# MIMO Operations in Molecular Communications: Theory, Prototypes, and Open
Challenges

Bon-Hong, Koo, Changmin, Lee, Ali E. Pusane, Tuna Tugcu, and Chan-Byoung Chae
B.-H. Koo, C. Lee, and C.-B. Chae are with Yonsei University, Korea. A. E.
Pusane and T. Tugcu are with Bogazici University, Turkey.

###### Abstract

The Internet of Bio-nano Things is a significant development for next
generation communication technologies. Because conventional wireless
communication technologies face challenges in realizing new applications
(e.g., in-body area networks for health monitoring) and necessitate the
substitution of information carriers, researchers have shifted their interest
to molecular communications (MC). Although remarkable progress has been made
in this field over the last decade, advances have been far from acceptable for
the achievement of its application objectives. A crucial problem of MC is the
low data rate and high error rate inherent in particle dynamics
specifications, in contrast to wave-based conventional communications.
Therefore, it is important to investigate the resources by which MC can obtain
additional information paths and provide strategies to exploit these
resources. This study aims to examine techniques involving resource
aggregation and exploitation to provide prospective directions for future
progress in MC. In particular, we focus on state-of-the-art studies on
multiple-input multiple-output (MIMO) systems. We discuss the possible
advantages of applying MIMO to various MC system models. Furthermore, we
survey various studies that aimed to achieve MIMO gains for the respective
models, from theoretical background to prototypes. Finally, we conclude this
study by summarizing the challenges that need to be addressed.

##  I Introduction

The future of beyond 6G and 7G (B6G/7G) networking is expected to enable novel
technologies related to health monitoring, where nanoscale networking has
emerged as a promising communication paradigm. Nano-communications primarily
constitutes the implementation of nanoscale devices and their utilization for
in vivo applications. On the other hand, recent studies show that
electromagnetic waves may not be compatible with nano-communication systems.
Techniques that use chemical particles as substitute messengers are therefore
of interest for communications technologies. A macroscopic view of the
trajectory and possible future directions of molecular communications (MC) are
presented in [1]. System design with analytical formulations [2] and testbed
studies [3, 4] are both ongoing with open problems and challenges. The main
challenge in this field over the next decade is expected to be technology
implementation with higher data rates and lower error rates. This article
discusses the tasks and challenges of applying multiple-input multiple-output
(MIMO) to MC in theory and prototypes, as well as research directions for
contemporary researchers.

Particle behaviors are dependent on diffusion and drift; thus, increasing the
data rate is a crucial challenge for implementing the MC protocols. In radio
frequency (RF) communications, the standard strategy to increase data rate is
to obtain independent information paths by exploiting the resources of power,
time, frequency, and space. An analogous strategy has also been used in MC;
molecular type can be one another resource in MC. It is noteworthy that
earlier studies on MC focused more on power, time, and type-based modulation
techniques, whereas spatial resources have been studied in recent years [1].

In [5], the authors introduced modulation techniques to exploit the variable
resources of molecular types and power. They claimed that both type- and
power-based modulation techniques could either increase the data rate or
reduce errors, and that a type domain ensured performance gain while remaining
within the same power constraints. The results were numerically validated. The
authors in [6] proposed and compared time-based modulation techniques with
power modulation. Owing to the high statistical noise from diffusion, the time
domain was shown to yield performance gains in both modulations, and their
testbed confirmed the results.

It is essential to investigate MIMO configurations to utilize spatial domain
resources. In MC with a diffusion environment, it can be argued that the MIMO
operation may not work as in RF communication because of the completely
different channel characteristics. However, the authors in [7] showed that it
is feasible to achieve performance gains in MC by applying MIMO systems in
practice. They proposed novel detection algorithms for MC with a 2$\times$2
MIMO configuration and implemented a prototype to test the results. Lee et al.
[8] designed learning-based algorithms to cope with unknown channel state
information (CSI), in addition to developments in [7]. Yu et al. [9] studied
an MC system with a 4$\times$4 configuration and demonstrated performance
enhancements. The authors in [10, 11] investigated general configurations and
considered mobility and asymmetry, respectively. To address the interference,
both studies successfully applied a zero forcing detector. Damrath et al.
provided analytic discussions on the array gain in MC [12]. These studies
showed promising results wherein a spatial domain could result in performance
gains. Therefore, we are motivated to find open problems in this research
area, whereas unknown CSI and interference could pose technical challenges.

The remainder of this article is organized as follows. We first provide an
overview of the MIMO-embedded MC system, including communication models,
technical hurdles, and testbed designs. Next, existing solutions are
discussed. Thereafter, we discuss the potential of molecular MIMO and conclude
this article by summarizing the open challenges.

Figure 1: Conceptual overview of B6G/7G and molecular MIMO communications.

##  II Applying MIMO to MC

As shown in Fig. 1, we expect the research area of MC to augment the B6G/7G
communication paradigm. In addition to the other MC techniques, we believe
that the role of MIMO technologies deserves special consideration. We briefly
introduce the potential gains of MIMO for RF communications and review the
applications of MC in various scenarios.

###  II-A Brief Review of MIMO Gain in RF Communications

In RF communications, multiple antennas can provide performance benefits via
array, diversity, and multiplexing gains. Array gain is the benefit of having
a high signal-to-noise ratio (SNR) at the receiver, which can be achieved by
coherently adding received signals at the antennas. A transmitter is required
to have CSI for signal coherence. Diversity gain offers a low error rate by
providing independent channel paths and reducing the fading effects. In
contrast, multiplexing can achieve an increase in the data rate using
simultaneous data streams through pairs of transmitter-receiver antennas. This
technique is also referred to as spatial multiplexing.

Knowledge on channel models, signal coherence, and antenna correlations is
required to apply MIMO technologies. In MC, a standard channel model is still
in the development stage. Furthermore, a diffusion-dominated environment makes
it difficult to achieve coherence. Therefore, channel, interference,
detection, and verification are prerequisites for applying MIMO schemes to MC.
The term ’antenna’ for MC in this article can physically be
chemical/biological transceivers (molecular emitters and detectors).

###  II-B MC System Model

We consider three models of interest as depicted in Fig. 2: three-dimensional
(3D) free-space, bounded space, and unestablished channel models (e.g.,
underwater). The first column shows the free-space channel model, where
molecules propagate through diffusion and drift. A possible target scenario
for the use of this model is tactical nano-robots because of its strength
against eavesdropping and energy efficiency. The second column presents a
vessel-bounded channel, that mimics in vivo applications. Health monitoring by
nano-robots with medical sensors and theranostics is a potential application
for this model. The third column describes underwater communication, in which
RF signal experiences severe degradation. In the bottom row, the corresponding
state-of-the-art testbeds are introduced. The first two testbeds are equipped
with 2$\times$2 MIMO configurations [8, 3] while the third [4] is equipped
with a single-input single-output (SISO) configuration.

Mimicking nature is one of the strong motivations for MC technology. For
instance, ants in a colony communicate with each other by pheromone molecules,
bio-organs in a body organize the system with hormone chemicals, and a shark
detects its target from a long distance with a minute amount of odor
molecules. From these examples, the following directions can be considered:
increasing the number of communication units that a network comprises,
expanding the size of a set of chemical compounds that the system employs, and
enabling position tracking functions with higher sensitivity.

In this article, we base our discussion on a 2$\times$2 symmetric
configuration for simplicity. Generalized designs are presented in the
following section. The transmitter antennas are regarded as point sources that
release messenger particles into the channel medium. The receiver antennas
were spherical in shape for analytical tractability. These antennas absorb the
contacted molecules and count their numbers over time. In addition to the
statistical counting noise, additional noise is considered to account for the
unmodeled phenomena. It is assumed that the transceivers are synchronized with
one another and are aware of the predefined system parameters, including the
required CSI and symbol duration.

Figure 2: Three types of channel model and comparisons in MC MIMO, from theory
to prototypes.

###  II-C Channel Model and CSI

Free space diffusion dynamics inherently have an indeterminacy of exact
movement, and analysis based on statistical characteristics is an alternative
approach to address this issue. In this regime, the channel that the
information carriers experience is the expected fraction of the number of
molecules that the receiver captures with respect to time. A closed-form
channel model solution for a case without drift and multiple antennas is
presented in [13]. Furthermore, Jamali et al. presented solutions for a
channel with drift and a non-absorbing receiver [2].

In MIMO configurations, molecular absorption at one receiver antenna induces
dependency on the others, and finding a closed-form channel model remains an
open problem. The studies presented in [7, 8] revealed that it is possible to
closely approximate the MIMO channel model by tuning the parameters using a
SISO solution.

The CSI required for the transmitter in this model comprises the drift
velocity, diffusion coefficient, distance, and MIMO parameters. The challenge
is to tune MIMO parameters for each topology, where the relational formula has
not yet been solved. The requirement of retuning parameters for varying
topologies makes the system sensitive to displacements of the communication
units. Machine learning-based parameter tuning algorithms were introduced in
[8], which manage the adjustment of the parameters given the communication
distances in the provided training data.

We consider in vivo applications, such as the communication units located in
blood vessels, where the dominance of the drift effect is high and boundary
restrictions affect the channel. The vessel-bounded channel space is regarded
as a straight cylinder [2, 7, 6]. Threshold-based detection algorithms were
proposed in [7], and learning-based algorithms were presented in [6] for SISO
configurations. In vessel-bounded MC, the set of channel state parameters
consists of the distance, diffusion coefficient, velocity profile, and vessel
radius.

One research direction for MC channels is the transition from mathematical
analysis to prototype implementations. In [2], the authors considered
advective flow and chemical reaction kinetics to provide vessel-bounded MC
channel responses. However, this becomes increasingly difficult as the channel
becomes more complicated, and another research approach is required.

An alternative approach of studying channels begins from a testbed with
numerous measurements and then involves determining correlations between sets
of input and output, as in [3, 14]. The authors in [3] discovered that the
velocity profile is related to the radius, and both studies showed
communication feasibility in vessel-bounded MC. Challenge in these research
directions is that prototypes must be developed beforehand.

Underwater environments with severe RF signal degradation are among the
prospective fields for the application of MC. The olfactory sense of sharks
outperforms any other alternative communication for the subaqueous positioning
task; thus, underwater MC is desirable in addition to acoustic/RF
communications [4]. The aforementioned channel models may not be feasible in
these environments. It is highly recommended to use a network with multiple
devices and antennas for long-distance communication. Therefore, it is
desirable to design communication transceivers with multiple components and
limited channel knowledge.

Figure 3: ISI and ILI models for MIMO operations in MC.

###  II-D Interference Sources and Mitigation Strategies

Diffusion-based MC suffers from statistical noise as a consequence of Brownian
motion. Particles that fail to reach their target within the desired time slot
are regarded as interference. Therefore, acquiring a higher data rate comes at
the cost of interference. As evident in the first column of Fig. 3, the
average receiver response to the single-shot transmission has a long tail,
which implies that MC suffers from severe interference and noise.

In SISO MC, the molecules that cannot arrive within the symbol duration are
the only interference sources, and are analogous to the inter-symbol
interference (ISI) in RF communications. The second column of Fig. 3 shows the
effect of a long tail on successive signal responses. Removing remnant
molecules with appropriate enzymes can mitigate interference while increasing
the system costs. Otherwise, the best available strategy to date is to exploit
the statistical channel characteristics and optimize the symbol duration. Kim
et al. proposed solutions to achieve a high data rate given the constraints on
the SNR level [5].

Applying MIMO schemes to MC yields additional spatial resources for the
system. Attaining an array or diversity gain by scheduling the transmitter
antennas and summing the receiver antenna signals is straightforward. Koo et
al. reported that achieving multiplexing gain is possible when inter-link
interference (ILI) is considered [7]. When the antenna of a device is paired
with the closest antenna of the communication counterpart, molecules at the
wrong destination are regarded as ILI, as shown in the last column of Fig. 3.
Note that the curves in Fig. 3 are averaged values obtained from numerous
observations at the receiver, whereas the actual receptions are random
variables. In [2], a Poisson random channel model was introduced to describe
the actual responses.

Based on an MC feature where the signal degradation as a function of range is
greater than that in RF communications, a simple idea for mitigation is to
consider ILI noise and apply a SISO threshold. The knowledge of ILI
characteristics results in even better performance, as shown in [11] with the
equalization method inspired by the zero-forcing method. Koo et al. also
proposed zero-forcing detection algorithms using statistical characteristics
only at the receiver under the assumption of partial CSI available at the
receiver [7]. The authors in [10] also exploited the mean value of the channel
and interference and proposed zero-forcing, minimum mean square error, and
least square detectors. They also showed that having decision feedback at the
transmitter can achieve enhanced performance by eliminating successive
interference.

A scenario with multiple transmitters and receivers also introduces an inter-
user interference (IUI). IUI can be regarded as an additional ILI, and
additional spatial multiplexing gain can be exploited when pairs of
communications are predefined.

As the medium drift speed increases, the ratio of ILI to the desired signal
decreases. In vessel-bounded channels, where drift dominates over diffusion,
the ILI is negligible when the antenna configuration is well aligned in a
single stream. Thus, SISO detection algorithms can mitigate ISI for the MIMO
setup. Example detection algorithms are provided in [14], where it can be
observed that the sensor’s chemical instability can also yield heavier tails.

We can also assume that communication units spread over multiple vessel
streams, which could exacerbate the ILI (or IUI) effect. Lee et al. introduced
a vessel testbed that used MC MIMO with intersecting vessels and empirically
demonstrated that multiplexing gain is achievable with CSI at both the
transmitter and receiver [3]. The issue of modeling and solving complex vessel
topologies is an open problem.

##  III Communication Transceiver Design

In this section, MC modulation techniques are presented, their capabilities
for MIMO applications are discussed, and we also introduce detection
algorithms.

###  III-A Modulations in MC

Modulation schemes can exploit, several domains simultaneously such as time,
molecular type, power, and space. The power in MC is proportional to the
number of molecules that are relevant to the concentrations. Power-based
modulation in MC is known as concentration shift keying (CSK), which resembles
to power amplitude-shift modulations in classical communications. The binary
modulation of CSK (BCSK) maps bit-1 into a fixed number of molecules and bit-0
into zero molecules. Sending zero molecules is not mandatory; however, it is a
popular option in terms of power and accuracy. Therefore, BCSK is used
interchangeably with on-off keying (OOK) in MC. A high order of modulation is
achievable using multiple molecular quantity levels.

The next common modulation source is the timing of molecular emission. One
such example is pulse position modulation (PPM) [15]. The system has a fixed
symbol time, which is divided into multiple time slots. A single-shot at one
of the slots per symbol time was used, and the slot position represented a
data symbol. Another example in [6] employed single-slot timing modulation,
which is equivalent to PPM with an infinite symbol time and indefinite
modulation order.

When a transmitter and a receiver can use multiple types of molecules,
additional degrees of freedom can be achieved by the type domain. In [5], the
authors proposed molecular type-based modulation. Each molecule represents a
different symbol. Assuming that the molecules do not interact with each other,
the type domain is independent of the others. Therefore, this domain is
typically used in combination with other domains. While the domain has
unlimited potential, we need to be cautious when planning to use the type
domain because the complexity growth is not yet quantifiable and some of the
chemicals may not be eligible for use in practice.

A device with multiple antennas yields another independent domain, thereby
contributing to the performance gains of the system. In [15], the authors
proposed index modulation, where each index denoted one transmitter antenna,
and the index represented an individual symbol. Yu et al. [9] also presented
space shift keying (SSK) modulation and designed joint modulations of SSK and
CSK for a 4$\times$4 MIMO configuration. Gursoy et al. addressed two types of
molecules using the index modulation in [15] and combined PPM with space in
their subsequent study.

High-order modulation is achievable by adopting more antennas per unit;
however, this increases the ILI and decreases the antenna separations. The
order of the modulation is also relevant to the channel and device functions.
We assumed an ideal case with $T$ transmitter and $R$ receiver antennas. The
maximum number of combinations that can be used for the modulation in theory
is $(R+1)^{T}$, where each transmit antenna can either choose one of the $R$
antennas or not. The combinations of transmitter antennas are preferred to be
uncorrelated so that the received signals at each antenna are separable by
having high directional transmissions to achieve the optimum.

Figure 4: Applying MIMO to MC increasing performance in all terms: array,
diversity, and multiplexing gains.

###  III-B Detection Algorithms

As stated in [7], the best detection algorithm that can be embedded in the
receiver is the maximum a posteriori algorithm with perfect CSI. To achieve
optimal performance, the knowledge of data statistics, channel governing
equations, channel state parameters, and unlimited receiver memory are
required. To obtain a practical detection algorithm, the constrained problems
must be solved under relaxed conditions. For example, when we have partial
CSI, unknown parameters can be estimated, albeit with uncertainty. Assuming
that a dataset is non-biased, and we have a reliable channel model, techniques
from RF communications such as zero forcing, coding combining [12], and the
Viterbi algorithm properly adapted to the MC environment can be applied.

The authors in [7] proposed and compared several detection algorithms for
cases in which a limited CSI set was provided. The objective was to obtain a
threshold for binary detection at the receiver for each bit slot. Increasing
the amount of CSI leads to improved performance, although communication is
feasible even with a modest amount of CSI. Farsad et al. [6] proved that
learning-based approaches can detect messages from empirical observations
without any prior information on CSI.

The main difference between MIMO and SISO detection algorithms is the presence
of multiple streams and the absence of an exact channel model. For example, in
pursuing multiplexing gain, it is assumed that the transceiver antennas are
paired and handled the ILI by considering it as additional noise. As mentioned
previously, this model is feasible under the condition of antenna pairing in
the aligned topology. This problem needs to be addressed to mitigate the ILI
when the configuration is not aligned, where the ILI can overwhelm the primary
signal.

Machine learning algorithms are compatible with MC with an unknown channel
model. This approach requires a lengthy measurement period for both prototypes
and numerical simulators. Here, the challenge is that a sufficiently large
dataset may not be available. To obtain the maximum amount of possible data,
device sharing or online data harvesting studies will be required in the
future. Furthermore, effective learning algorithms must be developed.

It was demonstrated in [3] that knowledge of the channel can reduce the burden
of training, making it possible to train on a smaller training dataset. Farsad
et al. stated that ensuring adequate memory at the receiver enables recurrent
neural networks (RNNs) to perform better. Lee et al. presented a learning
algorithm for molecular MIMO that trains MIMO channel tuning parameters in
combinations or independently. Therefore, further investigation of the channel
considering the developments in training neural networks is required.

###  III-C Exploitation of Spatial Resources

The number of paths that can be created using $T$ transmitter antennas and $R$
receiver antennas is $T\times R$. However, the antenna correlation limits
performance gains; the number of uncorrelated signals at the receiver is
bounded between $R$ and one. The MC channel attenuates highly over distance;
thus, it is sensitive to physical separation. Misalignment can also affect the
effectiveness of receivers.

To the best of our knowledge, spatial correlation studies between diffusive
signals have not yet been conducted. Antenna correlation studies can provide
an upper bound of the gains for general configurations and help decide the
order of priority to explore. Therefore, it is expected that characterizing
the correlation effects for transmitter and receiver antennas can result in
further progress in the theory and prototyping of molecular MIMO systems.

The effectiveness of the receiver can be further enhanced by ensuring the
transmitter antenna directivity. The number of uncorrelated signals at the
transmitter antennas depends on their correlation. It is easier to adjust the
transmitter antennas than the receiver antennas, because the presence of a
single transmitter antenna does not affect the others.

After obtaining the information paths, performance gains can be achieved by
applying MIMO strategies as in RF communications. The authors in [12] reported
that array gain is achievable by adding coding and receiver combining
techniques with the aforementioned detection algorithms, including threshold-
finding and learning-based algorithms. The numbers below SISO and MIMO in the
top part of Fig. 4 indicate the number of molecules required to achieve the
target accuracy. They proposed that the Alamouti-type code or repetitive-code
benefits the system, and a weighted combination of signals at the receiving
antennas introduces array gains of 3 dB with a 2$\times$2 MIMO configuration.
Their results also indicate that it is feasible to exploit resources for
diversity gains in MC MIMO.

We present the results from [9] in the middle part of Fig. 4 to show the
diversity gain effects, where the error rates of using SISO, 2$\times$2 MIMO,
and 4$\times$4 MIMO systems are compared under the same SNR. The numbers below
the configurations represent the symbol error rates. The results of [7] also
indicate that multiplexing gain is achievable, as shown at the bottom of Fig.
4. The numbers below the power indicate the number of molecules used to
transmit bit-1 while adopting OOK modulation, and the numbers under SISO and
MIMO indicate bps per molecule.

##  IV Validation by Prototypes

Three types of prototypes are presented for the three different representative
channel types and propagation modes. The first prototype is based on free-
space diffusion and drift. Its state-of-the-art version is equipped with a
2$\times$2 MIMO configuration. We expect its further applications in smart
dust and tactical nano-robots. The second prototype is a vessel-bounded
testbed. We anticipate that the advanced version will be used in in vivo
robots where biocompatibility is vital in the future. The third prototype can
be operated underwater. This system is capable of supporting futuristic
scenarios, including abyssal communications, where RF signal impairments are
severe.

###  IV-A Free-Space MIMO Testbed

Communication via free-space propagation is achieved with fans, programmable
sprays, and chemical sensors, as shown in the bottom part of Fig. 2. The fan
addresses the drift velocity, and its power can adjust the speed. The
programmable spray is controlled by an Arduino system on a chip to check the
interactive results in a timely manner, while the preprocessed codes are
embedded before use. The transmission power is varied by adjusting the size of
the spray outlet or spraying duration per shot. The external processors handle
the processing of received responses at the sensors; standalone nano-
processors can be investigated in future work.

There is wide potential extensibility in the spatial domain, but limited
progress has been achieved thus far. Researchers have investigated the
variation in performance using 2$\times$2 MIMO and SISO configurations and
proved that the results obtained using formulation-based analysis agree well
with the prototype results [7]. Future upgrade to the free-space MC testbed
would focus on increasing the number of adoptable antennas based on suitable
theory, while enabling gains from multiple domains.

###  IV-B In-Vessel MIMO Testbed

Researchers have built in-vessel MC systems at multiple scales. Farsad et al.
designed a meso-scale prototype utilizing base and acid molecules.
Programmable pumps introduced molecules into the channel, and pH sensors
captured the responses. The desired channel topologies can be expressed using
adjustable rubber pipes and joints. The authors applied machine learning for
detection, and the RNN significantly enhanced the performance by efficiently
mitigating the ISI. It is also worth noting that drift domination results in
the sharpness of the peak reactions. This implies high extensibility in the
time domain.

Lee et al. [3] expanded the prototype into a 2$\times$2 MIMO setup. The
developed testbed was appropriate for modeling various configurations of tube
environments such as the human blood vessel network. A 3D printer was used to
print the junction parts.

Koo et al. [14] implemented a prototype at the nanoscale. Most of the
components were analogous to those in [3]. One difference was that the sensor
was adaptively designed for MC at the nanoscale. In contrast with current
nano-sensors, their sensor was rapidly reactive, sensitive to changes in
concentration, and inexpensive. Their study is significant for demonstrating
the feasibility at the nanoscale and calling for interdisciplinary research
for further advancements.

###  IV-C Underwater Testbed

Guo et al. [4] introduced a macro-scale underwater MC with a prototype that
exploited gravity and buoyancy to convey molecules. The objective of this
study was to employ MC in liquid environments. In their implementation, two
nodes communicated with each other along the vertical axis. The buoy emitted
molecules with an initial velocity from the surface, and the molecules were
moved by gravity. In contrast, the submarine-unit emitted molecules could
float with the help of buoyancy.

Generally, most MC studies in a fluid environment assume laminar flow.
However, it is challenging to neglect turbulent flow when the physical size of
the application becomes enormous, e.g., tracking the target position beneath
the deep ocean. The turbulent flow complicates the analysis of the theoretical
channel model, and study on the case is a notable open problem.

##  V Open Challenges and Concluding Remarks

This study aims to provide insights into the research developments in MC,
particularly for exploiting spatial resources with multiple antennas. We
surveyed channel models and interference sources in MC and discussed potential
technical hurdles that need to be overcome. Next, we summarized the
communication strategies considered in MC research and listed open challenges
for further study. Because some of the system designs include intractable
tradeoffs, it is essential to develop prototypes to test their feasibility and
quantify the performances. Therefore, we presented testbed studies for three
prospective propagation environments for MC applications. The open challenges
identified herein can be summarized as follows:

  * •

Closed-form channel representations: Analytic characterizations of channels
remain open problems in many cases: free-space propagations with multiple
absorbing receiver antennas, vessel-bounded complex environments with
junctions and leakages, and undersea propagations.

  * •

Testbed design for feasibility study: Various types of hardware should be
developed to enable diverse practical applications. Underwater testbeds that
perform sensitive position tracking tasks or testbeds with the capability to
compose and sense multiple types of chemicals can be one example.

  * •

Theoretical studies for generalization: Physical principles that describe the
effects of deploying an arbitrary number of antennas are crucial to designing
general MIMO communications. For example, knowing the impact of signal
correlation between multiple antennas can optimize the MIMO configurations.

The current state of MC MIMO research indicates that performance gains from
spatial domain exploitation are possible and can be coupled to exploit power,
time, and molecular type. In [7], the multiplexing gain results in 1.7 to 1.9
times higher transmission rates with a 2$\times$2 MIMO system when compared
with the SISO system.

Joint optimization techniques with adaptive coding, modulation, and receiver
combining schemes can help achieve further efficiency. Joint modulations were
proposed and tested virtually in [9, 15]. We suggest two research directions
for further studies. The first involves determining a theoretical bound by
comparing the results of the signal correlations for the generalized
configurations and modulation orders. This will determine the capacity of the
system and provide researchers with insights regarding the areas where
research must be prioritized. The other direction is a prototype investigation
to obtain quantitative information to deploy multiple antennas in practice.

We foresee the potential of nano-communications in various scenarios. We also
anticipate problems in deploying communication systems in new and unexplored
environments. The findings of previous studies suggest that learning-based
approaches can address unknown channels, provided that we have sufficient
observation data. Machine learning is a widely expanding research field, and
synergetic effects can be achieved when the learning structure and hardware
are specialized for target applications. Hence, interdisciplinary research can
boost nano-communication performance, while an optimized learning network is
desired beforehand. Hence, we expect that MC hardware, training networks, and
transceiver design will be jointly optimized in the future.

## Acknowledgment

This work was supported in part by the Scientific and Technical Research
Council of Turkey (TUBITAK) under Grant 119E190 and part by the Basic Science
Research Program through the National Research Foundation of Korea funded by
the Ministry of Education (NRF-2020R1A2C4001941).

## References

  * [1] N. Farsad _et al._ , “A Comprehensive Survey of Recent Advancements in Molecular Communication,” _IEEE Commun. Surveys Tuts._ , vol. 18, no. 3, pp. 1887–1919, Feb. 2016.
  * [2] V. Jamali _et al._ , “Channel Modeling for Diffusive Molecular Communication-A Tutorial Review,” _Proc. IEEE_ , vol. 107, no. 7, pp. 1256–1301, Jul. 2019.
  * [3] C. Lee _et al._ , “Demo: In-Vessel Molecular MIMO Communications,” in _Proc. IEEE WCNC Workshops_ , Apr. 2020, pp. 6–7.
  * [4] W. Guo _et al._ , “Vertical Underwater Molecular Communications via Buoyancy: Gaussian Velocity Distribution of Signal,” in _Proc. IEEE ICC_ , Oct. 2020.
  * [5] N.-R. Kim _et al._ , “Novel Modulation Techniques using Isomers as Messenger Molecules for Nano Communication Networks via Diffusion,” _IEEE J. Sel. Areas Commun._ , vol. 31, no. 12, pp. 847–856, Dec. 2013\.
  * [6] N. Farsad _et al._ , “Capacity Limits of Diffusion-based Molecular Timing Channels with Finite Particle Lifetime,” _IEEE Trans. Mol. Bio. Multi-Scale Commun._ , vol. 4, no. 2, pp. 88–106, Jun. 2018.
  * [7] B.-H. Koo _et al._ , “Molecular MIMO: From Theory to Prototype,” _IEEE J. Sel. Areas Commun._ , vol. 34, no. 3, pp. 600–614, Mar. 2016.
  * [8] C. Lee _et al._ , “Machine Learning based Channel Modeling for Molecular MIMO Communications,” in _Proc. IEEE SPAWC_ , Jul. 2017, pp. 1–5.
  * [9] Y. Huang _et al._ , “Spatial Modulation for Molecular Communication,” _IEEE Trans. NanoBiosci._ , vol. 18, no. 3, pp. 381–395, Jul. 2019.
  * [10] S. M. R. Rouzegar _et al._ , “Diffusive MIMO Molecular Communications: Channel Estimation, Equalization, and Detection,” _IEEE Trans. Commun._ , vol. 67, no. 7, pp. 4872–4884, Jul. 2019.
  * [11] C. Wu _et al._ , “Signal Detection for Molecular MIMO Communications With Asymmetrical Topology,” _IEEE Trans. Mol. Bio. Multi-Scale Commun._ , vol. 6, no. 1, pp. 60–70, Jul. 2020.
  * [12] M. Damrath _et al._ , “Array Gain Analysis in Molecular MIMO Communications,” _IEEE Access_ , vol. 6, pp. 61 091–61 102, Sep. 2018\.
  * [13] H. B. Yilmaz _et al._ , “Three-Dimensional Channel Characteristics for Molecular Communications With an Absorbing Receiver,” _IEEE Commun. Lett._ , vol. 18, no. 6, pp. 929–932, Jun. 2014.
  * [14] B.-H. Koo _et al._ , “Deep Learning-based Human Implantable Nano Molecular Communications,” in _Proc. IEEE ICC_ , Jun. 2020.
  * [15] M. C. Gursoy _et al._ , “Index Modulation for Molecular Communication via Diffusion Systems,” _IEEE Trans. Commun._ , vol. 67, no. 5, pp. 3337–3350, May 2019.

Bon-Hong Koo is currently a Ph.D. student at the School of Integrated
Technology, Yonsei University, Korea. His research interests include molecular
communications, and machine learning.
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Changmin Lee is currently a Ph.D. student at the School of Integrated
Technology, Yonsei University, Korea. His research interests include testbed
implementations.
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Ali Emre Pusane is a Professor in the Department of Electrical and Electronics
Engineering, Bogazici University, Turkey. His research interests include
wireless communications, molecular communications, information theory, and
coding theory.
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Tuna Tugcu is a Professor in the Department of Computer Engineering, Bogazici
University, Turkey. His research interest includes nanonetworking, molecular
communications, wireless networks, and IoT.
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Chan-Byoung Chae is an Underwood Distinguished Professor at Yonsei University,
Korea. His research interest includes emerging technologies for 5G/6G and
molecular communications. He is now an EiC of the IEEE Trans. Molecular,
Biological, and Multi-scale Communications and an IEEE Fellow.
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