1 Role of Deep Learning in Wireless Communications Wei Yu Fellow IEEE Foad Sohrabi Member IEEE and Tao Jiang Graduate Student Member IEEE

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Role of Deep Learning in Wireless Communications

Wei Yu, Fellow, IEEE, Foad Sohrabi, Member, IEEE, and Tao Jiang, Graduate Student Member, IEEE

Abstract—Traditional communication system design has al-

ways been based on the paradigm of ﬁrst establishing a math-

ematical model of the communication channel, then designing

and optimizing the system according to the model. The advent

of modern machine learning techniques, speciﬁcally deep neural

networks, has opened up opportunities for data-driven system

design and optimization. This article draws examples from the

optimization of reconﬁgurable intelligent surface, distributed

channel estimation and feedback for multiuser beamforming, and

active sensing for millimeter wave (mmWave) initial alignment to

illustrate that a data-driven design that bypasses explicit channel

modelling can often discover excellent solutions to communication

system design and optimization problems that are otherwise

computationally difﬁcult to solve. We show that by performing

an end-to-end training of a deep neural network using a large

number of channel samples, a machine learning based approach

can potentially provide signiﬁcant system-level improvements as

compared to the traditional model-based approach for solving

optimization problems. The key to the successful applications

of machine learning techniques is in choosing the appropriate

neural network architecture to match the underlying problem

structure.

Index Terms—Active sensing, channel modelling, distributed

source coding, deep neural network, machine learning, massive

multiple-input multiple-output (MIMO), reconﬁgurable intelli-

gent surface, wireless communications.

I. INTRODUCTION

Modern machine learning techniques, speciﬁcally deep neu-

ral networks (DNNs), have enabled tremendous progress for

diverse applications, ranging from speech recognition, natural

language processing, image classiﬁcation, to data analytics

and self-driving cars, and many more. In this article, we ask

the following question: Is there a role for machine learning

in physical-layer wireless communications system design? If

so, where do opportunities lie, and where would the potential

beneﬁts come from?

Fundamental to the phenomenal success of the machine

learning techniques across a wide range of applications is

its apparent universal ability to approximate any functional

mapping from an input space to an output space, given

sufﬁciently complex neural network structure and enough

training data [1]. In fact, common characteristics of application

domains where machine learning has made the most impact,

are that the inputs to these tasks are high-dimensional complex

data, whose structure needs to be explored, while the outputs

of these tasks can either be categorical (e.g., classiﬁcation,

segmentation, sentiment analysis) or have complex structures

Manuscript to appear in IEEE BITS the Information Theory Magazine.

Wei Yu and Tao Jiang are with The Edward S. Rogers Sr. Department of

Electrical and Computer Engineering, University of Toronto, Canada. (e-mails:

weiyu@ece.utoronto.ca, taoca.jiang@mail.utoronto.ca) Foad Sohrabi is with

Nokia Bell Labs, New Jersey, USA. (e-mail: foad.sohrabi@gmail.com) This

work is supported by the Natural Sciences and Engineering Research Council

(NSERC) via the Canada Research Chairs program.

themselves (e.g., machine translation, image labelling). The

ﬁeld of machine learning has developed myriad techniques

to enable automatic feature extraction and to explore the

structure of the problem in order to efﬁciently train a DNN

to map the input to the desired output. The machine learning

paradigm essentially solves optimization problems by pattern

matching. This is a vastly different philosophy as compared to

the traditional model-based information theoretical approach

to communication system design.

This article aims to illustrate that machine learning has

an important role to play even in the physical-layer wireless

communications, which has traditionally been dominated by

model-based design and optimization approaches. This is so

for several reasons:

•First, traditional wireless communication design method-

ologies typically rely on the channel model, but models

are inherently only an approximation to the reality. In

applications where the models are complex and the chan-

nels are difﬁcult to estimate, a data-driven methodology

that allows the system design to bypass explicit channel

estimation can potentially be a better approach.

•Second, modern wireless communication applications of-

ten involve optimization problems that are high dimen-

sional, nonconvex, and difﬁcult to solve efﬁciently. By

exploiting the availability of training data, a machine

learning approach may be able to learn the solutions of

the optimization problems directly. This can lead to a

more efﬁcient way to explore the nonconvex optimization

landscape than the traditional model-based optimization

approaches.

•Third, traditional communication system designs are

based on the principle of source-channel separation and

the optimal design of compression and channel codes.

But when the encoder and the decoder are block-length

and/or complexity constrained, or when the overall com-

munication scenario involves multiple transmitters and

multiple receivers, the optimal design of practical encoder

and decoder is highly challenging. In this realm, there is

the potential for discovering better source and channel

encoders and decoders using machine learning, as many

of these code design problems boil down to solving

optimization problems over the codebook structure for

which data-driven methods may be able to identify better

solutions more efﬁciently.

The ﬁeld of machine learning for communication system

design has exploded in recent years [2]–[5]. We mention

some of the references here, e.g., in source and channel

coding [6]–[8], waveform design [9], signal detection [10]–

[12], resource allocation [13]–[18] and channel estimation

[19], [20], etc. This article does not attempt to do justice in

arXiv:2210.02596v1 [cs.IT] 5 Oct 2022

surveying the entire literature and the recent progress on this

topic. Instead, we focus on the questions of why and how

machine learning can beneﬁt wireless communication system

design by presenting the following three speciﬁc examples.

First, we consider communication scenarios in which a

naive parameterization of the channel would involve a large

number of parameters, thus making channel estimation a

challenging task. Speciﬁcally, we show that in a wireless

communication system involving a reconﬁgurable intelligent

surface (RIS), comprising of a larger number of reﬂective

elements, a machine learning approach that directly optimizes

the reﬂection coefﬁcients without ﬁrst estimating the channel

can signiﬁcantly improve the overall performance [21].

Second, we consider a distributed source coding problem in

the context of channel estimation and feedback for a massive

multiple-input multiple-output (MIMO) system, and show that

short block-length code design for distributed data compres-

sion with system-level objective is feasible and can result

in signiﬁcant performance improvements over the single-user

data compression codebook design [22].

Third, we use an active sensing problem for millimeter

wave (mmWave) initial alignment to illustrate the role of

machine learning in exploring the optimization landscape in

a complex sequential learning problem [23]. We show that

selecting the right neural network architecture to match the

problem structure is crucial for its success.

II. INFORMATION THEORETICAL APPROACH TO

COMMUNICATION SYSTEM DESIGN

Information theory has been the guiding principle in the

development of communication system design in the past

seventy years. The driving philosophy in information theory

has always been reductionist—putting it in words of a famous

quote: everything should be as simple as possible, but no sim-

pler. A celebrated example of this philosophy is the additive

white Gaussian noise (AWGN) channel model, in which the

choice of the Gaussian noise distribution is justiﬁed both by a

central limit theorem argument based on the assumption that

the overall noise is comprised of many independent small

components and by the fact that the Gaussian distribution

is the worst-case noise distribution for the additive channel.

The AWGN model is cherished in the research community

and has played a central role in many historical developments

in communication theory (e.g., from time-domain equaliza-

tion, to orthogonal frequency-division multiplex, to multiuser

detection), in coding theory (e.g., from maximum likelihood

decoding, to Viterbi algorithm, to Turbo, low-density parity-

check, and polar codes), and in multiuser information theory

(e.g., from multiple-access, to broadcast, and to interference

channel models).

The wireless channels are however much more complicated

than the AWGN channel model. The wireless channel can

be frequency selective; it is inherently time-varying; it often

involves multiple users and multiple antennas. Historically,

communication engineers have invested heavily in developing

models for various types of wireless channels. These mod-

els are often based on the physics of electromagnetic wave

propagation; many of these models are statistical in nature;

these channel models have played an important role in the

design, analysis, performance evaluation, and standardization

of generations of wireless systems [24].

Channel modelling is important in wireless communication

engineering because most modern wireless systems operate

under the framework of ﬁrst estimating the channel, then

feeding back the estimated channel to the transmitter, and

ﬁnally optimizing transmission and reception strategies to

maximize the mutual information between the input and the

output. In this article, we argue however that this model-then-

optimize approach is not necessarily always the best approach.

III. FROM MODEL-BASED OPTIMIZATION TO

LEARNING-BASED DESIGN

A. Model-Based Communication System Design

In traditional communication system design, maximizing the

capacity of a wireless link typically requires channel estima-

tion; the process of channel estimation always depends on

the channel model. Choosing which model to use is however

an art rather than science. This is because wireless channels

often have inherent structures that make certain models more

appropriate than others. For example, a MIMO channel with

Mtransmit antennas and Nreceive antennas can simply be

modelled as a M×Nmatrix. But a mmWave massive MIMO

channel often has a sparsity structure, corresponding to the

ﬁnite number of propagation paths from the transmitter to

the receiver, so that a sparse path-based model in the spatial

domain is a more efﬁcient representation of the channel.

Likewise, a frequency-selective channel can be modelled by

its channel response across the frequencies. But, the frequency

selectivity is usually a consequence of the different delays

across the multiple paths, so the channel variations across the

frequencies are correlated. Instead of estimating the channel

in the frequency domain, a multipath time-domain model may

be more appropriate.

Moreover, the channel estimation process requires specify-

ing a loss function. The squared-error metric is often adopted

for tractability reasons, but minimizing the mean-squared-

error (MSE) of the estimates of the channel parameters does

not necessarily correspond to maximizing the overall system

objective. For example, some parts of the channel may be more

important to describe than others. Clearly, the speciﬁc param-

eterization of the channel and the choice of the estimation

error metric have a signiﬁcant impact on the ultimate system

performance.

Traditionally, wireless researchers rely on experience and

engineering judgement in choosing the best channel model

and the best optimization formulation. The design decisions

need to balance the inherent trade-offs between: (i) how

complex the model is, e.g., the number of parameters in

the model; (ii) how well the model approximates the reality;

(iii) how easy it is to estimate the model parameters; (iv)

how easily the model can be used for subsequent transmitter

and receiver optimization. We emphasize that in a wireless

fading channel with limited coherence time/frequency, model

estimation comes at a signiﬁcant cost in term of the coherence

012345

0.2

0.4

0.6

0.8

1.2

1.4

model

objective

Model-Based Approach

Data-Driven Approach

solution

Fig. 1. Traditional wireless system design follows the paradigm of model-then-optimize, as shown in the top branch. The design problem is modelled

mathematically; the model parameters are then estimated, which allows the associated optimization landscape to be characterized; ﬁnally, the optimal solution

is obtained by mathematical programming. The machine learning approach aims to directly learn the optimal solution from a representation of the problem

instance, as shown in the bottom branch. The neural network is trained over many problem instances, by adjusting its weights according to the overall system

objective as a function of the representation of the problem instances.

slots occupied by pilot transmissions. For example, a highly

complex model may better approximate the reality, but may

require too many pilots for parameter estimation, hence may

not be worth the effort. The point is that there is no universal

theory about how to choose the best channel model and how

to best perform channel estimation. To characterize and to take

advantage of the underlying channel structure in the design of

the channel estimation process require engineering intuition

and are highly nontrivial tasks.

In contrast, this article shows that a machine learning

approach can be used to allow an automatic discovery of the

appropriate representation of the channel based on training

data. Further, it allows the optimization of the system metric

that actually matters (e.g., the achievable rate as opposed to

the MSE of the channel reconstruction) without having to ﬁrst

explicitly estimate the channel. This can have a signiﬁcant

advantage as illustrated in the example of optimizing the RIS

coefﬁcients directly based on received pilots in Section IV and

the application of neural networks for channel feedback for the

massive MIMO system in Section V.

B. Model-Based Optimization

In many communication system design problem, even if

the model parameters are perfectly estimated, the resulting

transmitter and receiver optimization problem may still be not

so easy to solve. The formulation of the optimization problem

is also an art rather than science. In fact, wireless engineers

often adopt optimization formulations, because the resulting

mathematical programming problem is amendable to either

analytic or computationally efﬁcient numerical solution. We

remark that a mathematical optimization problem can often

be parameterized in many different ways. The “holy grail” of

mathematical optimization is often thought of as to transform

a problem into a convex form, so that computationally efﬁcient

numerical procedures can be developed to ﬁnd the global

optimal solution of the resulting mathematical programming

problem. But there is no universal theory about how best to

transform the optimization landscape.

In contrast, this article shows that a machine learning ap-

proach can be used for the automatic discovery of the mapping

from the problem representation to the optimal solution based

on training data, as illustrated in the examples of optimizing

RIS coefﬁcients based on received pilots in Section IV, and

optimizing of beamformers based on channel feedback in

Section V, ﬁnally optimizing a sequence of active sensing

strategies in Section VI.

C. Data-Driven Communication System Design

The article advocates the viewpoint that a data-driven ap-

proach can circumvent many of the modelling and optimiza-

tion difﬁculties for wireless system design as mentioned in

the previous section. The main idea is as shown in Fig. 1.

Instead of the traditional model-then-optimize approach, which

involves choosing an appropriate parameter space, then char-

acterizing the associated optimization landscape, and ﬁnally

performing the resulting mathematical optimization, we adopt

a data-driven approach to directly map the problem instances

to the corresponding optimized solutions. By training such

a neural network over many problem instances, the task of

optimization is essentially turned into pattern matching. When

a new optimization task comes along, the trained neural

network can then simply output the corresponding solution.

This is akin to a human learner who is trained to use past

experience to perform future optimization tasks.

The advantages of the proposed data-driven paradigm are:

•It allows direct system-level optimization without the

intermediary step of channel estimation. The modelling

uncertainty and the channel estimation error are implicitly

taken into account in the overall optimization process.

•It allows an end-to-end design with a realistic system-

level objective function, instead of relying on some arbi-

trary metric in the model parameter estimation process.

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1RoleofDeepLearninginWirelessCommunicationsWeiYu,Fellow,IEEE,FoadSohrabi,Member,IEEE,andTaoJiang,GraduateStudentMember,IEEEAbstractTraditionalcommunicationsystemdesignhasal-waysbeenbasedontheparadigmofrstestablishingamath-ematicalmodelofthecommunicationchannel,thendesigningandoptimizingthesystemac...

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1 Role of Deep Learning in Wireless Communications Wei Yu Fellow IEEE Foad Sohrabi Member IEEE and Tao Jiang Graduate Student Member IEEE

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