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SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 1
Large Intelligent Surface-Based Index Modulation:A New Beyond
MIMO Paradigm for 6G
Ertugrul Basar, Senior Member, IEEE
Abstract—Transmission through large intelligent surfaces(LIS),
which modify the phases of incident waves in a deliberatemanner to
enhance the signal quality at the receiver, has beenrecently put
forward as a promising candidate for future wirelesscommunication
systems and standards. In this paper, we bringthe concept of
LIS-assisted communications to the realm ofindex modulation (IM) by
proposing LIS-space shift keying (LIS-SSK) and LIS-spatial
modulation (LIS-SM) schemes. These twoschemes are realized through
not only intelligent reflection ofthe incoming electromagnetic
waves to improve the signal qualityat the receiver but also
utilization of the IM principle for theindices of multiple receive
antennas in a clever way to improve thespectral efficiency. Maximum
energy-based suboptimal (greedy)and exhaustive search-based optimal
(maximum likelihood) de-tectors of the LIS-SSK/SM schemes are
formulated and a unifiedframework is presented for the derivation
of the theoreticalaverage bit error probability of the proposed
schemes using bothdetectors. Extensive computer simulation results
are provided toassess the potential of LIS-assisted IM schemes as
well as to verifyour theoretical derivations and remarks. Our
findings also revealthat LIS-based IM, which enables ultra-reliable
transmissionwith high spectral efficiency, can become a potential
candidate forfuture wireless communication systems in the context
of beyondmassive multiple-input multiple-output (MIMO)
solutions.
Index Terms—6G, beyond massive MIMO, index modulation(IM), large
intelligent surface (LIS), smart reflect-array, software-defined
surface, space shift keying (SSK), spatial modulation(SM).
I. INTRODUCTION
AS of the second quaterter of 2019, the first commer-cial fifth
generation (5G) wireless networks have beenalready deployed, in
part or as a whole, at certain coun-tries while the first 5G
compatible mobile devices are beingintroduced to the market.
Although the initial stand-alone5G standard, which was completed in
2018, has broughtmore flexibility to the physical layer by
exploiting millimeter-waves and multiple orthogonal frequency
division multiplex-ing (OFDM) numerologies, researchers have
already startedto explore the potential of alternative technologies
for laterreleases of 5G. These technologies include index
modulation(IM), non-orthogonal multiple access,
alternative/advancedwaveforms, low-cost massive multiple-input
multiple-output(MIMO) systems, terahertz communications, and new
antennatechnologies. At the first glance, the future 6G
technologies
Manuscript received April, 2019.The author is with the
Communications Research and Innovation Labora-
tory (CoreLab), Department of Electrical and Electronics
Engineering, KoçUniversity, Sariyer 34450, Istanbul, Turkey.
e-mail: [email protected]
This work was supported in part by the Scientific and
TechnologicalResearch Council of Turkey (TUBITAK) under Grant
117E869, the TurkishAcademy of Sciences (TUBA) GEBIP Programme, and
the Science AcademyBAGEP Programme.
Codes available at https://corelab.ku.edu.tr/tools
may seem as the extension of their 5G counterparts [1],
how-ever, new user requirements, completely new
applications/use-cases, and new networking trends of 2030 and
beyond maybring more challenging communication engineering
problems,which necessitate radically new communication paradigms
inthe physical layer.
Within the context of unconventional wireless commu-nication
paradigms, there has been a growing interest incontrolling the
propagation environment in order to increasethe quality of service
and/or spectrum efficiency. IM-basedemerging schemes such as
media-based modulation [2]–[4],spatial scattering modulation [5],
and beam index modulation(IM) [6], use the variations in the
signatures of received signalsby exploiting reconfigurable antennas
or scatterers to transmitadditional information bits in rich
scattering environments[7]. On the other hand, large intelligent
surfaces/walls/reflect-arrays/metasurfaces are smart devices that
intentionally controlthe propagation environment to boost the
signal quality at thereceiver [8], [9].
As a matter of fact, the large intelligent surface (LIS)-based
transmission concept, in which the large number ofsmall, low-cost,
and passive elements on a LIS only reflectthe incident signal with
an adjustable phase shift withoutrequiring a dedicated energy
source for RF processing, de-coding, encoding, or retransmission,
is completely differentfrom existing MIMO, beamforming,
amplify-and-forward re-laying, and backscatter communication
paradigms. Inspired bythe definition of software-defined radio,
which is given as“radio in which some or all of the physical layer
functionsare software defined” and considering the interaction of
theintelligent surface with incoming waves in a
software-definedfashion, we may also use the term of
software-defined surface(SDS) for these intelligent surfaces. In
other words, dueto the fact that reflection characteristics of
these intelligentsurfaces/walls/arrays in the physical layer can be
controlledby a software, they can be termed as SDS.
Transmission through intelligent walls is proposed in oneof the
early works by utilizing active frequency-selectivesurfaces to
control the signal coverage [10]. The promisingconcept of
communications over smart reflect-arrays withpassive reflector
elements is proposed in [11] as an alter-native to beamforming
techniques that require large numberof antennas to focus the
transmitted or received signals. Ithas been also demonstrated that
reflect-arrays can be usedin an effective way to change the phase
of incoming signalsduring smart reflection without buffering or
processing themand the received signal quality can be enhanced
through theadjustment of the phase shift of each reflector element
on thereflect-array. As a beyond massive MIMO solution, the LIS
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2 SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING
LIS
LIS
RF
LIS
D
...
D
...
D
...
S
...
(a)
(b)
(c)
RF
Fig. 1. Three conceptual LIS-based IM system realizations: a) IM
for source(S) transmit antennas, b) IM for LIS reflector regions,
c) IM for destination(D) receive antennas.
concept is proposed in [12] by exploiting the whole
contiguoussurface for transmission and reception1. The authors of
[13]–[15] considered a LIS-assisted downlink transmission
scenarioto support multiple users and focused on the maximizationof
sum-rate and energy efficiency. The selection of optimumLIS phases
is also investigated and low complexity algorithmsare considered
for the formulated non-convex optimizationproblems. Recently, the
interesting problem of joint activeand passive beamforming is
investigated in [16] and [17], andthe user’s average received power
is investigated. Even morerecently, the researchers focused on
outage probability [18]and asymptotic data rate [19] analyses for
LIS-based systems.Finally, we provided a mathematical framework in
[20] forthe calculation of average symbol error probability (SEP)
ofLIS-assisted systems. Furthermore, we proposed the
promisingconcept of using the LIS itself as an access point (AP)
byutilizing an unmodulated carrier for intelligent reflection.
The emerging IM concept also falls to the category of poten-tial
beyond 5G technologies and has been widely recognizedby both
academia and industry during the past few years[7], [21]–[23].
Contrary to the traditional modulation formats,the indices of the
available transmit entities, such as transmitantennas for space
modulation techniques [23] and subcarriersfor OFDM with IM [24],
are used to convey information
1It is important to note that the LIS structure considered in
this paper isconceptually different than that of [12].
for an IM scheme. The undeniable potential of both IM-and
LIS-based communication schemes has been the mainmotivation of this
study. With this purpose, we investigatedthree conceptual LIS-based
IM system realizations in Figs.1(a)-(c), in which we consider IM
for source transmit antennas,LIS regions, and destination receive
antennas, respectively.Since the first concept requires the
knowledge of activatedsource transmit antenna indices at LIS for
optimum reflectionand the second concept reduces the effective gain
of the LISby activating a part of the available reflectors, we
decided tofocus on the third approach in this preliminary work.
In this paper, we propose the visionary concept of LIS-basedIM
as a potential beyond MIMO solution by amalgamatingthe techniques
of transmission over LIS and IM for receiveantenna indices to
achieve ultra-reliable transmission with highspectral efficiency.
First, considering the LIS as an AP, wepropose LIS-space shift
keying (LIS-SSK) and LIS-spatialmodulation (LIS-SM) schemes by
exploiting the LIS not onlyto boost the signal quality in hostile
fading channels but alsoto realize IM by the selection of a
particular receive antennaindex according to the information bits.
Second, we formulatethe greedy and maximum likelihood (ML)
detectors of bothschemes and investigate their complexity. Third,
we present aunified framework for the calculation of the
theoretical errorperformance of the proposed schemes and provided
usefulinsights. Finally, extensive computer simulations are given
toassess the potential of the LIS-SSK and LIS-SM schemes.
The rest of the paper is organized as follows. In Section II,we
introduce the system model of LIS-based SSK/SM schemesand formulate
their detectors. Sections III and IV respectivelyfocuses on the
error performance of greedy and ML detectors.Computer simulation
results and comparisons are given inSection V. Finally, conclusions
are given in Section VI2.
II. SYSTEM MODEL
In this section, we present the system models of the pro-posed
LIS-based SSK and SM schemes and investigate theproblem of optimal
phase selection. We build the proposedschemes on the concept of
LIS-AP introduced in [20], wherethe LIS reflects the signals
generated by a near RF sourcein a deliberate manner to convey
information bits. We as-sume that the LIS is consisting of N
passive and low-costreflector elements, while the destination (D)
is equipped withnR receive antennas. The wireless fading channel
betweenthe lth receive antenna of D and ith reflector element
ischaracterized by gl,i = βl,ie−jψl,i for l = 1, 2, . . . , nR
and
2Notation: Bold, lowercase and capital letters are used for
column vectorsand matrices, respectively. (·)∗ (·)T, and (·)H
denote complex conjugation,transposition, and Hermitian
transposition, respectively. The real and imag-inary parts of a
complex variable X are denoted by X< (or
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SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 3
RF
LIS
D
...1 2 nR
1
N
log2nR bits
I/Q & RF
LIS
D
...1 2 nR
1
N
log2nR bits
Bit Splitter
log2M bits
log2nR + log2M bits
(a)
(b)
gl,i
gl,i
Fig. 2. LIS-based IM schemes: a) LIS-SSK, b) LIS-SM.
i = 1, 2, . . . , N , and follows CN (0, 1) distribution under
theassumption of flat Rayleigh fading channels. We also assumethat
all wireless channels are uncorrelated and perfect channelstate
information (CSI) is available at D if it is required bythe
utilized detector. The phase induced by the ith reflector isshown
by φi for i = 1, 2, . . . , N . For intelligent reflection, theLIS
has the knowledge of channel phases ψl,i for all l and i.
A. LIS-Assisted Space Shift Keying
In this scenario, the unmodulated carrier signal generatedby the
RF source, is reflected to D with the aim of maxi-mizing the
instantaneous received SNR at a specific receiveantenna, which is
selected according to the incoming log2 nRinformation bits, as
shown in Fig. 2(a). In other words, theLIS phase terms are adjusted
in such a way that the SNR atthe target receive antenna is
maximized, while the task of D isto detect the index of its receive
antenna with the maximizedinstantaneous received SNR.
For this system, the received baseband signal at the lthreceive
antenna of D is expressed as
rl =√Es
[N∑i=1
gl,iejφi
]+ nl, l ∈ {1, . . . , nR} (1)
where Es is the transmitted signal energy of the
unmodulatedcarrier and nl is the additive white Gaussian noise
(AWGN)sample at the lth receiver, which follows CN (0, N0)
distribu-tion. Here, the reflector phases {φi}Ni=1 are adjusted
accordingto the information bits to maximize the received SNR ata
specific receive antenna. For this purpose, the incominglog2 nR
bits specify the index m of a receive antenna andthe LIS adjusts
its phases according to this selected receiveantenna as φi = ψm,i
for i = 1, 2, . . . , N . More specifically,
the received instantaneous SNR at the lth receive antenna
isexpressed as
γl =
∣∣∣∑Ni=1 βl,iej(φi−ψl,i)∣∣∣2EsN0
. (2)
Considering∣∣∣∣∣N∑i=1
ziejξi
∣∣∣∣∣2
=
N∑i=1
z2i + 2
N∑i=1
N∑k=i+1
zizk cos(ξi − ξk) (3)
which can be maximized by ensuring ξi = ξ for all i, tomaximize
the instantaneous SNR at the mth receive antenna,we select φi =
ψm,i. This results in the following maximumSNR value at the
selected receive antenna:
γm =
∣∣∣∑Ni=1 βm,i∣∣∣2EsN0
. (4)
Later, we will also show that this selection of LIS phasesis
optimal in terms of error performance. We propose twodifferent
detectors for the LIS-SSK scheme.
i) Greedy Detector: This simple yet effective detector
elim-inates the need for channel estimation at D, that is,
performsnon-coherent detection, and simply detects the selected
receiveantenna as the one with the highest instantaneous
energy:
m̂ = arg maxm|rm|2 . (5)
As seen from (5), this detector does not require CSI, whichcan
be prohibitive at D for increasing N and nR.
In order to shed light on the derivation of the optimumLIS
phases, let us consider the selection of the mth receiveantenna of
D at the LIS and its erroneous detection as m̂. For
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4 SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING
this case, the corresponding pairwise error probability (PEP)can
be easily expressed from (5) as
P (m→ m̂) = P (|rm|2 < |rm̂|2)
=P
∣∣∣∣∣√EsN∑i=1
gm,iejφi +nm
∣∣∣∣∣2
<
∣∣∣∣∣√EsN∑i=1
gm̂,iejφi +nm̂
∣∣∣∣∣2(6)
where {φi}Ni=1 is determined according to the mth receiveantenna
(with a predefined method). As seen from (6), a logicalselection of
φi’s should minimize this PEP for the selectedreceive antenna m.
The above phase optimization problem canbe reformulated as follows
by ignoring the noise terms:
min{φi}Ni=1
P
∣∣∣∣∣N∑i=1
βm,iej(φi−ψm,i)
∣∣∣∣∣2
<
∣∣∣∣∣N∑i=1
βm̂,iej(φi−ψm̂,i)
∣∣∣∣∣2 .(7)
As seen from (7), even for a specific pair of m and m̂,
thisoptimization is not a straightforward task. Consequently, weaim
to maximize the first term by letting φi = ψm,i for all ito
minimize this probability. We will also show later that
thisselection maximizes the mean of the first term in (7),
whileproviding a zero-mean for the second one.
ii) ML Detector: The ML detector of the LIS-SSK schemeconsiders
the received signals at all receive antennas of D andperforms the
detection as follows:
m̂ = arg minm
nR∑l=1
∣∣∣∣∣rl −√Es[N∑i=1
gl,iejψm,i
]∣∣∣∣∣2
. (8)
Comparing (5) and (8), we observe that the ML detectorrequires
not only CSI but also ∼Nn2R real multiplications(RMs), while the GD
detector requires only nR squaredcomplex modulus operations (∼ nR
RMs). As we will showin later sections, the price paid for this
increased complexitycan be compensated with the improved error
performance.
B. LIS-Assisted Spatial Modulation
For the LIS-SM scheme, ordinary M -ary modulation for-mats are
also considered at the RF source to further improvethe spectral
efficiency. As shown in Fig. 2(b), the incominglog2 nR + log2M
information bits are partitioned into twogroups. While the first
group of log2 nR bits adjusts the LISphases according to the
selected receive antenna with indexm as done for the LIS-SSK
scheme, i.e., φi = ψm,i fori = 1, 2, . . . , N , the second group
of log2M bits is passedto the RF source for the generation of an
amplitude/phasemodulated signal through an RF chain. Consequently,
thereceived signal at the lth receive antenna of D is
expressedas
rl =
[N∑i=1
gl,iejφi
]x+ nl, l ∈ {1, . . . , nR} (9)
where x is the data symbol selected from M
-QAM/PSKconstellations, E[|x|2] = Es, and nl ∼ CN (0, N0) is
thenoise term. In a similar way, we propose the greedy and
MLdetectors of LIS-SM in the sequel.
i) Greedy Detector: This detector simplifies the receiverdesign
by detecting the selected receive antenna index and thetransmitted
symbol in a sequential fashion. For this purpose,the selected
receive antenna is determined similar to the LIS-SSK scheme: m̂ =
arg maxm |rm|2. After the detection of theselected receive antenna
index as m̂, this detector demodulatesthe transmitted data symbol
as
x̂ = arg minx
∣∣∣∣∣rm̂ −(
N∑i=1
βm̂,i
)x
∣∣∣∣∣2
. (10)
Here, compared to LIS-SSK, an additional (but minor) com-plexity
comes during the search for the constellation point x,however, due
to disjoint detection of m and x, the overall com-plexity still
linearly increases with nR and M . Furthermore,this detector
requires only channel amplitudes for detection.It is worth noting
that for constant-envelope constellationssuch as M -PSK, the
transmitted symbol can be detected evenwithout channel amplitudes
since
∑Ni=1 βm̂,i is a real variable:
x̂ = arg minx|rm̂ − x|2 . (11)
ii) ML Detector: This detector performs a joint search forthe
selected receive antenna index m and the transmitted datasymbol x
by considering all received signals as
(m̂, x̂) = arg min(m,x)
nR∑l=1
∣∣∣∣∣rl −[N∑i=1
gl,iejψm,i
]x
∣∣∣∣∣2
. (12)
As seen from (12), the ML detector of the LIS-SM schemerequires
the full CSI along with ∼ (N + M)n2R RMs whilemaking a joint
decision on (m,x).
III. GREEDY DETECTION: PERFORMANCE ANALYSIS
In this section, we investigate the theoretical bit error
prob-ability (BEP) of the proposed LIS-SSK and LIS-SM schemesin the
presence of greedy detection. We also provide usefulinsights
regarding the asymptotic behavior of the proposedschemes with this
type of detection.
A. Performance of LIS-SSK
Based on the detection rule given in (5), the correspondingPEP
is given in (6) for the erroneous detection of the selectedreceive
antenna index m as m̂. Considering φi = ψm,i fori = 1, 2, . . . , N
, (6) simplifies to
P (m→ m̂) = P(∣∣∣√EsB + nm∣∣∣2< ∣∣∣√EsB̂ + nm̂∣∣∣2) (13)
where B =∑Ni=1βm,i and B̂ =
∑Ni=1 βm̂,ie
j(ψm,i−ψm̂,i).Here, we resort to the central limit theorem (CLT)
under theassumption of N � 1 for the calculation of this PEP.
Underthe CLT, B and B̂ follow Gaussian distribution regardlessof
the distributions of their components. Specifically, sinceβm,i is a
Rayleigh distributed RV with E[βm,i] =
√π/2 and
Var[βm,i] = (4 − π)/4, we have B ∼ N (N√π/2, N(4 −
π)/4). Since ψm,i and ψm̂,i are independent and uniformly
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SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 5
distributed in (0, 2π), the distribution of ψ̄i = ψm,i − ψm̂,i
isobtained as
fψ̄i(x) =
{1
2π
(1 + x2π
), −2π < x < 0
12π
(1− x2π
), 0 < x < 2π.
(14)
Then defining B̂i = βm̂,iejψ̄i , we have E[B̂i] = 0 andVar[(B̂i)
2, we use the following union bound:
Pb ≤1
log2 nR
∑m̂
P (m→ m̂)e(m, m̂)
=nR2P (m→ m̂) (23)
where e(m, m̂) is the Hamming distance between the
binaryrepresentations of m and m̂. Here, we considered the fact
thatthe resulting PEP is independent of m and m̂, and identicalfor
all pairs (uniform error probability) and
∑m̂ e(m, m̂) =
(nR/2) log2 nR for all m due to bit symmetry. For simplicity,we
adopt natural mapping for receive antenna indices.
Remark 1: We observe from the exact and upper-boundedPEP
expressions of (16) and (22) that the resulting PEP isindependent
of nR for greedy detection of LIS-SSK. As seenfrom (23), doubling
nR doubles Pb in high SNR.
B. Performance of LIS-SM
To derive the theoretical BEP of the LIS-SM scheme withgreedy
detection, we consider the following approximation:
Pb ≈Pc(m)Ps
log2(MnR)+ 0.5Pe(m) (24)
where Pc(m) is the average correct detection probabilityof the
selected receive antenna with index m for LIS-SM,which is the same
for all m, Ps is the average symbol errorprobability (SEP)
conditioned on correct index detection, andPe(m) = 1−Pc(m) is the
erroneous index detection probabil-ity. Here, we followed a
conservative approach by assumingthat approximately 50% of the
transmitted bits are erroneouslydetected if the receive antenna
index is erroneously estimated,which is a valid assumption for
IM-based systems due to errorpropagation. Resorting to the union
bound on error probabilitywith uniform PEP values, we obtain
Pe(m) ≤nR∑
m̂=1,m̂6=m
P̄ (m→ m̂) = (nR−1)P̄ (m→ m̂) (25)
where P̄ (m→ m̂) is the PEP associated with index
detectionaveraged over all data symbols for LIS-SM. From (25),
Pc(m)is obtained as Pc(m) ≥ 1− (nR − 1)P̄ (m→ m̂).
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6 SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING
Assuming that x is transmitted, the PEP for erroneousdetection
of the selected receive antenna index m as m̂ isgiven as follows
considering (5), which is also valid for LIS-SM:
P (m→ m̂ |x) = P(∣∣Bx+ nm∣∣2 < ∣∣B̂x+ nm̂∣∣2) . (26)
Here, B and B̂ are as defined in (13). In what follows,
wecalculate (26) for different constellations.
i) BPSK: For this case, we have x ∈{±√Es}
and weobtain the same PEP derived from (17) or (21) for
LIS-SSK,which is independent of x.
ii) M -QAM: For this case, we have x = x< + jx= withE[|x|2] =
Es, and we may express the corresponding PEP as
P (m→ m̂ |x) = P (B21 +B22 −B23 −B24 < 0) = P (D <
0)(27)
where B1 = (Bx+ nm) 0) (38)
where we considered the fact that rl = Glx + nl for all l.Here,
G ∼ N (µG, σ2G) with µG = −
∑nRl=1
∣∣Glx− Ĝlx̂∣∣2 and
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SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 7
σ2G =∑nRl=1 2N0
∣∣Glx − Ĝlx̂∣∣2. Consequently, from P (G >0) = Q(−µG/σG), we
arrive at
P (m,x→ m̂, x̂) = Q
√∑nRl=1 ∣∣Glx− Ĝlx̂∣∣22N0
(39)which is analogous to classical SM-based systems [28].
Defin-ing Γ ,
∑nRl=1
∣∣Glx − Ĝlx̂∣∣2 and considering the alternativeform of the
Q-function, the unconditional (averaged overchannel coefficients)
PEP can be calculated as follows:
P̄ (m,x→ m̂, x̂) =∫ ∞
0
Q
(√Γ
2N0
)fΓ(Γ)dΓ
=
∫ ∞0
1
π
∫ π/20
exp
(−Γ
4 sin2 ηN0
)fΓ(Γ)dηdΓ
=1
π
∫ π/20
MΓ
(−1
4 sin2 ηN0
)dη. (40)
Here, we need the MGF of Γ (MΓ(s)) to perform this inte-gration.
This MGF can be derived by considering the generalquadratic form of
correlated Gaussian RVs and depends onerroneous or correct
detection of the receive antenna index m.
i) First Case (m 6= m̂): Let us rewrite Γ as Γ =
Γ1+Γ2+Γ3,where
Γ1 =
∣∣∣∣∣[N∑i=1
βm,i
]x−
[N∑i=1
gm,iejψm̂,i
]x̂
∣∣∣∣∣2
=∣∣Gmx− Ĝmx̂∣∣2
Γ2 =
∣∣∣∣∣[N∑i=1
gm̂,iejψm,i
]x−
[N∑i=1
βm̂,i
]x̂
∣∣∣∣∣2
=∣∣Gm̂x− Ĝm̂x̂∣∣2
Γ3 =
nR∑l=1(l 6=m,l 6=m̂)
∣∣Glx− Ĝlx̂∣∣2. (41)Here, Γ1, Γ2, and Γ3 respectively stand for
l = m, l = m̂, andl 6= m, l 6= m̂ in Γ. Different distributions of
Gl and Ĝl withrespect to l as well as the correlation among them
necessitatethe quadratic form of Gaussian RVs to derive MΓ(s).
Considering gl,i = βl,ie−jψl,i , let us rewrite Γ1 and Γ2 as
Γ1 = |γ1|2 = (γ1)2< + (γ1)2= =
∣∣∣∣∣N∑i=1
βm,i
(x− e−jψ̄i x̂
)∣∣∣∣∣2
Γ2 = |γ2|2 = (γ2)2< + (γ2)2= =
∣∣∣∣∣N∑i=1
βm̂,i
(xejψ̄i − x̂
)∣∣∣∣∣2
(42)
where ψ̄i = ψm,i−ψm̂,i has a triangle-shaped PDF defined in(14).
It is obvious from (42) and the CLT that γ1 and γ2 followcomplex
Gaussian distribution for increasing N , however, weneed to
consider the correlation among their components. Aftertedious but
straightforward calculations, the mean vector andthe covariance
matrix of g =
[(γ1)< (γ1)= (γ2)< (γ2)=
]Tare obtained respectively as follows:
m =[N√πx<2
N√πx=2 −
N√πx̂<2 −
N√πx̂=2
]T(43)
C =
σ21 σ1,2 σ1,3 σ1,4σ1,2 σ
22 σ2,3 σ2,4
σ1,3 σ2,3 σ23 σ3,4
σ1,4 σ2,4 σ3,4 σ24
(44)where
σ21 =N(4−π)x2<
4 +N |x̂|2
2 , σ22 =
N(4−π)x2=4 +
N |x̂|22
σ23 =N(4−π)x̂2<
4 +N |x|2
2 , σ24 =
N(4−π)x̂2=4 +
N |x|22
σ1,2 =N(4−π)x
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8 SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING
-35 -30 -25
SNR(dB)
10-6
10-5
10-4
10-3
10-2
10-1
BEP
LIS-SSK,N=128,nR
=2
LIS-SSK,N=128,nR
=8
LIS-SSK,N=128,nR
=32
LIS-SSK,N=128,nR
=64
-35 -30 -25
SNR(dB)
10-6
10-5
10-4
10-3
10-2
10-1
BEP
LIS-SM,N=128,nR
=2,M=2
LIS-SM,N=128,nR
=8,M=2
LIS-SM,N=128,nR
=32,M=2
LIS-SM,N=128,nR
=64,M=2
Fig. 3. Theoretical BEP performance of LIS-SSK and LIS-SM
systems withincreasing nR.
where e(m,x→ m̂, x̂) stands for the number of bits in errorfor
the corresponding pairwise error event.
Remark 3: The above analysis is general and can be consid-ered
for all constellations. Derivation of simplified expressionsfor
BPSK and QPSK (or M -PSK in general) is left tointerested
readers.
B. Performance of LIS-SSK
Considering x = x̂ =√Es (i.e., an unmodulated carrier in
the baseband) in (39), we obtain the conditional PEP of
theLIS-SSK scheme as
P (m→ m̂) = Q
√∑nRl=1Es∣∣Gl − Ĝl∣∣22N0
. (50)In light of this information, the analyses in Section IV.A
(forthe case of m 6= m̂) is also valid for ML detection of
LIS-SSKand the unconditional PEP P̄ (m→ m̂) can be easily
derivedfrom (40) with suitable modifications in MΓ(s). Then the
BEPupper bound of LIS-SSK can be calculated similar to (23) as
Pb ≤nR2P̄ (m→ m̂). (51)
Remark 4: We observe that unlike the greedy detector,increasing
nR for ML detection improves the PEP perfor-mance of LIS-SM and
LIS-SSK schemes through the MGFterms of (46) and (48), which
include nR in their exponents.Since increasing nR also improves the
data rate along withincreasing number of bit errors in (49) and
(51), we facean interesting trade-off among complexity,
performance, anddata rate. In Fig. 3, we show the theoretical BEP
performanceof LIS-SSK and LIS-SM schemes calculated from (49)
and(51) for N = 128 reflectors and increasing nR, with respectto
Es/N0. As seen from Fig. 3, increasing nR eventuallyimproves the
BER performance while providing a higher datarate, which is quite
unusual for legacy communication systems.In other words, increasing
nR both improves the spectralefficiency and overall BER performance
for LIS-SSK/SMsystems in the presence of ML detection.
-35 -30 -25 -20 -15
SNR(dB)
10-5
10-4
10-3
10-2
10-1
100
BE
R
LIS-SSK,GD,N=64,nR
=2
LIS-SSK,GD,N=64,nR
=4
LIS-SSK,GD,N=64,nR
=8
LIS-SSK,GD,N=64,nR
=16
LIS-SSK,GD,N=128,nR
=2
LIS-SSK,GD,N=128,nR
=4
LIS-SSK,GD,N=128,nR
=8
LIS-SSK,GD,N=128,nR
=16
Theoretical
Fig. 4. Theoretical and computer simulation results for LIS-SSK
with greedydetection.
-35 -30 -25 -20 -15 -10
SNR(dB)
10-5
10-4
10-3
10-2
10-1
100
BE
R
LIS-SM,GD,N=64,nR
=4,M=4
LIS-SM,GD,N=64,nR
=4,M=16
LIS-SM,GD,N=64,nR
=8,M=4
LIS-SM,GD,N=64,nR
=8,M=16
LIS-SM,GD,N=128,nR
=4,M=4
LIS-SM,GD,N=128,nR
=4,M=16
Theoretical
Fig. 5. Theoretical and computer simulation results for LIS-SM
with greedydetection.
V. SIMULATION RESULTS
In this section, we provide computer simulation results forthe
proposed LIS-based SSK and SM schemes and make com-parisons with
our theoretical results and reference schemes.We consider Es/N0 as
the SNR, similar to the classicaldiversity combining and space
modulation schemes.
In Figs. 4 and 5, we provide BER performance curves ofthe
LIS-SSK and LIS-SM systems for greedy detection andmake comparisons
with the theoretical results obtained from(23) and (24),
respectively. As seen from the given results, ourtheoretical
findings are quite accurate for both schemes andthe performance of
LIS-SSK and LIS-SM schemes degradewith increasing bits per channel
use (bpcu), or equivalentlynR, values (see Remarks 1 and 2). It is
worth noting thatBER performance of both schemes significantly
improves byincreasing the N value from 64 to 128, which is
consistentwith (22).
In Fig. 6, we focus on the performance of LIS-SSK andLIS-SM
schemes with ML detection and make comparisonswith the theoretical
results obtained from (49) and (51). Asseen from Fig. 6, while
increasing nR does not cause aremarkable BER degradation for the
LIS-SSK scheme, theeffect of increasing M is more evident for the
LIS-SM scheme.
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SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 9
-35 -30 -25 -20 -15 -10
SNR(dB)
10-5
10-4
10-3
10-2
10-1
100
BE
RLIS-SSK,MLD,N=64,n
R=2
LIS-SSK,MLD,N=64,nR
=8
LIS-SSK,MLD,N=128,nR
=2
LIS-SSK,MLD,N=128,nR
=8
LIS-SM,MLD,N=64,nR
=8,M=4
LIS-SM,MLD,N=64,nR
=8,M=16
LIS-SM,MLD,N=128,nR
=4,M=4
LIS-SM,MLD,N=128,nR
=4,M=16
Theoretical
Fig. 6. Theoretical and computer simulation results for LIS-SSK
and LIS-SMwith ML detection.
We compare the BER performances of greedy and MLdetectors for
both LIS-SSK and LIS-SM systems at variousbpcu values in Fig. 7. We
observe that the ML detector ofLIS-SSK provides approximately 2 dB
improvement in therequired SNR for the considered two setups (N =
64, nR = 2and N = 128, nR = 8). Although we observe a
similarimprovement for LIS-SM in case of N = 64, the difference
inBER performances of greedy and ML detectors is relativelysmaller
for the case of N = 128.
Finally, in Fig. 8, we present BER performance comparisonresults
for LIS-SSK, LIS-SM, LIS-AP [20], and conven-tional fully-digital
(zero-forcing) precoding-based receive SSK(RSSK) [29] at 3, 4, and
6 bpcu values with ML detection.We have several important
observations from Fig. 8. First,an interesting trade-off exists
between the receiver cost andthe BER performance for LIS-SSK and
LIS-SM schemes:while the former provides a better BER performance,
thelatter exhibits a slight degradation by using a less numberof
receive antennas at the same bpcu. Second, the LIS-APscheme
proposed in [20], which utilizes a single receiveantenna, cannot
compete with LIS-SSK/SM schemes since itcreates a virtual M -PSK
constellation by altering LIS phasesand suffers at high bpcu
values. Third, compared to LIS-based new schemes, a more than 15 dB
difference in requiredSNR is observed for the conventional
RSSK-MIMO scheme.Although utilizing a massive MIMO system, RSSK
forces theMIMO channels into zero to realize a pure SSK-like
reception,while LIS-based SM/SSK schemes constructively exploit
thewireless channels to boost the signal quality at the
intendedreceive antenna.
VI. CONCLUSIONS
The general concept of LIS-assisted IM has been proposedin this
paper as a new beyond massive MIMO paradigm fornext-generation
(potentially 6G or beyond) wireless networks.It has been shown by
comprehensive theoretical derivations aswell as computer
simulations that the proposed LIS-SSK andLIS-SM schemes have the
potential to provide considerablyhigh spectral efficiency at
extremely low SNR values througha smart and LIS-assisted indexing
mechanism for available
-35 -30 -25 -20 -15
SNR(dB)
10-5
10-4
10-3
10-2
10-1
100
BE
R
LIS-SSK,GD,N=64,nR
=2
LIS-SSK,MLD,N=64,nR
=2
LIS-SSK,GD,N=128,nR
=8
LIS-SSK,MLD,N=128,nR
=8
LIS-SM,GD,N=64,nR
=8,M=4
LIS-SM,MLD,N=64,nR
=8,M=4
LIS-SM,GD,N=128,nR
=4,M=4
LIS-SM,MLD,N=128,nR
=4,M=4
LIS-SM,GD,N=128,nR
=4,M=16
LIS-SM,MLD,N=128,nR
=4,M=16
Fig. 7. BER performance comparisons for greedy and ML detectors
of LIS-SSK and LIS-SM schemes.
-30 -25 -20 -15 -10 -5 0 5
SNR(dB)
10-5
10-4
10-3
10-2
10-1
100
BE
R
LIS-SSK,N=64,nR
=8
LIS-SM,N=64,nR
=4,M=2
LIS-AP,N=64,M=8
Conv.RSSK 64x8 MIMO
LIS-SSK,N=64,nR
=16
LIS-SM,N=64,nR
=4,M=4
LIS-AP,N=64,M=16
Conv.RSSK 64x16 MIMO
LIS-SSK,N=64,nR
=64
LIS-SM,N=64,nR
=16,M=4
LIS-AP,N=64,M=64
Conv.RSSK 128x64 MIMO
Fig. 8. BER performance comparison of LIS-SSK, LIS-SM, LIS-AP
[20], andconventional RSSK [29] schemes for 3, 4, and 6 bpcu.
receive antennas. We conclude that the effective use of
LIS-assisted IM schemes may be a game-changing paradigm
fornext-generation (6G) communication networks by eliminatingthe
need for sophisticated massive MIMO schemes that requireexpensive
and power-hungry components. The extremely lowSNR regions of
operation may also be a remedy to theincreasing need for advanced
channel coding schemes toachieve ultra-reliable communications. As
also discussed inIntroduction, potential application of IM for
transmit antennasand/or LIS regions along with other
advanced/generalizedschemes, the design of low-complexity receiver
architectures,and analyses in the presence of potential system
imperfections,remain as interesting and open research problems.
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Ertugrul Basar (S’09-M’13-SM’16) received theB.S. degree (Hons.)
from Istanbul University,Turkey, in 2007, and the M.S. and Ph.D.
degreesfrom Istanbul Technical University, Turkey, in 2009and 2013,
respectively. He is currently an AssociateProfessor with the
Department of Electrical andElectronics Engineering, Koç
University, Istanbul,Turkey and the director of Communications
Re-search and Innovation Laboratory (CoreLab). Hisprimary research
interests include MIMO systems,index modulation, waveform design,
visible light
communications, and signal processing for communications.Recent
recognition of his research includes the Science Academy
(Turkey)
Young Scientists (BAGEP) Award in 2018, Mustafa Parlar
FoundationResearch Encouragement Award in 2018, Turkish Academy of
SciencesOutstanding Young Scientist (TUBA-GEBIP) Award in 2017, and
the first-ever IEEE Turkey Research Encouragement Award in
2017.
Dr. Basar currently serves as an Editor of the IEEE
TRANSACTIONSON COMMUNICATIONS and Physical Communication
(Elsevier), and as anAssociate Editor of the IEEE COMMUNICATIONS
LETTERS. He served as anAssociate Editor for the IEEE ACCESS from
2016 to 2018.
https://arxiv.org/abs/1903.08925https://arxiv.org/abs/1903.08925https://arxiv.org/abs/1810.06934https://arxiv.org/abs/1810.10718https://arxiv.org/abs/1903.11456v1https://arxiv.org/abs/1810.05667v2https://arxiv.org/abs/1902.08463
I IntroductionII System ModelII-A LIS-Assisted Space Shift
KeyingII-B LIS-Assisted Spatial Modulation
III Greedy Detection: Performance AnalysisIII-A Performance of
LIS-SSKIII-B Performance of LIS-SM
IV Maximum Likelihood Detection: Performance AnalysisIV-A
Performance of LIS-SMIV-B Performance of LIS-SSK
V Simulation ResultsVI ConclusionsReferencesBiographiesErtugrul
Basar