IEEE Systems, Man and Cybernetics Magazine - October 2021 - 20

into wireless communication. One example is the use of
self-similar carriers (and, consequently, fractal modulation),
which had limited adoption [14]. The physical fractal
structure, however, has a long tradition in antenna design
for wireless communications.
A typical fractal antenna has a fractal shape and puts
to use two advantages of fractals: the existence of scaled
structures and space-filling properties. The self-similar
scaled structures offer different scales of length for the
antenna to work at, directly resulting in similar effects for
different wavelengths.
This does not necessarily mean good performance for
the said wavelengths, so the story of fractal antennas is
not that straightforward. The space-filling property is
related to the capability of all fractals to achieve dense
packing in some parts (in terms of antennas, it is the dense
packing of wires within a small surface area). For chaotic
signals, it was suggested that their transmission would be
robust to multipath effects and severe noise [15].
Cameos: Brain, Control, and Games
Wireless communications have a long-term relationship
with several disciplines heavily relying on dynamical systems.
This part of the story must not be overlooked, so we
examine control over wireless and game theory in the
wireless setting.
First, we note the cameo role of dynamical systems in
wireless communication as seen in differential games.
Defined as a game over a dynamical system, a differential
game can model, control, and optimize various processes
in wireless communications. Again, it is very often a
hybrid dynamical system the control is performed on,
dealing with external dynamics, such as drone or robotic
movement, but also the intrinsic " dynamics " of wireless,
including power control, transmission rates, and delays
[10]. To make it realistic and useful for practical considerations,
the models of the dynamical systems have to be
faithful to the reality. This means that differential game
theory eagerly awaits the results of everything dynamical
systems research can get from the wireless of the day.
Closely related to game theory is control over wireless:
it uses the wireless channel as the control signal medium
and has to deal with all of its peculiarities, determinism
and randomness alike (a timely example is that of teleoperation
[16]). The control engineers got rid of the wires cluttering
the factory and decreasing mobility, but they had to
face a whole new world of wireless communications, technologies,
and protocols. The distributed control system
just got another dynamical system on top of it, between its
nodes: the wireless.
The ubiquitous wireless sensor networks are essentially
control networks, just without actuators. There
again, dynamical systems emerge: the ones whose outputs
are measured by the sensors and those the sensory
data travel through.
Finally, one area of wireless communications that recognizes
the importance of dynamical systems and chaos is
at the crossroads of engineering and neuroscience, where
researchers both draw inspiration from the dynamical systems
and chaotic activity in the brain for bio-inspired network
and device design and seek ways to integrate modern
wireless communications with the human organism (the
brain in particular) for health-related applications of nextgeneration
communications [11].
Input
Nodes
Reservoir: State Nodes
Output
Nodes
Trained Interconnections
Fixed Interconnections
Figure 4. The reservoir computing principle.
Borrowing the structure from neural networks,
reservoirs are dynamical systems with temporal
dynamics and random fixed connections between
state nodes (randomly selected when the reservoir
is created and fixed for the future and unchanged
during training). Only the output connections (toward
the output nodes) are the result of training, which
reduces the complexity of learning and allows the
reservoir computer to use the large dynamic reservoir
for different dynamical systems.
20 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE October 2021
Learning Dynamical Systems
in Wireless Communications
The two decades of the new century saw a new artificial
intelligence spring, growing data availability, and an
increased capacity for data handling. In wireless communications,
an early major milestone was the pioneering
work on reservoir computing [17]. This concept, illustrated
in Figure 4, is the quintessential machine learning
model for dynamical systems: the intermediate stage
between inputs and outputs in this network is a dynamical
system on its own-it does not attempt to adapt to the
actual system, except for the subset of connections leading
to the outputs.
As such a general dynamical systems tool, reservoir
computing quickly left the realm of wireless communication
(only two reservoir computing applications were cited
in the most recent surveys of learning in this area [18],
[19]) and found greener pastures. It aims, together with
other machine learning paradigms, at providing a helping
hand in predicting the behavior of otherwise hard-to-anticipate
nonlinear systems, but we are still arguably waiting
for revolutionary results.
They are within reach once we offer a helping hand to
machine learning as well: we need better models of
IEEE Systems, Man and Cybernetics Magazine - October 2021

Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - October 2021
