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The road to6G: acomprehensive survey
ofdeep learning applications incell‑free
massive MIMO communications systems
Lazaros Alexios Iliadis1*, Zaharias D. Zaharis3, Sotirios Sotiroudis1, Panagiotis Sarigiannidis2,
George K. Karagiannidis3 and Sotirios K. Goudos1*
1 Introduction
Massive Multiple-Input-Multiple-Output (M-MIMO) communications systems play a
fundamental role in improving today’s wireless network communications, and different
variants have been proposed for beyond 5G and 6G telecommunications [1]. Some of
their advantages over previous configurations are the following: (i) high spectrum effi-
ciency, (ii) power efficiency and high reliability [1]. However, M-MIMO networks follow
the classical cellular paradigm, which results in large rate variations, inter-cell interfer-
ence and often a poor quality of service [1, 2]. Although there are many discussions in
the literature about overcoming these challenges, at this moment the most promising
idea seems to be the Cell-free (CF) networking and especially the CF M-MIMO technol-
ogy [2].
e key idea behind CF M-MIMO lies on the notion of distributed operation [2–6].
In the CF M-MIMO framework,
L
distributed access points (APs) serve
K
users such
Abstract
The fifth generation (5G) of telecommunications networks is currently commercially
deployed. One of their core enabling technologies is cellular Massive Multiple-Input-
Multiple-Output (M-MIMO) systems. However, future wireless networks are expected to
serve a very large number of devices and the current MIMO networks are not scalable,
highlighting the need for novel solutions. At this moment, Cell-free Massive MIMO (CF
M-MIMO) technology seems to be the most promising idea in this direction. Despite
their appealing characteristics, CF M-MIMO systems face their own challenges, such as
power allocation and channel estimation. Deep Learning (DL) has been successfully
employed to a wide range of problems in many different research areas, including
wireless communications. In this paper, a review of the state-of-the-art DL methods
applied to CF M-MIMO communications systems is provided. In addition, the basic
characteristics of Cell-free networks are introduced, along with the presentation of the
most commonly used DL models. Finally, future research directions are highlighted.
Keywords: Cell-free massive MIMO, Deep learning, User-centric cell-free massive
MIMO, 6G
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REVIEW
Iliadisetal. J Wireless Com Network (2022) 2022:68
https://doi.org/10.1186/s13638‑022‑02153‑z
EURASIP Journal on Wireless
Communications and Networking
*Correspondence:
liliadis@physics.auth.gr;
sgoudo@physics.auth.gr
1 ELEDIA@AUTH, School
of Physics, Aristotle University
of Thessaloniki, Thessaloniki,
Greece
2 Department of Informatics
and Telecommunications
Engineering, University
of Western Macedonia, Kozani,
Greece
3 Department of Electrical
and Computer Engineering,
Aristotle University
of Thessaloniki, Thessaloniki,
Greece
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Iliadisetal. J Wireless Com Network (2022) 2022:68
that
L≫K
distributed over space. In such a configuration, neither cells nor cell-bound-
aries exist. A central processing unit (CPU) is connected with the APs via the backhaul
network, while all users are served based on a cooperation between the APs which use
time-division duplexing (TDD) mode. e main benefits over the classical cellular tech-
nology are: (i) smaller SNR variations, (ii) managing interference and (iii) increased SNR
values [2–6].
Deep Learning (DL) is a subset of Machine Learning (ML) class of computational
methods and recently has achieved impressive results in many different research areas.
DL is based on neural networks’ architectures, using multiple layers (“deep”) of artificial
neurons [7]. DL has been utilized in the field of wireless communications too, introduc-
ing a data driven approach and offering new insights, such as new system’s modeling [8,
9] and distributed computation [10]. In this context, there is ongoing research in the
applications of DL in CF M-MIMO, thus providing new insights in the current research.
Fig. 1 depicts the number of papers referring to DL applications in CF M-MIMO
systems.
1.1 Related work
e applicability of CF M-MIMO to 6G vision is thoroughly discussed in [3]. An exten-
sive presentation of the foundations of user-centric CF M-MIMO is provided in [2]. In
[4] the authors provide a survey of the state-of-the-art literature on CF M-MIMO along
with the characteristics of such systems. e applications of DL in wireless communica-
tions are presented in [8].
To the best of our knowledge this is the first study that discusses explicitly the applica-
tions of DL methods to the field of CF M-MIMO, providing at the same time an intro-
duction to both CF M-MIMO systems and current DL architectures.
1.2 Paper motivation andcontributions
e motivation behind this work may be framed in the need to study in depth the ideas
behind future 6G vision. In particular, both CF M-MIMO and DL methods are consid-
ered viable solutions for many design and optimization problems, such as resource allo-
cation, energy efficiency and managing interference.
Fig. 1 Number of papers referring to DL applications in CF M-MIMO
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Iliadisetal. J Wireless Com Network (2022) 2022:68
is paper considers the application of DL models for CF M-MIMO systems. e
main contributions of this work are summarized as follows:
• An introduction to CF M-MIMO and user-centric CF M-MIMO networks is pre-
sented here.
• An extended review of the work around DL methods for CF M-MIMO systems is
provided. Among the DL methods, special focus is given on federated learning and
its utilization in resource management, and channel estimation
• Future research directions are discussed, including research challenges and the
incorporation of DL methods to the 6G vision
e rest of this paper is structured as follows: DL models are briefly described in sect.2. In
sect.3 the details of CF M-MIMO configurations are provided. In addition, the user-cen-
tric approach is also presented. Section4 considers the application of DL in CF M-MIMO
networks, sect.5 discusses the future research challenges and also concludes this work.
2 DL models
ere are three main DL models that are mostly employed in the current CF M-MIMO
literature; feed-forward neural networks (FFNNs), recurrent neural networks (RNNs)
and convolutional neural networks (CNNs). In this section, the details about these mod-
els are briefly discussed, providing further references for the interested reader. In addi-
tion, Reinforcement Learning (RL), one of the three major ML paradigms (the other two
are Supervised Learning and Unsupervised Learning), is briefly presented in this section.
2.1 Feed‑forward neural networks
e key component of every DL architecture is the notion of the artificial neuron. Arti-
ficial neurons are computational units (functions) that try to mimic in mathematical
terms the behavior of biological neurons. e functionality of such a unit is very simple;
the neuron takes some input and produces an output (or an activation, with respect to
the action potential of a biological neuron). For inputs in vector form, each individual
input is weighted in a separated way, and then the sum is passed through a nonlinear
function known as an activation function [7].
A FFNN is the first proposed architecture comprised of multiple artificial neurons. In
such a model, the connections between the nodes do not form a cycle or a loop and the
information is transferred only forward. Both the training and the learning are achieved
through the stochastic gradient descent (SGD) algorithm. e pseudo-code for the SGD
algorithm is given in Alg. 1.
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Iliadisetal. J Wireless Com Network (2022) 2022:68
where
η
is the learning rate, w the weight and C the loss function (cost) which com-
putes the distance between the current output of the algorithm and the expected output.
ere are many techniques for making FFNNs work efficiently, but the most fre-
quently used is the back-propagation [7] algorithm. For the loss function, back-propaga-
tion technique utilizes the chain rule from calculus, computing the gradient one layer at
a time, iterating backward from the last layer. In Fig.2, the basic architecture of a FFNN
with one hidden layer is shown.
e mathematical formulation of FFNNs (that can be extended to other DL architec-
tures) considers an input vector
x
, a set of weights
w
, a bias b and an activation function
f. e output of the last layer is
As mentioned before this output is compared with the expected output vector.
2.2 Recurrent neural networks
As stated before FFNNs’ architecture does not contain either cycles or loops (acyclic
graphs). A different approach is introduced with Recurrent Neural Networks (RNNs).
RNNs adopt a notion of memory by utilizing their internal state to process variable
length sequences of inputs [7, 11]. is characteristic makes them suitable for tasks
such as time series forecasting, handwriting recognition or speech recognition [11].
ere are many RNN architectures, such as Gated Recurrent Units (GRUs), Bi-direc-
tional RNNs, Hopfield networks, etc.
A very successful variant of RNNs are the long short-term memory (LSTM) net-
works [12, 13]. e building blocks of LSTMs are cells which have an input gate, an
output gate and a forget gate. e main advantage over classical RNNs is that this
type of cell is capable of remembering values over arbitrary time intervals. In addi-
tion, the flow of information is regulated by the three aforementioned gates [12].
(1)
y=f(wT·x+b)
Fig. 2 FFNN with one hidden layer
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In mathematical terms, a LSTM network can be formulated in the following way.
For an input vector
xt∈
R
N
at time step t, and M hidden layers, the forget gate’s acti-
vation vector
Ft∈(0, 1)M
is given by
where
WF
and
UF
are matrices of weights,
qt∈(
0, 1
)M
is the hidden state vector and
bF
is the bias vector.
In addition, the input/update gate’s activation vector
It∈(
0, 1
)M
and the output’s
activation vector
Ot∈(
0, 1
)M
are expressed in a similar way,
and
where the subscripts I and O mean input and output, respectively, and the other symbols
have the same meaning as previously.
A LSTM unit has also a cell input activation vector
Ct∈(−
1, 1
)M
, which is given by,
Combining the above equations, the cell state vector and the hidden state vector are
updated with the following rules
where
◦
denotes the Hadamard product,
S0=0
and
q0=0
. Finally,
Although the DL research field seems to move towards replacing LSTMs with Trans-
formers for many tasks [14], LSTMs still remain one of the most commonly used
architectures.
2.3 Convolutional neural networks
e ImageNet Large Scale Visual Recognition Challenge (ILSVRC), has been proved
a driving force for many advancements in computer vision (CV) [15]. e dominant
paradigm in this field is the application of convolutional neural networks (CNNs).
CNNs utilize the convolution operation instead of the general matrix multiplication
[7, 16]. CNNs have found success not only in CV tasks but also in time series fore-
casting, video processing, natural language processing, etc. [7].
CNNs are composed of at least one convolutional layer and often fully connected lay-
ers and pooling layers, as shown in Fig.3. e latter reduces the size of the incoming
data. In contrast to a fully connected layer, in a convolutional layer exists the so-called
neuron’s receptive field, which means that every single neuron receives input from only a
restricted area of the previous layer.
(2)
Ft
=σ(W
F
x
T
t
+U
F
q
T
t−1
+b
F)
(3)
It
=
σ(WIxT
t
+
UIqT
t−1
+
bI)
(4)
Ot=σ(WOxT
t+UOqT
t−1+bO)
(5)
Ct
=σ(
WCxT
t
+
UCqT
t−1
+
bC)
(6)
St=Ft◦St−1+It◦Ct
(7)
qt=Ot◦tanh(St)
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Most CNNs use at some point as an activation function the Rectified Linear Unit
(ReLU) function, or variants. ReLU is simply defined as [7],
Despite its mathematical simplicity, its use has been proved valuable in order to avoid
over-fitting.
2.4 Reinforcement learning
Reinforcement Learning (RL) is one of the three major ML paradigms [7]. In this frame-
work, a learning agent is able to act within its environment, take actions and learn
through trial and error. Finding a balance between exploration of an “unknown space”
and exploitation of its “current knowledge”, the agent maximizes a cumulative reward
[17]. Recently the combination of DL architectures with RL (DRL) in a unified setup has
provided solutions to many difficult problems [18].
RL has many similarities with the fields of dynamic programming and optimal con-
trol [19]. In this context, the environment is often modeled as Markov decision process
(MDP). However, RL methods do not always assume the knowledge of an exact model of
the environment. Formally, a MDP is defined as a 4-tuple
(S,A,P,Q)
, where S is the state
space, A is the action space, Q is the immediate reward and the probability that action
a1
in state
s1
at time t will lead to state
s2
at time t + 1 is given by
Deep Q-Learning (DQL) is a branch of DRL which is utilized for many tasks in different
areas, including wireless communications. In DQL, a Q-value is an estimation of how
good it is to take the action A at the state S at time t. In this way, a matrix is created
where the agent can refer to in order to maximize its cumulative reward [17].
e realization that the matrix entries have an importance relative to the other entries,
leads us to approximate the matrix values with a deep neural network.
Another frequently used DRL method that exploits DQL characteristics is the deep
deterministic policy gradient (DDPG) algorithm. DDPG is an “off-policy” method that
(8)
f(x)=max(0, x)
(9)
Pa1(s
1
,s
2
)=Pr(st+
1
=s
2
|st=s
1
,at=a
1
)
(10)
Q
π(St,At)=E
k
γkRt+1+k|St,At,k=0, 1,
...
Fig. 3 Convolutional neural network
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Iliadisetal. J Wireless Com Network (2022) 2022:68
consists of two entities; the actor and the critic. e actor is modeled as a policy network
and its input is the state and its output the exact continuous action (instead of a prob-
ability distribution over actions). e critic is a Q-value network that takes in state and
action as input and outputs the Q-value. [20].
3 CF M‑MIMO
In this section, the basic characteristics of CF M-MIMO networks and user-centric CF
M-MIMO networks are discussed. For a detailed analysis of the fundamentals of cellular
M-MIMO networks the interested reader may refer to [1], while for CF M-MIMO [2, 3]
and [4].
3.1 Conventional CF M‑MIMO
Current wireless communications systems are based on the cellular architecture, where
the coverage area is divided into cells. Cell-free technology has been proposed as a
change of paradigm in communications engineering, trying to meet the beyond 5G
telecommunications’ demands [21]. Fig.4 shows the number of papers referring to CF
M-MIMO technology.
Following [2], CF M-MIMO can be described as an ultra-dense wireless network
where joint transmission and reception are achieved through the cooperating APs which
serve the user equipment (UE). A benefit of the CF M-MIMO is that the system as a
whole makes use of the physical layer concepts from the cellular M-MIMO area. More
specifically, a CF M-MIMO network consists of numerous distributed APs which are
connected to a central processing unit (CPU). In this way, there is no need for cells and
the users are served simultaneously by all APs, as illustrated in Fig.5. e motivation
behind this idea is to provide an, as uniform as possible, quality of service in the given
space.
CF M-MIMO brings a change of paradigm in wireless communications, offering many
advantages over the classical cellular telecommunications systems. In particular, CF
M-MIMO technology offers (i) smaller SNR variations, (ii) managing interference and
(iii) increased SNR values [2–6].
Fig. 4 Number of papers referring to CF M-MIMO
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Smaller SNR variations are achieved through uniform SNR across the coverage area.
e joint transmission from multiple APs, helps suppressing the inter-cell interfer-
ence. e involvement of APs, with weaker channels in the transmission, results in an
increased signal-to-interference-and-noise ratio (SINR). In the cellular paradigm, only
the AP with the best channel is utilized. In addition, having a much larger number of
antennas than users, has the effect of creating many spatial degrees of freedom to sepa-
rate the UE in space. As a result the transmitted and received signals can be processed
using linear methods [2].
3.1.1 Conventional TDD‑based CF M‑MIMO
Most CF M-MIMO scenarios consider a time division duplexing (TDD) operation. Here,
the basic system model is introduced. For a discussion of FDD operation, one can refer
to [3].
Considering the deployment of a CF M-MIMO network, it is going to consist of
L
distributed APs, each equipped with
M
antennas serving
K
single-antenna users. e
scenario considering multi-antenna users can be modeled in the same way, by just add-
ing more single-antenna users.
Each AP acquires channel state information (CSI) between itself and all users via the
uplink channel estimation method. e channel between the l-th AP and the k-th user
is denoted by
hkl ∈
C
N
. e channel is considered approximately constant during coher-
ence time
τc
and follows a correlated Rayleigh fading distribution,
(11)
hkl ∼NC(0
,
Corkl )
Fig. 5 CF M-MIMO network
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In the above equation,
Corkl
is simply the spatial correlation matrix composed of the
small-scale fading and large-scale fading.
For channel estimation we use
τp
mutually orthogonal pilots
q
1
,...,q
τ
p
, such that
||
q
j
||
2
2
=τ
p
,
j=1, ...,τp
and
τp
is the length of the pilot. e uplink received signal cor-
responding to the pilot signal at the l-th AP is [2]
where
pk≥0
the transmit power of the k-th user,
np
l
∈C
N
×τ
p
is the additive noise and
each element is considered i.i.d.
However, despite their appealing amenities CF M-MIMO networks face serious chal-
lenges regarding their practical implementation. e main one is that this configuration
is not scalable as the number of users increases [2]. As a result, they cannot be deployed
for the future 6G wireless networks.
3.2 User‑centric CF M‑MIMO
As previously stated, the main challenge that CF M-MIMO systems face, is the fact
that they are not scalable, thus making them impractical for 6G applications. In order
to overcome this problem, user-centric CF M-MIMO has been proposed. In this new
setup, a subset of APs is transmitted to the UE. As a result, the fronthaul signaling is
reduced, while at the same time the performance loss is negligible. Stated differently,
user-centric CF M-MIMO makes use of dynamic cooperation clustering, where a subset
of APs serves the user k. In [2], one proved that this new configuration is scalable.
Cellular M-MIMO communication systems make use of two emerging phenomena:
(i) Channel hardening and (ii) favorable propagation, which explain the resulting perfor-
mance gain. Channel hardening explains the situation where a fading channel has almost
the same effects with a non-fading channel. Favorable propagation is defined in the case
of the vector-valued channels [22, 23]. ese two properties are extended in the user-
centric CF M-MIMO framework, since the above characteristics remain. However, a
proper mathematical analysis is needed.
e mathematical formulation of user-centric function extends the results obtained
in the previous section, but also utilizes the concept of dynamic cooperation clustering
(DCC) [24]. DCC refers to the idea that every user selects which antennas should serve
them.
Let us consider the scenario discussed previously and a set of diagonal matrices
Dkl ∈
C
N×N
. ese matrices establish the connection between users and antennas. If an
antenna is allowed to serve the k-th user then the matrix
Dkl
is transformed to the iden-
tity matrix. e DCC framework allows only a subset of the APs to participate [3], so the
received downlink signal at k-th user is given by [2],
(12)
Y
p
l=
K
k=1
p1/2
khklqT
jk+np
l
,
(13)
yk=
L
l=1
hH
kl
K
k=1
Dklwkl sk+n
k
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where
wkl
is the precoding vector,
sk
is the transmitted signal and as before
nk∼CN (0, σ2)
is the additive Gaussian noise.
It is evident that if
Dkl =0
, the k-th user is not served by l-th AP.
4 DL forCF M‑MIMO systems
DL has been recently applied in many tasks in the field of wireless communications [8].
In addition DL is considered a main component of beyond 5G communications systems.
In this section, the application of DL models in CF M-MIMO systems is reviewed. In
Table1, the results presented in this section are summarized.
4.1 Resource allocation andpower eciency
In wireless networks, power allocation is a very important factor for the system’s overall
efficiency [45, 46]. When power allocation is properly performed, signal communication
can take place in a near-optimum way. e allocation of power to the individual users
should take into consideration two things: (i) the maximization of the minimum capacity
guaranteed to each of them and (ii) the channel’s dynamics [1]. Exploiting the character-
istics of DL techniques one can approximate the power allocation and control problem.
e sum rate maximization problem indirectly maximizes the spectral efficiency of the
system. A solution to this problem is discussed in [25]. e sum rate describes the sum-
mation of the achievable rates of multiple concurrent transmissions and the problem of
its maximization is a non-convex one. In that research paper, power allocation prob-
lem is converted into a standard geometric program (GP) and the channel statistics is
exploited to design the respective power elements. Employing large-scale-fading (LSF)
with a CNN allows to determine a mapping from the LSF coefficients and the optimal
power through solving the sum rate maximization problem.
e uplink power control is studied in [26]. In the Supervised Learning framework,
a FFNN is trained to learn the pairs of input-output data. In this particular setting, the
optimal solution of the power allocation strategy is the goal of the FFNN’s training. In a
similar manner, the same problem is tackled in [27]. e authors train a LSTM, taking
into consideration different scenarios.
A different approach is given in [28]. An Unsupervised Learning setting is estab-
lished, where a FFNN is designed to learn the optimum user power allocations which
maximize the minimum user rate. In this way there is no need to know in advance the
optimal power allocations. An alternative research direction in problem of downlink
power allocation is provided in [29]. First the authors proved a generalization of max-
imum ratio precoding and then they trained a NN for every AP. e goal is to mimic
system-wide max-min fairness power allocation. One major benefit of that paper over
Table 1 DL methods for CF M-MIMO systems
Applications DL architectures Research papers
Resource allocation FFNNs, LSTM, RL [25–35]
Channel estimation FFNN, CNN, Unsupervised Learning [36–40]
Federated learning FL [41, 42]
Other FFNN, RL [43, 44]
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other candidate solutions, is the use of only local information, outperforming the
state-of-the-art power allocation algorithms for CF M-MIMO scenarios.
Maximum ratio transmission (MRT) as a concept for multiple antenna systems was
introduced in [47]. MRT combined with a CF M-MIMO network results in smaller
fronthaul overhead. e work proposed in [30] considers the task of finding practi-
cal near-optimal power control utilizing DL methods. e whole procedure consists
of a CNN whose input is the channel matrix of large-scale fading coefficients and
its outputs are the total transmit power of each AP. is information is then used
to compute the downlink power control for each user, with a low-complexity convex
program.
RL has also been employed in resource allocation problems. More specifically, in
[31] DQL is utilized. e allocation of the downlink transmission powers in a CF
M-MIMO configuration is achieved by making use of a DQN. e sum spectral effi-
ciency optimization problem is discussed. Spectral efficiency refers to the maximum
number of bits of data that can be transmitted to a specified number of users per
second per Hz while maintaining an acceptable quality of service. Exploiting the RL
framework of trial-and-error interactions with the environment over time, the DQN
is trained taking as input of the long-term fading information and then it outputs the
downlink transmission power values.
A similar approach is used in [32]. e proposed DQN and the deep deterministic
policy gradient (DDPG) methods are employed for the task of dynamic power alloca-
tion. e goal here is to maximize the sum-spectral efficiency. e numerical results
showed a competitive performance with the state-of-the-art weighted minimum
mean square error (WMMSE) algorithm.
Another important factor in the operation of wireless networks is the power effi-
ciency and the long-term energy efficiency. e long term energy efficiency of the
uplink beamforming is addressed in [33]. Exploiting the information obtained from
the MMSE algorithm, an estimation of SINR is given. en the long-term energy effi-
ciency is defined as a function of the beamforming matrix. As a final step, the authors
utilize DRL algorithm based on deep deterministic policy gradient to model the
dynamic beamforming design.
In the current literature model-based approaches regarding power control have
prevailed. However, in [34] the authors exploit a model-free solution for downlink
power control, using also the deep deterministic policy gradient algorithm (DDPG)
with FFNNs.
Industrial Internet of ings (IIoT) is developed in parallel with other IoT networks.
e architecture and optimization of such networks are considered as difficult prob-
lems, hence DL techniques are often applied. Cell-free architectures have been proposed
for IIoT networks. In [35] a systematic study of DRL in CF M-MIMO IIoT is presented.
In particular, considering a cross-layer optimization scenario (power allocation in the
physical layer and random access in the medium access layer), a dual deep deterministic
policy gradient (DDPG) algorithm is designed for resource management tasks.
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4.2 Channel estimation
Channel estimation is a fundamental concept in wireless communications and refers
to the process of characterizing the dynamics of the wireless channel [23].
e authors of [36] formulate the concept of channel mapping in space and fre-
quency. Considering a scenario with two sets of antennas with different frequency
bands, the channels and the frequencies of the first one are mapped to the channels
and frequency bands of the other set of antennas. Leveraging the results of their pro-
posed analysis, a FFNN was utilized for channel mapping in a CF M-MIMO model.
is DL method managed to reduce both the downlink training/feedback and the
fronthaul signaling overhead.
In [37] the authors employ a flexible denoising convolutional neural network (FFD-
Net) for the task of channel estimation in a CF M-MIMO framework. e results
showed that the time spent for the FFDNet training is much less than the time that is
needed from the state-of-the-art channel estimators, such as CNN, achieving at the
same time similar performance. In order to remove the need for relative reciprocity
calibration based on the cooperation of antennas, a cascade of two FFNNs is pro-
posed in [38].
Unsupervised Learning is employed for the task of decentralized beamforming in
[39]. e authors propose two different deep neural networks models, one fully dis-
tributed and the other partially distributed. e training is performed in an unsu-
pervised framework and each model is able to perform decentralized coordinated
beamforming with zero or limited communication overhead between APs and the
network controller, for both fully digital and hybrid precoding. e proposed meth-
ods achieve a near-optimal sum-rate while also reducing significantly the complexity.
For the case of enhanced normalized conjugate beamforming, the authors in [40]
derived an exact closed-form expression for an achievable downlink spectral effi-
ciency. To achieve such a result, they assumed independent Rayleigh fading chan-
nels. DL could be proved useful for other cases, where such a modeling would not be
sufficient.
4.3 Federated learning
Federated Learning (FL) is a sub-field of ML algorithms, where the models are trained
across multiple decentralized devices, while at the same time they hold only local
data, without exchanging them (offering advanced security). is is an alternative
approach compared to traditional centralized ML techniques where all the local data-
sets are uploaded to one server [48].
Wireless FL faces many challenges. In [41] a novel scheme for CF M-MIMO net-
works is proposed. is scheme tries to establish a stable operation in any FL frame-
work by allowing each instant of all the iterations of the FL framework to happen in a
large-scale coherence time. e authors take into account an existing FL framework
as an example and target FL training time minimization for this framework.
e authors in [42] try to answer the following question: How does a wireless net-
work support multiple FL groups? eir proposal is CF M-MIMO network to estab-
lish a stable operation of multiple FL processes. en, a novel scheme is developed
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Iliadisetal. J Wireless Com Network (2022) 2022:68
which asynchronously executes the iterations of FL processes under multi-casting
downlink and conventional uplink transmission protocols. As a final step, an optimal
low-complexity resource allocation algorithm is used.
4.4 Other applications
Apart from the aforementioned DL applications in CF M-MIMO, there are some
insights in other possible use-case scenarios. Considering the case of a large scale CF
M-MIMO network, a FFNN is utilized in [43] for pilot assignment. e goal is to maxi-
mize the sum spectral efficiency.
Examining the advantages of joint cooperation clustering and content caching in CF
M-MIMO, a DRL approach is discussed in [44] demonstrating good energy efficiency
performance with no prior information requirements.
5 Future directions andconclusions
ere is a consensus among researchers in the field of communications engineering that
CF M-MIMO will play a very important role in the deployment of beyond 5G networks.
As a result, a growing number of papers relative to these issues are being published
every year. Although DL methods seem to offer a data-driven approach, thus improving
the overall performance, it is likely that standalone techniques will not be proved suffi-
cient. On the contrary, advanced signal processing techniques, compressed sensing and
DL methods employed in a combined way which leverages the individual characteristics
of each method are more likely to offer solutions in the near future.
e main drawback of practical implementation of DL models in wireless communica-
tions is their computational cost. Reducing the required memory and utilizing results
from a “classical” analysis will provide better resource usage. In addition power alloca-
tion and energy efficiency will be central in the near-future research, while DL applica-
tions focusing only on user-centric CF M-MIMO are also expected.
Another factor that will enable future research in this field is the publication of the
codes and the rest computational tools that were used along with the published works.
Publicly available datasets and simulation codes have helped other fields to grow rapidly.
It is inevitable that such practices will boost the research activity in wireless communi-
cations in general.
In this article, an extensive review of the work around DL methods for CF M-MIMO
systems was provided. More specifically, DL architectures applied on the field of CF
M-MIMO technology were reviewed and the basic information about the CF MIMO
systems was discussed, including the user-centric variant. e model’s equations were
presented for both conventional systems and the user-centric approach. e survey was
focused on resource allocation, channel estimation and federated learning problems. In
these three areas, DL methods seem to achieve better results. Finally, future research
directions were highlighted, offering insights for further study.
Abbreviations
5G Fifth generation
6G Sixth generation
MIMO Multiple-input-multiple-output
CF M-MIMO Cell-free massive MIMO
DL Deep learning
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Iliadisetal. J Wireless Com Network (2022) 2022:68
ML Machine learning
NN Neural networks
FL Federated learning
AP Access point
TDD Time division duplex
FDD Frequency division duplex
CPU Central processing unit
FFNN Feed-forward neural network
RNN Recurrent neural network
CNN Convolutional neural network
LSTM Long short-term memory
RL Reinforcement learning
DRL Deep reinforcement learning
WMMSE Weighted minimum mean square error
DCC Dynamic cooperation clustering
IoT Internet of things
IIoT Industrial Internet of things
ReLU Rectified linear unit
CSI Channel state information
Author contributions
All authors read and approved the final manuscript
Funding
This research was supported by the European Union, through the Horizon 2020 Marie Skłodowska-Curie Research and
Innovation Staff Exchange Programme “Research collaboration and mobility for beyond 5G future wireless networks
(RECOMBINE)” under grant agreement no. 872857.
Availability of data and materials
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
Declarations
Competing interests
The authors declare that they have no competing interests.
Received: 8 June 2022 Accepted: 27 July 2022
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