# Implementation and Performance Analysis of a Low Resolution OFDM System
Prototype With Low Cost Hardware

Eder O. de Souza, João T. Dias, Demerson N. Gonçalves Eder O. de Souza (ORCID:
0009-0001-8733-2854; e-mail: eder.souza@aluno.cefet-rj.br), João T. Dias
(ORCID: 0000-0001-9391-9830; e-mail<EMAIL_ADDRESS>and Demerson N.
Gonçalves(ORCID: 0000-0001-9130-7363; e-mail<EMAIL_ADDRESS>are with Federal Center for Technological Education of Rio de Janeiro
(CEFET/RJ).Digital Object Identifier: 10.14209/jcis.2023.17

###### Abstract

The present work focus on the implementation and analyze of performance of a
low-resolution OFDM system prototype with low-cost hardware. A software
defined radio (SDR) system was chosen in this implementation due to its
various advantages over a traditional radio system. Among the options of SDR
devices available, the use of universal software radio peripherals (USRP) was
avoided due to its high cost, despite its popularity in this field of
research. Alternatively, a combination of two low-cost SDRs, “Hackrf One” and
“RTL-SDR Blog V3” with the GNU Radio, a popular, free and open source radio
software, were used. Thus, it was possible to emulate the behavior of a low
resolution ADC in the receiver, characterize its performance and estimate its
energy savings. This allowed us to determine the feasibility of building a
component with the analog-to-digital conversion function with few bits of
resolution. We conclude that the performance of an ADC with at least 5 bits of
resolution is pretty reasonable and that this reduction in the number of bits,
in comparison to 8-bit ADC, represents a fairly expressive energy saving.

###### Index Terms:

SDR, USRP, GNU Radio, HackRF One, RTL-SDR, OFDM.

##  I Introduction

New applications of low latency, high connection density and ubiquitous
connectivity are present in various services of 5G networks, among them we can
highlight the internet of things (IoT), autonomous vehicles, telemedicine and
industry $4.0$. These applications require an efficient and flexible
communication system, since the characteristics of the physical (PHY) and
medium access (MAC) layers in a network architecture model (like OSI and
TCP/IP) affect the overall performance of the system in terms of energy
efficiency, spectral efficiency, achievable throughput, quality of service
(QoS), etc. [1].

An important factor in regard to energy efficiency aspect is the analog-to-
digital converter (ADC) resolution, once the energy consumption is
proportional to the number of bits [2]. In this sense, some works have been
take into account the power consumption mitigation provided by low resolution
ADCs in potential 5G technologies [3], [4].In Reference [3], an algorithm for
channel estimation in broadband millimeter wave multiple input multiple output
(MIMO) systems with few-bits ADCs is proposed and simulation results are
presented, while in [4], important issues of systems relying on low-resolution
ADCs are discussed. Other works are dedicated to show practical results by
means of prototyping, usually with the use of SDRs. Both References [5] and
[6] are examples of such strategy, while [5] introduces a architecture that
can interface different antennas to a SDR, [6] proposes a SDR platform for
transmission and acquisition of wideband signals. In Reference [7], the
authors implemented the IEEE 802.11ah (Wi-Fi HaLow) standard, an extension of
the Wi-Fi protocol focused on providing IoT-like connectivity on midrange
sites (up to 1 km), simulation and experimental measurements towards
evaluating the performance and limitations in interference and noise
environments. Although these works show practical results, they lack the
addressing of low resolution ADCs.

The flexibility offered by SDRs make them capable of prototyping very diverse
communication technologies. Their category may range from low complexity/low
cost to very advanced and expensive equipment. Perhaps the most popular ones,
in terms of paper publications, are the USRP models from National
Instruments/Ettus Research. Conversely, a low cost alternative is the HackRF
One, which is popular among hobbyists but with very fewer related
publications. The References [8] and [9] are some examples of works based on
this device, they address long range (LoRa) collision decoding and the peak-
to-average power ratio (PAPR) reduction, respectively. However, once again,
the ADC issue is not considered.

Finally, [10] focuses on both algorithm design and system implementation in
the field of low-resolution quantization communication. The work reports the
construction of a proof-of-concept prototyping system used to conduct over-
the-air (OTA) tests, but, overall, expensive hardware is applied. A summary of
the topics discussed is shown in Table I, where is notable that none of them
meet the combination of prototyping, low cost hardware and low resolution ADC.
That combination of factors is exactly what this work proposes, by the
implementation of a prototyping system in order to emulate and analyse the
performance of a low resolution ADC.

TABLE I: Works comparison summary.

Work | Simulation | Prototyping | Low cost hardware | Low resolution ADC
---|---|---|---|---
Mo et al. [3] | Yes | No | No | Yes
Zhang et al. [4] | Yes | No | No | Yes
Gaber et al. [5] | No | Yes | No | No
Diouf et al. [6] | No | Yes | No | No
Nervis et al. [7] | Yes | Yes | No | No
Chen et al. [8] | No | Yes | Yes | No
Ishkaev et al. [9] | No | Yes | Yes | No
Wang et al. [10] | No | Yes | No | Yes
Proposed system | Yes | Yes | Yes | Yes

Preliminary studies of this research were presented in References [11] and
[12]. In this work, we show the feasibility of implementing an actual low-
resolution ADC and also supports further investigations in future works. The
rest of the work is divided as follows: the OFDM communication system model is
presented in Section II; Section III presents the development of this model
and a brief description of the implemented quantizer; in Section IV, some
performance results of the prototyping performed are presented; in Section V
the conclusions of the work are made.

##  II Q-OFDM

The block diagram of the proposed quantized OFDM (Q-OFDM) system is shown in
Fig.1. In this system, $b$ is the bit to be transmitted, $s$ is the frequency
domain data symbols, $x$ is the time domain data samples, $y$ is the time
domain received signal, $y_{q}$ is the quantized signal , $\hat{s}$ is the
received signal in the frequency domain and $\hat{b}$ are the estimated bits.

The preamble is the size of an OFDM symbol and it is inserted before the data
sequence. The receiver knows the preamble and uses this information to
synchronize the beginning of the data symbols, correct phase and frequency
deviations, as well as perform the first channel estimation.

Figure 1: Block diagram of the proposed Q-OFDM system.

The OFDM is a multicarrier modulation scheme based on dividing the serial data
stream into parallel groups of streams that are transmitted on orthogonal
subcarriers. When an OFDM signal crosses a time-dispersive or frequency-
selective channel, the subcarriers are only affected by a constant or
frequency flat channel. In this type of channel, the signal can be distorted
by intersymbolic interference (ISI). This problem is solved in OFDM by
inserting a copy of the last part of the symbol, also known as a cyclic prefix
(CP), at the beginning to absorb the channel delay spreads. The OFDM signal
can be expressed in the time domain by [13]

$\it{x}[n]=\displaystyle\sum_{k=0}^{K-1}\it{s}_{k}e^{j2\pi\frac{k}{K}n},$ (1)

where $\it{s}_{k}$ is the data symbol on the $k$-th subcarrier and $K$ is the
number of subcarriers in the OFDM symbol.

The signal at the receiver input can be written by

$\it{\mathbf{y}}=\it{\mathbf{x}}*\it{\mathbf{h}}+\it{\mathbf{\omega}},$ (2)

where $\it{\mathbf{y}}\in\mathbb{C}^{(K+CP+N_{p}-1)\times 1}$, $CP$ is the
length of the cyclic prefix, and $N_{p}$ is the number of paths considered in
the channel, $\it{\mathbf{x}}\in\mathbb{C}^{(K+CP)\times 1}$,
$\it{\mathbf{h}}\in\mathbb{C}^{(N_{p})\times(1)}$ is the channel impulse
response, $*$ is the convolution operation, and
$\it{\mathbf{\omega}}\in\mathbb{C}^{(K+CP+N_{p}-1)\times 1}$ is additive white
Gaussian noise (AWGN).

###  II-A Low resolution ADC

In this section, the low resolution ADC considered in this work and its main
characteristics will be described. The choice of the linear quantizer Mid-
Riser is due to its wide use, easy implementation and good performance [14].
This quantizer divides the signal to be mapped into equidistant quantization
levels, with a step size $\Delta$ and total number of quantization levels
($V$) given by $V=2^{\flat}$, where $\flat$ is the number of quantization bits
used in the ADC. For uniform and symmetric Mid-Riser quantizers, the quantizer
output levels are given by the equation

$v_{i}=\frac{-V\Delta}{2}+(i-\frac{1}{2})\Delta.$ (3)

The quantizer input limits are defined by $\tau_{1}=-\infty$,
$\tau_{L+1}=\infty$ and $\tau_{i}=v_{i}+\frac{\Delta}{2}$, for $i=2,3,...,V$
[14]. Therefore, for a discrete input signal $y$, the characterization of this
quantizer is given by the Eq. ( 4) and illustrated in Fig. 2.

$Q(y[n])=\begin{cases}v_{1},&y\leq\tau_{1},\\\
v_{i},&\tau_{i-1}<y\leq\tau_{i},\\\ v_{L},&y>\tau_{L+1}.\end{cases}$ (4)

Figure 2: Characterization of the uniform and symmetrical Mid-Riser quantizer.

The signal after the quantizer will take the form

$\it{\mathbf{y}}_{q}=\mathcal{Q}_{c}(\it{\mathbf{y}}),$ (5)

where $\mathcal{Q}_{c}(.)$ denotes the elementary complex-valued quantizer
mapping function, which comprises two parallel real-valued quantizers
$\mathcal{Q}(.)$ that independently quantize the real and imaginary parts of
each analog input sample [15].

The received signal in the frequency domain can be written as

$\it{\mathbf{\hat{s}}}=g(\mathbf{F}\it{\mathbf{y}}_{q}),$ (6)

where $\mathbf{F}$ is the discrete Fourier transform (DFT), a unitary matrix
of dimension $K\times K$ and $g(.)$ is the function of the equalizer.

Due to the fact that the decision feedback equalizer (DFE) is native to the
OFDM library in GNU Radio [16] and the objective is to observe in the MatLab
simulation the behavior of the bit error rate (BER) that must be found in the
prototyping, the OFDM system was simulated with the same DFE equalizer present
in the GNU Radio library, that is, the simple DFE (SDFE).

In the SDFE, for each symbol $t$ and for each subcarrier $k$ in each symbol,
if it is a pilot carrier then we update the channel state for $k$ to be

$\it{H[k]}=\alpha\it{\hat{H}[k]}+(1-\alpha)\frac{\hat{s}_{t,k}}{p_{k}},$ (7)

where $\it{H[k]}$ is the frequency response of the channel, $\alpha$ is a
parameter normally set to $0.1$, $\it{\hat{H}[k]}$ is a channel response
estimation obtained and applied in the forward filter, ${p_{k}}$ is the pilot
symbol corresponding to the $k$th index, and $\hat{s}_{t,k}$ is the estimated
received symbol. The expression $(1-\alpha)\frac{\hat{s}_{t,k}}{p_{k}}$ is
obtained and applied in the feedback filter.

If the subcarrier is not a pilot subcarrier, then we update the channel in a
similar way. First, let the equalized symbol just be
$\frac{\bar{s}_{t,k}}{\it{H_{t}[k]}}$, where $\bar{s}_{t,k}$ is the received
symbol after the FFT and before the equalizer. Next, we use the constellation
mapper to essentially “snap” the complex item to a complex item that we know.
Now that we know what this symbol really was (the decision), we can use this
feedback to update our channel slightly, via the same equation above, Eq.(7),
just using the snapped complex number instead of the pilot symbol. The Fig. 3
shows the simplified diagram of SDFE.

Figure 3: Simplified diagram of SDFE.

We believe that the choice of GNU Radio for the DFE equalizer is due to two
disadvantages for OFDM systems free of intercarrier and intersymbol
interference. First, a longer guard interval than the delay channel has to use
in each OFDM symbol period, thus resulting in a considerable loss in bandwidth
utilization efficiency. Second, FFT-based demodulation methods, although
computationally simple, do not use enough statistics for channel equalization,
which degrades performance [17].

##  III Q-OFDM system prototyping with SDRs

Here we discuss the details of the implementation of our prototype system. In
order to better organize the information we divided this section into three
subsections: characteristics of the hardware [III-A], development of the low
resolution ADC block [III-B] and, finally, the description of the transmitter
and receiver projects [III-C].

###  III-A Hardware used

The SDRs devices selected for this work were the HackRF One [18] and the RTL-
SDR Blog V3 [19]. Some information about these devices is shown in the Table
II, where we notice that there is a window of compatibility between the SDRs
in relation to the values of the operating frequency and the sampling rate.
The chosen sampling rate was $1.8\,\mbox{MS/s}$ (Mega Samples/seconds) and the
chosen operating frequency was dependent on the antennas.

TABLE II: Basic characteristics of the SDRs

| HackRF One | RTL-SDR Blog V3
---|---|---
Communication | half duplex | simplex reception
Operating frequency | 1 MHz - 6 GHz | 500 kHz - 1766 MHz
Converter resolution | A/D - 8 bits | A/D - 8 bits
D/A - 8 bits
Sample rate | 20 MS/s | 2.4 MS/s

The antennas used in the transmitter and receiver were both simple monopole
telescopic antennas with SMA connector. In the case of HackRF One, which acted
as the transmitter, in addition to the antenna, a DC-Blocker was also used, in
order to provide a purely AC signal to the antenna.

The performance of the chosen antenna was characterized in the range from
$350$ to $450\,\mbox{MHz}$ using the NanoVNA-H Rev3.6 [20], a cheap Vector
Network Analyzer. And by using the NanoVNASaver [21], a software tool for the
NanoVNA, we saved a Touchstone file, analyzed the data and plotted the Smith
chart and the VSWR graph, shown in the Fig. 4 and Fig. 5, respectively. Based
on this analysis we decided that $410\,\mbox{MHz}$ was good operating
frequency for our prototype, because in this frequency the antenna yields the
minimum VSWR value ($1.238$) and has an impedance that is close enough to the
input impedance of both SDR devices ($50\,\Omega$).

$0.2$$0.5$$1$$2$$5$$0$$0.2$$0.5$$1$$2$$5$$-0.2$$-0.5$$-1$$-2$$-5$$1.17-j0.157$@$410\,\mbox{MHz}$Antenna
Impedance Figure 4: Smith chart - antenna analysis between $350$ and
$450\,\mbox{MHz}$.
$340$$360$$380$$400$$420$$440$$460$$1.5$$2$$2.5$$1.238$@$410\,\mbox{MHz}$frequency
[MHz]VSWRAntenna VSWR Figure 5: VSWR graph - antenna analysis between $350$
and $450\,\mbox{MHz}$.

The notebooks used in this work were the CCE Win T54P+, which combined with
the HackRF One formed the transmitter SDR system; and the Lenovo idepad 310 -
14ISK notebook, which combined with the RTL-SDR Blog V3 formed the receiver
SDR system. The Table III summarizes some basic technical characteristics of
both computers. The version 3.10 of GNU Radio was installed in both of them.

TABLE III: Specifications of computers used

Notebook 1 | CCE Win T54P+
---|---
CPU | processor | Intel® CoreTM i5 M 450
cores | 4
frequency | 2,4 GHz
RAM | (2$\times$) 2 GB DDR3 - 1333 MHz SODIMM
Operating System | Ubuntu 22.04.2 LTS
Notebook 2 | Lenovo idepad 310 - 14ISK
CPU | processor | Intel® CoreTM i3-6100U
cores | 4
frequency | 2,3 GHz
RAM | 4 GB DDR4 - 2133 MHz SODIMM
Operating System | Ubuntu 22.04.2 LTS

The Fig. 6 shows the complete setup of the prototype system. The transmitter
SDR was placed on the left side and the receiver SDR on the right side, with a
distance of 1 m between the antennas.

Figure 6: SDR system prototype setup.

###  III-B Low resolution ADC block

The Fig. 7 shows the GNU Radio Companion (GRC) project of the low resolution
ADC block implemented by the authors.

Figure 7: Low resolution ADC block diagram.

Note that this block is actually composed by others blocks, which the GNU
Radio documentation classifies as a “Hierarchical Block” [22]. The signal flow
passes through two main blocks: the “Root Raised Cosine Filter”, which has the
function of simulating a DA conversion; and the “Quantizer”, that quantizes
the signal. The latter was created by the authors from an “Embedded Python
Block” [23], a special type of GNU Radio block that allows the user to
customize it through a Python script.

Thus, the low resolution ADC block was available locally in the GRC library
under the name of “Low Resolution Converter” and was used in the receiver
design with different resolution bits.

###  III-C Transmitter and receiver designs

The GNU Radio code and projects used in this work are publicly available on
the GitHub platform [24]. The transmitter design is shown in Fig. 8. Specific
blocks are used for each stage of an OFDM transmission and, on purpose, the
resource of an error correcting code is not used. The interface with HackRF
One is done through the “osmocom Sink” block.

The transmission consisted of sending 10 randomly generated binary files of
$50\,\mbox{B}$ each for every noise level increment at the receiver side. In
the reception, each received file had a size of $15\,\mbox{kB}$, which means
$300$ repetitions of the transmitted file. To calculate the BER of each noise
level we first calculated the BER related to each of the $10$ files of that
specific level and then we averaged the results. This process, repeated at
various noise levels.

Figure 8: Block diagram of transmitter.

The Fig. 9 shows the receiver design and configuration that allows the
collection of data from three distinct events: the average signal power, the
low resolution ADC performance estimation and the receiver SDR performance.
The information regarding the average signal power is given by the “Probe Avg
Mag^2” block [25]. The “Low Resolution Converter” block emulates the behavior
of an ADC with variable bit resolution. By disabling it from the project it is
possible to collect data directly from the RTL-SDR’s 8-bit ADC. Similar to the
transmitter design, specific blocks are used for each stage of an OFDM
reception with the omission of an error correction and the interface with the
SDR done by the “osmocom Source” block. Furthermore, there was also the
addition of the Gaussian noise, through the “Noise Source” block, to provide
different levels of signal to noise ratio (SNR).

Figure 9: Block diagram of receiver.

Thus, knowing the noise levels and the average power of the signal it was
possible to calculate the SNR and the survey of the BER curves shown in
Section IV. The measurements were performed with a distance of 1 meter between
the antennas.

##  IV Results

First, to evaluate the impact of the number of quantizer bits on the power
consumption of the ADC, the power consumption curve per number of quantization
bits was drawn up. To this end, the expression described in [26] was used,
which lists the energy consumed by an ADC in relation to the number of
resolution bits:

$P_{ADC}=cf_{s}2^{\flat},$ (8)

where $\flat$ represents the number of bits of resolution, $c$ is a constant
associated with the noise merit figure, and $f_{s}$ is the sampling rate.

This simulation was carried out with $f_{s}=1.8$ MHz and $c=496$ fJ/conv-step
(Fento Joule / conversion-step) [27]. As we can see in Fig. 10, the impact of
power consumption is more significant when the number of bits is greater than
$5$ bits.

$2$$4$$6$$8$$0$$0.5$$1$$1.5$$2$$2.5$$\cdot 10^{-4}$Number of quantization
bitsADC power consumption [W/conv-step]

Figure 10: ADC power consumption as a function of the number of quantizer
bits.

In order to validate the proposed system and analyze its performance by
varying the number of bits, BER curves were initially created by simulation in
MatLab considering the parameters shown in the Table IV:

TABLE IV: Simulation parameters. number of subcarriers [K] | 64
---|---
subcarrier modulation | QPSK
preamble modulation | BPSK
cyclic prefix length in number of subcarriers | 16
number of quantization bits [$\flat$] | 1 to 8
Equalizer | SDFE

To choose the channel model used in the simulation, all multipath channel
models presented in Annex $4$ of the ITU-R BT.2035 [28] document, for the
scenario in question, were analyzed and we came to the conclusion that the
model that presented the characteristics closest to those we had in our
laboratory was an adaptation with the first 4 taps of the ”Brazil D” model,
which is described in the Table V.

TABLE V: Channel Brazil D. Delay [$\mu$s] | $0.15$ | $0.63$ | $2.22$ | $3.05$
---|---|---|---|---
Attenuation [dB] | $0.1$ | $3.8$ | $2.6$ | $1.3$

The Fig. 11 shows the performance of the BER as a function of the SNR in the
MatLab simulation.

$0$$10$$20$$30$$10^{-2}$$10^{-1}$SNR
[dB]BER1-bit2-bit3-bit4-bit5-bit6-bit7-bit8-bit

Figure 11: BER performance with the number of quantization bits ranging from 1
to 8.

The satisfactory results of the simulation motivated the realization of
practical tests with hardware, that is, with the prototype based on SDRs.

The results of our prototype system are shown in the Fig. 12, where the
performance of the receiver SDR is indicated by the “Hardware” curve and the
other curves are results for different resolution bits in the “Low Resolution
Converter” block of the receiver project, which is indicated in the graph
legend by the term “LRC” followed by the number of bits used in each
measurement.

Due to the fact that the 1 and 2 bit resolution curves present very poor BER
performance and generate a plateau with a very high BER value during the
simulation with MatLab, Fig.11, they were not considered in our tests with the
prototype.

As the MatLab simulation results show that the 6, 7 and 8 bit resolution
curves present overlapping in the BER performance, Fig.11, and these cases
imply greater energy consumption, as we see in fig.10, in addition to the fact
that we observed overrun problems for resolutions greater than 5 bits in
several tests carried out. For these reasons, we removed 6, 7 and 8 bit
resolutions curves from our analysis.

As described in the session III-C, to generate the curves were sent bursts of
10 randomly generated binary files of $50\,\mbox{B}$ each for every noise
level increment at the receiver side. In the reception side, for each received
burst, an frame of size of $15\,\mbox{kB}$, which means $300$ repetitions of
the transmitted file is used to obtain the SNR and BER calculate. All curves
of the graph in Fig. 12 falls within the SNR range from $16.456~{}\mbox{dB}$
to $26.403~{}\mbox{dB}$. The “LRC 3b” curve starts with a BER of $4.2498\times
10^{-2}$ and after a SNR of $20~{}\mbox{dB}$ it reaches a plateau around a BER
of $2.5\times 10^{-3}$. The “LRC 4b” curve starts with a BER of $1.3923\times
10^{-2}$ and we did not observe the occurrence of a plateau, in agreement with
what was observed in the MatLab simulation, Fig.11. The “LRC 5b” curve starts
with a BER of $7.3375\times 10^{-3}$ and presents a BER performance very close
to the “Hardware” curve that starts with a BER of $5.7167\times 10^{-3}$, as
we expected.

$16$$18$$20$$22$$24$$26$$10^{-2.5}$$10^{-2}$$10^{-1.5}$SNR [dB]BERHardwareLRC
3bLRC 4bLRC 5b

Figure 12: Prototype system performance with $1\,\mbox{m}$ distance between
the antennas.

##  V Conclusion

Based on the prototyping work presented in this research, it is safe to say
that there is a basis for creating critical hardware for systems that require
high energy efficiency, that is, an ADC with less than 8 bits of resolution.
It is possible to reinforce the importance of the subject discussed, since it
can strongly impact the prototyping of radio systems in the laboratory. The
use of SDRs allows flexibility to test different radio communication systems
with the same device. And although SDRs such as USRP are already widely used
in research, this work has shown that there are low-cost devices on the market
that can fulfill this function. The contents presented here demonstrate that
many other researches can still be carried out on prototyping using low-cost
SDRs, due to the importance of the topic and numerous contributions to the
academic environment. As an example of future work, one can consider
implementing a receiver in GNU Radio that takes into account the quantization
noise and thus improves the performance of the presented system even when
running in low resolution.

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Eder Oliveira de Souza was born in the city of Rio de Janeiro, Brazil, on July
1st, 1990. He received his bachelor’s degree in Telecomunication Engeneering
from Fluminense Federal University (UFF) in 2016. In 2022, he received his
bachelor’s degree in Electronic Engineering from Federal Center for
Technological Education of Rio de Janeiro (CEFET/RJ). His research interests
are digital signal processing and digital transmission systems.

João Terêncio Dias was born in Tarumirim, Minas Gerais, Brazil, on April 10,
1971. Graduated in Telecommunications Engineering from the Fluminense Federal
University (UFF), in 2002, MSc in Electrical Engineering (Digital
Communication Systems) from the Military Engineering Institute (IME), in 2006,
PhD in Electrical Engineering (Digital Signal Processing) from the Federal
University of Rio de Janeiro (UFRJ), in 2013, and post-doctorate in Electrical
Engineering (Digital Signal Processing Applied to Communications Systems) at
Pontifical Catholic University of Rio de Janeiro (PUC-Rio) in 2016, all in Rio
de Janeiro, Brazil. He joined the teaching staff of the Rio de Janeiro
Technical School Support Foundation (FAETEC) in 2002, where he worked as a
Telecommunications Professor until 2008, when he transferred to the Federal
Center for Technological Education of Rio de Janeiro (CEFET/RJ), where he is
now Full Professor. Between 2006 and 2008 he was a Substitute Professor at the
Faculty of Engineering at the State University of Rio de Janeido (UERJ) and in
January 2017 he was a visiting researcher at the University of York, in
England. He prepared and reviewed questions for the National Student
Performance Exam (ENADE) for Engineering and Computing. He was also a member
of the Mathematics team for preparing and reviewing the National High School
Exam (ENEM). He is currently leader of the Quantum Communication Research
Group (CQRG) and develops extension and research projects in
Telecommunications and Computing. His research interests include low-
resolution converters, quantum algorithms, wireless communication systems,
communication theory, and digital signal processing. João has been a member of
the Brazilian Telecommunications Society (SBrT) since 2003 and a member of the
Institute of Electrical and Electronic Engineers (IEEE).

Demerson Nunes Gonçalves is a professor in the Mathematics Department at
CEFET/RJ since 2015. He holds a bachelor’s degree in Mathematics Education
from the Federal University of Espírito Santo (2002), a master’s degree in
Computational Modeling from the National Laboratory for Scientific Computing
(2005), and a doctorate in Computational Modeling from the National Laboratory
for Scientific Computing (2009). His research interests lie at the
intersection of mathematics, scientific computing and quantum physics, with a
focus on both practical and theoretical applications. His work involves the
development of advanced methods and algorithms to solve complex problems in
the areas of computational group theory, quantum algorithms, quantum error-
correcting codes, and quantum machine learning.