Camera Ready IEEE WCNC 2019

# Sampling Free TDOA Localization in Millimeter Wave Networks

Shree Prasad M.∗, Trilochan Panigrahi∗, Mahbub Hassan†, Ming Ding‡ ∗Dept. of
Electronics and Communication Engineering, National Institute of Technology
Goa, India
†School of Computer Science and Engineering, University of New South Wales,
Sydney, Australia
‡ Data61, CSIRO, Sydney, Australia
Email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Time difference of arrival (TDOA) is a widely used technique for localizing a
radio transmitter from the difference in signal arrival times at multiple
receivers. For TDOA to work, the individual receivers must estimate the
respective signal arrival times precisely, which requires sampling the signal
at least double the rate of its highest frequency content, commonly known as
the Nyquist rate. Such sampling is less practical for the millimeter wave band
comprising of frequencies in 30-300 GHz range. In this paper, we propose an
energy detection architecture for accurately estimating the time of arrival
from a single picosecond Gaussian pulse, which enables TDOA localization
without sampling at the receiver. We derive the closed form expression of the
estimated time of arrival and validate it via simulation. We demonstrate that
the proposed sampling-free TDOA can localize millimeter wave transmitters as
accurately as the conventional sampling-based TDOA.

###### Index Terms:

Millimeter Wave Communication, Time Difference of Arrival (TDOA), Time of
Arrival (TOA).

##  I Introduction

Millimeter wave (mmWave), a newly released spectrum band in the frequency
range of 30-300 GHz, is fast becoming a popular choice of networking for a
range of applications [1]. The huge bandwidth of mmWave opens up new
opportunities for not only high data rate applications but also high precision
localization [2, 3]. With ultra-wide bandwidth, mmWave nodes can emit a very
short pulse on the order of picoseconds for precise time resolution at the
receiver [4]. The arrival times recorded at multiple base stations (BSs) then
can be used by the widely used algorithm, called time difference of arrival
(TDOA), to localize the mmWave transmitter.

While TDOA has been used successfully for existing frequency bands, it poses a
serious implementation challenge for the mmWave band. Conventional TDOA
requires the BSs to sample the incoming signal at least at Nyquist rate, which
is twice the rate of the highest frequency content of the signal. Thus, for
mmWave, TDOA would require at least 600 GHz sampling, or even higher if more
precise localization is required. Such a high sampling rate cannot be achieved
with existing analog-to-digital converters (ADCs) [5].

In this paper, we propose an energy-detection-based TDOA that obviates the
need for sampling. In the proposed architecture, time of arrival (TOA) is
precisely estimated through a bank of time-delayed energy detectors, which
estimate the reception of the pulse (energy) at progressively narrower
intervals through many iterations enabled by the delay circuits. By
dimensioning the delay bank, desired TOA and TDOA localization accuracies can
be achieved.

We obtain closed-form expression of the estimated TOA as a function of the
delay bank parameters. The validity of the closed-form expression is achieved
via numerical simulations, which confirm that the estimated TOA converges to
the true value with increasing iterations (energy detection banks with more
elements). By simulating TDOA for many randomly located nodes within a 2mx2m
area, we demonstrate that the proposed sampling-free TDOA can localize
millimeter wave transmitters as accurately as the conventional sampling-based
TDOA.

The rest of the paper is structured as follows. Related work is presented in
section II, followed by the system model in section III. Simulation results
are presented and discussed in Section IV. We conclude the paper in Section V.

##  II Related Works

Different localization techniques such as direction of arrival (DOA), TOA, and
received signal strength have been used in Impulse Radio (IR) communication
systems [6, 7]. The estimation of DOA of source node transmitting higher order
Gaussian pulses in the higher frequency band of mmWave (100 - 325 GHz) and in
terahertz band (0.1 - 10 THz) is studied in [8, 9, 11, 10]. In [12], TOA
estimation technique is investigated for different IR mmWave pulse waveforms
(with center frequency 28 GHz and 78 GHz). Both of these DOA and TOA
estimation techniques require the IR pulse to be sampled beyond the Nyquist
rate, which is not possible with the available state of the art data
converters. Hence, sub-Nyquist sampling rate TOA estimation schemes based on
low complexity energy detectors is investigated in [13, 14], but they require
a large number of pulses in order to improve the signal-to-noise ratio (SNR)
to provide accurate position estimates [15]. To our knowledge, TDOA estimation
from a single pulse without requiring sampling has not been addressed in the
literature.

The closest work in the literature is the proposal of a synchronization
architecture for pulse-based communication in the terahertz band (0.1-10 THz)
[16]. The authors of [16] used an electronically tunable voltage controlled
delay (VCD) in conjunction with continuous time moving average (CTMA)
detectors. CTMAs allow detection of the pulse in a given interval and the VCDs
help narrow down the interval successively with multiple pulse transmissions
in the preamble. This architecture allows precise TOA estimation without
sampling. We build on the core principles of VCD-CTMA-based TOA estimation as
proposed in [16], but it is extend for TDOA estimation with a single pulse.

##  III System Model

Figure 1: mmWave Network Topology.

###  III-A Network Topology

The network topology consisting of three mmWave BSs for TDOA based
localization of a mmWave node is shown in Fig. 1. BS 1 is located at the
origin and the position coordinates of BS 2 and 3 are $\left(0,L\right)$ and
$\left(L,0\right)$, respectively. The coordinates of mmWave node to be
localized is $\left(x_{s},y_{s}\right)$. Both the BSs and the mmWave node
employ based graphene-based plasmonic transceivers, which have been recently
shown to support efficient wireless communications at very high frequencies
above 100 GHz [17]. The mmWave node transmits higher order Gaussian pulses and
the TDOA is achieved by estimating the TOA of the pulse at the BSs.

###  III-B Channel Model

mmWave channel is still not known very well, especially for the very high
frequency range above 100 GHz. Most work in the literature is focused on lower
ranges of the mmWave band (below 60 GHz) using existing channel models.
However, as electromagnetic waves at frequencies over 100 GHz coincide with
the resonance frequencies of many molecules in the air, some recent works used
radiative transfer theory to model such high frequency channels [18], which is
used in our system. Channel response and noise of this model are explained
below.

The channel response $H\left(f,R_{i}\right)$ accounts for both spreading loss
$H_{spread}\left(f,R_{i}\right)$ and molecular absorption loss
$H_{abs}\left(f,R_{i}\right)$ and is represented in frequency domain as

$H\left(f,R_{i}\right)=H_{spread}\left(f,R_{i}\right)H_{abs}\left(f,R_{i}\right)$

(1)

$H_{spread}\left(f,R_{i}\right)=\left(\frac{c_{o}}{4\pi
R_{i}f_{c}}\right)\exp\left(-\frac{j2\pi R_{i}}{c_{o}}\right)$

(2)

$H_{abs}\left(f,R_{i}\right)=\exp(-0.5k\left(f\right)R_{i})$

(3)

where $f$ denotes frequency, $R_{i}$ is the path length between
$i^{\text{th}}$ mmWave BS and mmWave node, $c_{o}$ is the velocity of light in
vacuum, and $k\left(f\right)$ is the medium absorption coefficient. The medium
absorption coefficient $k\left(f\right)$ of the mmWave channel at frequency
$f$ composed of $J$ type molecules is given as

$k\left(f\right)=\sum\limits_{j=1}^{J}a_{j}K_{j}\left(f\right).$

(4)

where $a_{j}$ is the mole fraction of molecule type $j$ and $K_{j}$ is the
absorption coefficient of individual molecular species. The channel response
$h\left(t,R_{i}\right)$ is obtained by taking inverse Fourier transform of
$H\left(f,R_{i}\right)$. Since, this inverse Fourier transform does not have
an analytical closed form expression, the channel response
$h\left(t,R_{i}\right)$ is computed numerically. The ambient noise affecting
the propagation of mmWave pulse in mmWave band arises due to the propagating
of pulse itself and is defined as molecular absorption noise. The total
molecular absorption noise power spectral density (p.s.d.)
$S_{N}\left(f,R_{i}\right)$ affecting the transmitted pulse is the sum of
background atmospheric noise p.s.d $S_{N_{B}}\left(f,R_{i}\right)$ and the
self induced noise p.s.d. $S_{N_{G}}\left(f,R_{i}\right)$ and is given as[18]

$S_{N}\left(f,R_{i}\right)=S_{N_{B}}\left(f,R_{i}\right)+S_{N_{G}}\left(f,R_{i}\right)$

(5)

$S_{N_{B}}(f,R_{i})=\lim\limits_{R_{i}\rightarrow\infty}k_{B}T_{0}\left(1-\exp\left(-k\left(f\right)R_{i}\right)\right)\left(\frac{c_{0}}{\sqrt{4\pi}f_{c}}\right)^{2}$

(6)

$S_{N_{G}}\left(f,R_{i}\right)=S_{G}\left(f\right)\left(1-\exp\left(-k\left(f\right)R_{i}\right)\right)\left(\frac{c_{0}}{4\pi
R_{i}f_{c}}\right)^{2}$

(7)

where $k_{B}$ is the Boltzmann constant, $T_{0}$ is the room temperature and
$S_{G}\left(f\right)$ represents p.s.d. of transmitted pulse.

The noise $n\left(t,R_{i}\right)$ effecting the propagation of mmWave pulse is
modeled as zero mean additive white Gaussian noise and its power or variance
$\sigma^{2}$ is computed as

$\sigma^{2}\left(R_{i}\right)=\int\limits_{B}S_{N}(f,R_{i})df$ (8)

where $B$ represents the bandwidth of the graphene-based plasmonic
transceiver.

Based on this channel model, the pulse received at the mmWave BSs is
represented as [18]

$v\left(t,R_{i}\right)=g_{p}\left(t\right)\ast
h\left(t,R_{i}\right)+n\left(t,R_{i}\right)$ (9) $R_{i}=\tau_{i}c_{o}$ (10)

where $\tau_{i}$ is the true TOA between mmWave node and $i^{\text{th}}$
mmWave BS, $g_{p}\left(t\right)$ represents time derivative of a Gaussian
pulse with derivative order $p$, $h\left(t,R_{i}\right)$ is the mmWave channel
response and $n\left(t,R_{i}\right)$ is the molecular absorption noise created
between mmWave node and $i^{\text{th}}$ mmWave BS.

###  III-C CTMA Pulse Detector vs. Sampling

Fig. 2 illustrates the difference between CTMA pulse detection and sampling.
The CTMA pulse detector is modeled as a linear time-invariant system and its
input to output relation is given as[18]:

$x\left(t\right)=\int\limits_{t-T_{p}}^{t}v^{2}\left(t\right)dt$ (11)

where $x\left(t\right)$ is the output of CTMA, $T_{p}$ is the total pulse
duration of higher order Gaussian pulse and $v\left(t\right)$ is the input to
the CTMA. Equation (11) can be approximated by a second order low pass filter
(LPF) with impulse response $h_{lpf}\left(t\right)=\beta^{2}te^{-\beta t}$,
where $\beta=1.4615/T_{P}$. Using energy storage elements, such as capacitors,
it is possible to hold the maximum value of $x\left(t\right)$ within a certain
time interval. A mmWave pulse is detected within the observation time interval
$t\in\left[0,T_{\text{ob}}\right]$, if
$\text{max}\left\\{x\left(t\right)\right\\}$ exceeds a predefined threshold
voltage. Thus a CTMA can be used to obtain the
$\text{max}\left\\{x\left(t\right)\right\\}$, which we will use later in our
proposed sampling-free TDOA architecture.

Figure 2: CTMA pulse detector and sampling based TOA estimation.

In the sampling based TOA estimation method, on the other hand, the output of
LPF $h_{lpf}\left(t\right)$ is sampled above Nyquist rate and the TOA is
estimated as the time instant at which the output of LPF
$h_{lpf}\left(t\right)$ is maximum. But this method requires very high
sampling rates which is not possible with the existing state of the art ADCs.
Thus in this paper, a sampling free approach for TOA estimation is proposed by
using an array of VCDs and CTMA pulse detectors.

###  III-D Proposed Sampling free TDOA Estimation

Figure 3: Proposed mmWave BS architecture for TOA Estimation using single
mmWave pulse. Figure 4: Timing diagram illustrating observation time interval
selected by CTMAs for $M=3$ at first iteration with
$T_{\text{win}}=T_{\text{ob}}/3$.

TDOA requires TOA estimations (TDOA details explained in Section III-E). Fig.
3 shows the proposed scheme to obtain the TOA estimate at the mmWave base
station (BS). In our architecture, there are two delay blocks. The VCDs in the
fixed delay block delays the mmWave pulse by $T_{\text{ob}}$ and thus provide
a copy of the single mmWave pulse to the next block ever $T_{\text{ob}}$
seconds. In contrast, the delay introduced by VCDs in TOA estimation block is
tuned for every $T_{\text{ob}}$. Without loss of generality, the procedure for
obtaining the TOA estimate at a mmWave BS $i$ is described as follows. Here,
it is assumed that the mmWave pulse arriving at all the three mmWave BSs is
contained within $T_{\text{ob}}$.

During the first iteration, TOA of mmWave pulse is estimated within
$T_{\text{ob}}$. The delay introduced by VCDs in TOA estimation block is
$T_{\text{ob}}/M$ and observation window duration $T_{\text{win}}$ of CTMA is
$T_{\text{ob}}/M$. Hence, $m_{i}^{\text{th}}$ CTMA computes its output
$y\left(t\right)$, for
$t\in\left[\left(M-m_{i}\right)T_{\text{ob}}/M,\left(M-\left(m_{i}-1\right)\right)T_{\text{ob}}/M\right]$.
Thus, together all the CTMAs computes its output in contiguous time intervals
over entire $T_{\text{ob}}$. In the proposed scheme, the CTMA that yields the
maximum output when compared to other CTMAs is said to have detected the
mmWave pulse. In general, the decision rule for selecting the CTMA at
$j^{\text{th}}$ iteration is given as

$\hat{m}_{i,j}=\operatorname*{arg\,max}_{0\leq m_{i}\leq
M}\>\>\left\\{\text{max}\left\\{x_{m_{i}}\left(t\right)\right\\}\right\\}$
(12)

The timing diagram in Fig.4 illustrates the observation time interval selected
by CTMAs for $M=3$ at the first iteration. After first iteration, the coarse
TOA estimate $\hat{\tau}_{i,1}$ of the pulse at the $i^{\text{th}}$ mmWave BS
is given as

$\hat{\tau}_{i,1}=\frac{\left(M-\hat{m}_{i,1}\right)T_{\text{ob}}}{M}$ (13)

where $\left(M-\hat{m}_{i,1}\right)T_{\text{ob}}/M$ is the start time interval
of the $\hat{m}_{i,1}$ CTMA pulse detector that yielded the maximum output
value when compared to the other CTMAs. It should be noted here that, the
start time of mmwave pulse can computed as $\hat{\tau}_{i,1}-T_{p}$. Further,
either $\hat{\tau}_{i,1}$ or $\hat{\tau}_{i,1}-T_{p}$ can be used in TDOA
based localization.

The coarse TOA estimate obtained from the first iteration can be made finer if
more pulses were available. Hence the fixed delay block along with switch
block is used to obtain delayed copies of the single mmWave pulse. The switch
in the switch block changes its position for every $T_{\text{ob}}$. In the
second iteration, the TOA estimate of mmWave pulse is estimated within a
narrower time interval
$\left[\left(M-\hat{m}_{i,1}\right)T_{\text{ob}}/M,\left(M-\left(\hat{m}_{i,1}-1\right)\right)T_{\text{ob}}/M\right]$.

In the second iteration, the single pulse delayed by $T_{\text{ob}}$ is given
as input to the TOA block. In this iteration the observation window of the
CTMA detector $T_{\text{win}}$ is set to $T_{\text{ob}}/M^{2}$. The VCD in the
first line introduces a delay of
$\left[\left(\hat{m}_{i,1}-1\right)T_{\text{ob}}/M+T_{\text{ob}}/M^{2}\right]$
and the remaining VCDs introduces delay of $T_{\text{ob}}/M^{2}$. Thus the
total delay in the $m^{\text{th}}$ VCD is
$\left(\hat{m}_{i,1}-1\right)T_{\text{ob}}/M+mT_{\text{ob}}/M^{2}$. Thus,
$m_{i}^{th}$ CTMA computes its output $y\left(t\right)$, for
$t\in\left[\hat{\tau}_{i,1}+\left(M-m_{i}\right)T_{\text{ob}}/M^{2},\>\hat{\tau}_{i,1}+\left(M-\left(m_{i}-1\right)\right)T_{\text{ob}}/M^{2}\right]$.
Let $\hat{m}_{i,2}$ represent the CTMA detector that yielded the maximum
output value when compared to the other CTMAs. Thus finer TOA estimate
$\hat{\tau}_{i,2}$ of the pulse after the second iteration is given as

$\hat{\tau}_{i,2}=\hat{\tau}_{i,1}+\frac{\left(M-\hat{m}_{i,2}\right)T_{\text{ob}}}{M^{2}}$
(14)

Based on the logic described in the first two iterations, the TOA estimate
$\hat{\tau}_{i}$, at the $i^{\text{th}}$ mmWave BS after $Q+1$ iterations is
given as

$\hat{\tau}_{i}=\hat{\tau}_{i,Q+1}=\sum\limits_{q=1}^{Q+1}\frac{\left(M-\hat{m}_{i,q}\right)T_{\text{ob}}}{M^{q}}$
(15)

From Equation (15), we can see that the time resolution of the proposed TDOA
architecture is basically governed by $M^{Q+1}$, which is further illustrated
in Fig. 5 with a true TOA of 7.5685 ns. In the first iteration, the output of
CTMA $m=3$ will be the maximum and hence the TOA is estimated as
$\hat{\tau}_{1,1}=7\>\text{ns}$. In the second iteration, the TOA is estimated
within the narrower interval of $\left[7\>\text{ns},8\>\text{ns}\right]$.
Given that the CTMA $m=5$ has the maximum output among all CTMAs, TOA estimate
at the second iteration is obtained as $\hat{\tau}_{1,1}=7.5\>\text{ns}$. Thus
for the third iteration, the TOA estimation time interval further narrows to
$\left[7.5\>\text{ns},7.6\>\text{ns}\right]$. In the third iteration, since
$T_{\text{win}}<T_{p}$, the mmWave pulse is spread across more than three time
slots, but CTMA 1 will yield the maximum output when compared to other CTMAs
because, although the time interval for CTMA 1 is
$t_{\text{int}}\in\left[7.59\>\text{ns},7.6\>\text{ns}\right]$, its
convolution integral interval is
$\left[t_{\text{int}}-T_{p},t_{\text{int}}\right]$.

Figure 5: Illustration of iterative procedure for estimation of TOA of tenth
order Gaussian pulse with center frequency 200 GHz at mmWave BS 1. The number
of CTMAs $M=10$ and fixed VCDs $Q=2$.

###  III-E TDOA Localization Algorithm

The TDOA localization algorithm [19], uses the TOA estimates of the mmWave
pulse at mmWave BS to estimate the position coordinates of the mmWave node. In
TDOA localization algorithm all mmWave BS are synchronized by a common clock.
The TDOA of mmWave pulse at mmWave BS $i$ with respect to reference mmWave BS
1 located at the origin is given as

$\tau_{i1}=\tau_{i}-\tau_{1}$ (16)

where $\tau_{i}$ is the true TOA at $i^{\text{th}}$ mmWave BS. The distance
difference $R_{i1}$ is defined as

$R_{i1}=R_{i}-R_{1}=\tau_{i1}c_{o}$ (17)

Now, we define the following terms that will be used in obtaining the position
estimate of mmWave node.

$\boldsymbol{H}=\begin{bmatrix}x_{2}&y_{2}\\\
x_{3}&y_{3}\end{bmatrix},\boldsymbol{c}=\begin{bmatrix}-R_{2i}\\\
-R_{3i}\end{bmatrix},\boldsymbol{d}=0.5\begin{bmatrix}b_{2}^{2}-R_{21}^{2}\\\
b_{3}^{2}-R_{31}^{2}\end{bmatrix}$

where $\left[x_{i},y_{i}\right]$ are coordinates of $i^{\text{th}}$ mmWave BS
and $b_{i}^{2}=x_{i}^{2}+y_{i}^{2}$. Using these terms, the estimate of
position coordinates of the mmWave node is obtained according to the following
equation

$\begin{bmatrix}\hat{x}_{s}\\\
\hat{y}_{s}\end{bmatrix}=\left(\boldsymbol{H}^{T}\boldsymbol{H}\right)^{-1}\boldsymbol{H}^{T}\left(R_{1}\boldsymbol{c}+\boldsymbol{d}\right)$
(18)

##  IV Simulation Results

The proposed sampling-free TDOA algorithm is implemented in MATLAB 2014a.

###  IV-A Parameters and Performance metrics

In the simulation, three mmWave BS with coordinates $\left(0,0\right)$,
$\left(0,L\right)$, and $\left(L,0\right)$ with $L=2\>m$ is considered [12].
The mmWave pulse considered in simulation is a second order Gaussian pulses
with its center frequency $f_{c}=200\>GHz$ and half power bandwidths
$f_{l}=123.38\>GHz$ and $f_{h}=288.30\>GHz$. The power of the second order
Gaussian pulse is 1 $\mathrm{\SIUnitSymbolMicro}$W. The Molecular absoprtion
coefficient $k\left(f\right)$ of the mmWave channel
$\left(100-300\>\text{GHz}\right)$ for standard summer air with 1.86%
concentration of water vapor is obtained from high-resolution transmission
molecular absorption (HITRAN) database [20]. Further, the performance of the
proposed sampling free TDOA estimation algorithm is compared with sampling
based method.

We simulate 10 node positions located randomly in the 2mx2m area. For each
position, we repeat the simulation 500 times. The TDOA localization accuracy
is then defined in terms of average Euclidean distance error (AEDE) as
follows:

$\text{AEDE}=\frac{1}{N_{pos}}\sum\limits_{i=1}^{N_{pos}}\left\\{\frac{1}{N_{run}}\sum\limits_{j=1}^{N_{run}}\sqrt{\left(\left(\hat{x}\left(i,j\right)-x\left(i\right)\right)^{2}+\left(\hat{y}\left(i,j\right)-y\left(i\right)\right)^{2}\right)}\right\\}$

(19)

where $N_{pos}$ is the number of random locations,
$\left[x\left(i\right),y\left(i\right)\right]$ the true coordinates of the
$i^{\text{th}}$ location, $N_{run}$ the number of times simulation is repeated
for each location, and
$\left[\hat{x}\left(i,j\right),\hat{y}\left(i,j\right)\right]$ the estimated
coordinates of the $i^{\text{th}}$ node in the $j^{\text{th}}$ repetition. For
$L=2\>m$, the observation interval is $T_{\text{ob}}=\left[0,10\>ns\right]$.
Here, $10\>ns>R_{max}/c_{o}$, where $R_{max}$ is the longest possible distance
between the mmWave node and mmWave BS within $L\times L$ area.

###  IV-B TOA Estimation

The main source of TDOA localization error stems from errors in estimating the
TOA of the arriving pulse. As explained by Equation (15), TOA accuracy is
strictly influenced by $M^{Q+1}$, i.e., the accuracy can be improved by
allowing larger $M$ and $Q$ in the architecture. For a node located at
$\left[0.5\>m,0.75\>m\right]$, Figure 6 plots TOA estimates as a function of
$M^{Q+1}$. We make the following observations: (1) with only a single CTMA
(m=1) and no iteration (Q=0), the TOA estimation accuracy is very poor, (2)
TOA estimate improves very quickly and becomes close to the ground truth with
the addition of only a few CTMAs and/or iterations, and (3) the improvement
then slows down and it would take many more CTMAs and/or iterations to further
reduce the gap between the ground truth and the estimate.

Figure 6: Estimated TOA verus $M^{Q+1}$. Coordinates of the mmWave node
transmitting 1 $\mathrm{\SIUnitSymbolMicro}$W power second order Gaussian
pulse with $f_{c}=200\>\text{GHz}$ is $\left[0.5\>m,0.75\>m\right]$

###  IV-C Localization Accuracy

Fig. 7 plots AEDE for 10 random locations as a function of $M^{Q+1}$. As
expected, the localization error of the proposed TDOA decreases with
increasing $M^{Q+1}$ in a similar way the TOA improves in Figure 6. To compare
the performance of the proposed sampling-free TDOA against the conventional
sampling-based method, we also plot the localization errors achieved by the
sampling-based method for different sampling rates starting from 300 GHz. We
can see that for Nyquist rate equal to 600 GHz, the proposed TDOA can match
the performance of sampling-based TDOA with $M^{Q+1}=4096$, which could be
achieved for example with only 2 CTMAs subjected to 11 iterations (Q=10). The
proposed TDOA can match the sampling-based TDOA for higher than Nyquist-rate
samplings by simply increasing the number of CTMAs and/or iterations.

Figure 7: AEDE [m] versus $M^{Q+1}$. (The AEDE values at different $f_{s}$ and
the $M^{Q+1}$ that yields AEDE value closest to the AEDE obtained using
different $f_{s}$ is i)
$f_{s}=300\>\text{GHz},\text{AEDE}=0.6903\>\text{mm},\alpha=1728$, ii)
$f_{s}=600\>\text{GHz},\text{AEDE}=0.188\>\text{mm},\alpha=4096$, iii)
$f_{s}=1000\>\text{GHz},\text{AEDE}=0.123\>\text{mm},\alpha=10000$, iv)
$f_{s}=2000\>\text{GHz},\text{AEDE}=0.0632\>\text{mm},\alpha=16384$, and
v)$f_{s}=3000\>\text{GHz},\text{AEDE}=0.0326\>\text{mm},\alpha=20736$)

##  V Conclusion

We have proposed an energy-detection-based TDOA architecture that obviates
sampling requirement at the receiver. The proposed TDOA method, therefore, is
more suitable for high frequency bands, such as mmWave band. The TOA accuracy
of the proposed architecture can be estimated using closed-form expression.
Using numerical simulations, we have demonstrated that the proposed sampling-
free TDOA can localize millimeter wave transmitters as accurately as the
conventional sampling-based TDOA.

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# Video Prediction Models as General Visual Encoders

James Maier
Carnegie Mellon University
<EMAIL_ADDRESS>
Nishanth Mohankumar
Carnegie Mellon University
<EMAIL_ADDRESS>

###### Abstract

This study explores the potential of open-source video conditional generation
models as encoders for downstream tasks, focusing on instance segmentation
using the BAIR Robot Pushing Dataset. The researchers propose using video
prediction models as general visual encoders, leveraging their ability to
capture critical spatial and temporal information which is essential for tasks
such as instance segmentation. Inspired by human vision studies, particularly
Gestalt’s principle of common fate, the approach aims to develop a latent
space representative of motion from images to effectively discern foreground
from background information. The researchers utilize a 3D Vector-Quantized
Variational Autoencoder (3D VQ-VAE) video generative encoder model conditioned
on an input frame, coupled with downstream segmentation tasks. Experiments
involve adapting pre-trained video generative models, analyzing their latent
spaces, and training custom decoders for foreground-background segmentation.
The findings demonstrate promising results in leveraging generative pretext
learning for downstream tasks, working towards enhanced scene analysis and
segmentation in computer vision applications.

##  1 Introduction

Over the past five years, large-scale pretraining on unlabeled data has
significantly transformed the landscape of language modeling [7] [21]. While
strides have been made in the realm of visual understanding through models
like CLIP [12] and BLIP [5], which leverage multi-modal data such as organic
image captions, these approaches still contend with issues related to labeler
intent and bias, inherent ambiguity in text-image pairs as well as the
expensive nature of labelling [13]. However, the realm of video generation
presents a distinct advantage due to the absence of ambiguity in pixel values
within real video data. This suggests that video generation could serve as a
well-structured task for generative pretraining of visual modeling systems,
implicitly encapsulating information relevant to various downstream vision
tasks such as instance segmentation, mask classification, and depth
perception.

Moreover, the abundance of video data available online, estimated to
constitute a large majority of internet traffic, offers a vast resource for
training such models. This stands in stark contrast to text data, where even
the largest datasets are dwarfed by the sheer volume of video content created
daily. Given this landscape, our project aims to explore the potential of
open-source video generation models as adaptable encoders for downstream tasks
like instance segmentation, particularly focusing on the BAIR Robot Pushing
Dataset. Instance segmentation[3], a cornerstone in computer vision
applications, holds immense significance across diverse domains, from
autonomous vehicles to medical image analysis. This task to classify specific
objects within an image enriches systems’ abilities to comprehend visual
complexities and extract implicit information.

Figure 1: System Overview: leveraging pre-trained video prediction model as an
encoder for downstream task of mask segmentation

The primary contributions of this work are as follows:

  * •

The VideoGPT open source video prediction model is analyzed and two distinct
latent spaces are proposed as inputs to downstream task-specific models

  * •

The BAIR Robot Pushing dataset is selected as a testbed, and a custom dataset
of 250 frame/segmentation mask pairs is created.

  * •

A variety of segmentation head neural architectures are proposed and evaluated

  * •

Results from full system compared with UNet [14] architecture as baseline

###  1.1 Core Idea

Image representation learning models are recognized for effectively capturing
information within an image, including details about the scene and objects
present. However, they are not equipped to represent dynamic information such
as optical flow, which requires temporal context. Conversely, video
representation models, exemplified by 3D inflated Convolutional layers [18],
excel at representing both spatial and temporal data as they can capture
images along a third axis, time in our case. Specifically, they can capture
critical information associated with how a scene is expected to change in the
future, which is beneficial for tasks that need to understand how objects
move, such as instance segmentation.

Our proposed approach aims at leveraging a latent space conditioned on a
single input frame to effectively discern foreground from background
information. However, a key challenge emerges: to incorporate temporal data
from a standalone frame. To address this, we propose employing a 3D Vector-
Quantized Variational Autoencoder(3D VQ-VAE) video generative encoder model
conditioned on an input frame. We then utilize the downsampled latent space
generated from the 3D VQ-VAE and feed it into a segmentation head to achieve
the task of foreground vs background segmentation.

###  1.2 Intuition

At a fundamental level, we are inspired by human vision studies, particularly
the Gestalt principle of common fate [9], which suggests that humans tend to
associate pixels of an image as part of the same object if they exhibit a
common motion relative to each other. This concept is observed not only in
adults but also in infants and individuals who have recently gained sight
through experiments [15] [8]. Based on these findings, we hypothesize that
developing a latent space representative of the motion of an object from
images could effectively represent crucial aspects such as object
segmentation, optical flow, depth perception, object occlusion, and other
dynamic characteristics of a scene.

By leveraging this latent space, we aim to capture the underlying temporal
dynamics of a visual scene that are essential for tasks like object
segmentation. This approach aligns with the principles observed in human
visual perception, where motion and spatial relationships play a key role in
perceptual organization and object recognition. Ultimately, our goal is to
harness these insights to enhance computer vision systems, enabling them to
better understand and interpret visual information akin to human and animal
perception.

###  1.3 Relation to Prior Work

As far as our research indicates our implementation of foreground vs
background segmentation using video generational models is novel, but this
idea was inspired by several advancements in the fields of Generative
Artificial Intelligence and the sciences of human vision:

#### Downstream Natural Language Tasks with Large language models:

In recent years, the rapid advancement of large language models has brought
about a transformative impact on the field of natural language processing [1].
By pre-training these models on extensive, unlabeled datasets of natural
language, they have acquired the capacity to comprehend, manipulate, and
generate human language, thereby becoming fundamental tools for a broad
spectrum of downstream NLP applications [4], including machine translation,
chatbots, and text summarization.

Notably, there have been instances where pre-trained language models have been
fine-tuned specifically for tasks such as sentiment analysis [21]. In our
study, we aim to extend this paradigm into the realm of computer vision by
adapting and fine-tuning a suitable video generation model for the task of
foreground versus background segmentation using still images.

Drawing inspiration from the success of language models in NLP tasks, our
objective is to leverage the transferability of pre-training and fine-tuning
techniques to enhance the capabilities of vision models. By applying similar
methodologies to visual data, we seek to equip video generation models with
the ability to discern foreground objects from the background in still images.

#### Representing learning from Motion and Videos:

The human visual system exhibits a learning process that heavily relies on
observing objects in motion rather than static images, as evidenced by studies
conducted by Ostrovsky et al. [8]. Furthermore, experiments involving infants
[15] and newly sighted congenitally blind individuals [8] demonstrate that the
tendency to over-segment images diminishes once objects are perceived in
motion. This insight highlights the importance of temporal information in
informing instance segmentation.

A notable contribution to this understanding comes from the work of Pathak et
al. [11], where they successfully segmented foreground versus background and
performed other tasks by leveraging low-level motion-based grouping to learn
effective visual representations from images. They introduced the concept of
"pseudo ground truth" by encoding motion representations derived from video
data through a motion-based unsupervised learning approach. Their method
involved generating representations that encapsulate motion-related
information, which was then fed into established architectures for tasks such
as object detection and segmentation as Fast R-CNN and AlexNet. The resulting
representations exhibited strong performance in their respective tasks. The
significance of this approach lies in its ability to enhance visual
representation learning by incorporating motion cues derived from video data.
By leveraging temporal dynamics, models can better discern object boundaries
and relationships within an image, thereby improving segmentation accuracy and
overall scene understanding.

#### Learning from Video Generation:

The field of next-frame prediction has seen considerable research activity,
with approaches that leverage pretext learning of motion and scene dynamics.
Pathak et al. explored image inpainting as a means to learn scene dynamics
from images [10]. Wang et al. [17] trained convolutional networks to
distinguish between pairs of tracked patches within a single video versus
pairs of patches from different videos. Misra et al. [6] designed a network to
correctly arrange shuffled frames of a video into their original temporal
sequence. Another prevalent pretext task involves predicting future frames, as
demonstrated by Goroshin et al. [2] predicting pixels of upcoming frames and
Walker et al. [16] predicting dense future trajectories.

However, a key concern when utilizing generation models for such tasks is that
nearby frames in a video often exhibit visual similarity. This similarity can
lead these methods to focus on learning low-level features rather than the
high-level information crucial for our specific task [6].

In our study, we aim to address this challenge by implementing techniques that
encourage the learning of more abstract and meaningful representations from
videos. By leveraging advancements in video generation and representation
learning, we seek to extract rich, high-level information related to object
segmentation, optical flow, and scene dynamics. This involves designing
tailored architectures and training strategies that emphasize the extraction
of semantically meaningful features, ultimately enhancing the model’s ability
to discern complex visual relationships and improve the quality of foreground-
background segmentation in still images.

##  2 Methodology

Since our ultimate goal was to adapt the latent space of a video prediction
model to the task of moving object segmentation, we had some specific
constraints on the video model that we would start with. First, since we
wanted to run mask inference on single images (rather than a video), we needed
a video model which could generate a sequence of frames conditioned on a given
initial frame. Second, since our goal was to leverage a low-dimensional
representation of our input image, we needed a model with an encoder-decoder
architecture. These constraints ultimately led us to two models: MAGVIT [20]
and VideoGPT [19]. Since MAGVIT is SOTA on several modern video modeling
benchmarks [20], we initially chose MAGVIT.

Since MAGVIT does not have publicly available weights, our effort in the
project began with an effort to train a MAGVIT model from scratch that would
serve as our video prediction model. As it turned out, this effort proved to
be a significant resource sink since the computational load to train the
MAGVIT model was significant (In the MAGVIT paper, the authors note the model
requires roughly 2 weeks to train on a V100 GPU)[20]. When we attempted to
replicate the author’s results we did not see good results even after copying
the author’s published hyperparameters and training regime(see Fig 2), most
likely due to a lack of compute (We trained the model on Geforce RTX 4070).
Since the goal of our project was to focus on adapting an existing video
prediction model to downstream tasks rather than training a video prediction
model from scratch, we pivoted to focus on using the VideoGPT model rather
than MAGVIT.

Figure 2: Custom trained MAGVIT [20] output after 10,000 steps training to fit
a single frame sequence. We were not able to get a MAGVIT model trained that
would overfit to a single sequence, and switched to VideoGPT to focus on our
goal of video model adaptation. Figure 3: Two different options for latent
spaces in VideoGPT to serve as inputs to our model [19]. The box on the left
labeled (1) is the output of a 3D Resnet model wihch is then fed into a
transformer before being decoded. The box on the right labeled (2) denotes the
latent space defined as the output of the pretrained transformer model. We
experimented with learning segmentation masks from each of these latent
spaces.

Like MAGVIT, VideoGPT comprises a 3D VQVAE encoder-decoder architecture with a
transformer-based sequence model operating on that latent space [19]. Unlike
MAGVIT, however, VideoGPT provides publicly available weights for a model
trained to generate videos conditioned on initial frames sampled from the BAIR
Robot Pushing dataset. We conducted some initial exploratory tests on VideoGPT
by pulling single frames from BAIR Robot Pushing videos and generating
predicted frame sequences conditioned on these initial frames. We saw
promising results (i.e. the VideoGPT pretrained model was able to generate
plausible predicted sequences from the initial frames, see [FIGURE]) and that
gave us confidence that we would be able to adapt the VideoGPT model as an
encoder for our downstream tasks. Since the pretrained VideoGPT model was
trained to generate video predictions from frames of the BAIR Robot Pushing
dataset, we created a custom hand-labeled dataset of 250 images and
segmentation masks for the BAIR Robot Pushing dataset that we would attempt to
infer from the VideoGPT latent representation.

Figure 4: Bair frame sequences generated by Video GPT conditioned on same
input image (left). credit:[19]

Figure 5: Example frame from our custom dataset with robot segmentation mask

In order to adapt VideoGPT as an encoder for downstream tasks, we had to
decide which set of logits would provide the best latent representation.
VideoGPT, like MAGVIT, is an encoder-decoder architecture with a 3D ResNet-
based encoder and decoder, and then a transformer operating on the latent
space between encoding and decoding. Because of this, we could either use the
output activations of the transformer or the ResNet output activations
directly as the input to our model. Our initial intuition was that the output
of the transformer would be a more processed representation of the input frame
and would therefore provide superior performance, but we evaluated our system
with both options. For our segmentation network, we experimented with a number
of different architectures including a linear probe, a shallow convolutional
network, a fully connected layer followed by a sequence of convolutional
layers, and a multi-head self attention layer followed by a sequence of
convolutional layers. We took our top performing decoder model from initial
tests with a frozen encoder, and we trained a model with the same decoder
architecture and a fully finetuned VideoGPT model as an encoder. We also
deployed a U-Net model as a baseline.

In order to ensure that our model was not "memorizing the dataset", we swapped
out the dataset with generated noise images paired them with segmentation
masks from the real dataset. We trained models to predict masks from noise in
order to understand the representational capacity of the decoder by itself. If
we were able to achieve non-zero IOU scores with a decoder working from
encoded noise, we would know that our dataset was too small/simple and we
would need to label more data. The output of all of our segmentation networks
was a binary mask which was intended to show the location of the robot in the
input frame.

###  2.1 Model Architecture and Training Details

In the course of developing our custom decoder module we experimented with a
number of different decoder architectures. The details of these model
architectures are as follows.

  1. 1.

Frozen 3D ResNET encoder with transfomer (pretrained from VideoGPT)

     * •

Linear probe: input dim=4x32x32, output dim=64x64, sigmoid activation

     * •

Lightweight Convolutional Decoder: Fully connected layer with output
dim=4x32x32; ReLU; 2D Convolutional layer with output dim=1x32x32 and 3x3
kernel; ReLU; 2D Transpose Convolutional Layer with output dim=64x64; sigmoid
activation

     * •

Heavyweight Convolutional Decoder: Fully connected layer with output
dim=64x64; ReLU; 4 layer convolutional encoder with output dim=4x4x512; ReLU;
4 layer convolutional decoder with output dim=64x64 and skip connections
between corresponding feature maps in encoder; sigmoid activation

  2. 2.

Frozen 3D ResNET encoder (pretrained from VideoGPT)

     * •

Linear probe: input dim=16x16x240, output dim=64x64, sigmoid activation

     * •

Lightweight Convolutional Decoder with fully connected initial layer: Fully
connected layer with output dim=16x16x240; ReLU; 2D Transpose Convolutional
layer with output dim=128x32x32 and 3x3 kernel; ReLU; 2D Transpose
Convolutional Layer with output dim=32x64x64 and 3x3 kernel; ReLU; 2D
Convolutional Layer with output dim=64x64 and 3x3 kernel; sigmoid activation

     * •

Lightweight Convolutional Decoder with multi-head attention initial layer:
eight head multi-head attention layer with output dim=16x16x240; ReLU; 2D
Transpose Convolutional layer with output dim=128x32x32 and 3x3 kernel; ReLU;
2D Transpose Convolutional Layer with output dim=32x64x64 and 3x3 kernel;
ReLU; 2D Convolutional Layer with output dim=64x64 and 3x3 kernel; sigmoid
activation

  3. 3.

Noise samples, Frozen 3D Resnet encoder with transfomer (pretrained from
VideoGPT)

     * •

Lightweight Convolutional Decoder: Fully connected layer with output
dim=4x32x32; ReLU; 2D Convolutional layer with output dim=1x32x32 and 3x3
kernel; ReLU; 2D Transpose Convolutional Layer with output dim=64x64; sigmoid
activation

  4. 4.

Finetuned 3D Resnet encoder (pretrained from VideoGPT)

     * •

Lightweight Convolutional Decoder with multi-head attention initial layer:
eight head multi-head attention layer with output dim=16x16x240; ReLU; 2D
Transpose Convolutional layer with output dim=128x32x32 and 3x3 kernel; ReLU;
2D Transpose Convolutional Layer with output dim=32x64x64 and 3x3 kernel;
ReLU; 2D Convolutional Layer with output dim=64x64 and 3x3 kernel; sigmoid
activation

##  3 Results

We defined our baseline as a UNET model given the miniature size of our self-
annotated dataset–250 self-segmented images from the BAIR dataset performed
with an IOU score of 0.83. Our best-performing model (Unfrozen 3D inflated
ResNET component of the 3D-VQVAE with a lightweight Self-Attention and
Convolutional layer decoder architecture) matched that score. Both these
models converged to a negligible training loss within 50 thousand epochs.

Model Encoder-Decoder |
---|---
Encoder | Decoder | IOU Score
Noise Input | Linear Layer + Conv. Layers | 0
Transformer Included | Linear Layer | 0.17
Transformer Included | Linear Layer + Conv. Layers | 0.225
Transformer Included | Linear Layer + UNET | 0.35
3D ResNET Included(Frozen) | Linear Layer | 0.17
3D ResNET Included(Frozen) | Linear Layer + Conv. Layers | 0.38
3D ResNET Included(Frozen) | Transformer Layer + Conv.Layer | 0.79
3D ResNET Included(Unfrozen) | Transformer Layer + Conv.Layers | 0.83*
—-Full | UNET— | 0.83(Baseline)
Table 1: Ablation Study of Model Architectures: Here Transformer Included
indicates that the encoder consists of both the 3D ResNET as well as the
Axial-Attention (Transformer) mechanism of the 3D-VQVAE. While, 3D ResNET
Included indicates that only the 3D Inflated ResNET was used the Attention
Component was not used. Frozen and Unfrozen indicate the state of the encoder
parameters while training.

Figure 6: Example outputs from our best network (finetuned Resnet with
transformer-convolutional decoder). Left: predicted masks, Center: mask
labels, Right: input images

##  4 Discussion

The dimensions of the latent space of the 3D VQVAE of the VideoGPT model were
similar to that of a convolutional encoder– BxCxHxW– which led us to initially
experiment with a simple linear layer and convolutional layers to match the
output of the self annotated masks. This specific model did end up learning a
segmentation mask which served as a proof of concept albeit the performance
was rather poor with an IOU score of 0.225. Since our dataset was rather small
we wanted to test if our 3D-VQVAE latent space was meaningful, i.e. encoded
informative representation of the image. To examine this we trained the
decoder on total noise to see whether our model could learn a segmentation
mask, the decoder model could not learn a segmentation mask and had an IOU
value of 0.0. We further attempted to add to the decoder complexity by adding
residual connections, adding more convolutional layers and even attempted to
develop a UNET-inspired decoder architecture. Beyond that we attempted several
combinations of objective loss functions –DICE loss, Positive Weighted Binary
Cross Entropy loss, and Jaccard loss– and several optimizers –SGD, ADAM, and
ADAMW. Finally, we conducted a hyperparameter sweep logging our results to
Weights and Biases and arrived at the best-performing model which was the
UNET-inspired decoder with ADAMW optimizer. Unfortunately, upon training this
model provided an IOU score of 0.35 which was far below our UNET baseline.
After this, we switched to a custom trained transformer layer instead of the
pretrained one that we had been using, and we produced much better results
which matched the performance of the UNET model.

##  5 Future Work and Conclusion

In this study, we demonstrate the effectiveness of utilizing generative
pretext learning for downstream tasks, particularly in the context of
segmentation. Initially, we harbored doubts regarding our approach of
employing generative models to capture high-level scene information, given the
visual similarity of adjacent frames in videos, which could potentially lead
the model to learn low-level representations. However, our findings proved
otherwise, as the model successfully acquired an appropriate representation of
the scene.

As part of our future work, we propose the replication of this implementation
using the encoder from the MAGVIT (Multimodal Attentional Generative Video
Inpainting Transformer) model, which is the current state-of-the-art
performance in terms of Frechet Video distance (FVD) values on several
datasets [20]. Leveraging such an encoder could further enhance the quality
and richness of learned representations, thereby improving the effectiveness
of the pretext learning approach for segmentation tasks.

Additionally, we recommend scaling up the training process by utilizing a
larger and more diverse segmentation dataset, such as COCO (Common Objects in
Context). Training on a larger dataset can facilitate the model’s ability to
generalize and capture a broader range of scene dynamics and object
interactions, ultimately leading to more robust and versatile segmentation
performance.

By incorporating these suggestions into future research endeavors, we aim to
advance the understanding and capabilities of pretext learning methods in
computer vision, paving the way for improved performance and applicability in
various real-world applications of scene analysis and segmentation.

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##  Appendix A Appendix / supplemental material

For the link to the code as well as a partial dataset used for training please
visit:
https://anonymous.4open.science/r/anonymous_VPT-5E85/