1
A Tutorial on Interference E xploitation via
Symbol-Level Precoding: Overview, State-of-the-Art
and Future Directions
Ang Li, Member, IEEE, Danilo Spano, Member, IEEE, Jevgenij Krivochiza, Student Member, IEEE,
Stavros Domouchtsidis, Student Member, IEEE, Christos G. Tsinos, Member, IEEE, Christos Masouros, Senior
Member, IEEE, Symeon Chatzinotas, Sen ior Member, IEEE, Yongh ui Li, Fellow, IEEE,
Branka Vucetic, Life Fellow, IEEE, and Bj¨orn Ottersten, Fellow, IEEE
Abstract—Interference is tradition ally viewed as a perfor-
mance limiting factor in wireless communication systems, which
is to be minimized or mitigated. Nevertheless, a recent line of
work has shown that by manipulating the interfering signals
such that they add up constructively at the receiver side, known
interference can be made beneficial and further improve the
system performance in a variety of wireless scenarios, achieved
by symbol-level precoding (SLP). This paper aims to provide
a tutorial on interference exploitation techniques from the
perspective of precoding design in a multi-antenna wireless
communication system, by beginning with the classification of
constructive interference (CI) and destructive interference (DI).
The definition for CI is presented and the correspon ding math-
ematical characterization is formulated for popular modu lation
types, based on wh ich optimization-based precoding techniques
are discussed. In addition, the extension of CI precoding to oth er
application scenarios as well as for hardware efficiency is also
described. Proof-of-concept testbeds are demonstrated for the
potential practical implementation of CI precoding, and finally
a list of open problems and practical challenges are presented to
inspire and motivate further research directions in this area.
Index Terms—MIMO, constructive interference, symbol-level
precoding, optimization, application, faster-than-Nyquist, hard-
ware efficiency, proof-of-concept testbed.
I. INTRODUCTION
Manuscript received July 03, 2019; revised October 21, 2019; January 15,
2020 and March 04, 2020; accepted March 09, 2020. The associate editor
coordinating the review of this paper and approving it for publication was
Prof. Fabrizio Granelli. (Corresponding author: Ang Li.)
A. Li is with the Faculty of Electronic and Information Engineering, Xi’an
Jiaotong University, Xi’an, China. (e-mail: ang.li.2020@xjtu.edu.cn).
D. Spano, J. Krivochiza, S. Domouchtsidis, C. G. Tsinos, S. Chatzino-
tas and B. O ttersten are with the Interdisciplinary Centre for Security,
Reliability, and Trust, University of Luxembourg, 1855 Luxembourg, Lux-
embourg. (e-mail: {danilo.spano, jevgenij.krivochiza, stavros.domouchtsidis,
christos.tsinos, symeon.chatzinotas, bjorn.ottersten}@uni.lu)
C. Masouros is with the Department of Electronic and Electrical Engineer-
ing, University College London, Torrington Place, London, WC1E 7JE, UK.
(email: c.masouros@ucl.ac.uk)
Y. Li, and B. Vucetic are with the S chool of Electrical and Information
Engineering, University of Sydney, NSW 2006, Australia. (email: {yonghui.li,
branka.vucetic}@sydney.edu.au)
This work was supported in part by the Engineering and Physical Sciences
Research Council (EPSRC) Project under Grant EP/R007934/1, in part by the
FNR, Luxembourg under the projects INTER CI-PHY and CORE ECLECTIC,
in part by the Australian Research Council (ARC) under Grant DP150104019
and Grant DP190101988, in part by the ARC Laureate Fellowship under Grant
FL160100032, and in part by the Science and Technology Program of Shaanxi
Province under Grant No. 2019KW-007.
P
RECODING is able to support data transmission s to mul-
tiple receivers simultaneously in m ulti-antenna wireless
communication systems, which has attracted significant inter-
est in their development towards 5G [1]. The term ‘precoding’
usually refe rs to the transmit signal design that directs the
desired data symbols to the intended users while limiting
the inter-user interference, by exploiting the channel state
informa tion (CSI) and potentially the information of the d ata
symbols. In the literature, the dirty paper coding (DPC) tech-
nique is known to b e capable of a chieving the ch annel capacity
theoretically [2]. Despite its o ptimality, DPC is d ifficult to
implement in practical wireless communication systems, due
to (i) the impractical assum ption of an infinite source alphabet
and (ii) the prohibitive computational complexity incurred
by sequential encoding. Therefor e , lin ear precoding methods,
where the prec oded signals are linear combinations of the
informa tion symbols, have becom e appealing and attracted
more research attention because of their low complexity [3]-
[5]. In the literature, while the maximum ratio tran smission
(MRT) precoding offers the lowest computational cost [3],
it does no t fu lly eliminate the mu lti-user interference , which
leads to an error floor at medium-to-high sig nal-to-noise ratio
(SNR) regions. Zero -forcing (ZF) precoding is able to improve
the performance of MRT prec oding by fully eliminating the
multi-user interference via inverting the channel [4], whose
performance can be further improved via the regularized ZF
(RZF) precoding by including a regularization factor in the
matrix inversion, which alleviates the noise amplification effect
that ZF precoding suffers [5].
In addition to these closed-form precoders, linear prec od-
ing methods based on optimization have rec e ived increas-
ing research a ttention recently beca use of their flexibility to
achieve various performance targets, where the most popular
two design targets are power minimization (PM) and signal-
to-interference-plus-noise ratio (SINR) balancin g (SB) [6]-
[9]. For unicast applications where the base station (BS)
transmits individual informatio n to each receiver, PM aims
to minimize the total transmit power at the BS subject to
a c ommon m inimum SINR target fo r all the receivers [6]
or an individual SINR target for each user [7], while SB
targets at maximizing the min imum SINR for each receiver
while satisfying a total transmit power requirement [8] or
a per-antenna power constraint [9] at the BS. Given the
2
Fig. 1: Var ious asp e cts of interference exploitation via symbol-level precoding
capability of adaptation to various wireless communica tion
scenarios, optimization-based precoding sch emes have been
extended to a variety of research areas such as cognitive
radio (CR) [10], simultaneous wireless information an d power
transfer (SWIPT) [11], [ 12], physical-layer (PHY) security
[13]-[16], full-duplex (FD) communications [17]-[19], radar
and com munication coexistence [20], [21], etc., which will be
overviewed in the correspon ding chapters in the following.
For bo th closed- form linear precoding methods [3]-[5] and
optimization-based schemes [6]-[9] described above, it is
observed that only the information of the channel is exploited
for the precoding design, and these precoding methods all
treat interference as a detrimental effect. Nevertheless, it
has already been observed in non-linea r precoding methods
such as Tomlinson-Harashima precoding (THP) [22]-[24] and
vector perturbation (VP) precoding [25]-[27] that both the CSI
and the data symbols have be e n included in the sy mbol-by-
symbol precod ing design, i.e., the informatio n of the data
symbols is also exploited. However, the problem for non-
linear precoding schemes is that they are still difficult to be
implemented in practical wireless communication systems, due
to the complica ted e ncoding and decodin g process that lea ds
to unfavora ble computatio nal costs. Th erefore, it is natural to
ask: Is it possible for lin ear precoding methods to potentially
exploit the information of the data symbols as well, or more
specifically exploit the interference based on the knowledge
of the data symbols to further im prove the performance?
To answer the above question, this paper provides a tutorial
on a recently proposed concept termed ‘constructive interfer-
ence’ (CI) and the corresponding CI precoding techniques, as
well as the ir applications to a n umber of current and future
wireless communication scenarios, as illustrated in Fig. 1.
Compared with a previous survey paper [28] on symbo l-level
precod ing (SLP) which includes 1) the compa rison between
traditional block-level precoding and emerging SLP regarding
their application in both unicast and multicast scenarios, 2)
directional modulation based on SLP, 3) the symbol-level PM
problem based on CI for PSK modulations, and 4) the tra nsmit
architecture for SLP techniques, the focus of this tutorial
paper is on 1) the illustration, definition, characterization
and classification of CI for different modulation types, 2)
the exploitation of the CI effect in a variety of wireless
communication scenarios including VP, PM, SB, CR, SWIPT,
PHY security, etc., an d 3) the proof-o f-concept testbeds for
CI.
We begin with a brief review on precod ing, followed by the
introdu ction of CI, its potential bene fits and current limitations
in Section I. Section II then intro duces the c la ssification and
mathematical characterization of CI for various modu la tion
types, based on which Section III formulates the optimization
problems for CI exploitation, whose solution can be obtaine d
via convex optimization tools. Section IV describes the appli-
cations of CI exploitation techniques in traditional small-scale
multiple-input multiple-ou tput (MIMO) systems, and Section
V extends the application to large-scale antenna systems for
hardware efficiency. Section VI describe the proof-of-concept
testbed for practical implementation of CI exploitation via
SLP, developed by University College London and University
of Luxembourg, respectively. Section VII discusses some open
problems and challenges to be explored, followed by Section
VIII tha t concludes the paper. For clarity, we first summarize
the notations that are employed in the subsequent sections in
Ta ble I .
A. Pre liminaries on Precoding
Before we introduce CI, in this section we firstly review
how precoding works in the downlink transmission of a
multi-antenna system as preliminaries, where the traditional
ZF precoding scheme is also introduced as a simple an d
illustrative examp le .
For notational convenience, we consider a generic multi-
user multiple-input single-output (MU-MISO) system in the
downlink, where the BS equipped with N
T
transmit antennas
communicates with a total number of K single-antenna users
in the same time-frequency resource. Since users are usually
separate and do not cooperate in the downlink transmission,
in order to manage the potential multi- user interference, the
BS needs to perform som e signal proce ssing techniques on the
data symbols prio r to transmission based on the CSI, and this
is where the term ‘ precoding’ comes fro m. Mathematically,
3
the precoded signal vector x ∈ C
N
T
×1
to be transmitted at the
antenna ports can be expr e ssed as [6]
x =
K
X
k=1
w
k
s
k
= Ws, (1)
where w
k
∈ C
N
T
×1
is the precoding vector for user k’s d ata
symbol s
k
, which is drawn from a specific modulation constel-
lation. W = [w
1
, w
2
, ··· , w
K
] ∈ C
N
T
×K
is the concaten a te d
precod ing matrix and s = [s
1
, s
2
, ··· , s
K
]
T
∈ C
K×1
is the
data symbol vector. Subsequently, the signal for user k at the
receiver side can be expressed as [6]
y
k
= h
T
k
x + n
k
= h
T
k
Ws + n
k
, (2)
where y
k
is the received signal for user k, h
k
∈ C
N
T
×1
is
the channel vector between the BS and user k, and n
k
is the
additive Gaussian noise w ith zero mean and variance σ
2
at
the receiver side. (2) can also be written in a c ompact matrix
form as
y = H Ws + n, (3)
where y ∈ C
K×1
is the received signal vector, H ∈ C
K×N
T
is
the concatenated channel matrix, and n ∈ C
K×1
is th e additive
noise vector.
Precoding approaches aims to design the precoding matrix
W to achieve certain targets, which include linear closed-form
precod ing schemes such as MRT, ZF and RZF [3]-[5], non-
linear precoding schemes such as THP [22]-[24] and VP [25]-
[27], and optimization-based precoding designs such as PM
and SB [6]-[9], as already mentioned above. In th is section, we
briefly review ZF precoding as an illustrative example, which
can be viewed as a special case of CI-based prec oding, as
shown later in Section III-F. To be mor e specific, the precoding
matrix for ZF precoding c an be expre ssed as [5]
W
ZF
=
1
f
ZF
· H
H
HH
H
−1
, (4)
where f
ZF
is the normalization factor that guarantees tha t the
power of the transmit signal is not increased after precoding,
TABLE I: Notations
a Scalar
a Column vector
A Matrix
(·)
∗
Conjugate
(·)
T
Transpose
(·)
H
Conjugate transpose
(·)
−1
Inverse
(·)
+
Pseudo-inverse
diag (·) Transformation of a vector into a diagonal matrix
⊗ Kronecker product
|·| Absolute value or modulus
k·k
2
ℓ
2
-norm
k·k
∞
Uniform norm
ℜ {·} Extraction of the real part
ℑ {·} Extraction of the imaginary part
I
K
K × K identity matrix
j Imaginary unit
C
n×n
Set of n × n complex-valued matrices
R
n×n
Set of n × n real-valued matrices
card {·} Cardinality of a set
which is also k nown as the noise amplification factor. For
traditional ZF precoding, f
ZF
is calculated a s
f
ZF
=
r
tr
n
(HH
H
)
−1
o
, (5)
which is obtained based on the assumption of Gaussian
signaling [5], where we note that the expression for f
ZF
can
be different if we no rmalize the precoded signa l on a symbol
level. By substituting (4) into (3), we obtain the received signal
vector for ZF precoding as
y
ZF
=
1
f
ZF
·HH
H
HH
H
−1
s + n =
1
f
ZF
· s + n, (6)
where we observe that ZF precoding forces the multi-user
interference to be zero for eac h user, which is thus ter med
as ‘ZF’.
For an arbitrary constellation, the received signal vector
y needs to be fu rther rescaled f or correct demodulation,
expressed as
r = β ·y , (7)
where r is the received symbol vector r eady for demodulation,
and β is the rescaling factor. When closed-form pre coding
schemes such as ZF are adopted, β is e qual to the normal-
ization factor included in the pr e coding matrix, i.e., β = f
ZF
if the BS employs ZF precoding. On the other hand, when
optimization-based precoding appr oaches are employed, β is
obtained by minimizing the M SE between the received and
transmit symbol vector, which can be expressed in a closed
form as [29]
β =
ℜ
x
H
H
H
s
kHxk
2
2
+ Kσ
2
, (8)
We note that the above rescaling operation (7) is not neces-
sarily required for PSK constellations, since it is sufficient to
demodulate the received symbols based on their phases when
a PSK modulation is adopted. We refer the interested re aders
to the overview papers [28], [30] and [31] for a more detailed
description on precodin g techniques.
In what follows, we introduce CI and interference exploita-
tion techniques by first illustrating a simple example that
characterizes CI, as detailed below.
B. Interference in Wireless Commu nications - Is It All Harm-
ful?
Traditionally, interference is usually viewed as a perfor-
mance limiting factor in wireless commu nication systems. In a
typical multi-user transmission, the existence of interference is
based on the observation that the transmit signals for different
users are superimposed in w ireless communication channels.
Precoding strategies are designed based on th e fact that, with
CSI known at the BS and potentially with the information
of the data symbols as well, multi-user interference is able
to be predicted prior to transmission. I n fact, information
theoretical an alysis in [2] shows tha t whe n CSI is available at
the transmitter, known interference will not affect the capacity
of the broadcast channel. More specifically, the DPC method
implies that it is optimal to code along interference, instead of
attempting to mitigate or cancel interference. Nevertheless, the
4
majority of existing linear precoding sch emes still aim to elim-
inate, avoid or limit the interference [3]-[9]. In these trad itional
precod ing sche mes, the precoding matrix is designed based on
the CSI only and therefore op e rate on a block level. In other
words, the same precoding matrix is applied across a bloc k of
symbols and is updated when the ch annel changes. This means
that only the power of the interferen ce can be con trolled, which
leads to the statistical view tha t the effect of interfer ence is
similar to noise. On the other hand, if we observe interference
from an instantaneous instead of statistical point of view,
recent studies have shown that CI preco ding via SLP is able
to control both the power and the direction of the interfering
signals on the received complex plane on a symbol level, such
that the interference can act as an additional source of th e
desired signal power and contribute to the symbol detection,
which therefore fu rther improves the system performance [32],
[33]. Based on the above descrip tion, interference exploitatio n
techniques are foreseen to be most useful in systems where
interference c an be p redicted and manipulated. To motivate
the exploitation of interferen ce in precoding design s, we firstly
present illustrative examples to demonstrate how instantaneous
interference can be divided into CI and destructive interference
(DI) b e low, followed by the system a tic CI c haracterization in
Section II.
Let’s first consider a simple example wh ere the desired
symbol u is from a nominal BPSK con stellatio n [34], and
without lo ss of generality we assume u = 1. We express the
received signal as [35]
y = u + i + n = r + n , (9)
where i is the inte rfering signal, r denotes the received sign al
excluding noise, and n denotes the additive noise at the
receiver side. We consider two distinct cases: (i) i > 0 and
(ii) i < 0. When i > 0 , the resulting noiseless received
signal r > 1, which means that the interfer e nce has pushed r
further away from the detection threshold of BPSK, comp ared
with the original data sy mbol u. In this case, the interfering
signal i contributes to the useful signal p ower and is in fact
‘constructive’. Given a fixed noise power, y = u + i + n
is mor e likely to be correctly detected than the interfe rence-
free ca se ˜y = u + n, and a n improved performance can be
expected. On the other hand, when i < 0, the interfering signal
causes the received signal r to move closer to the detection
threshold, where the interfering signal reduces the useful sig nal
power and is therefore ‘destructive’. In this case, the noiseless
received signal r = u + i is mor e vulnerable to noise than
˜r = u.
The above examples have only considered the effect o f
interfering symbols. To make the concept of interf e rence
exploitation more explicit, in the following example we fu r-
ther take the e ffect of wireless channels into account. In
this example, we consider a geometrical representation of
an interfer ence scenario w ith random channels, as shown in
Fig. 2, where for simplicity we still assume that u = 1 is
the desired data sy mbol, i = 1 is the data symbol from
the interferer, h
u
denotes the wireless channel betwe e n the
transmitter and the receiver, while h
i
and
˜
h
i
represent th e
channel betwee n the interferer and the receiver for achieving
Fig. 2: T he geometrical representation of CI and DI
DI and CI, respectively. Accordingly, the received signal can
be expressed as [35]
y
DI
= h
u
u + h
i
i, y
CI
= h
u
u +
˜
h
i
i, (10)
where we have assumed a noiseless case to focus on the effect
of interfere nce. In Fig. 2, DI is achieved when the channel
between the interferer and the r eceiver is h
i
. To be more
specific,
~
OA = h
u
u is the useful signal wh ile
~
OB = h
i
i
is the interferin g sign al.
~
OC = y
DI
is the received signal,
and
~
OD represents its projection on the axis of h
u
, whose
amplitude directly determines the detection performance. Ge-
ometrically, we observe that |
~
OD| < |
~
OA|, and consequently
the interference is de structive sin c e it reduces the useful signal
power. To take a closer look, we can project the interfering
signal
~
OB onto the axis of h
u
, and it is then observed that
the direction of the effective interfering signal
~
OE = e
i
is to
the opposite side of th e desired sign a l
~
OA, which is similar
to the case of (ii) i < 0 discussed in the p revious examp le
and results in DI. On the other hand, when the interfering
channel is shifted from h
i
to
˜
h
i
, the interfering signal becomes
constructive to the desired data symbol u, since they add up
constructively and yield a received symbol whose amplitude
is larger than that of the original tra nsmit signal, as shown
in Fig. 2 where |
~
O
˜
D| > |
~
OA|. This can also be observed
from the fact that
~
O
˜
E = ˜e
i
, which is the projection of the
interfering signal
~
O
˜
B onto h
u
, is in the same direction as
the useful signal
~
OA, which is similar to the case of (i)
i > 0 discussed in the previous example and leads to CI.
The above observation implies tha t f or a given data symbol
combination, some channel realizations may lead to CI while
some other channe l realizations may yield DI. Based on the
above two simple examples, it is important to note that the
classification of interference into constru c tive or destructive
depends both on the data symbol combination and the CSI, as
will be mathematically shown in Section II.
C. CI Exploitatio n v ia Symbol-Level Precoding
With the two example s illustrated above, we are now able to
give the definition of CI: CI is the interference that pushes the
received signals away from all of their corresponding decision
boundaries of the modulated-symbol constellation, which thus
5
contributes to the useful signal power
1
. Moreover, to exploit
CI in the precodin g design, firstly it should be highlighted
that CI-based precoding has to be shifted from block-level
operation to sym bol-level operation, i.e., SLP is the method
to achieve the CI effect. It should be noted that SLP is not
limited as a metho d to explo it CI effects only, but also find s
its application in hardware-efficient BS architecture , a s will be
discussed in Section V.
Early works on CI precoding techniques have focused on
the adaptation of simple linear pre c oding methods such as
ZF and RZF for CI exploitation [36]-[38]. In [36] and [37],
for the first time the instantaneous interference in a MIMO
system is characterized and classified into CI and DI, and
a selective precodin g is proposed where the CI is retained
while the DI is cancelled via ZF. A mor e advanced approach
termed correlation-rotation prec oding is proposed in [38],
where instead of being canc e lled as in [36] and [37], the DI is
manipulated an d further rotated to be aligned with the desired
data sym bols such that DI becomes CI. Compared with the
selective pre coding in [36] and [37] that exploits interference
only when it is constructive, the correlation-rotation preco ding
proposed in [38] directly co ntrols interference such that all the
interference for each user becomes constructive in the system.
The concept of CI has subsequently been applied to the
non-lin ear THP method in [23], [24] and VP precoding in
[39]. The interference-optimized THP (IO-THP) proposed in
[23] introduces a com plex scaling to the first user such that the
interfering signals are better aligned to the symbols of interest,
and by optimizing the complex scaling factor to minimize
the power of the modified transm it signals, IO-THP reduces
the power loss of the conventional THP schemes. As a step
further, the power-efficient THP (PE-T H P) method proposed
in [24] allows complex scalin g for a number of users, instead
of for the first user only as in [23]. Compared with IO-THP in
[23], the per formance improvements come from th e fact that
PE-THP allows a larger number of variables to be optimized
jointly within the constructive area and the signal-to-noise ratio
(SNR) threshold, which generally leads to a better and more
power-efficient THP solution. [39] proposes CI techniques in
the context of V P precoding by substituting the search for
the perturbation vectors with a linear scaling precoder, which
removes the sophisticated sphere-search process and is the first
optimization-based CI techn ique that involves a linear symbol-
scaling operation based on qua dratic programming (QP).
More recently, CI-based precoding techniqu e s have been
widely combined with optimization to achieve further per for-
mance improvements [40]-[46]. In [41] and [42], the authors
firstly propose a CI-MRT precoding method that impr oves the
performance of correlation-rotation precoding by avoiding the
ZF operation. In a ddition, PM o ptimization and weighted SB
optimization based on the same CI metric are further discussed
in [42]. It is worth mentioning that for CI precoding designs
in [41] and [42], the received signals are force d to be strictly
aligned to the desire d data symbols with an increase in the
amplitude for achieving CI, which follows the CI metric in
1
Based on this definition, for multi-level modulations only the outer
constellation points can exploit CI, which will be discussed later in Section
II-B.
[38] and is later shown to be sub-optimal and term ed ‘strict
phase rotation’ in [58] (Fig. 4a). A mo re advanced CI me tric is
introdu ced in [43] and [44], where the concept of ‘constructive
region’ is charac te rized for PSK constellatio ns, within which
all the interfere nce is shown to be constructive. T his relaxed CI
metric reveals that it is no longe r necessary for the interfering
signals to be strictly aligned to the symbols of interest, which
leads to further performance gains and is superior to the
‘strict phase-rotation’ CI metric in [38], [41] and [42]. This
advanced CI metric is later termed ‘non-strict phase rotation’
in [58] (Fig. 4b) , and is widely a dopted in the subseque nt
precod ing designs for CI exploitation [51], [52], [58]-[63] and
its applications. Meanwhile, a similar and sub-optimal relaxed
CI metric is also presented in [45], [46], w here the ‘relaxed
detection region’ metr ic that is determined by a phase margin
related to the SNR target is introduced.
It should be noted that the above works [23], [24], [36]-
[38], and [41]-[46] h ave all focused on PSK constellations
for CI precoding based on the ‘phase-rotation’ m etric, which
is not applicable to QAM modulations since only the real
or imaginary part of some constellation points from QA M
modulation can explo it CI (Fig. 3). To this end, the extensio n
to multi-level modulations su c h as QAM has re cently been
discussed in [47], [48] and [59]-[64], where the ‘symbol-
scaling’ CI metric is adopted. Interestin gly, in contrast to
claims that CI precoding may not be promising for higher-
order QAM modulations since only the outer constellation
points benefit from CI, [60] shows that substan tial gains can
still be observed even for a 64QAM constellation, which will
also be num erically shown in Section III. This is bec ause CI
exploitation precoding not only allows the outer constellation
points to benefit from CI, but more importantly also re duces
the noise amplification effect, which is more prominent for a
high-order QAM modulation. CI precoding has further been
extended to gen eric two-dimension constellations with any
shape and size in [56], where the CI metric is ter med ‘distance
preserving CI region’ (DPCIR). Additional studies on CI
precod ing include per-antenna power constraint [49], MMSE-
based CI [50], noise-robust CI [51], symbol error rate (SER)
minimization [52], non-linear channels [53], CI for generic
constellations [54], multi-group multicasting [65], closed-form
and iterative CI solutions [57]-[62], etc., and we summarize
the major research outputs on CI precoding in Table II.
Meanwhile, a similar concept coined as ‘directional modu-
lation’ [66]-[68], which was studied in th e past in the context
of ana log RF and antenna components, has also emerged
as a promising hardware-efficient approach, whe re the phase
and amplitude of the transmitting signal on eac h antenna
are directly designed such that multiple interferenc e-free or
interference-limited symbols c a n be transmitted to the receiver,
which will be discussed in more detail in Section V-F.
D. Benefits of CI and S y m bol-Level Precoding
With the ab ility to transform the power of the interfering
signals into useful signal power without the need of investing
additional transmit power, CI precoding has b ecome an appeal-
ing PHY technique for wireless communications. Since future
