CSI

    channel state information
UE

    user equipment
UL

    uplink
BS

    basestation
TDD

    time division duplex
FDD

    frequency division duplex
ECC

    error-correcting code
MLD

    maximum likelihood decoding
HDD

    hard decision decoding
IF

    intermediate frequency
RF

    radio frequency
SDD

    soft decision decoding
NND

    neural network decoding
CNN

    convolutional neural network
ML

    maximum likelihood
GPU

    graphical processing unit
BP

    belief propagation
LTE

    Long Term Evolution
BER

    bit error rate
SNR

    signal-to-noise-ratio
ReLU

    rectified linear unit
BPSK

    binary phase shift keying
QPSK

    quadrature phase shift keying
AWGN

    additive white Gaussian noise
MSE

    mean squared error
LLR

    log-likelihood ratio
MAP

    maximum a posteriori
NVE

    normalized validation error
BCE

    binary cross-entropy
CE

    cross-entropy
BLER

    block error rate
SQR

    signal-to-quantisation-noise-ratio
MIMO

    multiple-input multiple-output
OFDM

    orthogonal frequency division multiplex
RF

    radio frequency
LOS

    line of sight
NLoS

    non-line of sight
NMSE

    normalized mean squared error
CFO

    carrier frequency offset
SFO

    sampling frequency offset
IPS

    indoor positioning system
TRIPS

    time-reversal IPS
RSSI

    received signal strength indicator
MIMO

    multiple-input multiple-output
ENoB

    effective number of bits
AGC

    automatic gain control
ADC

    analog to digital converter
ADCs

    analog to digital converters
FB

    front bandpass
FPGA

    field programmable gate array
JSDM

    Joint Spatial Division and Multiplexing
NN

    neural network
IF

    intermediate frequency
LoS

    line-of-sight
NLoS

    non-line-of-sight
DSP

    digital signal processing
AFE

    analog front end
SQNR

    signal-to-quantisation-noise-ratio
SINR

    signal-to-interference-noise-ratio
ENoB

    effective number of bits
PCB

    printed circuit board
EVM

    error vector mangnitude
CDF

    cumulative distribution function
MRC

    maximum ratio combining
MRP

    maximum ratio precoding
MRT

    maximum ratio transmission
DeepL

    deep-learning
DL

    deep learning
SISO

    single-input single-output
SGD

    stochastic gradient descent
CP

    cyclic prefix
MISO

    Multiple Input Single Output
LMMSE

    linear minimum mean square error
ZF

    zero forcing
USRP

    universal software radio peripheral
RNN

    recurrent neural network
GRU

    gated recurrent unit
LSTM

    long short-term memory
NTM

    neural turing machine
DNC

    differentiable neural computer
TCN

    temporal convolutional network
FCL

    fully connected layer
MANN

    memory augmented neural network
RNN

    recurrent neural network
DNN

    dense neural network
FIR

    finite impulse response
BPTT

    back-propagation through time
GAN

    generative adversarial network
ELU

    exponential linear unit
tanh

    hyperbolic tangent
BICM

    bit-interleaved coded modulation
OTA

    over-the-air
IM

    intensity modulation
DD

    direct detection
RL

    reinforcement learning
SDR

    software-defined radio
WGAN

    Wasserstein generative adversarial network
BMD

    bit-metric decoding
BMI

    bit-wise mutual information
LDPC

    low-density parity-check
IDD

    iterative demapping and decoding
JSD

    Jensen-Shannon divergence
MMSE

    minimum mean square error
FFT

    fast Fourier transform
IFFT

    inverse fast Fourier transform
QAM

    quadrature amplitude modulation
EMD

    earth mover’s distance
TDL

    tapped delay line
KL

    Kullback-Leibler
PRACH

    physical random access channel
URLLC

    ultra-reliable low-latency communication
ANOMA

    asynchronous non-orthogonal multiple access
FEC

    forward error correction
PAPR

    peak-to-average power ratio
APP

    a posteriori probability
COTS

    commercial off-the-shelf
PLL

    phase locked loop
STO

    sampling time offset
SFO

    sampling frequency offset
CFO

    carrier frequency offset
CPO

    carrier phase offset
CSI

    channel state information
GNSS

    global navigation satellite system
ELAA

    extremely large aperture array
UE

    user equipment
DICHASUS

     Distributed Channel Sounder by University of Stuttgart
JCAS

    Joint Communication and Sensing

# A Distributed Massive MIMO Channel Sounder for “Big CSI Data”-driven Machine
Learning

Florian Euchner, Marc Gauger, Sebastian Dörner, Stephan ten Brink
Institute of Telecommunications, Pfaffenwaldring 47, University of Stuttgart,
70569 Stuttgart, Germany
<EMAIL_ADDRESS>
###### Abstract

A distributed massive multiple-input multiple-output (MIMO) channel sounder
for acquiring large channel state information (CSI) datasets, dubbed
Distributed Channel Sounder by University of Stuttgart (DICHASUS), is
presented. The measured data has potential applications in the study of
various machine learning algorithms for user localization, Joint Communication
and Sensing (JCAS), channel charting, enabling massive MIMO in frequency
division duplex (FDD) operation, and many others. The proposed channel sounder
architecture is distinct from similar previous designs in that each individual
single-antenna receiver is completely autonomous, enabling arbitrary,
spatially distributed antenna deployments, and offering virtually unlimited
scalability in the number of antennas. Optionally, extracted channel
coefficient vectors can be tagged with ground truth position data, obtained
either through a global navigation satellite system (GNSS) receiver (for
outdoor operation) or through various indoor positioning techniques.

##  I Introduction

To study massive MIMO channels, accurate wireless channel measurements from a
multitude of receive antennas are required. Such channel measurements,
referred to as CSI, are acquired through a process known as channel sounding.
Ever since the concept of massive MIMO was first introduced, the scientific
community has placed significant effort into obtaining reliable and large CSI
datasets. Early massive MIMO channel sounding experiments have been carried
out since 2012 [1] [2] [3], followed by many more advanced channel sounders
developed by different research groups in the subsequent years [4] [5] [6].
Nowadays, real-time massive MIMO testbeds have become commercially available
[7] [8] [9], albeit at a rather expensive price point. More recently, an open
source initiative for massive MIMO development, with a channel sounder based
on hardware components from Skylark Wireless [9], was launched by a research
group at Rice University [10]. All of these channel sounders, including a
previous channel sounder developed at our institute [11], are primarily
targeted at centralized massive MIMO deployments where all receivers are
concentrated in a single antenna array.

While the idea of cell-less wireless networks is not new, in combination with
massive MIMO, the concept has seen a surge in research interest over the last
years. Research results, though only of theoretical nature, suggest that cell-
less massive MIMO, also known as distributed massive MIMO, has advantages over
network architectures based on small cells [12]. One objective of our channel
sounder, DICHASUS, is to facilitate research into various distributed antenna
deployment schemes, such as extremely large aperture arrays, where antennas
are distributed along building facades or embedded into building structures as
holographic antennas, as well as truly distributed antenna deployments across
multiple buildings.

Therefore, DICHASUS was designed with a decentralized system architecture in
mind: Rather than collecting all measurements at a central node, each receiver
acquires and stores the samples from each antenna autonomously while staying
tightly synchronized to a reference signal transmitter. This over-the-air
synchronization method not only provides the flexibility to build distributed
setups, but also enables straightforward scalability in the number of antennas
and reduces overall system set-up complexity, which allows for rapid
deployments of the channel sounder. A breakdown of the system architecture and
a simple verification experiment are presented in Sections II through VI.

Figure 1: Massive MIMO system set-up with single-antenna, mobile transmitter
(MOBTX), reference transmitter (REFTX) and one or multiple individual antennas
or antenna arrays with receivers (AARX) and USB flash storage.

Captured DICHASUS datasets, one of which is described in Section VII, are made
freely available to the scientific community111Datasets, tutorials and sample
code can be downloaded from https://dichasus.inue.uni-stuttgart.de.. In
addition to the acquired CSI, we provide accurate labels such as position
tags. In Section VIII, we demonstrate one possible application of the captured
CSI data, namely neural network (NN)-based localization.

##  II Overall System Set-up

DICHASUS covers the frequency range from 70 MHz to 6 GHz and every receiver
has an analog to digital converter (ADC) bit depth of $12\,\mathrm{bit}$. As
depicted in Fig. 1, it consists of

  1. a)

one or several groups of antenna arrays (AARX) as receivers, mimicking
distributed base stations, described in detail in Section III,

  2. b)

a reference transmitter (REFTX) for frequency, phase and timing calibration,
at a location that ensures a low-attenuation propagation path to all AARX
antennas, explained in Section IV and

  3. c)

a mobile transmitter (MOBTX) with one transmit antenna in the field, which
resembles a user equipment (UE), described in Section 6.

The MOBTX continuously transmits cyclic prefix (CP)- orthogonal frequency
division multiplex (OFDM)-modulated pilot symbols with a configurable number
of subcarriers $N_{\mathrm{sub,mob}}$ and a maximal bandwidth of 50 MHz,
enabling the extraction of CSI per subcarrier at the receiver antenna array.
Also, the transmitter can embed its position, e.g., GNSS coordinates, into the
transmit signal, making it possible to obtain CSI data together with position
tags, which can later be used for supervised machine learning. The REFTX is
placed in such a way that there is a good propagation path to each AARX
receive antenna, e.g., a direct line-of-sight path. It also transmits CP-OFDM-
based pilot signals with $N_{\mathrm{sub,ref}}=128$ subcarriers at a bandwidth
of $2\,\mathrm{MHz}$, but in a different, non-overlapping frequency range,
that is, MOBTX and REFTX are frequency-multiplexed. At all times, the AARX can
receive both the signal from the MOBTX (through the channel of interest) as
well as the signal from the REFTX. The individual single-antenna AARX
receivers operate in an autonomous fashion, i.e., without a central clock, but
with clock signals that are purely derived from each receiver’s built-in
crystal oscillator. Therefore, they rely on regular over-the-air frequency,
phase and timing calibration using the REFTX’s transmit signal, called REFTX
broadcast. While the REFTX frequency may be inaccurate in absolute terms due
to its own oscillator drift, by synchronizing every receiver to the same
frequency reference, the relative offsets between receivers disappear.

##  III Massive MIMO Receiver (AARX)

Figure 2: Photo of 64-antenna AARX array (only 32 antennas of which are
connected) on the left and autonomous AARX receivers on the right.

The AARX, shown in Fig. 2, is entirely built from comparably inexpensive
commercial off-the-shelf (COTS) hardware components. Central to the AARX are
Analog Devices’ ADALM-PLUTO software-defined radios [13] that capture raw I/Q
samples in a configurable frequency band received by the antennas. Each ADALM-
PLUTO contains a Cortex-A9 microprocessor running a Linux-based firmware, on
top of which a custom application is responsible for managing the sample
capture. This way, all real-time signal processing functions can be performed
by the receiver itself. Captured I/Q data is first transferred to the device’s
RAM, where $200\,\mathrm{MB}$ per device are allocated for sample buffering,
and later stored onto one or multiple USB storage devices attached to each
ADALM-PLUTO. While each ADALM-PLUTO is capable of capturing samples with a
bandwidth of over $50\,\mathrm{MHz}$ to RAM, tests with typical USB storage
devices show that a continuous writing speed of up to
$15\,\nicefrac{{\mathrm{MB}}}{{\mathrm{s}}}$ is realistic. Real-time 12-bit
I/Q sample capture is hence possible for capture rates of up to approximately
$5\,\mathrm{MHz}$. By, instead, only capturing short bursts, i.e., operating
with a certain duty cycle, higher bandwidths are achievable. For example, even
for a capture bandwidth of $50\,\mathrm{MHz}$, the RAM buffer can hold more
than one second of continuous I/Q samples.

All receivers are managed by a central controller, connected through Ethernet.
The central controller does not perform any signal processing, but provides a
graphical user interface through which all parameters of the data capture can
be configured. Once the process of automatic calibration and capturing has
been started, however, individual receivers can operate autonomously thanks to
the reference transmitter (REFTX) concept, making this architecture easily
scalable in the number of deployed AARX elements. In fact, since receivers
store data in a decentralized fashion on their own USB flash storage devices,
there is no need for high-speed networking for collecting data at a central
node. During the channel sounding operation, the user interface on the central
controller can be used for monitoring system parameters such as each antenna’s
signal-to-noise-ratio (SNR), buffer state or storage write speed.

Within one measurement campaign, all recordings are performed with fixed gain
configurations at all transmitters and receivers so that channel attenuations
are comparable between measurements at different points in time and space,
i.e., automatic gain control (AGC) is disabled.

##  IV REFTX and Channel Model

time [ms]0100200300400500600syncsyncI/Qcapt.I/Qcapt.I/Qcapt.$\cdots$$\cdots$
Figure 3: Typical frequency / timing synchronization and I/Q sample capture
burst schedule

With DICHASUS, multiple receivers can be deployed in a spatially distributed
manner as long as reception of the REFTX broadcast signal is ensured. The
REFTX signal is used for synchronization both in _real time_ and later in an
_off-line_ postprocessing step, compare Fig. 4. In real time, the REFTX
broadcast is used for two aspects of synchronization:

  * •

Timing synchronization: The receivers typically do not record continuously,
but in bursts, following a predefined schedule such as the one shown in Fig.
3. All receivers align this schedule to the received REFTX broadcast in time,
with an accuracy that corresponds to the duration of one I/Q sample.

  * •

Frequency synchronization: Each receiver’s sampling and local oscillator clock
are derived from an internal crystal oscillator through a phase locked loop
(PLL). By adjusting the PLL’s fractional-$n$ divider, local oscillator and
sampling clock frequencies are synchronized with the REFTX down to
approximately 0.025ppm.

Compared to off-line frequency correction, real time carrier frequency offset
(CFO) and sampling frequency offset (SFO) correction has the advantage that
SFO, the correction of which in digital processing is computationally
expensive, becomes negligible over the short capture burst duration. The
subsequent off-line postprocessing step improves synchronization by performing
even more timing offset corrections, namely:

  * •

CFO correction down to significantly less than 0.025ppm

  * •

Phase correction so that the local oscillators of all receivers after
correction can be considered to be phase-synchronous, except for the phase
shift of the mostly flat channel between REFTX and receiver.

  * •

Sub-sample sampling time offset (STO) correction so that the sampling
instances can be considered to be identical across all receivers, except for
the delay of the channel between REFTX and receiver.

This off-line synchronization is only possible due to the fact that the AARX
receivers capture and store raw I/Q samples for the complete capture
bandwidth, i.e., containing both REFTX and MOBTX signals.

Raw I/Q Sampleson USB StorageRaw I/Q Sampleson USB StorageRaw I/Q Sampleson
USB StorageRaw I/Q Sampleson USB StorageRaw I/Q Sampleson USB StorageRaw I/Q
Sampleson USB StorageAARXreal-timePhase / Freq.CalibrationChannelEstimationCSI
Storageoffline Figure 4: Massive MIMO receiver architecture: Distributed
sampling and raw data storage, centralized synchronization and analysis.
REFTX$h_{\mathrm{ref},0}$$\tau_{\mathrm{ref},0}$$h_{\mathrm{ref},1}$$\tau_{\mathrm{ref},1}$$h_{\mathrm{ref},2}$$\tau_{\mathrm{ref},2}$$h_{\mathrm{ref},3}$$\tau_{\mathrm{ref},3}$$h_{\mathrm{ref},4}$$\tau_{\mathrm{ref},4}$$h_{\mathrm{ref},5}$$\tau_{\mathrm{ref},5}$$h_{\mathrm{ref},6}$$\tau_{\mathrm{ref},6}$$h_{\mathrm{ref},7}$$\tau_{\mathrm{ref},7}$AARX
antenna elements Figure 5: Illustration of different-length line-of-sight
channels between REFTX and AARX array antenna elements for $M=8$ AARX
antennas.

The channels between REFTX antenna and the $M$ AARX antenna elements may not
all be perfectly identical, which is important to consider when performing STO
and phase correction based on the REFTX broadcast. In a distributed setup,
individual antennas may be separated by distances of several meters or more.
Even under perfect line-of-sight conditions without scatterers, if the REFTX
is not located at an equal distance to all AARX antenna elements, the
different distances between REFTX antenna and AARX antenna elements will lead
to a fixed delay $\tau_{\mathrm{ref},m}$, phase shift and path loss in the
received signal specific to antenna $m$ as illustrated in Fig. 5. After STO
correction, which removes the effect of $\tau_{\mathrm{ref},m}$, the channel
experienced by a single subcarrier is approximately frequency-flat. For
subcarrier index $i$, its effect is described only by a channel coefficient
$h_{\mathrm{ref},m,i}\in\mathbb{C}$. With transmitted and received symbols
$s_{\mathrm{ref},i}(k)\in\mathbb{C}$ and
$r_{\mathrm{ref},m,i}(k)\in\mathbb{C}$ for subcarrier $i$ at time instance
$k$, our channel model is

$r_{\mathrm{ref},m,i}(k)=h_{\mathrm{ref},m,i}~{}s_{\mathrm{ref},i}(k).$ (1)

For all antenna elements and subcarriers, the value of $h_{\mathrm{ref},m,i}$
is unknown but assumed to be constant over time $k$. In practice, this is
ensured by keeping REFTX and AARX at static positions and making sure that the
propagation environment does not change. Due to the small REFTX bandwidth of
$2\,\mathrm{MHz}$ and due to the strong propagation path between REFTX and
each AARX antenna, the channel can be assumed to be approximately flat over
all subcarriers, i.e., we assume

$h_{\mathrm{ref},m}\approx h_{\mathrm{ref},m,i}~{}\text{for all
$i=0,\ldots,N_{\mathrm{sub,ref}}-1$}.$ (2)

##  V MOBTX and Channel Coefficient Extraction

Figure 6: Exemplary channel coefficient vectors for an indoor, mostly line of
sight-channel with a few clearly visible notches. Each color represents one of
the 32 AARX receive antennas. 1024 subcarriers are equally spaced over a
bandwidth of $50\,\mathrm{MHz}$.

The channels between MOBTX and each AARX antenna fluctuate as the MOBTX moves
in the field. For the channel between MOBTX and each AARX receive antenna, we
use a channel model similar to the one in Eq. 1, except that the channel
coefficients are no longer constant, but dependent on time index $k$:

$r_{\mathrm{mob},m,i}(k)=h_{\mathrm{mob},m,i}(k)~{}s_{\mathrm{mob},i}(k)$ (3)

In Eq. 3, $s_{\mathrm{mob},i}(k)$ denotes the symbol transmitted by the MOBTX
at time instance $k$ on subcarrier $i$, $r_{\mathrm{mob},m,i}(k)$ denotes the
corresponding received symbol for the AARX antenna with index $m$ and
$h_{\mathrm{mob},m,i}(k)$ is the time-dependent channel coefficient. After the
sampled received baseband signals for each antenna have been synchronized in
time, frequency and phase during postprocessing, subcarrier-specific channel
coefficients $h_{\mathrm{mob},m,i}(k)$ can be extracted in another off-line
processing step. To this end, a perfect reconstruction of the MOBTX transmit
signal is produced. This is achieved by performing a maximal-ratio combining
of the MOBTX receive signal of all antennas and then demodulating it. Through
the use of error correction codes and checksums, the received symbols on all
OFDM subcarriers, even those that are not pilots, can be traced back to their
ideal constellation points. The effect of the channel is then computed based
on Eq. 3 with known $r_{\mathrm{mob},m,i}(k)$ and $s_{\mathrm{mob},i}(k)$, for
all antennas and all subcarriers. If the duration of each OFDM symbol is much
shorter than the channel coherence interval, multiple channel coefficient
vectors within the same coherence interval that are captured within the same
burst may be averaged to improve the SNR. The extracted CSI for a single
coherence interval, referred to as a _datapoint_ , is tagged with a timestamp
and possibly some additional labels such as the position of the MOBTX. As
illustrated in Fig. 6, the CSI for a particular time instance consists of
multiple vectors of channel coefficients, one per AARX receive antenna. For
the $m$th receive antenna, the channel coefficient vector is given by
$\mathbf{h}_{\mathrm{mob},m}\in\mathbb{C}^{N_{\mathrm{sub,mob}}}$, where the
$i$th entry, $h_{\mathrm{mob},m,i}$, contains the estimated channel
coefficient for the MOBTX subcarrier with index $i$.

The use of a reference transmitter instead of distributing clock signals has
important ramifications on the interpretation of the extracted channel
coefficient phases: All receivers are synchronized in time and phase to their
received REFTX broadcast, but, due to the different channels between REFTX and
each AARX antenna as expressed in Eq. 1, they are not necessarily synchronous
in absolute terms, i.e., in phase and sampling instances. The REFTX channel’s
phase shift leads to a constant, antenna-specific phase rotation. Moreover,
the different propagation path delays between REFTX and AARX antennas lead to
a receiver-specific STO, which manifests itself as a subcarrier-dependent
phase shift that increases or decreases linearly over the subcarrier
frequency.

However, by ensuring the propagation environment between REFTX and AARX is
static, all phase rotations remain constant and can be accounted for or even
be removed through calibration. In many applications, including precoding for
massive MIMO and CSI-fingerprinting-based positioning, phase differences
between antennas that are accurate in absolute terms are not even required, as
long as they are correct in relative terms. That is, phase offsets of
individual antennas and subcarriers caused by the REFTX propagation path need
to be constant over time and irrespective of the MOBTX position, which is the
case.

We denote the REFTX-_adjusted_ channel coefficient vector between MOBTX and
AARX antenna $m$, i.e., the true channel coefficients that are unaffected by
the channel between REFTX and AARX, by $\mathbf{a}_{\mathrm{mob},m}$.
Neglecting the propagation delay, the channel between REFTX and AARX antenna
$m$ is described by a single channel coefficient $h_{\mathrm{ref},m}$ (compare
Eq. 2), which only leads to a constant phase rotation. If $h_{\mathrm{ref},m}$
is known, the adjusted MOBTX channel coefficient vector
$\mathbf{a}_{\mathrm{mob},m}$ can be computed as

$\mathbf{a}_{\mathrm{mob},m}=\mathbf{h}_{\mathrm{mob},m}\mathrm{e}^{\mathrm{j}\arg\\{h_{\mathrm{ref},m}\\}}~{}\text{for
$\tau_{\mathrm{ref},m}\approx 0$}.$ (4)

If, as is usually the case, the propagation path delays through the REFTX
channel $\tau_{\mathrm{ref},m}$ are not negligible, the effect of a constant
STO relative to other AARX receivers also has to be accounted for. For small
STO values and narrow subcarrier spacing $\Delta f_{\mathrm{sub,mob}}$, if
$\tau_{\mathrm{ref},m}$ is known, the effect of STO can be accounted for by
undoing the phase shift it causes to subcarrier $i$ with
$i=0,\ldots,N_{\mathrm{sub,mob}}-1$:

$a_{\mathrm{mob},m,i}=h_{\mathrm{mob},m,i}~{}\mathrm{e}^{\mathrm{j}(\arg\\{h_{\mathrm{ref},m}\\}+2\pi
i\tau_{\mathrm{ref},m}\Delta f_{\mathrm{sub,mob}})}$ (5)

On the other hand, the amplitudes of the coefficients
$\mathbf{h}_{\mathrm{mob},m}$ are not influenced by the REFTX propagation
path, because measuring them does not require timing synchronization. In our
datasets, all channel coefficient amplitudes are provided relative to an
arbitrary, but constant reference amplitude level that is specific to each
measurement campaign.

##  VI Verification: Phase Stability

We carried out a set of experiments to verify that the proposed and
implemented system architecture provides accurate and repeatable measurement
results. One particularly insightful experiment demonstrates long-term phase
stability and repeatability of CSI measurements. For this experiment, a MOBTX
center frequency of $1.27\,\mathrm{GHz}$ with a bandwidth of $8\,\mathrm{MHz}$
and $N_{\mathrm{sub,mob}}=1024$ subcarriers was chosen and the REFTX operated
at $1.262\,\mathrm{GHz}$.

For a small-scale indoor test setup, the delay spread between multiple
propagation paths is very small and the path delay between MOBTX and $m$th
AARX antenna element is assumed to only lead to a phase shift. According to
the channel model given in Eq. 3, this phase shift is dependent on the
subcarrier index $i$. For illustration purposes, we averaged the phases of all
subcarriers, resulting in an average phase shift $\vartheta_{m}(k)$ perceived
by the $m$th antenna at time index k, given by

$\vartheta_{m}(k)=\arg\left\\{\sum_{i=0}^{N_{\mathrm{sub,mob}}-1}h_{\mathrm{mob},m,i}(k)\right\\}.$
(6)

The measured average phases $\vartheta_{m}(k)$ of 17 out of 32 antennas, as a
function of time elapsed since the start of the experiment, are shown in Fig.
7. In the beginning of the experiment, the MOBTX together with the REFTX and a
single, concentrated 32-antenna array as AARX were placed in a static
environment (a seminar room). The initial MOBTX placement is referred to as
_Position A_. Channel measurements are acquired continuously throughout the
experiment. After $50\,\mathrm{s}$ of waiting, the MOBTX is moved to a
different position in the same room, referred to as _Position B_. In Fig. 7,
the change in received MOBTX phases is clearly visible. After approximately
$30\,\mathrm{s}$ at this new position, the MOBTX is returned to its original
location, Position A. As can be observed from Fig. 7, all phases return to
their original value, illustrating repeatability and spatial consistency of
the set-up.

050100150$-$3$-$2$-$10123MOBTX moved to pos. BMOBTX moved back to pos. Atime
[s]relative phase $\vartheta_{m}$ [rad] Figure 7: Relative phases
$\vartheta_{0},\ldots,\vartheta_{16}$ from 17 (out of 32) antennas as measured
in the experiment, plotted over time, verifying stability and spatial
consistency. The other 15 antennas exhibited similar behavior and are only
omitted as to not overload the diagram with too many colors.

##  VII Dataset Description

At the point of writing, several datasets, measured in both indoor and outdoor
environments, have been collected using DICHASUS. As an example that conveys
what a typical dataset looks like, some characteristics of one particular
indoor dataset will be outlined in the following. This dataset, called
dichasus-015x, was collected using a robot, on top of which the MOBTX was
mounted. The robot was programmed to drive along a meandering path inside
certain areas of the room, while CSI was acquired by the AARX. This procedure
was repeated multiple times, resulting in CSI datasets for multiple _round
trips_ of the robot, with a duration of 10 to 20 minutes each. Channel
coefficients from $N_{\mathrm{sub,mob}}=1024$ subcarriers, spanning a
bandwidth of $50\,\mathrm{MHz}$, were acquired. In total, CSI was collected
over a duration of $5467\,\mathrm{s}$ amounting to 77607 datapoints or
$20.4\,\mathrm{GB}$ of uncompressed, single precision complex floating point
numbers. On average, more than 14 datapoints were collected per second with
each datapoint containing channel coefficients averaged over complete capture
bursts containing 90 MOBTX symbols. In addition to the channel coefficients,
each datapoint is tagged with two MOBTX antenna position labels, one derived
from a LiDAR that is part of the robot and one generated by a tachymeter
tracking the antenna, as well as a timestamp, SNR and CFO information.

##  VIII Verification: NN-based Positioning

FlattenDenseDenseDenseDense$\left[\,\overline{h}_{\mathrm{mob},m,\ell}\,\right]_{m,\ell}\in\mathbb{C}^{32\times
64}$$(\hat{x},\hat{y})$$\left[\,\overline{P}_{\mathrm{mob},\ell}\big{|}_{\mathrm{Np}}\,\right]_{\ell}\in\mathbb{R}^{64}$$32\times
64\times 2$$4096$$512$$128$$128$$2$$64$

Figure 8: Architecture of the NN used for CSI-based MOBTX localization.

In another experiment, we verified that CSI and ground truth labels are
suitable for a practical application based on CSI data, namely CSI-based
positioning using NNs. We apply multiple robot round trips of aforementioned
dichasus-015x dataset to this task. As a network architecture, the simple NN
with four dense layers shown in Fig. 8 is used. We do not provide the channel
coefficients for all 1024 subcarriers directly to the network, but only
features derived from them, which are computed in a feature extraction stage.
These features are:

  * •

Mean normalized channel coefficients: For each antenna $m=0,\ldots,M-1$, the
channel coefficients of $p$ adjacent subcarriers are summed and then
normalized over all antennas $n=0,\ldots,M-1$. We obtain averaged, normalized
channel coefficients with
$\ell=0,\ldots,\nicefrac{{N_{\mathrm{sub,mob}}}}{{p}}-1$:

$\overline{h}_{\mathrm{mob},m,\ell}=\frac{\sum_{i=p\ell}^{p\ell+p-1}h_{\mathrm{mob},m,i}}{\sqrt{\sum_{n=0}^{M-1}\left|\sum_{i=p\ell}^{p\ell+p-1}h_{\mathrm{mob},n,i}\right|^{2}}}$
(7)

The normalization ensures that
$\sum_{m=0}^{M-1}|\overline{h}_{\mathrm{mob},m,\ell}|^{2}=1~{}\forall\ell$. As
the numeric values of channel coefficients span several orders of magnitude
for typical radio environments, this input normalization greatly improves NN
performance.

  * •

Subcarrier powers: The mean power over all antennas of the averaged channel
coefficients before the normalization in Eq. 7 in logarithmic units:

$\overline{P}_{\mathrm{mob},\ell}\big{|}_{\mathrm{Np}}=\mathop{\mathrm{ln}}\left(\sum_{m=0}^{M-1}\left|\sum_{i=p\ell}^{p\ell+p-1}h_{\mathrm{mob},m,i}\right|^{2}\right)$

The intention of providing these power values is to give the network an
indication of the distance between MOBTX and AARX.

We choose $p=16$, yielding $\nicefrac{{N_{\mathrm{sub,mob}}}}{{p}}=64$
averaged normalized channel coefficients for our dataset with 1024
subcarriers. Since we provide the real and imaginary parts of
$\overline{h}_{\mathrm{mob},m,\ell}\in\mathbb{C}$ for all $M=32$ antennas
separately to the NN, the averaged normalized channel coefficient input
tensor’s dimensionality is
$M\times\nicefrac{{N_{\mathrm{sub,mob}}}}{{p}}\times 2$.

$-6$$-4$$-2$$0$$-2$$0$$2$$x$-coordinate [m]$y$-coordinate
[m]$0$$0.1$$0.2$$0.3$$0.4$$0.5$Error [m] Figure 9: Absolute localization error
for an exemplary dataset with concentrated AARX antenna array (black
rectangle) at position $(x,y)=(0,0)$.

Training is performed on a training set that contains all datapoints from two
complete round trips, with batch sizes 32, 64, 256, 1024 and 4096 and 20
epochs per batch size. The trained network then estimates positions based on
CSI from a third round trip, our test set. While the robot always stays inside
the same part of the room during every round trip, it may drive along a
different path, hence the visited locations from one round trip do not
precisely match those from previous trips. By training and evaluating on
different robot round trips, the network is presented inputs from positions in
the room that it has never seen before during training. Fig. 9 illustrates the
quality of the position estimates $(\hat{x},\hat{y})$ generated by the NN for
the outlined scenario. Over the complete test set, we achieve a mean absolute
error of less than $0.2\,\mathrm{m}$.

##  IX Summary and Outlook

The system architecture of a distributed massive MIMO channel sounder with
over-the-air synchronization, suitable for researching cell-less massive MIMO
systems and various antenna deployments, has been presented. To verify the
suitability of our approach, first captured datasets have been generated and
analyzed. The captured datasets can be used to tackle open research questions
in a variety of domains and to empirically verify theoretical results.

Two particularly interesting applications are channel charting [14] and
enabling massive MIMO in FDD operation [15]. CSI captured by DICHASUS may be
used to verify results previously only obtained through simulations with real-
world measurement data.

## References

  * [1] X. Xie, E. Chai, X. Zhang, K. Sundaresan, A. Khojastepour, and S. Rangarajan, “Hekaton: Efficient and practical large-scale MIMO,” in _Proceedings of the 21st Annual International Conference on Mobile Computing and Networking_ , 2015, pp. 304–316.
  * [2] C. Shepard, H. Yu, N. Anand, E. Li, T. Marzetta, R. Yang, and L. Zhong, “Argos: Practical many-antenna base stations,” in _Proceedings of the 18th annual international conference on Mobile computing and networking_ , 2012, pp. 53–64.
  * [3] S. Malkowsky, J. Vieira, L. Liu, P. Harris, K. Nieman, N. Kundargi, I. C. Wong, F. Tufvesson, V. Öwall, and O. Edfors, “The world’s first real-time testbed for massive MIMO: Design, implementation, and validation,” _IEEE Access_ , vol. 5, pp. 9073–9088, 2017.
  * [4] P. Harris, W. B. Hasan, S. Malkowsky, J. Vieira, S. Zhang, M. Beach, L. Liu, E. Mellios, A. Nix, S. Armour _et al._ , “Serving 22 users in real-time with a 128-antenna massive MIMO testbed,” in _2016 IEEE International Workshop on Signal Processing Systems (SiPS)_. IEEE, 2016, pp. 266–272.
  * [5] J. Vieira, S. Malkowsky, K. Nieman, Z. Miers, N. Kundargi, L. Liu, I. Wong, V. Öwall, O. Edfors, and F. Tufvesson, “A flexible 100-antenna testbed for massive MIMO,” in _2014 IEEE Globecom Workshops (GC Wkshps)_. IEEE, 2014, pp. 287–293.
  * [6] X. Jiang, F. Kaltenberger, R. Knopp, and H. Maatallah, “OpenAirInterface massive MIMO testbed: A 5G innovation platform,” in _Proceedings of the 21st International ITG Workshop Smart Antennas, Berlin, Germany_ , 2017, pp. 15–17.
  * [7] Nutaq. (2015) 5G Massive MIMO Testbed. [Online]. Available: https://nutaq.com/5g-massive-mimo-testbed
  * [8] NI. What Is the MIMO Prototyping System? [Online]. Available: https://www.ni.com/de-de/shop/wireless-design-test/what-is-the-mimo-prototyping-system.html
  * [9] Skylark wireless. [Online]. Available: https://skylarkwireless.com/products/research/
  * [10] (2019) RENEW: Reconfigurable Eco-system for Next-generation End-to-end Wireless. [Online]. Available: https://renew.rice.edu/
  * [11] M. Arnold, J. Hoydis, and S. ten Brink, “Novel massive MIMO channel sounding data applied to deep learning-based indoor positioning,” in _SCC 2019; 12th International ITG Conference on Systems, Communications and Coding_. VDE, 2019, pp. 1–6.
  * [12] H. Q. Ngo, A. Ashikhmin, H. Yang, E. G. Larsson, and T. L. Marzetta, “Cell-free massive MIMO versus small cells,” _IEEE Transactions on Wireless Communications_ , vol. 16, no. 3, pp. 1834–1850, 2017.
  * [13] _ADALM-PLUTO SDR Active Learning Module_ , Analog Devices. [Online]. Available: https://www.analog.com/media/en/news-marketing-collateral/product-highlight/ADALM-PLUTO-Product-Highlight.pdf
  * [14] C. Studer, S. Medjkouh, E. Gönültas, T. Goldstein, and O. Tirkkonen, “Channel Charting: Locating Users within the Radio Environment using Channel State Information,” _CoRR_ , vol. abs/1807.05247, 2018. [Online]. Available: http://arxiv.org/abs/1807.05247
  * [15] M. Arnold, S. Dörner, S. Cammerer, S. Yan, J. Hoydis, and S. ten Brink, “Enabling FDD massive MIMO through deep learning-based channel prediction,” _arXiv preprint arXiv:1901.03664_ , 2019.

  *[MIMO]: multiple-input multiple-output
  *[CSI]: channel state information
  *[DICHASUS]: Distributed Channel Sounder by University of Stuttgart
  *[JCAS]: Joint Communication and Sensing
  *[FDD]: frequency division duplex
  *[GNSS]: global navigation satellite system
  *[NN]: neural network
  *[ADC]: analog to digital converter
  *[UE]: user equipment
  *[CP]: cyclic prefix
  *[OFDM]: orthogonal frequency division multiplex
  *[COTS]: commercial off-the-shelf
  *[SNR]: signal-to-noise-ratio
  *[AGC]: automatic gain control
  *[PLL]: phase locked loop
  *[CFO]: carrier frequency offset
  *[SFO]: sampling frequency offset
  *[STO]: sampling time offset
  *[NNs]: neural network