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2023 The 23rd International Conference on Control, Automation and Systems (ICCAS 2023)
Yeosu Venezia Hotel & Utop Marina Hotel, Yeosu, Korea, Oct. 17∼20, 2023
Performance Analysis and Deep-Learning-Based Real-Time Evaluation
for Multihop MIMO Full-Duplex Relay Networks with Short-Packet URLLCs
Ngo Hoang Tu1and Kyungchun Lee2∗
1Department of Electrical and Information Engineering, Seoul National University of Science and Technology,
Seoul, 01811, Republic of Korea (ngohoangtu@seoultech.ac.kr)
2Department of Electrical and Information Engineering and Research Center for Electrical and Information Technology,
Seoul National University of Science and Technology,
Seoul, 01811, Republic of Korea (kclee@seoultech.ac.kr) ∗Corresponding author
Abstract: This work investigates multihop multiple-input multiple-output full-duplex relay (FDR) networks using short-
packet communications in accordance with ultra-reliability and low-latency communications. To comprehensively capture
the performance trend of the considered systems, the end-to-end block-error rate of the considered FDR is analyzed and
compared with that of half-duplex relaying systems, from which the effective throughput (ETP), energy efficiency (EE),
reliability, and latency are also studied. However, the derived analytical expressions contain non-elementary functions,
making them intricate for practical implementations, particularly in real-time configurations. Motivated by this, we in-
troduce a deep multiple-output neural network with a short execution time, low computational complexity, and highly
accurate estimation. This network can serve as an efficient tool to rapidly respond to the necessary system parameters,
such as transmit power and blocklength, when the services request specific ETP, EE, reliability, and latency. To validate
the correctness of the theoretical analysis, extensive simulation results are provided under varying impacts of system
parameters.
Keywords: Short-packet communication, ultra-reliable and low-latency, multiple-input multiple-output, multihop relay,
full-duplex relay, deep learning.
1. INTRODUCTION
In large-scale networks, multihop multiple-input
multiple-output (MIMO) relaying is a key idea that not
only enables reliable connectivity but also offers a viable
solution for energy savings and coverage extension of
wireless networks [1]. Ordinarily, multihop MIMO relay
systems operate in half-duplex relay (HDR) mode, where
each relay receives and transmits signals over orthogonal
resources, such as different time slots and orthogonal-
frequency channels. Although multihop MIMO HDR
networks can provide enhanced reliability and coverage,
the end-to-end (E2E) transmission rate decreases dramat-
ically as the number of hops increases, leading to a sig-
nificant loss of spectrum efficiency. Motivated by the
enormous advances in self-interference cancellation tech-
niques [2], full-duplex relay (FDR) systems, where each
relay node receives and transmits signals simultaneously
and over the same frequency band, have been investi-
gated as a promising method to overcome the spectrum-
efficiency loss of HDR.
In conventional wireless systems, long-packet com-
munications (LPCs) have primarily been examined; how-
ever, they are limited to supporting ultra-reliable and low-
latency communications (uRLLCs) for fifth-generation
(5G) and beyond networks. Inspired by the rigorous re-
quirements of 5G uRLLCs applications with an ultra-
reliability of at least 99.999% (five nines) and a very low
latency of ∼1−10 ms [3], short-packet communications
(SPCs) have been investigated as a new service [4].
This work was supported in part by the Basic Science Re-
search Program through the National Research Foundation of Ko-
rea (NRF) funded by the Ministry of Education under Grant NRF-
2019R1A6A1A03032119 and in part by the NRF Grant funded by the
Korean Government (MSIT) under Grant NRF-2022R1A2C1006566.
Recently, deep learning (DL) has been recognized as
a powerful data-driven approach for real-time configu-
rations in future wireless communications when closed-
form expressions for performance metrics may become
infeasible. Simulation and numerical-integration meth-
ods can be leveraged as alternative methods for eval-
uating system performance. However, the simulation
method suffers from long execution times, whereas the
numerical-integration method is hindered by high com-
plexity. In contrast, DL offers high accuracy in estimat-
ing nonlinear functions with reduced complexity, over-
coming the limitations of model-based approaches [5].
This study is the first to exploit the benefits of multihop
MIMO FDR networks using SPCs in accordance with 5G
uRLLCs. In addition, a deep multiple-output neural net-
work (DMNN) is designed to effectively and simultane-
ously predict multiple performance metrics. Our main
contributions are summarized as follows:
•This work investigates multihop MIMO FDR networks
with short-packet uRLLCs over Rayleigh fading chan-
nels, where the closed-form expressions for E2E block-
error rate (BLER), effective throughput (ETP), energy ef-
ficiency (EE), reliability, and latency are derived.
•An effective DMNN framework is designed to simul-
taneously predict performance metrics, such as ETP, EE,
and reliability, which can facilitate real-time IoT appli-
cations. The numerical results show that the designed
DMNN estimator achieves equivalent performance while
substantially reducing the execution time, compared with
the conventional analysis and simulation methodologies.
•Our model-based analysis is verified by Monte Carlo
simulations. Based on numerical results, the advantages
of multihop MIMO FDR systems in accordance with
uRLLC requirements are discussed, where the compet-
978-89-93215-26-7/23/$31.00ⓒICROS
1099
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itive tradeoff between HDR and FDR for these networks
has been indicated.
Notations: |·|,∥·∥2, and (·)Hdenote the magnitude,
ℓ2-norm, and Hermitian transpose, respectively. The
(i, j)th element of a matrix is denoted by [·]i,j , whereas
the ith column of a matrix is denoted by [·]i. Notation
∼and arg mean distributed as and argument, respec-
tively. Besides that, E(·)represents the expectation op-
erator. ℜ{·} represents the real part. Furthermore, Cx×y
represents the space of x×ycomplex matrices. If we
do not specify otherwise, k= 1, K + 1,i= 1, NT, and
j= 1, NRare assumed throughout this paper.
2. SYSTEM MODEL
We consider a multihop MIMO FDR system with
SPCs, where the source and destination communicate
with each other through the assistance of Kdecode-and-
forward relays over Rayleigh fading channels. For conve-
nience, we denote R1, R2, ..., RKas a sequence of relays,
R0as a source, and RK+1 as a destination. Each relay
node is equipped with NTisolated transmit antennas and
NRisolated receive antennas to enable the FDR mode,
whereas the source and destination nodes in HDR mode
are equipped with only NTtransmit and NRreceive an-
tennas, respectively. We assume that the direct links from
node Rkto node Rk+2 and beyond for k= 1, ..., K −1
are significantly weak and can be ignored because of ob-
stacles, severe shadowing, and the path-loss effect. In
other words, direct links only exist between two consec-
utive nodes; the communication from node R0to node
RK+1 requires K+ 1 hops.
Let Hk∈CNR×NTand Gk∈CNR×NTdenote
the channel coefficient matrices of communication link
Rk−1→Rkand self-loop interference (SLI) link, re-
spectively. Over Rayleigh fading channels, [Hk]i,j
2
and [Gk]i,j
2
follow the exponential distribution with
the characteristic parameters λ(i,j)
k=E[Hk]i,j
2
and Ω(i,j)
k=E[Gk]i,j
2, respectively. We assume
that the channel coefficients of each hop are independent
and identically distributed (i.i.d.), yielding λ(i,j)
k=λk
and Ω(i,j)
k= Ωk,∀i, j.
In the FDR mode, the received signal at each relay
is affected by the SLI. Although some techniques have
been proposed to cancel SLI, e.g., natural isolation, time-
domain cancellation, and spatial suppression [6], ideal
cancellation is challenging. Consequently, certain resid-
ual SLI remains. When the ith transmit antenna of node
Rk−1is selected for transmission by the transmit-antenna
selection (TAS) scheme [7, 8], the received signals at re-
lay Rkwith k= 1, K and destination RK+1 are ex-
pressed, respectively, as
y(i)
k=pPk−1[Hk]ixk−1+pPk[Gk]˜sxk+n(i)
k,
y(i)
K+1 =pPKHK+1ixK+n(i)
K+1,(1)
where ˜sdenotes the selected transmit antenna of node
Rkby the TAS scheme, Pk−1is the transmit power
of node Rk−1,xkis a scalar complex baseband sig-
nal transmitted from Rkwith zero mean and unit vari-
ance, i.e., En|xk|2o= 1,n(i)
kis a zero-mean ad-
ditive white Gaussian noise signal at Rkwith covari-
ance matrix N0INR,∀i, k, i.e., n(i)
k∼ CN (0,N0INR),
and INRdenotes the identity matrix of size NR. We
consider the maximum-ratio combining (MRC) scheme
[7, 8] at the receiver side, i.e., [Hk]H
iy(i)
k/
[Hk]i
2and
HK+1H
iy(i)
K+1/
HK+1i
2. As a result, the output
signal-to-interference-plus-noise ratios (SINRs) at link k
with k= 1, K and link K+ 1 are given by
γk=ρk−1Xk
ρkYk+ 1 and γK+1 =ρKXK+1,(2)
where ρk=Pk/N0,Xk= max
1≤i≤NTn
[Hk]i
2
2o, and
Yk=[Hk]H
ik[Gk]˜sk
2/
[Hk]ik
2
2. Here, ik= arg Xk
and ˜sk= arg Xk+1 indicate the selected transmit an-
tenna index of Xkand Xk+1, respectively. Accordingly,
the cumulative-distribution functions for γkand γK+1 are
calculated, respectively, by
Fγ(1)
k
(γ) = 1 +
NR−1
X
n=0
ak,n
NT−1
X
m=0 NT−1
mm(NR−1)
X
ℓ=0
ξℓm
·
V
X
v=0
ςvcα−v
k
nℓ
X
u=0 nℓ
ubnℓ−u
k
ρf(u,v)
ℓ
k−1
exp (m+ 1) bkγ
λ2
kρk−1
·Θ(k,u,v)
ℓ,m,n γf(u,v)
ℓ+nΓ−g(u,v)
n,(m+ 1) bkγ
λ2
kρk−1,(3)
Fγ(1)
K+1
(γ) = (1−exp −γ
zNR−1
X
n=0
1
n!γ
zn)NT
,
(4)
where α= 2NR/(NR+ 4),ϖk= (NR/2 + 2) λkΩk,
ak,n =Γ(n+α)NT
Γ(α)(NR−1)!n!ϖkρk
ρk−1n
,bk=ρkϖk−λk,
ck=λk+bk,nℓ=ℓ+NR−1,V=⌈α⌉is the upper
rounding of α,g(u,v)
n=−u−v+n+α−1,t(u,v)
n,ℓ =
2g(u,v)
n+ 2nℓ+ 2,f(u,v)
ℓ=α−v+nℓ−u,Θ(k,u,v)
ℓ,m,n =
(m+ 1)g(u,v)
nλ−t(u,v)
n,ℓ
kℜn(−1)h(u,v)
ℓ,m o,h(u,v)
ℓ,m =f(u,v)
ℓ+
m+ 1,ςv=Γ(α+1)
Γ(v+1)Γ(α−v+1) ,ξℓm =Pbℓm
κ=aℓ
ξℓ(m−1)
(ℓ−κ)!
is the recursion coefficient with ξℓ0=ξ0ℓ= 1,ξℓ1=
1/ℓ!,ξ1ℓ=ℓ,aℓ= max {0, ℓ −(NR−1)},bℓm =
min {ℓ, (m−1) (NR−1)},z=ρKλK+1, and Γ (·,·)
denotes the upper incomplete gamma function. The
proofs of (3) and (4) can be found in [9], which are omit-
ted here due to the page limitation.
3. PERFORMANCE ANALYSIS
3.1 Average BLER
According to Shannon’s theory, errors can be avoided
when the transmission rate is lower than the Shannon ca-
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pacity. In such a scenario, the outage probability would
be an appropriate performance metric. When it comes
to SPC in the finite-blocklength regime, the error prob-
ability is always non-zero, even when the transmission
rate is below the Shannon capacity. Given this context,
the desired BLER can be alternatively calculated using
the achievable rate, blocklength (BL), Shannon capac-
ity, and channel dispersion [4]. By considering SPC at
hop k, where Rk−1transmits Tinformation bits over
a BL with βchannel uses (CUs) to Rk,βneeds to re-
main at least 100 CUs to balance the reliability and la-
tency [10]. According to [11], when βis sufficiently large
(i.e., β > 100 CUs), the average BLER at hop kcan
be tightly approximated as ¯εk≈E(Q C(γk)−R
qV(γk)/β !),
where Q(·)denotes the Gaussian Q-function, C(γk)∆
=
log2(1 + γk)denotes the Shannon capacity, V(γk)∆
=
1−1
(1+γk)2(log2e)2is the channel dispersion, and R
represents the coding rate. We note that HDR and FDR
have different BL and coding rates [12], which need to be
clarified for the performance comparison. Specifically, if
the BL of each information packet in FDR mode is given
by β, the BL for HDR mode is calculated as β/2. Ac-
cordingly, the coding rates for the FDR and HDR modes
are determined by T/β and 2T/β, respectively.
It is intractable to directly characterize ¯εkin a closed-
form expression because of the complicated Gaussian Q-
function. We are thus inspired to apply a tight approx-
imation QC(γk)−R
√V(γk)/β ≈Ψ (γk)given by Ψ (γk) =
1, γk≤φL,
0.5−ξ√β(γk−τ), φL< γk< φH,
0, γk≥φH,
where ξ=
2π22R−1−1/2,τ= 2R−1,φH=τ+1/2ξ√β,
and φL=τ−1/2ξ√β[10]. With such a feasible ap-
proximation, we subsequently utilize the partial integra-
tion method, which yields ¯εk≈ξ√βRφH
φLFγk(γ)dγ.
Notably, ¯εkis still very strenuous to calculate directly
due to the complicated form of Fγk(γ). When β > 100
CUs, it is observed that φH−φL=p2π(22R−1) /β is
very small. Therefore, it is valid to utilize the first-order
Riemann integral approximation for ¯εk,k= 1, K [13],
which yields
¯εk≈ξpβ(φH−φL)FγkφH+φL
2
=Fγk(τ).(5)
Subsequently, ¯εK+1 can be directly calculated by
¯εK+1 ≈1 + ξpβ
NT
X
m=1 NT
m(−1)m^
X
(NR,m) m
Y
t=1
1
jt!!
·
ΥSm+ 1, a(m)
K+1φH−ΥSm+ 1, a(m)
K+1φL
mSma(m)
K+1
,(6)
where ^
P
(NR,m)
=
NR−1
P
j1=0 ·· ·
NR−1
P
jm=0
,Sm=
m
P
t=1
jt,a(m)
K+1 =
m
ρKλK+1 and Υ (·,·)denotes the lower incomplete gamma
function.
By adopting the selective decode-and-forward mech-
anism [7, Prop. 1], where an error occurs by incorrect
decoding at the relays or destination, the E2E BLER of
the proposed multihop MIMO FDR network is given by
¯εE2E = ¯ε1+
K+1
X
k=2 ¯εk·
k
Y
m=2
(1 −¯εm−1)!.(7)
3.2 Effective Throughput and Energy Efficiency
As reported in [3], ETP characterizes the effective rate
of a network (i.e., the actual useful data delivered through
a network per unit of time), which is measured in bits per
CU (BPCU). By considering the latency-limited trans-
mission mode with a transmission rate R=T/β, ETP
can be modeled as
δ= (1 −¯εE2E)R.(8)
To investigate the trade-off between effective rate and
total energy consumption for performing communica-
tions in the proposed systems, we present the average EE,
denoted by µ. Mathematically, the average EE, measured
in BPCU per watt (BPCU/W), is defined as the ratio be-
tween effective throughput and total energy consumption
[13]. In particular, we obtain
µ=(1 −¯εE2E )R
Pc+ (K+ 1)
K+1
P
k=1
Pk−1
,(9)
where Pcrepresents the total static power consumed by
the circuit components.
3.3 Reliability and Latency
The key objectives of SPCs over conventional LPCs
are ultra-reliability and low latency [3]. Reliability is de-
termined by the probability that a transmitted signal is re-
ceived and decoded correctly at the destination, whereas
latency is defined as the duration of the data transmission
and decoding required to traverse from the source to the
destination. As a result, the reliability and latency are
given, respectively, by
χ= (1 −¯εE2E)·100%,(10)
L=T
δ=β
1−¯εE2E
.(11)
We note that the above latency expression holds under
the assumption of an unlimited number of retransmission
times.
4. DL-BASED REAL-TIME EVALUATION
4.1 Motivation and Description of DMNN Framework
The DMNN framework is designed to realize the real-
time prediction of system performance. Although closed-
form expressions are available, it is not straightforward
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