming through a vector
$\mathbf{w}$ designed to provide nearly constant gain over a wide circular
sector. Therefore, at the Rx, the array response from Tx to the target is a
complex constant, i.e., $g_{p}=\mathbf{a}^{\mathrm{H}}(\phi_{p})\mathbf{w}$,
which can be absorbed in the channel gain coefficient, as $h_{p}\triangleq
g_{p}\epsilon_{p}$. The effective channel gain thus becomes independent on the
AoD $\phi_{p}$, i.e., $\mathbf{G}(f_{\mathrm{D}_{p}},\tau_{p},\theta_{p})$.

The vector of sensing parameters related to the target $p$ to be estimated is
defined as $\boldsymbol{\Theta}_{p}\leavevmode\nobreak\ =\leavevmode\nobreak\
(|h_{p}|,\angle{h_{p}},f_{\mathrm{D},p},\tau_{p},\theta_{p})$, so the ML
estimate of the set $\boldsymbol{\Theta}_{p}$ involves a search in the space
$\Gamma\triangleq\mathbb{C}\times\mathbb{R}^{3}$ [10]

$\boldsymbol{\Theta}_{\mathrm{ML}}=\underset{\boldsymbol{\Theta}_{p}\in\Gamma}{\arg\min}\;\left\|\mathbf{\underline{y}}-\sqrt{\frac{P_{\mathrm{t}}G_{\mathrm{t}}G_{\mathrm{r}}}{K}}h_{p}\mathbf{G}(f_{\mathrm{D}_{p}},\tau_{p},\theta_{p})\mathbf{\underline{x}}\right\|^{2}_{2}.$
(11)

One possible solution of (11) can be obtained through a generalized maximum
likelihood (GML) approach. It consists of estimating the sensing parameters of
interest in $\boldsymbol{\Theta}_{p}$ by maximizing the log-likelihood
function with respect to the channel gain coefficient $h$. This reduces the
sensing parameters ML estimation to the solution of the following problem

$\left(\hat{f}_{\mathrm{D}_{p}},\hat{\tau}_{p},\hat{\theta}_{p}\right)=\mathrm{arg}\;\underset{(f_{\mathrm{D}},\tau,\theta)\in\Psi}{\mathrm{max}}\;\frac{|\boldsymbol{\xi}(\tau,f_{\mathrm{D}})\mathbf{b}^{*}(\theta)|^{2}}{\mathbf{\underline{x}}^{\mathrm{H}}\mathbf{b}^{\mathrm{H}}(\theta)\mathbf{b}(\theta)\mathbf{\underline{x}}}$
(12)

where $\Psi$ is a grid composed of a set of $(f_{\mathrm{D}},\tau,\theta)$
tuples, and
$\boldsymbol{\xi}(\tau,f_{\mathrm{D}})=\left[\mathbf{\underline{x}}^{\mathrm{H}}\mathbf{T}^{\mathrm{H}}(\tau,f_{\mathrm{D}})\mathbf{Y}^{\mathrm{T}}\right]$,
with
$\mathbf{Y}=\left[\mathbf{\underline{y}}_{1}[0,0],\dots,\mathbf{\underline{y}}_{N_{\mathrm{r}}}[M-1,K-1]\right]\in\mathbb{C}^{N_{\mathrm{r}}\times
KM}$. The position of the target $p$ is thus obtained from the estimate of the
bistatic range $\hat{r}_{p}=\hat{\tau}_{p}c$ and AoA $\hat{\theta}_{p}$, by
first computing the distance from target $p$ to Rx, as

$\hat{\gamma}_{p}=\frac{\hat{r}^{2}_{p}-L^{2}}{2\left(\hat{r}_{p}+L\sin{(\hat{\theta}_{p}-\pi/2)}\right)}$
(13)

where $L$ is the distance between Tx and Rx, commonly referred to as
_baseline_. Then, the estimated position of the target with respect to the Rx
is
$\mathbf{\hat{p}}_{p}=[\hat{\gamma}_{p}\cos{(\hat{\theta}_{p})},\hat{\gamma}_{p}\sin{(\hat{\theta}_{p})}]^{\mathrm{T}}$.

###  II-E Position Error Bound

Let us consider the received signal in (7), and define
$\mathbf{\underline{s}}=\leavevmode\nobreak\
\sqrt{\frac{P_{\mathrm{t}}G_{\mathrm{t}}G_{\mathrm{r}}}{K}}h_{p}\,\mathbf{G}(f_{\mathrm{D}_{p}},\tau_{p},\theta_{p})\,\mathbf{\underline{x}}\in\mathbb{C}^{N_{\mathrm{r}}KM\times
1}$ as the vector of mean values of $\mathbf{\underline{y}}$. The Cramér-Rao
lower bound (CRLB) on the estimation of the unknown parameters in
$\mathbf{\Theta}_{p}$ is

$\mathrm{var}[{\hat{\Theta}_{p_{i}}}]\geq\mathrm{CRLB}(\hat{\Theta}_{p_{i}})=I_{p_{ii}}^{-1}\qquad
i=1,\dots,\mathrm{card(\mathbf{\Theta}_{p})}$ (14)

where ${\hat{\Theta}_{p_{i}}}$ is the estimate of the $i$-th parameter
contained in $\boldsymbol{\Theta}_{p}$, and $I_{p_{ii}}^{-1}$ represents the
$i$-th element on the main diagonal of the inverse of the Fisher information
matrix (FIM) $\mathbf{I}_{p}$. The generic $ij$-th element of $\mathbf{I}_{p}$
can be computed as [11, 12]

$I_{p_{ij}}=\frac{2}{\sigma^{2}_{\tilde{n}}}\mathfrak{Re}\Biggl{\\{}\sum_{k,m,n}\biggl{(}\frac{\partial
s_{n}[k,m]}{\partial\Theta_{p_{i}}}\biggr{)}^{\ast}\biggl{(}\frac{\partial
s_{n}[k,m]}{\partial\Theta_{p_{j}}}\biggr{)}\Biggl{\\}}$ (15)

where $s_{n}[k,m]$ is the $(n,k,m)$ element of a 3D array obtained starting
from the $N_{\mathrm{r}}KM\times 1$ vector $\mathbf{\underline{s}}$ and given
by

$s_{n}[k,m]=\sqrt{\frac{P_{\mathrm{t}}G_{\mathrm{t}}G_{\mathrm{r}}}{K}}h_{p}e^{j2\pi(mT_{\mathrm{s}}f_{\mathrm{D}_{p}}-k\Delta
f\tau_{p})}b_{n}(\theta_{p})x[k,m]$ (16)

being $b_{n}(\theta_{p})$ the $n$-th element of the array response vector
$\mathbf{b}$. After computing the inverse of the FIM $\mathbf{I}_{p}$, the
bound on position estimation accuracy, hereinafter referred to as position
error bound (PEB), is given by
$\mathrm{PEB}=\sqrt{\mathrm{CRLB}(\mathbf{\hat{p}}_{p})}$, where the CRLB of
position estimate can be found as [13]

$\displaystyle\mathrm{CRLB}(\mathbf{\hat{p}}_{p})$
$\displaystyle=\operatorname{Tr}(\mathbf{J}_{\mathrm{\Omega}}^{-1}[\mathbf{I}_{p}^{-1}(\boldsymbol{\Theta}_{p})]_{4:5,4:5}[\mathbf{J}_{\mathrm{\Omega}}^{-1}]^{\mathrm{T}})$
$\displaystyle=\operatorname{Tr}([\mathbf{I}_{p}^{-1}(\boldsymbol{\Theta})]_{4:5,4:5}[\mathbf{J}_{\mathrm{\Omega}^{-1}}]^{\mathrm{T}}\mathbf{J}_{\mathrm{\Omega}^{-1}})$
(17)

being $\mathbf{J}_{\mathrm{\Omega}}$ the Jacobian of the transformation
$\Omega:\leavevmode\nobreak\ \mathbf{\hat{p}}_{p}\leavevmode\nobreak\
=\leavevmode\nobreak\ (x_{p},y_{p})\rightarrow(\tau_{p},\theta_{p})$, and
$\mathbf{J}_{\mathrm{\Omega}^{-1}}$ the Jacobian of the inverse transformation
$\Omega^{-1}:(\tau_{p},\theta_{p})\rightarrow\mathbf{\hat{p}}_{p}=(x_{p},y_{p})$,
defined as111Note that the following property holds
$\mathbf{J}_{\mathrm{\Omega}^{-1}}=\mathbf{J}_{\mathrm{\Omega}}^{-1}$, and
vice versa.

$\mathbf{J}_{\mathrm{\Omega}^{-1}}=\begin{bmatrix}\frac{\partial
x_{p}}{\partial\tau_{p}}&\frac{\partial x_{p}}{\partial\theta_{p}}\\\
\frac{\partial y_{p}}{\partial\tau_{p}}&\frac{\partial
y_{p}}{\partial\theta_{p}}\end{bmatrix}.$ (18)

##  III Two-stage Method for Ambiguity Problem Management

The advantage of using huge bandwidths at THz is beneficial for both the
communication and the sensing functionalities of the OFDM-based ISAC system.
From a communication viewpoint, wider bandwidths increase channel capacity and
enhance robustness by exploiting multipath propagation. In contrast, for what
concerns the sensing part, larger bandwidths enable higher range resolution,
making it possible to distinguish targets that may be very close to each
other. In fact, an OFDM system with a bandwidth of the order of GHz can
achieve cm-level range resolution, according to $r_{\mathrm{res}}=c/B$, for a
bistatic configuration. Moreover, a larger bandwidth also increases
performance in terms of root mean square error (RMSE) on position estimation,
with a lower PEB. Increasing the subcarrier spacing $\Delta f$ seems a natural
choice to increase the bandwidth without compromising system complexity,
especially when a ML estimation approach is considered.

It’s important to note that while increasing $\Delta f$ is feasible at THz due
to the coherence band being of the order of hundreds of MHz [14], it can lead
to an ambiguity problem in target position estimation. This problem persists
even in relatively small areas, as the maximum unambiguous range, in these
conditions, is less than the maximum distance that can be estimated in the
area of interest. For instance, the maximum unambiguous bistatic range in an
OFDM-based radar is $r_{\mathrm{unamb}}=c/\Delta f$. To solve this problem,
which can cause the impossibility of correctly estimating the target position,
a two-stage ML estimation algorithm is proposed in this work. The approach
consists of a novel two-stage transmission scheme and a two-stage ML
estimation approach at the receiver. In the first phase, a coarse target
estimation exploits a transmitting signal that uses a sub-band with narrow
subcarrier spacing to avoid the ambiguity problem. Then, in the second phase,
the transmission exploits the full system bandwidth, and at the receiver, a
refined super-resolution estimation is performed around the coarse estimate.

The considered OFDM ISAC system operates over a large bandwidth $B$, of the
order of GHz, with a large number of equispaced subcarriers $K$ and subcarrier
spacing $\Delta f$, in the order of few MHz. However, such a system manages
the complexity using a relatively small number $K^{\prime}$ of active
subcarriers out of the $K$ available, as shown in Fig. 1. The remaining
subcarriers can be used for communication purposes. The two phases are
summarized below.

  * •

_Coarse target estimation_ : Localization of target $p$ with coarse resolution
over a search area $A$ by using a sub-band $B_{\mathrm{coarse}}$ of the system
bandwidth $B$ around the carrier frequency $f_{\mathrm{c}}$, with $K^{\prime}$
contiguous active subcarriers within $B_{\mathrm{coarse}}$ and considering a
subcarrier spacing $\Delta f$. The ML target position estimation according to
(12) is performed without range ambiguity by properly designing
$B_{\mathrm{coarse}}$ such that
$B_{\mathrm{coarse}}\leq(cK)/r_{\mathrm{unamb}}$, where $r_{\mathrm{unamb}}$
is the maximum unambiguous bistatic range compatible with the search area $A$.

  * •

_Fine target estimation_ : Localization of target $p$ with refined resolution
and without range ambiguity around the target position estimated in the coarse
stage. Here, the system uses the same number $K^{\prime}$ of properly
equispaced active subcarriers out of the $K$ over the overall bandwidth $B$,
with $\rho\Delta f$ subcarrier spacing, where $\rho\triangleq
B/B_{\mathrm{coarse}}$. The search interval222Note that, the search interval
width should be properly set, e.g., by considering the PEB of the coarse
stage, computed according to Section II-E. is centered in the target position
estimated in the previous stage, and the width of the bistatic range search
interval must be less than double the maximum unambiguous range, by
considering the system working on the overall bandwidth $B$, i.e.,
$<2r_{\mathrm{unamb}}\leavevmode\nobreak\ =\leavevmode\nobreak\ (2cK)/B$.
Again, the ML approach in (12) is here used for target position estimation.

Figure 1: Illustration of the proposed two-stage method with $\rho=2$.

This way, the proposed system can exploit an ultra-wide bandwidth at THz to
achieve highly precise and unambiguous range localization while maintaining
low system complexity.

(a) RMSE of target $p$ position estimation and PEB vs SNR

(b) RMSE of target $p$ position estimation and PEB vs RCS $\sigma_{p}$

Figure 2: RMSE compared to the PEB related to position estimation
$\mathbf{\hat{p}}_{p}$ of target $p$ as a function of SNR (a) and RCS
$\sigma_{p}$ (b), considering $r_{\mathrm{t},p}=r_{p,\mathrm{r}}=7.9\,$m,
$\phi_{p}=18.4^{\circ}$, $\theta_{p}=-26.5^{\circ}$, and
$|\mathbf{v}_{p}|=0\,$km/h as target parameters.

##  IV Numerical Results

Numerical simulations are performed to evaluate the sensing performance of the
proposed two-stage ultra-wideband system at THz frequencies. In particular, we
consider $f_{\mathrm{c}}=0.3\,$THz, $B=2\,$GHz,
$B_{\mathrm{coarse}}=400\,$MHz, $\Delta f=6.25\,$MHz, $K=320$,
$K^{\prime}=64$, $M=50$, $N_{\mathrm{t}}=N_{\mathrm{r}}=64$,
$P_{\mathrm{t}}G^{a}_{\mathrm{t}}=1\,$W, $G_{\mathrm{r}}=1$, $N_{0}=4\cdot
10^{-20}\,$W/Hz, and $\rho=5$. The cyclic prefix duration has been set to
$T_{\mathrm{cp}}=19.5\,$ns, according to the channel delay spread, here
approximated as $T_{\mathrm{cp}}=(r_{\mathrm{bis,max}}-L)/c$, where
$r_{\mathrm{bis,max}}$ is the maximum bistatic range within the considered
squared area $A$ of $10\times 10\,$ m2. In addition, quadrature phase shift
keying (QPSK) constellation, and a scenario as the one described in Section II
are considered. The target $p$ is assumed to be stationary (i.e.,
$|\mathbf{v}_{p}|=0$), inside the designated area and located at a distance of
$7.9\,$m from both Tx and Rx units, with $\phi_{p}=18.4^{\circ}$ and
$\theta_{p}=-26.5^{\circ}$ as AoD and AoA, respectively, with the Tx and Rx
placed in the bottom left and top right corners of the area.

The analysis is performed through curves of RMSE of target position estimation
$\mathbf{\hat{p}}_{p}$ and PEB as a function of the SNR and target RCS
$\sigma_{p}$. When the SNR is varied, this is normalized as explained in
Section II-C. Conversely, when $\sigma_{p}$ is varied the considered SNR is
given according to (10), as a function of $\sigma_{p}$, $\mathbf{p}$, and the
system parameters above.

The obtained results are shown in Fig. 2. In particular, in Fig. 2(a), it can
be observed that the considered ISAC system with the proposed two-stage ML
estimation method, exhibits good position estimation performance up to
$\mathrm{SNR}=-39\,$dB, where the RMSE curve related to the target position
estimation $\mathbf{\hat{p}}_{p}$ nearly coincides with the PEB curve. The
possibility of correctly estimating the target in correspondence with
extremely low values of SNR is especially valuable at THz, where the path loss
significantly affects the performance. Furthermore, it is worth noting that
such a system can reach a mm accuracy on the position estimation, without
range ambiguities, for values of SNR greater than $-10\,$dB, under the above
simulation parameters and conditions. Note that the bistatic range resolution
is $15\,$cm, thanks to the use of a $B=2\,$GHz bandwidth. In Fig. 2(b), the
RMSE on position estimation $\mathbf{\hat{p}}_{p}$ is plotted as a function of
the RCS of the target. As it can be observed, the proposed two-stage ISAC
system can correctly estimate, with sub-cm accuracy, the position of the
target with an RCS approximately greater than $1\,$m2 at a distance of
$7.9\,$m from both the Tx and Rx, showing performance very close to the
theoretical bound.

##  V Conclusion

This work introduced a two-stage ML-based estimation approach for managing
range ambiguity in a bistatic MIMO-OFDM ISAC system at THz frequencies that
use a GHz-wide bandwidth. Initially, a coarse target position is estimated
using a small sub-band to avoid ambiguity within the monitored area. The
estimation is then refined using the system’s full bandwidth to enhance
position accuracy and resolution. The approach maintains low computational
complexity and uses a small fraction of the subcarriers to save resources for
communication. Numerical results confirm that the method effectively resolves
range ambiguity, achieving near-optimal RMSE performance even at very low SNR
regimes.

## References

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  *[THz]: terahertz
  *[ISAC]: integrated sensing and communication
  *[OFDM]: orthogonal frequency-division multiplexing
  *[MIMO]: multiple-input multiple-output
  *[ML]: maximum likelihood
  *[Tx]: transmitter
  *[Rx]: receiver
  *[ULA]: uniform linear array
  *[CP]: cyclic prefix
  *[FFT]: fast Fourier transform
  *[ICI]: inter-carrier interference
  *[ISI]: inter-symbol interference
  *[AWGN]: additive white Gaussian noise
  *[AoD]: angle of departure
  *[LoS]: line of sight
  *[RCS]: radar cross section
  *[AoA]: angle of arrival
  *[SNR]: signal-to-noise ratio
  *[GML]: generalized maximum likelihood
  *[CRLB]: Cramér-Rao lower bound
  *[FIM]: Fisher information matrix
  *[PEB]: position error bound
  *[RMSE]: root mean square error
  *[QPSK]: quadrature phase shift keying


# ChatGPT Application in Summarizing an Evolution of Deep Learning Techniques
in Imaging: A Qualitative Study

Arman Sarraf
Department of Electrical and Software Engineering
University of Calgary
Calgary, AB T2N 1N4, Canada
<EMAIL_ADDRESS>
Amirabbas Abbaspour
Department of Electrical and Software Engineering
University of Calgary
Calgary, AB T2N 1N4, Canada
<EMAIL_ADDRESS>
Corresponding Author

###### Abstract

The pursuit of article or text summarization has captured the attention of
natural language processing (NLP) practitioners, presenting itself as a
formidable challenge. ChatGPT 3.5 exhibits the capacity to condense the
content of up to 3000 tokens into a single page, aiming to retain pivotal
information from a given text across diverse themes. In a conducted
qualitative research endeavor, we selected seven scientific articles and
employed the publicly available ChatGPT service to generate summaries of these
articles. Subsequently, we engaged six co-authors of the articles in a survey,
presenting five questions to evaluate the quality of the summaries compared to
the original content. The findings revealed that the summaries produced by
ChatGPT effectively encapsulated the crucial information present in the
articles, preserving the principal message of each manuscript. Nonetheless,
there was a slight diminishment in the technical depth of the summaries as
opposed to the original articles. As a result, our conclusion underscores
ChatGPT’s text summarization capability as a potent tool for extracting
essential insights in a manner more aligned with reporting than purely
scientific discourse.

_Keywords_ Text Summerization $\cdot$ ChatGPT $\cdot$ Deep Learning

##  1 Introduction

Text summarization is a pivotal application of NLP that condenses lengthy
documents or articles into shorter, coherent representations while retaining
the essential information. Through various algorithms and techniques, NLP
models identify significant sentences, key phrases, or essential concepts
within the text to generate concise summaries. Extractive summarization
involves selecting and stitching together important segments directly from the
original text, often based on relevance, importance, or frequency of
occurrence. On the other hand, abstractive summarization goes beyond
extraction, generating novel sentences that convey the core meaning while
potentially rephrasing and restructuring the content. NLP-powered
summarization systems play a crucial role in information retrieval, aiding in
quick comprehension and accessibility of vast amounts of text across diverse
domains such as news articles, research papers, and legal documents.
ChatGPT boasts impressive text summarization capabilities, harnessing its
advanced Natural Language Processing (NLP) architecture to distill lengthy
conversations, articles, or documents into concise, coherent summaries.
Leveraging its vast understanding of language semantics, context, and syntax,
ChatGPT effectively identifies key points, essential information, and
significant passages within the text. Its summarization prowess encompasses
extractive and abstractive techniques, allowing it to select important
segments directly from the input while generating novel, coherent sentences
that capture the essence of the content. This functionality enables ChatGPT to
offer streamlined and comprehensive summaries across various topics and
sources, facilitating quicker comprehension and accessibility of information
for various purposes, from research and study aids to content curation and
information

##  2 Method

Qualitative research is a versatile and nuanced methodology that emphasizes
understanding phenomena from the perspective of those being studied. It
involves an in-depth exploration of experiences, attitudes, beliefs, and
behaviors through interviews, observations, and analysis of texts or
artifacts. Unlike quantitative methods focusing on numerical data and
statistical analysis, qualitative research delves into the richness of human
experiences, seeking to uncover underlying meanings, patterns, and contexts
within a particular social or cultural setting. Researchers often employ
various approaches, such as grounded theory, phenomenology, ethnography, or
narrative analysis, allowing them to immerse themselves in the subject matter
and gather detailed, descriptive data. This method prioritizes flexibility,
enabling researchers to adapt their strategies based on emerging insights and
the evolving nature of the study, ultimately providing a deeper understanding
of complex human phenomena.
In this work, we selected seven articles, and we had access to the co-authors
to conduct a qualitative research study to explore the quality of ChatGPT to
summarize scientific articles. The theme of the articles selected focused on
various techniques of deep learning in imaging over time, where the evolution
of techniques was captured. We prepared five questions to survey six co-
authors of the articles. We asked them the questions and requested them to
provide a score from 1 to 5 where 1 represents the lowest and 5 represents the
highest. During the interviews, we collected crucial insights into articles
from the co-authors for our discussion section. The list of questions is as
follows:

  * •

ChatGPT preserved the keywords in the summary

  * •

ChatGPT correctly captured the objective of the articles

  * •

ChatGPT produced a summary that includes enough details

  * •

ChatGPT’s summary is highly technical, preserving the technical terms

  * •

The overall satisfaction with the articles’ summaries

In order to generate the summary, we used the text summarization capability of
ChatGPT 3.5. This tool only accepts text with less than 3000 tokens (words);
therefore, we split the long articles into segments with proper lengths.
ChatGPT is often generated around one page of summary per request and usually
ends with a user asking if there is any specific information we are seeking.
Although the inference latency of ChatGPT is out of the scope of this study,
the online API produced the summary in a very appropriate time, usually less
than five seconds.

##  3 Results

First, we asked the interviewees to review the seven articles and provided
them with a summary of each article generated by ChatGPT. Once the
interviewees reviewed the original and summary of the articles, we initiated
the interview process to capture their responses to the survey questions. The
summary of each article is presented in the following section, where the
summary length is highly proportionate with the length of the original
article.

###  3.1 Template Matching Advances and Applications in Image Analysis

The article discusses the significance of template matching in computer vision
and image analysis, emphasizing its role in determining similarities between
different objects or images. It covers various approaches and mathematical
methods involved in template matching, focusing on both feature-based and
area-based techniques. The piece delves into measures of match, such as cross-
correlation and normalized cross-correlation, highlighting their importance in
image processing.
Additionally, the article explores challenges in template matching, including
scale and rotation invariance, and discusses methods like Fourier-Mellin
transform for achieving scale invariance and techniques for rotation
invariance using polar coordinate transforms. It also touches upon efficiency
considerations and computational complexities of different template matching
algorithms.
The applications of template matching span diverse fields, from object
recognition in computer vision to medical imaging, illustrating its relevance
in various real-world scenarios.
In essence, the article provides an extensive overview of template matching
methods, their mathematical underpinnings, challenges, and practical
applications across different domains in computer vision and image analysis.
The article discusses template matching algorithms and their applications
across various fields, emphasizing their role in image analysis, computer
vision, and medical imaging. It outlines:

  1. 1.

Scale and Translation Invariance: It describes equations showing the scaled
Fourier transform of 2D signals, introducing logarithmic representations to
handle translation versions.

  2. 2.

Rotation Invariance: By applying polar coordinate transforms and complex log
mapping, rotation and scaling become translations in the transformed domain.

  3. 3.

Deformable Template Models: The concept of deformable templates addresses
shape deformations and variations, allowing more powerful techniques for shape
matching in computer vision.

  4. 4.

Applications:

    1. (a)

Face Detection: Emphasizes the importance of facial features and emotions in
detection methods.

    2. (b)

Eye Detection: Discusses template-based eye detection for various
applications.

    3. (c)

License Plate Recognition: Details the use of template matching for license
plate detection and recognition systems.

    4. (d)

Bare PCB Board Testing: Discusses how template matching helps in inspecting
bare PCBs for loose connections and defects.

    5. (e)

Breast and Mammogram Positioning: Highlights the use of template matching in
medical imaging to locate and evaluate symmetry between breast mammograms.

    6. (f)

Brain Network Extraction: Explores the use of template matching techniques in
extracting brain networks from MRI images, particularly focusing on resting-
state fMRI.

  5. 5.

Conclusion: Emphasizes the importance of post-classification or decision-
making steps to improve the accuracy of template matching systems and suggests
different approaches based on the nature of the data being matched.

Overall, the article demonstrates the versatility of template matching
algorithms and their significance in a wide range of applications, from
computer vision to medical imaging Hashemi et al. (2016); Sarraf et al. (2021,
2023, 2020a); Sarraf (2020a).

###  3.2 A Comprehensive Review of Deep Learning Architectures for Computer
Vision Applications

It seems like a comprehensive overview of the principles and methodologies in
computer vision, particularly in image classification. You’ve touched upon
various techniques from preprocessing and feature extraction to supervised and
unsupervised learning methods. The breakdown of SVM, ANN, and Decision Trees
provides a good comparison between these methods.
If you’re aiming to delve deeper into the nuances of deep learning and
convolutional neural networks (CNNs), it might be beneficial to elaborate on
those topics further. CNNs, in particular, have been groundbreaking in image
classification due to their ability to automatically learn features from raw
data, significantly impacting fields like computer vision and pattern
recognition.
Highlighting specific architectures within CNNs, like AlexNet, VGG, ResNet,
and explaining how these architectures have improved the efficiency of image
classification could be valuable. Additionally, discussing transfer learning—a
technique where a model trained on one task is adapted for another—and its
impact on image classification might add depth to your exploration.
Do you plan to focus more on CNNs and their applications in image
classification, or are you considering a broader perspective on deep learning
in computer vision? Both paths could provide valuable insights depending on
your target audience or the depth of understanding you aim to offer.
That’s an extensive exploration of CNNs and their diverse applications across
various domains, from computer vision to natural language processing and
speech recognition. The breakdown of each application area and how CNNs have
improved performance in tasks like image classification, detection,
segmentation, and even handling low-resolution images provides a comprehensive
view of their versatility.
The emphasis on CNNs’ ability to solve feature extraction problems in image
classification compared to older machine learning techniques is well
highlighted. It’s interesting to note how CNNs’ deep training capabilities
have addressed the challenges of extracting nuanced features and handling
multi-class classification scenarios.
The potential for CNNs in diagnosing diseases like Alzheimer’s based on brain
scans is a fascinating and promising area. It’s great to see how these
advanced neural networks are contributing significantly to medical science.
As a concluding thought, considering the ongoing advancements in machine
learning and neural networks, the prospects for further refining algorithms
and enhancing predictive capabilities for diagnosing diseases like Alzheimer’s
seems highly promising.
If you’re planning to expand this further, perhaps delving into recent
breakthroughs or ongoing research leveraging CNNs in medical diagnostics or
exploring how these networks are evolving to handle new challenges could be
interesting. Additionally, discussing any limitations or ethical
considerations in using CNNs across these domains might add depth to your
analysis Sarraf et al. (2021); Sarraf and Kabia (2023); Aghakhani et al.
(2023); Sarraf (2022); Sarraf and Noori (2021); Sarraf (2020b); Sarraf et al.
(2020b).

###  3.3 Recent Applications of Deep Learning Algorithms in Medical Image
Analysis

Your abstract and introduction provide a comprehensive overview of the
intersection between deep learning, medical imaging, and the diagnosis of
brain disorders using advanced techniques like convolutional neural networks
(CNNs) and semantic segmentation. Here are some observations and suggestions:

  * •

Comprehensive Introduction: Your introduction provides an excellent overview
of deep learning, its applications, and the prominence of CNNs in various
fields such as image classification, semantic segmentation, and medical
imaging.

  * •

Explanation of CNNs and Semantic Segmentation: You’ve done a great job
explaining the significance of CNNs in image processing, particularly in
semantic segmentation. Elucidating the difference between image classification
and semantic segmentation along with the key models used in deep learning
(SAE, DBN, CNN, RNN) adds depth to the discussion.

  * •

Focus on Medical Imaging Modalities: Your discussion of medical imaging
modalities like CT scans, PET scans, and MRI is insightful. It’s good to
emphasize the importance of high-resolution imaging for deep learning models
in diagnosing brain disorders.

  * •

Case Studies on Disorders: The specific examples and case studies you’ve
presented, particularly in the context of diagnosing Alzheimer’s and stroke,
are illustrative and add practical insights to the discussion.

  * •

Visual Aid: Incorporating figures to illustrate classification, localization,
and semantic segmentation adds visual clarity to your explanations.

  * •

Suggestions for Improvement: You might consider expanding on the challenges
faced in medical imaging, such as dealing with noise or variations in imaging
quality, and how deep learning techniques mitigate these challenges.
Additionally, discussing the ethical considerations or limitations of using
deep learning in medical diagnoses could further enrich the discussion.

  * •

Future Directions: It would be beneficial to briefly touch upon the potential
future advancements or areas of exploration in this field, such as the
integration of multi-modal imaging or the use of generative models for medical
image synthesis.

Your work provides a solid foundation for understanding the role of deep
learning, CNNs, and semantic segmentation in medical imaging and diagnosing
brain disorders. Expanding on certain areas and discussing future trends could
enhance the depth and breadth of your exploration.
Your exploration of deep learning applications in diagnosing brain disorders,
specifically Alzheimer’s disease, Mild Cognitive Impairment (MCI), and autism
spectrum disorder (ASD), provides a detailed understanding of the advancements
made in medical imaging and diagnostics. Here are some observations and
suggestions:

  * •

Comprehensive Disease Overview: Your breakdown of Alzheimer’s, MCI, and Autism
provides a clear understanding of these disorders, their symptoms, and their
impact on brain patterns. It helps set the context for the importance of
accurate diagnosis using deep learning techniques.

  * •

Deep Learning in Disease Diagnosis: Your discussion of deep learning models,
particularly CNNs like LeNet and GoogleNet, showcases their effectiveness in
diagnosing these brain disorders. Providing accuracy rates for different
models strengthens the argument for their potential in medical imaging.

  * •

Focus on Disease Stages: Highlighting the importance of identifying specific
stages of diseases like Alzheimer’s and MCI showcases the depth of analysis
needed in medical diagnosis. The mention of MCADNNet and its high accuracy in
classifying different stages is a compelling point.

  * •

Application of LeNet-5 in Autism Diagnosis: Explaining the application of
LeNet-5 in diagnosing Autism from brain MRI samples and achieving a high
accuracy rate adds depth to the discussion, showcasing the versatility of deep
learning models in different disorders.

  * •

Visual Representation: The inclusion of figures demonstrating CNN
architectures and their functions adds visual clarity to complex concepts,
aiding in better comprehension for readers.

  * •

Conclusion and Future Implications: The conclusion summarizes the advancements
made and hints at the potential for productizing these techniques. Adding a
section on future implications or areas of further research could offer
insights into what lies ahead in this field.

  * •

Ethical Considerations: Discussing ethical considerations or limitations of
using deep learning in medical diagnoses could add depth to your discussion.
Privacy concerns, biases in datasets, or the need for expert validation could
be valuable points to consider.

Your work effectively highlights the capabilities of deep learning models in
diagnosing brain disorders, backed by accuracy rates and specific models used.
Expanding on ethical considerations and potential future directions could
further enrich your discussion. Overall, it’s a comprehensive overview of the
current landscape in medical imaging and deep learning applications in brain
disorder diagnoses Sarraf et al. (2020a); Sarraf (2019a); Sarraf et al.
(2019); Sarraf (2019b, 2018); Yang et al. (2018).

###  3.4 Deep Learning-based Pipeline to Recognize Alzheimer’s Disease using
fMRI Data

This paper you’ve presented highlights the application of Convolutional Neural
Networks (CNNs) in classifying Alzheimer’s disease (AD) from normal control
data using functional MRI (fMRI) images. Here’s a summary and some key points
to consider:

  * •

Objective: The primary objective of the study is to distinguish AD brains from
healthy brains using CNNs and LeNet-5 architecture.

  * •

Data Acquisition and Preprocessing: The study uses data from the ADNI dataset,
involving 28 AD patients and 15 normal control subjects. The fMRI data
undergoes standard preprocessing steps including motion correction, skull
stripping, spatial smoothing, and alignment to standard space.

  * •

Deep Learning with CNNs: The paper explains the fundamentals of CNNs,
emphasizing their use in processing 2D images like fMRI scans. LeNet-5
architecture is chosen for its application in binary classification of AD
versus normal control data.

  * •

Results: The CNN model achieved an average accuracy rate of 96.8588% across
five runs of cross-validation. Figures depicting learning rates, loss, and
accuracy during training are provided, demonstrating the robustness and
reproducibility of the model.

  * •

Feature Extraction and Complexity: CNNs are praised for their ability to
simultaneously extract high-level features and perform classification,
addressing challenges in traditional medical image processing. The complexity
of the CNN architecture is acknowledged, offering both strong feature
extraction and classification capabilities.

  * •

Conclusion: The study concludes with the successful classification of AD data
with high accuracy using a CNN-based deep learning approach. It highlights the
potential of this method for further prediction tasks and emphasizes the need
for more complex architectures for addressing more challenging problems.

This paper provides a comprehensive overview of the methodology, data
processing steps, and results achieved through deep learning techniques
applied to fMRI data for Alzheimer’s classification. It’s commendable for the
high accuracy achieved and the potential for further improvements in complex
network architectures Sarraf and Tofighi (2016a); Anderson et al. (2017);
Sarraf (2017a, b); Sarraf and Ostadhashem (2016).

###  3.5 DeepAD: Alzheimer’s Disease Classification via Deep Convolutional
Neural Networks using MRI and fMRI

This is an extensive paper detailing the application of deep learning methods
for distinguishing Alzheimer’s disease from healthy brain data using MRI and
fMRI. It covers various aspects, including the challenges in classification
due to similarities between Alzheimer’s-related brain changes and normal aging
effects, the use of convolutional neural networks (CNNs) for feature
extraction, data acquisition methodologies, and a review of related work in
the field.
The paper presents two subsets of data from the ADNI database, one involving
rs-fMRI data from 144 subjects and the other involving MRI data from 302
subjects, both aged over 75. The study reports impressive accuracy rates
achieved through deep learning pipelines for both fMRI (99.9%) and MRI
(98.84%) data, showcasing significant improvements over previous studies in
Alzheimer’s classification. Subject-level classification, crucial for clinical
application, also demonstrated high accuracy rates of 94.32% and 97.88% for
fMRI and MRI, respectively.
The use of deep learning architectures, such as CNNs, is explained in detail,
including their role in extracting high-level features from imaging data. The
paper refers to notable CNN architectures like LeNet-5 and GoogleNet,
emphasizing their effectiveness in image classification tasks.
The related work section discusses various studies that utilized deep learning
techniques for Alzheimer’s classification using MRI and PET data. The
accuracies reported in these studies range from approximately 75% to 95%,
demonstrating the effectiveness of deep learning methodologies in this domain.
Overall, this paper seems comprehensive and provides a robust exploration of
using deep learning for Alzheimer’s disease prediction based on neuroimaging
data.
This excerpt details an elaborate process for Alzheimer’s disease image
classification, involving extensive preprocessing of both functional (fMRI)
and structural (MRI) data, followed by training and testing CNN-based models.
The methods aim to accurately differentiate Alzheimer’s patients from healthy
individuals.
The steps involve converting raw data into suitable formats, eliminating non-
brain regions, correcting artifacts, performing slice timing correction,
spatial smoothing, registration, and aligning images to a standard space. This
comprehensive preprocessing is crucial to extract meaningful features from the
data.
The convolutional neural network (CNN) models (LeNet and GoogleNet) were
trained and tested using different datasets derived from these preprocessed
images. The models achieved very high accuracy rates, particularly with the
GoogleNet architecture, showcasing the potential effectiveness of these
methods in classification tasks related to Alzheimer’s disease.
The results suggest that spatial smoothing with an optimal kernel size notably
improves classification accuracy. Visualizing filter weights and network
activations helps interpret the convolutional layer’s results, indicating the
network’s progress and potential overfitting.
Additionally, the discussion emphasizes the importance of preprocessing and
feature learning in distinguishing Alzheimer’s disease-related brain changes
from normal aging effects. The provided visualizations of filter weights and
features aid in understanding how the trained models identify relevant
patterns in brain images.
This detailed methodology establishes robust pipelines for consistent and
reproducible results, highlighting the significance of rigorous preprocessing
and feature extraction in the accurate classification of Alzheimer’s disease
images.
That’s an incredibly detailed and thorough research paper about distinguishing
Alzheimer’s disease from healthy brains using MRI and fMRI data! It covers a
wide range of topics from preprocessing to classification and even delves into
subject-level recognition and decision-making algorithms. The rigorous
preprocessing steps applied to both fMRI and MRI data seem to have
significantly enhanced the accuracy of the classifiers. Moreover, the subject-
level classification, which is more relevant to clinical applications,
displayed high accuracy rates even after considering slices at the subject
level rather than individual image slices.
The utilization of deep learning models like LeNet and GoogleNet has shown
impressive accuracy rates, surpassing previous methodologies in the field.
Also, the incorporation of the decision-making algorithm seems to have further
improved the accuracy at the subject level, making the predictions more robust
Sarraf et al. (2016a); Saverino et al. (2016); Sarraf and Sun (2016); Moosavi-
Zadeh et al. (2023); Sarraf and Tofighi (2016b); Sarraf et al. (2016b).

###  3.6 MCADNNet: Recognizing Stages of Cognitive Impairment through
Efficient Convolutional fMRI and MRI Neural Network Topology Models

It looks like you’ve shared an extensive research paper focused on developing
a deep learning algorithm, MCADNNet, for the simultaneous recognition of Mild
Cognitive Impairment (MCI), Alzheimer’s Disease (AD), and normally aging
brains in adults over 75 years old using functional and structural magnetic
resonance imaging (fMRI and MRI) data. The paper goes into detail about the
methodology, data preprocessing steps, neural network architecture, and
previous related works in the field.
The research involves several significant components:

  * •

Problem Statement: Recognizing MCI, AD, and normal aging brains using
neuroimaging data.

  * •

Approach: Employing an optimized convolutional neural network (CNN)
architecture, MCADNNet, to classify these conditions.

  * •

Data Used: Utilizing data from the Alzheimer’s Disease Neuroimaging Initiative
(ADNI) database, with different groups of subjects for fMRI and MRI
modalities, including Alzheimer’s patients, healthy controls, and MCI
patients.

  * •

Preprocessing: Extensive preprocessing of both fMRI and MRI data, involving
steps like converting data formats, removing non-brain tissues, motion
artifact correction, slice timing correction, spatial smoothing, registration,
and normalization.

  * •

Neural Network Design: Using a CNN architecture inspired by the human visual
system, structured with convolutional layers, pooling layers, normalization
layers, and fully connected layers.

  * •

Previous Works: Discussing related studies and methodologies used in
diagnosing MCI and AD, including various deep learning architectures and their
accuracies.

The paper emphasizes the need for accurate diagnosis and early intervention in
cognitive impairment, highlighting the potential of artificial intelligence,
particularly deep learning, in enhancing diagnostic capabilities using
neuroimaging data.
The excerpt you’ve shared delves deep into the methodology and results of
using CNN-based architectures like DeepAD and MCADNNet for the classification
of MRI and fMRI data in distinguishing between different brain conditions like
MCI, AD, and NC. It seems like they’ve meticulously detailed the entire
pipeline, from data conversion and augmentation to the specific architecture
of the neural networks used for classification. They’ve even employed a
decision-making algorithm for subject-level recognition after the
classification.
The use of CNNs for processing medical imaging data has shown promising
results in various studies. It’s interesting how they’ve noted the impact of
data size, preprocessing steps like spatial smoothing, and the architecture
complexity on the model’s performance. The decision-making algorithm applied
post-classification seems to significantly improve subject-level accuracy
rates.
In terms of future work, considering MCI subcategories and creating a more
robust pipeline that’s less sensitive to preprocessing steps could be
intriguing avenues for further research Sarraf et al. (2019, 2016c, 2016a,
2014a, 2014b, 2009).

###  3.7 OViTAD: Optimized Vision Transformer to Predict Various Stages of
Alzheimer’s Disease Using Resting-State fMRI and Structural MRI Data

Your abstract outlines a compelling study on Alzheimer’s disease diagnosis
using an optimized vision transformer architecture applied to neuroimaging
data. The focus on predicting the disease stage and employing efficient
pattern extraction methods like transformers is a significant step forward.
Your methods cover a comprehensive preprocessing pipeline for both resting-
state functional MRI (rs-fMRI) and structural MRI data, optimizing the data
for the vision transformer. The step-by-step description ensures clarity
regarding how the data was prepared for modeling.
The introduction effectively contextualizes the significance of early
Alzheimer’s detection, highlighting the challenges faced by traditional
methods and the potential of AI in neuroimaging. The detailed review of
related work provides a solid foundation for your study’s novelty in adopting
an optimized vision transformer (OViTAD) for Alzheimer’s prediction.
Your study provides a detailed exploration of various transformer-based
architectures in predicting Alzheimer’s disease stages using both functional
and structural MRI data.
The introduction of DeepViT and CaIT, both employing unique attention
mechanisms within vision transformers, enriches the comparison and
benchmarking process, enhancing the study’s comprehensiveness. DeepViT
introduces re-attention, while CaIT incorporates class-attention layers,
showcasing different approaches to leverage attention mechanisms within the
vision transformer architecture.
The meticulous preprocessing pipelines for both fMRI and structural MRI,
followed by data decomposition and model building, are thorough and
structured. The creation of 2D images from the 4D fMRI data and decomposition
of 3D structural MRI data into 2D images pave the way for utilizing these
formats with the vision transformer architectures.
The model training, evaluation, and comparison across different architectures,
especially focusing on multiclass prediction for AD, HC, and MCI, as well as
binary classification experiments, are detailed and systematic. The use of AWS
SageMaker for model development on robust computing infrastructure enables
efficient training and testing.
Your subject-level evaluation, aggregating predictions to generate subject-
level performance metrics, adds depth to the analysis. The tables and figures
provided in the appendices succinctly present the results for both fMRI and
structural MRI models, allowing for a comprehensive comparison of performance
metrics across experiments and repetitions.
It’s impressive how you’ve accounted for multiple repetitions and presented
averaged results, offering a clearer understanding of the models’ stability
and generalizability. The tables summarizing model-level performance for both
fMRI and structural MRI experiments are highly informative and allow for easy
comparison.
Your detailed methodology enables readers to follow each step of the process,
ensuring transparency and reproducibility in research. It would be interesting
to learn more about any insights or conclusions drawn from the comparison of
the different vision transformer architectures and their impact on predictive
performance across the various experiments. Additionally, any insights gleaned
from the subject-level evaluation and its implications for clinical
applications would be valuable to discuss. Your study outlines a comprehensive
approach employing vision transformers (VT) for Alzheimer’s disease stage
prediction using fMRI and structural MRI data. The systematic exploration
encompasses aggressive preprocessing, data decomposition, VT model
development, and postprocessing steps.
The optimization of the vision transformer architecture was thoughtful,
considering input size and patch dimensions to fit the data. This strategy
effectively reduced trainable parameters by 28% compared to vanilla VTs and
DeepViT while enhancing performance in fMRI experiments and maintaining
competitiveness in structural MRI ones.
Performance evaluations at both slice and subject levels were insightful,
showcasing the importance of postprocessing, notably the significant
improvement in subject-level performance. This aligns with existing literature
and reinforces the idea that data decomposition and transformation from slice
to subject levels significantly enhance predictive quality.
Your comparison with recent literature and state-of-the-art models highlights
the strength of your optimized VT (OViTAD) across broader classifications,
demonstrating its superior performance. This reinforces the potential clinical
significance of the developed model.
The observation regarding combining AD, HC, and MCI brains for binary
classifications provided interesting insights into the similarities between HC
and MCI functional data, and how your models effectively addressed aging
effects.
Visualization of attention mechanisms at both local and global levels added
depth to the analysis, allowing exploration of crucial brain areas and
offering valuable insights into the model’s decision-making process.
You acknowledge limitations, such as the number of repetitions for model
development and the computational cost of postprocessing. Additionally, you
propose future directions, suggesting exploration of other datasets and the
potential use of 3D vision transformers.
In conclusion, your study introduces an optimized vision transformer that
significantly reduces complexity while outperforming or competing with
existing state-of-the-art models in predicting various stages of Alzheimer’s
disease. The insights gained from this work and the methodological approach
presented offer significant potential for clinical applications and further
research in this domain Sarraf et al. (2023, 2016a, 2019); Sarraf and Kabia
(2023); Krishnan et al. (2016).

##  4 Discussion

We collected the interviewees’ insights and the scores provided for each
question. Table 1 shows the details of the scoring. As seen in the table,
article 6 achieved the highest score, suggesting that the summary generated by
ChatGPT could attract the interviewees’ attention more than other articles.

Table 1: The overall scores provided by the interviews

Criteria | Co-author 1 | Co-author 2 | Co-author 3 | Co-author 4 | Co-author 5 | Co-author 6 | Average
---|---|---|---|---|---|---|---
| Q1 | 4 | 3 | 5 | 4 | 3 | 2 |
| Q2 | 2 | 2 | 4 | 5 | 3 | 4 |
| Q3 | 5 | 3 | 5 | 3 | 2 | 4 |
| Q4 | 4 | 3 | 2 | 2 | 2 | 5 |
Article 1 | Q5 | 4 | 5 | 4 | 3 | 3 | 3 | 3.43
| Q1 | 3 | 5 | 5 | 3 | 3 | 3 |
| Q2 | 3 | 5 | 4 | 4 | 4 | 3 |
| Q3 | 3 | 4 | 5 | 4 | 5 | 3 |
| Q4 | 5 | 4 | 5 | 4 | 5 | 4 |
Article 2 | Q5 | 4 | 4 | 5 | 4 | 4 | 4 | 4.03
| Q1 | 4 | 4 | 5 | 4 | 4 | 4 |
| Q2 | 5 | 5 | 4 | 5 | 4 | 4 |
| Q3 | 5 | 5 | 5 | 5 | 5 | 4 |
| Q4 | 4 | 4 | 5 | 5 | 5 | 4 |
Article 3 | Q5 | 5 | 4 | 5 | 5 | 5 | 4 | 4.53
| Q1 | 5 | 4 | 5 | 4 | 4 | 5 |
| Q2 | 4 | 5 | 4 | 4 | 5 | 5 |
| Q3 | 5 | 4 | 5 | 4 | 4 | 4 |
| Q4 | 4 | 4 | 4 | 5 | 5 | 5 |
Article 4 | Q5 | 4 | 4 | 4 | 5 | 4 | 5 | 4.43
| Q1 | 5 | 4 | 5 | 4 | 4 | 4 |
| Q2 | 4 | 5 | 5 | 4 | 5 | 4 |
| Q3 | 5 | 4 | 4 | 5 | 5 | 4 |
| Q4 | 4 | 4 | 4 | 4 | 4 | 5 |
Article 5 | Q5 | 5 | 4 | 4 | 4 | 5 | 4 | 4.37
| Q1 | 5 | 4 | 4 | 5 | 4 | 5 |
| Q2 | 5 | 4 | 5 | 5 | 5 | 4 |
| Q3 | 5 | 5 | 5 | 4 | 5 | 5 |
| Q4 | 5 | 4 | 5 | 4 | 5 | 5 |
Article 6 | Q5 | 5 | 5 | 5 | 5 | 5 | 5 | 4.73
| Q1 | 4 | 4 | 4 | 5 | 4 | 5 |
| Q2 | 5 | 5 | 4 | 4 | 5 | 4 |
| Q3 | 5 | 4 | 5 | 4 | 4 | 4 |
| Q4 | 4 | 5 | 5 | 5 | 4 | 4 |
Article 7 | Q5 | 4 | 5 | 5 | 5 | 5 | 4 | 4.47

The summary of interviewees’ opinions about each article is as follows:

  * •

The summary of Article 1 missed some important details in techniques while
preserving the details in the application of template matching. The article
focused on the techniques rather than the applications; however, the summary
could still send the overall message.

  * •

The summary of Article 2 could preserve the overall message from the original
content; however, the interviewees felt the technical language changed into a
more non-specialist language.

  * •

The summary of Article 3 was very well structured and could preserve and share
the message of original content. This summary is among the top-scored
articles.

  * •

The summary of Article 4 was well structured and could preserve and share the
message of original content.

  * •

The summary of Article 5 is comprehensive and longer than a normal summary
because of the length of the original paper. Although the summary makes sense,
the interviewees’ believed that ChatGPT slightly shifted the conclusion.

  * •

According to the interviewees, the summary of Article 6 is the top content
generated by ChatGPT in this study. It is very well structured and preserves
the main message and details of the article.

  * •

The summary of Article 7 is comprehensive and longer than a normal summary
because of the length of the original paper. The summary preserves and shares
the main message of the article.

##  5 Conclusion

This qualitative study aimed to assess the quality of summaries for scientific
manuscripts generated by ChatGPT. We interviewed six co-authors of those
manuscripts and posed five questions to compare the summary with the original
content. The overall conclusion drawn by the interviewees is that ChatGPT
could summarize the scientific content; however, it slightly changes the
summary tone from a scientific to a non-specialist language. We acknowledged
that our study has limitations, including the number of manuscripts,
interviewees, and questions, and some responses might be subjective, but our
findings align with the current perception of ChatGPT text summarization
capability. Also, we conclude that this capability can allow scientists to
have a quick and fairly informal summary of a scientific manuscript, but we
could not conclude that this capability can or should be used for content
generation and academic publication.

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