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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1
Decentralized Blockchain-Based Dynamic Spectrum
Acquisition for Wireless Downlink Communications
Miao Jiang, Yiqing Li, Qi Zhang, Member,IEEE, Guangchi Zhang, and Jiayin Qin
Abstract—Wireless network virtualization is a promising so-
lution to improve spectrum efficiency. For a wireless downlink
communication system with multiple mobile virtual network
operators (MVNOs), we propose a decentralized blockchain-
based dynamic spectrum acquisition scheme. Our proposed
scheme aims to minimize the sum transmit power at all MVNOs
while satisfying the average data transmission rate thresholds.
For each MVNO, the required wireless spectrum to provide
customized services to the mobile users (MUs) is predicted
using the half-range Gauss-Hermite quadrature. Based on the
predicted values, all the MVNOs carry out a blockchain-based
distributed alternative direction method of multipliers to obtain
the global optimal solution to the aforementioned sum transmit
power minimization problem. To examine the effectiveness of
our proposed scheme, with known system parameters, we also
theoretically derive the semi-closed-form solution to the actually
required sum transmit power minimization problem subject to
data transmission rate constraints. Simulation results illustrate
that our proposed dynamic spectrum acquisition scheme achieves
almost the same minimum sum power as the non-causal scheme,
which assumes the number of active MUs in all cells and all
the channels are known non-causally for the optimal dynamic
spectrum allocation.
Index Terms—Alternating direction method of multipliers
(ADMM), blockchain, dynamic spectrum acquisition, wireless
network virtualization.
I. INT ROD UC TI ON
With the popularity of smartphones, an exponential traffic
growth is generated by wireless applications in the fifth-
generation (5G) networks and beyond [1]–[5]. To cope with
the dramatic growth of wireless traffic and massive access
of mobile users, base stations are expected to be densely
deployed [6]. Because of densely deployed base stations, the
spectrum is becoming crowded and at the same time, the cost
This work was supported in part by the National Natural Science Foundation
of China under Grant 61672549, in part by the China Postdoctoral Science
Foundation under Grant 2020M682612, in part by the Guangdong Natural
Science Foundation under Grant 2018B0303110016, in part by the Special
Support Plan for High-Level Talents of Guangdong Province under Grant
2019TQ05X409, and in part by the Guangzhou Science and Technology
Program under Grant 201804010445.
M. Jiang and Y. Li are with the School of Electronics and Informa-
tion Technology, Sun Yat-sen University, Guangzhou 510006, Guangdong,
China, and also with the School of Information Engineering, Guangdong
University of Technology, Guangzhou 510006, Guangdong, China (e-mail:
jmiao@mail2.sysu.edu.cn, liyiq5@mail2.sysu.edu.cn). Q. Zhang is with the
School of Electronics and Information Technology, Sun Yat-sen University,
Guangzhou 510006, Guangdong, China (e-mail: zhqi26@mail.sysu.edu.cn).
G. Zhang is with the School of Information Engineering, Guangdong U-
niversity of Technology, Guangzhou 510006, Guangdong, China (e-mail:
gczhang@gdut.edu.cn). J. Qin is with the School of Electronics and Infor-
mation Technology, Sun Yat-sen University, Guangzhou 510006, Guangdong,
China, and also with the Xinhua College, Sun Yat-sen University, Guangzhou
510520, Guangdong, China (e-mail: issqjy@mail.sysu.edu.cn).
to acquire the exclusive right for spectrum usage is becoming
high [5]. On the other hand, the actual licensed spectrum
is largely under-utilized in vast temporal and geographic
dimensions. A method to solve the issue of spectrum scarcity
and under-utilization is to allow dynamic spectrum utilization,
either by spectrum auction or spectrum sharing. Note that the
conventional spectrum sharing using a centralized database is
not flexible, scalable, and is vulnerable to a single point of
failure [5].
A dynamic spectrum utilization application is wireless net-
work virtualization [7]–[9]. Wireless network virtualization fa-
cilitates multiple network operators in the sharing of common
resources, e.g., licensed spectrum. The virtualized wireless
networks commonly consist of multiple mobile network oper-
ators (MNOs) and multiple mobile virtual network operators
(MVNOs) [10]. The MNO owns the physical cellular infras-
tructure and radio resources, and it executes the virtualization
by leasing the isolated virtualized network resources to the
MVNO. The MVNO leases the resources from the MNO and
then assigns the resources to the mobile users (MUs). The
spectrum resources that belong to one or more MNOs are
virtualized and split into slices. The MVNO utilizes the slices
leased from MNOs depending on the quality-of-service (QoS)
required by the MUs. Recently, wireless network virtualization
has attracted increasing attention from the research community
[11]–[14]. In [11], an active sharing of physical infrastructure
and the spectrum was proposed, where MNOs share the
network resources and provide wholesale access to MVNOs,
allowing them to provide voice and data services using part
of the available resources. The work in [12] introduced a
novel scheme for slicing and scheduling by developing an
efficient resource allocation scheme. In [13], an efficient low-
complexity scheme was put forward to virtualize the wireless
resource blocks and share them between MUs of multiple
MNOs. The scheme aims to maximize the throughput while
maintaining access with proportional fairness among MUs
as well as MNOs. In [14], a two-stage spectrum leasing
problem with the goal of maximizing the average profit of an
MVNO was investigated. Besides the use in terrestrial cellular
networks, wireless network virtualization was considered as a
technique for more flexible integration and interworking in
air-to-ground heterogeneous networks [15].
In wireless network virtualization, it is important to precise-
ly predict the required wireless spectra to provide customized
services to the MUs in their respective service cells. In this
paper, we propose to model that the MUs arrive at the service
cells with a spatio-temporal Poisson process and the sojourn
time of each MU before its departure follows an independent
IEEE TRANSACTIONS ON SIGNAL PROCESSING 2
exponential distribution. Since the instantaneous data rate
expression includes the instantaneous channel, by employing
stochastic geometry, we express the cumulative distribution
function (CDF) and the probability density function (PDF)
of the channel gain by Kummer’s function [16]. Thus, the
expected data transmission rate involves the integral of Kum-
mer’s function, whose closed-form expression is difficult to
obtain. In this paper, we propose to apply the half-range Gauss-
Hermite quadrature (HR-GHQ) to approximate the aforemen-
tioned integral [17], [18].
To allow multiple MVNOs to share the limited wireless
spectrum, we propose to divide the whole communication pro-
cess into multiple periods, each measured in minutes. At the
beginning of each period, MVNOs should predict and acquire
the necessary wireless spectrum. It is well known that there ex-
ists a trade-off between the bandwidth and the transmit power
in the sense that one can compensate for the other. Therefore,
we formulate the dynamic spectrum acquisition optimization
problem that minimizes the sum transmit power at all MVNOs
while satisfying the average data transmission rate thresholds.
The optimization problem can be solved in a centralized
manner. However, in wireless network virtualization, a vast
number of MVNOs may join the network or leave the network
in a very short time duration. On the other hand, only adjacent
MVNOs may compete for the same wireless spectrum, because
the wireless spectrum can be reused by two MVNOs that
are far away from each other. Furthermore, different MVNOs
may belong to different entities, i.e., different enterprises or
different persons. The information exchange among different
MVNOs should be as limited as possible. Therefore, it is
reasonable that the formulated dynamic spectrum acquisition
optimization problem is solved in a decentralized manner. In
this paper, we propose a decentralized alternative direction
method of multipliers (ADMM) to obtain the globally optimal
solution [19]. Note that only by expressing the expected data
transmission rate using the HR-GHQ, the centralized and
decentralized schemes are applicable.
The decentralized dynamic spectrum acquisition may fail
under the Byzantine attack and double-spending attack [20].
The Byzantine attack means that the participants provide
misleading answers for reaching a consensus on dynamic
spectrum acquisition. The double-spending attack means that
the same wireless spectrum is erroneously shared by more
than one MVNO. To make the decentralized system robust
to the Byzantine attack and double-spending attack, we pro-
pose a smart contract-enabled permissioned blockchain-based
dynamic spectrum acquisition scheme [20]–[30]. Note that in
the permissioned blockchains, only consensus among adjacent
MVNOs are required to be created because only adjacent
MVNOs may compete for the same wireless spectrum.
The using of blockchain to deal with spectrum challenges
is a growing application area [5], [31]–[34]. In [31], a
blockchain-enabled spectrum sharing in 5G heterogeneous
networks was proposed. In [32], a multi-operator spectrum
sharing using a consortium blockchain was studied to improve
spectrum utilization. In [33], a proactive blockchain-based
spectrum sharing protocol that leverages a blockchain to
provide security against spectrum sharing data falsification
attacks in cognitive radio based Internet of Things (IoT) was
put forward. In [34], a blockchain radio access network as an
advanced wireless access paradigm was presented. In [5], the
state-of-art applications of blockchain in 5G wireless networks
were reviewed.
The permissioned blockchain-based dynamic spectrum ac-
quisition problem was also considered in [30], where an MNO
leases its owned spectrum to a secondary unmanned aerial
vehicle (UAV) network in exchange for some revenue from
the UAV operators. It is noted that in [30], each UAV operator
only maximizes its own utility function, which is a logarithm
function modeled payoff/benefit gained from allocated spec-
trum minus the cost incurred due to buying the spectrum. The
dynamic spectrum prediction, which is significantly important
in wireless network virtualization, is missing.
The main contributions of this paper can be summarized as
follows:
•For an MVNO in its respective service cell with randomly
distributed MUs, we propose a method to predict the
required wireless spectrum, where the CDF and the PDF
of the channel gain are expressed by Kummer’s function.
To facilitate the centralized and decentralized dynamic
spectrum acquisition optimization, we propose to express
the expected data transmission rate using the HR-GHQ.
•To allow multiple MVNOs to share the limited wireless
spectrum, we formulate the dynamic spectrum acquisition
optimization problem that minimizes the sum transmit
power at all MVNOs while satisfying the average data
transmission rate thresholds. Furthermore, we propose
a decentralized ADMM to obtain the globally optimal
solution to the aforementioned optimization problem.
•To combat the Byzantine attack and double-spending
attack in a decentralized network, we propose a smart
contract-enabled permissioned blockchain-based dynamic
spectrum acquisition scheme.
The remainder of the paper is organized as follows. The
system model is described in Section II. We propose the dy-
namic spectrum prediction method in Section III. The dynamic
spectrum acquisition optimization problem is formulated and
solved in Section IV. We propose the smart contract-enabled
permissioned blockchain-based dynamic spectrum acquisition
scheme in Section V. With known system parameters, the
optimal power and spectrum allocation is theoretically derived
in Section VI. Section VII provides simulation results to
validate the effectiveness of our proposed scheme. Section VIII
concludes this paper.
Notation: Boldface lowercase letters denote vectors. (·)T
denotes the transpose operation. ∥·∥1and ∥·∥2represent the
ℓ1and ℓ2norm of a vector, respectively.
II. SYSTEM MO DE L
Consider a wireless downlink communication system with
MMVNOs. Each MVNO serves the MUs in a cell via orthog-
onal multiple access (OMA), such as time-division multiple
access (TDMA), frequency-division multiple access (FDMA),
or code-division multiple access (CDMA), which avoids multi-
user interference. In this paper, we consider that FDMA is em-
ployed. The mth transmission cell, m∈ M ={1,2,· · · , M },
IEEE TRANSACTIONS ON SIGNAL PROCESSING 3
is assumed to be a fixed circular region, denoted as Dm∈R2,
whose radius is denoted as rm. The mth MVNO is located at
the cell center.
With wireless network virtualization operation, the whole
communication process is divided into multiple periods, each
measured in minutes. At the beginning of each period,
MVNOs should predict the required wireless spectrum to
provide customized services to the MUs in their respective
service cells. Based on the predicted values, MVNOs acquire
wireless spectrum. Denote the bandwidth of wireless spectrum
acquired by the mth MVNO as wm, for m∈ M. We have
M
m=1
wm≤W, (1)
where Wdenotes the total available bandwidth.
To predict the required wireless spectrum accurately in a
period is a difficult problem in general [35], [36]. To make it
easy to tackle, we assume that all MUs arrive at the service
cells with a spatio-temporal Poisson process, the movement
of each MU can be modeled as independent Markov process
and the sojourn time of each MU before its departure follows
an independent exponential distribution. Based on the above
assumption, the number of active MUs in a service cell
describes a spatial birth-and-death process, whose stationary
distribution is a Poisson point process (PPP) [37], [38]. Thus,
the number of active MUs in the mth cell is modeled as a
PPP with density λm. This is a very common assumption
in wireless network modeling and performance analysis [39],
[40].
Suppose that transmitted signals are affected by both large-
scale path-loss and small-scale flat Rayleigh fading. Thus, the
channel between the nth MU and its associated mth MVNO
is denoted by
hmn =gmn
1 + Lα
mn
,(2)
where Lmn denotes the distance between the mth MVNO and
the nth MU in the mth cell, αdenotes the path-loss decay
factor, and gmn denotes a complex Gaussian random variable
with zero mean and unit variance. The instantaneous data rate
for the nth MU in the mth MVNO is given by
Rmn =bmn log21 + qmn |hmn |2
Γbmnσ2
0,(3)
where bmn and qmn denote the bandwidth and power of
the nth MU allocated by the mth MVNO, respectively, Γ
denotes the signal-to-noise ratio (SNR) gap to the information
theoretical channel capacity owing to the non-ideal coding and
modulation in practice [41], and σ2
0denotes the power spectral
density of additive white Gaussian noise at all MUs.
III. DY NAM IC SP EC TRUM PREDICTION
For the required wireless spectrum prediction, since we have
no information on the channels, hmn, we employ the uniform
bandwidth allocation and power allocation for the MUs in each
cell. Thus, in the mth cell,
bmn =wm
Nm
and qmn =pm
Nm
,(4)
where Nmdenotes the number of active MUs in the mth cell
and pmdenotes the total transmission power budget at the mth
MVNO. Since the active MUs in the mth cell are modeled as
a PPP with density λm, the average number of MUs in the
mth cell is
E[Nm] = Λm=πr2
mλm.(5)
Accordingly, the expected data transmission rate of the nth
MU in the mth cell is expressed as
E[Rmn] =
∞
Nm=1
Ω
Nm
Pr[Nm],(6)
where
Ω = ∞
0
wmlog21 + pmx
wmσ2f|hmn|2(x)dx, (7)
Pr[Nm] = (Λm)Nm
Nm!exp (−Λm).(8)
In (7), σ2= Γσ2
0and f|hmn|2(x)is the PDF of the random
variable |hmn|2. According to [16], we have
∞
Nm=1
1
Nm
Pr[Nm] = ϕm,(9)
where
ϕm= (Ei (Λm)−ln (Λm)−C) exp (−Λm).(10)
In (10), Ei (x)is the exponential integral function whose series
expansion is [16, 5.1.10]
Ei (x) =
∞
n=1
xn
n·n!+ ln x+C(11)
and Cdenotes the Euler-Mascheroni constant.
Denote the average data transmission rate threshold for each
MU in the mth cell as ¯
Rm, for m∈ M. To predict the required
wireless spectrum, we should calculate the minimum wmthat
ensures
E[Rmn]≥¯
Rm.(12)
Given pm, to ensure (12) requires the computation of Ωin (7).
To proceed, we first introduce the following proposition.
Proposition 1: The CDF of |hmn|2is
F|hmn|2(x) = 1 −Ψ2
α,1 + 2
α,−xrα
me−x,(13)
where Ψ (a, b, z)denotes Kummer’s function [16].
Proof : See Appendix A.
Using Proposition 1, by taking the first-order derivative with
respect to x,f|hmn|2(x)is
f|hmn|2(x) =Ψ 2
α,1 + 2
α,−xrα
me−x
−dΨ2
α,1 + 2
α,−xrα
m
dx e−x.(14)
From [16, 13.4.8], we know
dΨ (s, t, y)
dy =s
tΨ (s+ 1, t + 1, y ).(15)
IEEE TRANSACTIONS ON SIGNAL PROCESSING 4
Thus, we have
f|hmn|2(x) = e−xκ(x),(16)
where
κ(x) =Ψ 2
α,1 + 2
α,−xrα
m
+2rα
m
2 + αΨ1 + 2
α,2 + 2
α,−xrα
m.(17)
Substituting (16) into (12), we obtain
ξ≥¯
Rm,(18)
where
ξ=ϕm∞
0
wmlog21 + pmx
wmσ2e−xκ(x)dx. (19)
It is noted that, on the left-hand side of (18), the integral
result ξis difficult to obtain. Furthermore, when the integrand
has a non-negligible tail, even the numerical integration is
complicated and time-consuming. In this paper, we propose
to apply the HR-GHQ to approximate the integral on the left-
hand side of (18) with high accuracy [17], [18].
Based on [18], a K-point HR-GHQ can be written as
∞
0
e−t2ζ(t)dt ≈
K
k=1
akζ(tk),(20)
where both the weights {ak}K
k=1 and abscissas {tk}K
k=1 are
real numbers. By letting x=t2, we have
ξ=ϕm∞
0
2wmtlog21 + pmt2
wmσ2e−t2κt2dt. (21)
Applying the K-point HR-GHQ, we obtain
ξ≈
K
k=1
wmηmk log21 + pmt2
mk
wmσ2,(22)
where ηmk = 2ϕmamktmk κt2
mk, and both the weights
{amk}and abscissas {tmk }are real numbers.
From (18) and (22), in the mth cell, given pm, we can
predict the required bandwidth of wireless spectrum.
IV. DEC EN TR AL IZ ED DYNAMIC SPECTRU M ACQUISITION
Because there exists a trade-off between the bandwidth and
the transmit power, to allow multiple MVNOs to share the
limited wireless spectrum, we propose to minimize the sum
transmit power at all MVNOs while satisfying the average
data transmission rate thresholds. By substituting (22) into the
constraint E[Rmn]≥¯
Rm, i.e., (18), the dynamic spectrum
acquisition optimization problem is
min
p,w
M
m=1
pm
s.t.
K
k=1
wmηmk log21 + pmt2
mk
wmσ2≥¯
Rm,
M
m=1
wm≤W, pm≥0, wm≥0,∀m∈ M.(23)
Problem (23) is convex in terms of optimization variables p
and w. It can be solved efficiently using the interior point
method [42] in a centralized manner. However, a decentralized
dynamic spectrum acquisition scheme is preferable. This is be-
cause a vast number of MVNOs may join the network or leave
the network in a very short time duration in wireless network
virtualization. On the other hand, only adjacent MVNOs may
compete for the same wireless spectrum, because the wireless
spectrum can be reused by two MVNOs that are far away
from each other. Furthermore, different MVNOs may belong to
different entities, i.e., different enterprises or different persons.
The information exchange among different MVNOs should be
as limited as possible. Therefore, we propose a decentralized
ADMM to obtain the globally optimal solution to the dynamic
spectrum acquisition optimization problem [19].
By introducing an auxiliary variable z= [z1, z2,· · · , zM]T,
(23) is reformulated as
min
p,w,z
M
m=1
pm(24a)
s.t.
K
k=1
wmηmk log21 + pmt2
mk
wmσ2≥¯
Rm,(24b)
M
m=1
zm≤W, (24c)
w−z=0,(24d)
pm≥0, wm≥0, zm≥0,∀m∈ M.(24e)
Denote the feasible region of constraint (24c) and zm≥0,
∀m∈ M as Z, its indicator function is defined as
IZ(z) = 0,if z∈ Z,
∞,otherwise.(25)
Similarly, denote the feasible region of constraint (24b), pm≥
0and wm≥0,∀m∈ M as C, its indicator function can be
defined as
IC(p,w) = 0,if (p,w)∈ C,
∞,otherwise.(26)
With (25) and (26), (24) can be rewritten in ADMM form as
follows
min
p,w,z
M
m=1
pm+IZ(z) + IC(p,w)(27a)
s.t. w−z=0.(27b)
Thus, the augmented Lagrangian (using the scaled dual vari-
able) of (27) is given by
Lν(p,w,z,u) =
M
m=1
pm+IZ(z) + IC(p,w)
+ν
2∥w−z+u∥2
2,(28)
where u= [u1, u2,· · · , uN]Tis the dual variable for the
constraint (27b) and ν > 0is the penalty parameter. From
(27), it is observed that the variables can be split into two
groups: {p,w}and z. Furthermore, the objective function can
be separable accordingly. Therefore, the ADMM algorithm can
IEEE TRANSACTIONS ON SIGNAL PROCESSING 5
be applied to solve (27) by iteratively updating p,w,z, and
u.
In the (l+1)th iteration, given {p(l),w(l),z(l),u(l)}, which
is optimal in the lth iteration, the optimization variables are
updated sequentially as follows.
Step 1: Given {z(l),u(l)}, we solve the following optimiza-
tion problem
{p(l+1),w(l+1) }= arg max
p,wLνp,w,z(l),u(l).(29)
Problem (29) is equivalent to
min
p,w
M
m=1
pm+ν
2
M
m=1 wm−z(l)
m+u(l)
m2
s.t. (24b), wm≥0, pm≥0,∀m∈ M.(30)
It is noted that (30) can be decomposed into Msubproblems.
Each subproblem solves
min
pm,wm
pm+ν
2wm−z(l)
m+u(l)
m2
s.t.
K
k=1
wmηmk log21 + pmt2
mk
wmσ2≥¯
Rm,
wm≥0, pm≥0.(31)
Problem (31) is a convex problem and can be solved efficiently
using the interior point method [42].
Step 2: Given {p(l+1),w(l+1),u(l)}, we solve the following
optimization problem
z(l+1) = arg max
zLνp(l+1),w(l+1) ,z,u(l).(32)
Problem (32) is equivalent to
min
z
w(l+1) −z+u(l)
2
2(33)
s.t. ∥z∥1≤W, zm≥0,∀m∈ M.(34)
Problem (33) is a convex ℓ1ball projection problem [43]. Its
closed-form solution is obtained as follows.
If ∥w(l+1) +u(l)∥1> W , we have
z(l+1)
m= max w(l+1)
m+u(l)
m−β, 0,(35)
where
β=1
ττ
m=1
φm−W,(36)
τ= max
1≤i≤Mi
φi−1
ii
m=1
φm−W>0,(37)
and φ= [φ1, φ2,· · · , φM]Tdenotes the vector obtained by
sorting w(l+1) +u(l)in descending order.
If ∥w(l+1) +u(l)∥1≤W, we have
z(l+1)
m=w(l+1)
m+u(l)
m.(38)
Step 3: Given {w(l+1),z(l+1)}, the dual variable can be
updated as
u(l+1) =w(l+1) −z(l+1) +u(l).(39)
A reasonable termination criterion is that the primal and
dual residuals are small enough, i.e., [44]
w(l+1) −z(l+1)
max
w(l+1)
,
z(l+1)
≤ϵp,
ν(z(l+1) −z(l))
u(l+1)
≤ϵd,
(40)
where ϵp>0and ϵd>0are predefined convergence tolerance
for the primal and dual residuals, respectively.
V. SM ART CO NT RAC T-ENAB LE D PERMISSIONED
BLOCKCHAIN-BA SE D DYNAMIC SPECTRU M ACQUISITION
The decentralized dynamic spectrum acquisition may fail
under the Byzantine attack and double-spending attack. For
example, although the proposed ADMM based decentralized
dynamic spectrum acquisition scheme in Section IV is a
distributed scheme, an aggregator is still needed to compute
and broadcast the global variable zand dual variable u. When
the aggregator is under the Byzantine attack, the broadcasted
zand umay be corrupted, which leads to the divergence
of ADMM. To make the decentralized system robust to the
Byzantine attack and double-spending attack, we propose a s-
mart contract-enabled permissioned blockchain-based dynamic
spectrum acquisition scheme.
Blockchain, which was invented by Satoshi Nakamoto in
2008, is an emerging technology to build consensus between
disparate individuals [21]. The blockchain technologies have
been extensively used in many areas, such as Bitcoin and
Ethereum [22]–[27]. Both Bitcoin and Ethereum belong to
public blockchains [28]. Due to numerous participants, achiev-
ing consensus in public blockchains is time-consuming and
power-intensive, which restricts the application of blockchains
in many scenarios. Apart from public blockchains, another
primary type of blockchain is permissioned blockchains [29].
Due to the limited number of predefined participants and
controllable trust among them, a more efficient consensus
algorithm can be employed.
In this paper, we assume that most of MVNOs, which are
predefined participants of a smart contract-enabled permis-
sioned blockchain, are reliable. All the participants build the
consensus via the low complexity consensus algorithms, e.g.,
practical Byzantine fault tolerance (PBFT) based consensus
algorithms [45], [46] and Raft [47], which are based on
electing and voting. The leader is the only participant that
should bundle transactions into a block. The leader is elected
after a period of voting. Once a participant is elected by
majority participants, the participant will become the leader
and all other participants take a follower role. When the
leader creates a block, the block is set to be the new head
of the blockchain only after the block has been verified by the
majority of followers [47]. Due to the limited number of partic-
ipants and low complexity consensus algorithms, permissioned
blockchain can handle as high as thousands of transactions per
second [48], [49], which can satisfy the practical demand in
wireless downlink communication systems.
The proposed smart contract-enabled permissioned
blockchain-based dynamic spectrum acquisition scheme is
summarized in Algorithm 1.
IEEE TRANSACTIONS ON SIGNAL PROCESSING 6
Algorithm 1 Smart Contract-Enabled Permissioned
Blockchain-Based Dynamic Spectrum Acquisition
1: Initialize:z(0)
m= 0 and u(0)
m= 0,∀m∈ M;l= 0;
ϵp>0,ϵd>0, and ν > 0;
2: Loop:
Local Computation:
Get z(l)
mand u(l)
mfrom blockchain;
Obtain p(l+1)
mand w(l+1)
mby solving (31);
Send w(l+1)
mto SC1on blockchain;
Blockchain Computation:
SC1: Update z(l+1) via (35) and (38);
Update u(l+1) via (39);
Compute the primal and dual residuals;
If (40) is satisfied
A final agreement is achieved;
Terminate iteration;
Call SC2with z(l+1);
Endif
l=l+ 1;
Endloop
3: SC2:For m∈ M
Send transaction to the mth MVNO with z(l+1)
m;
If Get paid from the mth MVNO successfully
Authorize the spectrum to the mth MVNO;
Endif
Endfor
In Algorithm 1, both SC1and SC2are smart contracts
deployed on the permissioned blockchain. SC1and SC2will
run on all MVNOs. Smart contract SC1receives the local
computational result w(l+1)
msent from each MVNO as input,
and computes z(l+1) and u(l+1). Based on the assumption
that most MVNOs are reliable, the final correctness of z(l+1)
and u(l+1) can be guaranteed even there exist some malicious
participants due to the consensus mechanism. If the convergent
condition is satisfied, the result will be sent to smart contract
SC2. If not, the result will be sent back to MVNOs. Smart
contract SC2receives the convergent result sent from SC1as
input. Then it charges all MVNOs and authorizes them to
use their acquired spectrum according to the final convergent
result.
Unlike the MNO in the traditional centralized spectrum
acquisition situation, smart contracts SC1and SC2take all
network demands into consideration, where w(l+1) and z(l+1)
can be viewed as the spectrum demand of MVNOs and the
spectrum MNO can provide to MVNOs, respectively. The
iteration is similar to the negotiation process between MNO
and MVNOs in the traditional centralized spectrum acquisi-
tion situation. After several rounds of negotiations, when the
spectrum that MNO can provide for all MVNOs approximates
the spectrum demand of all MVNOs, the algorithm converges,
which means a final agreement is achieved.
VI. OP TI MA L POWE R AN D SPE CT RUM ALLOCATION WITH
KNOW N SYS TE M PARAMETERS
In this paper, we propose a dynamic spectrum acquisition
scheme. To fairly compare the performance of our proposed
scheme with the fixed spectrum allocation scheme and other
schemes, with known system parameters, we propose to in-
vestigate the actually required minimum sum transmit power
of MMVNOs subject to that the data transmission rate
thresholds for all MUs in Mcells are satisfied. With our
proposed dynamic spectrum acquisition scheme and other
spectrum allocation schemes, the bandwidth of wireless spec-
trum of the mth MVNO, i.e., wm, is known. Thus, the
aforementioned optimization problem is decoupled into M
transmit power minimization subproblems. For the transmit
power minimization subproblem of the mth MVNO, with
known system parameters, we should study the power and
spectrum allocation optimization problem among all MUs
in the mth cell subject to that the data transmission rate
thresholds for all MUs in the mth cell are satisfied.
In the mth cell, when the actual number of MUs, Nm,
and the channel between the nth MU and its associated mth
MVNO, hmn, are known for n∈ Nm={1,2,··· , Nm},
the power and spectrum allocation optimization problem is
formulated as
min
qm,bm
Nm
n=1
qmn (41a)
s.t.
Nm
n=1
bmn ≤wm,(41b)
bmn log21 + qmn |hmn |2
bmnσ2≥˜
Rm,(41c)
qmn ≥0, bmn ≥0,∀n∈ Nm,(41d)
where ˜
Rmdenotes the data transmission rate threshold for
each MU in the mth cell, qm= [qm1, qm2,··· , qmNm]T,
and bm= [bm1, bm2,· · · , bmNm]T. To continue, we need the
following proposition.
Proposition 2: For (41), the optimal qmand bmshould
satisfy that constraint (41c) are all active, i.e.,
bmn log21 + qmn |hmn|2
bmnσ2=˜
Rm,∀n∈ Nm.(42)
Proof : See Appendix B.
From Proposition 2, (41) is equivalently written as
min
bm
Nm
n=1
bmnσ2
|hmn|22
˜
Rm
bmn −1
s.t.
Nm
n=1
bmn ≤wm, bmn ≥0,∀n∈ Nm.(43)
Problem (43) is convex. In the following proposition, we
propose to solve it using the bisection search.
IEEE TRANSACTIONS ON SIGNAL PROCESSING 7
Proposition 3: The closed-form optimal solution to (43),
denoted by bo
mn, is
bo
mn =˜
Rmln 2
1 + Wµo|hmn|2−σ2
eσ2,∀n∈ Nm,(44)
where W(x)denotes the Lambert Wfunction of x[50] and
µo>0is a constant which satisfies Nm
n=1 bmn =wm.
The value of µocan be found by the bisection search over
[µmin, µmax ]with
µmin =χ
maxn|hmn|2and µmax =χ
minn|hmn|2,(45)
where
χ=σ2Nm˜
Rmln 2
wm
−1exp Nm˜
Rmln 2
wm+σ2.(46)
Proof : See Appendix C.
VII. SIM UL ATIO N RES ULTS
In this section, we evaluate the performance of our pro-
posed dynamic spectrum prediction, decentralized dynamic
spectrum acquisition, and smart contract-enabled permissioned
blockchain-based dynamic spectrum acquisition schemes.
A. Simulation Results of Dynamic Spectrum Prediction and
Decentralized Dynamic Spectrum Acquisition Schemes
We consider a wireless downlink communication system
with M= 6 MVNOs. Each MVNO serves the MUs in
a cell. Since each MVNO uses different wireless spec-
trum for transmission, there is no co-channel interference.
Thus, the overlap of different cells will not cause a prob-
lem. We assume that the radii and the corresponding user
densities of the M= 6 cells are (r1= 80 m, λ1=
1200 persons/km2),(r2= 80 m, λ2= 800 persons/km2),
(r3= 100 m, λ3= 800 persons/km2),(r4= 100 m, λ4=
1000 persons/km2),(r5= 120 m, λ5= 1000 persons/km2),
and (r6= 120 m, λ6= 1200 persons/km2). The total avail-
able bandwidth is 100 MHz. The path-loss decay factor is 3.76
[52]. We assume that σ2= Γσ2
0=−150.9dBm/Hz [52]. In
(20), a K= 500-point HR-GHQ is employed. If not specified,
the average data transmission rate threshold in (12) and the
data transmission rate threshold in (41) are ¯
R1=˜
R1= 2
Mbps, ¯
R2=˜
R2= 0.5Mbps, ¯
R3=˜
R3= 0.5Mbps,
¯
R4=˜
R4= 1 Mbps, ¯
R5=˜
R5= 1 Mbps, and ¯
R6=˜
R6= 2
Mbps.
Remark: In this paper, the chosen user densities of cells
follow a case of broadband access in dense areas [51, 4.2.6
Table 2].
In Fig. 1, we show the convergence performance of our
proposed decentralized dynamic spectrum acquisition scheme.
From Fig. 1, it is observed that our proposed scheme converges
at about 10 iterations. Furthermore, the parameters and final
convergent results are summarized in Table I. For an MVNO,
the larger the throughput expected, the more bandwidth is
needed in most cases. Particularly, the throughput expected
to provide for an MVNO can be computed by multiplying the
0 2 4 6 8 10 12 14 16
0
5
10
15
20
25
30
35
40
45
50
Iterations
Bandwidth (MHz)
The 6th MVNO
The 5th MVNO
The 4th MVNO
The 3rd MVNO
The 2nd MVNO
The 1st MVNO
Fig. 1. Bandwidth versus iterations; the convergence performance of our
proposed decentralized dynamic spectrum acquisition scheme.
average number of MUs in the cell with the average data trans-
mission rate threshold, i.e., E[Nm]¯
Rm. In addition, compared
with the 5th MVNO, although the throughput expected for the
1st MVNO is larger, the required bandwidth is less. The reason
is that the service cell radius of the 1st MVNO is much smaller
than that of the 5th MVNO. In large service cells, to satisfy
the QoS constraints for cell-edge MUs, more power will be
used to compensate the distance-related large-scale path-loss.
Therefore, in order to minimize the sum transmit power used
in all MVNOs, more spectrum should be allocated to cells
with larger radii.
TABLE I
SUM MARY O F PARA MET ER S AND RE SU LTS IN FI G. 1
MVNO rmλmE[Nm]¯
RmE[Nm]¯
Rmwm
m persons/km2persons Mbps Mbps MHz
1 80 1200 24 2 48 13.51
2 80 800 16 0.5 8 2.2
3 100 800 25 0.5 12.5 4.44
4 100 1000 31 1 31 11.21
5 120 1000 45 1 45 20.14
6 120 1200 54 2 108 48.5
In Fig. 2, we present the minimum sum power comparison
of different schemes for different values of the average data
transmission rate threshold in the 6th cell, ¯
R6. In the legend,
“DSA” denotes our proposed dynamic spectrum prediction and
decentralized dynamic spectrum acquisition schemes. “Unifor-
m” denotes that the total available bandwidth is uniformly
allocated to M= 6 MVNOs. “Proportional” denotes that
the total available bandwidth is allocated to MVNOs propor-
tionally according to E[Nm]¯
Rm. “Non-Causal” denotes that,
assuming the number of active MUs in all cells and all the
channels, hmn,∀n∈ Nm, m ∈ M, are known non-
causally, we solve the joint sum transmit power minimization
and bandwidth allocation optimization problem subject to that
the data transmission rate thresholds for all MUs in Mcells
are satisfied. From Fig. 2, it is observed that our proposed
dynamic spectrum acquisition scheme achieves almost the
IEEE TRANSACTIONS ON SIGNAL PROCESSING 8
0.5 1 1.5 2 2.5 3
12
14
16
18
20
22
24
26
28
30
¯
R6(Mbps)
Minimum Sum Power (dBm)
Uniform
Proportional
DSA
Non−Causal
Fig. 2. Minimum sum power versus ¯
R6; comparison of our proposed
dynamic spectrum prediction and decentralized dynamic spectrum acquisition
schemes, the “Uniform” scheme, the “Proportional” scheme, and the “Non-
Causal” scheme.
1 2 3 4 5 6
0
5
10
15
20
25
30
35
40
45
50
The number of MVNOs
Bandwidth (MHz)
Uniform
Proportional
DSA
Non−Causal
Fig. 3. Bandwidth allocation comparison of our proposed dynamic spectrum
prediction and decentralized dynamic spectrum acquisition schemes, the
“Uniform” scheme, the “Proportional” scheme, and the “Non-Causal” scheme
when ¯
R6= 2 Mbps.
same minimum sum power as the “Non-Causal” scheme.
In Fig. 3, we present the bandwidth allocation comparison
of different schemes with parameters shown in Table I. From
Fig. 3, it is found that the allocated bandwidth of our pro-
posed dynamic spectrum prediction and decentralized dynamic
spectrum acquisition schemes is almost the same as that of
the “Non-Causal” scheme. This is because the average of the
simulated data transmission rate is accurately predicted by the
expected data transmission rate using (22), i.e., our proposed
dynamic spectrum prediction is accurate. Furthermore, our
proposed decentralized dynamic spectrum acquisition scheme,
which takes all the statistical information of MUs’ distributions
and channel gain distributions into consideration, achieves the
globally optimal solution to (23).
In Fig. 4, we present the minimum sum power comparison
800 1000 1200 1400 1600 1800
14
16
18
20
22
24
26
28
λ6 (persons/km2)
Minimum Sum Power (dBm)
Uniform
Proportional
DSA
Non−Causal
Fig. 4. Minimum sum power versus λ6; comparison of our proposed dynamic
spectrum prediction and decentralized dynamic spectrum acquisition schemes,
the “Uniform” scheme, the “Proportional” scheme, and the “Non-Causal”
scheme when ¯
R1=˜
R1= 2 Mbps, ¯
R2=˜
R2= 0.5Mbps, ¯
R3=˜
R3= 0.5
Mbps, ¯
R4=˜
R4= 1 Mbps, ¯
R5=˜
R5= 1 Mbps, and ¯
R6=˜
R6= 2 Mbps.
800 1000 1200 1400 1600 1800
0
10
20
30
40
50
60
λ6 (persons/km2)
Bandwidth (MHz)
The 6th MVNO
The 5th MVNO
The 4th MVNO
The 3rd MVNO
The 2nd MVNO
The 1st MVNO
Fig. 5. Bandwidth allocation of all MVNOs versus λ6; our proposed dynamic
spectrum prediction and decentralized dynamic spectrum acquisition schemes
when ¯
R1=˜
R1= 2 Mbps, ¯
R2=˜
R2= 0.5Mbps, ¯
R3=˜
R3= 0.5Mbps,
¯
R4=˜
R4= 1 Mbps, ¯
R5=˜
R5= 1 Mbps, and ¯
R6=˜
R6= 2 Mbps.
of different schemes. Particularly, we vary the value of λ6
while keeping the rest of the parameters in Table I unchanged.
In Fig. 5, we present the corresponding bandwidth allocation
of our proposed dynamic spectrum prediction and decentral-
ized dynamic spectrum acquisition schemes for all MVNOs.
From Fig. 4, it is shown that almost the same minimum
sum power is obtained by our proposed dynamic spectrum
acquisition scheme and the “Non-Causal” scheme.
B. Simulation Results of Smart Contract-Enabled Permis-
sioned Blockchain-Based Dynamic Spectrum Acquisition
In this subsection, our proposed system is simulated on the
Quorum blockchain system [53] with Istanbul Byzantine fault
tolerance (IBFT) [46] consensus protocol on a Dell Precision
IEEE TRANSACTIONS ON SIGNAL PROCESSING 9
0 2 4 6 8 10 12 14 16
Iterations
0
10
20
30
40
50
60
70
80
90
100
Bandwidth (MHz)
The 1st MVNO
The 2nd MVNO
The 3rd MVNO
The 4th MVNO
The 5th MVNO
The 6th MVNO
Fig. 6. Bandwidth versus iterations; the iteration behavior of our proposed
decentralized dynamic spectrum acquisition scheme when the aggregator is
under the Byzantine attack.
T3630 workstation with an Intel Core i7-8700 3.2 GHz CPU
and 16 GB memory. Each MVNO runs in a virtual machine
on the workstation. All smart contracts are implemented via
Solidity and can be interacted via Web3 [54] in Python. In
Algorithm 1, (31) is solved by CVXPY [55] in Python.
It is noted that, compared with other conventional methods,
using permissioned blockchains achieves the following advan-
tages at the expense of extra computation and storage costs in
each MVNO:
•By delegating all the computation and data operation
tasks to the blockchain and MVNOs, management costs
can be saved at the MNO.
•Spectrum acquisition, charging, and authorization can be
performed automatically with the help of smart contracts
deployed on the blockchain. The processing delay de-
creases significantly, making real-time dynamic spectrum
access possible.
•Due to the transparency of the blockchain, the MVNOs
can be ensured that they are charged fairly.
•During the spectrum acquisition process, MUs’ related
data are not exchanged in the network. Therefore, MUs’
privacy can be protected.
•Permissioned blockchains are more robust to cyber at-
tacks. The network is safe and reliable unless most of
the MVNOs have been controlled by the attacker.
In Fig. 6, we show the iteration behavior of our proposed
decentralized dynamic spectrum acquisition scheme when
the aggregator is under the Byzantine attack. The attack is
simulated by adding zero-mean and unit-variance Gaussian
random variables to each element of z(l+1) in the (l+ 1)th
iteration. From Fig. 6, it is observed that the decentralized
dynamic spectrum acquisition scheme cannot converge. As
a consequence, the MVNOs cannot reach a consensus on
dynamic spectrum acquisition and the spectrum cannot be
properly allocated to the MVNOs.
In Fig. 7, we show the primal residual and dual residual evo-
0 5 10 15 20 25 30 35 40 45 50
Iterations
10-10
10-8
10-6
10-4
10-2
100
102
Primal and Dual Residuals
Dual residual, DSA
Primal residual, DSA
Dual residual, Blockchain DSA
Primal residual, Blockchain DSA
Fig. 7. Primal and dual residuals versus iterations; the convergence per-
formance comparison of our proposed smart contract-enabled permissioned
blockchain-based dynamic spectrum acquisition scheme and decentralized
dynamic spectrum acquisition scheme when the aggregator is under the
Byzantine attack.
lutions of our proposed smart contract-enabled permissioned
blockchain-based dynamic spectrum acquisition scheme and
decentralized dynamic spectrum acquisition scheme, denoted
as “Blockchain DSA” and “DSA”, respectively, when the
aggregator is under the Byzantine attack. From Fig. 7, it is
observed that the primal residual and dual residual of our
proposed “Blockchain DSA” scheme almost monotonically
decrease with the increase in iterations, whereas those of the
“DSA” are larger than 10−2when the number of iterations is
50.
In Fig. 8, we present the transaction throughput of our pro-
posed smart contract-enabled permissioned blockchain-based
dynamic spectrum acquisition scheme with IBFT and Raft
consensus algorithms for different numbers of MVNOs, M,
where the transaction throughput is defined as the number of
transactions successfully processed by the blockchain network
per second. The results are averaged by sending 50000 trans-
actions from MNO to MVNOs with the help of Chainhammer
[56]. From Fig. 8, it is found that the blockchain with IBFT
consensus algorithm has lower transaction throughput than
that with Raft consensus algorithm. This is because IBFT,
used in the simulations of Fig. 7, needs more voting rounds
to handle the possible Byzantine attacks, which causes the
longer processing delay, whereas Raft is a crash fault-tolerant
algorithm that cannot handle the Byzantine attacks. From Fig.
8, it is also shown that both consensus algorithms can achieve
over 200 transactions per second when there are 8 MVNOs.
In our proposed smart contract-enabled permissioned
blockchain-based scheme, the number of transactions required
for each dynamic spectrum acquisition is (L+ 1)M, where
Ldenotes the number of iterations for convergence of the
ADMM. Therefore, when M= 8, our proposed scheme can
be accomplished in less than half a second. Since the spatio-
temporal Poisson process of MUs in a cell may vary on the
time scale of minutes, our proposed scheme is applicable. It
IEEE TRANSACTIONS ON SIGNAL PROCESSING 10
45678
M
200
250
300
350
400
450
Throughput (transactions per second)
Raft
IBFT
Fig. 8. Transaction throughput versus M; performance of our proposed
smart contract-enabled permissioned blockchain-based dynamic spectrum
acquisition scheme with IBFT and Raft consensus algorithms.
is noted that, in simulations, each MVNO runs in a virtual
machine on the workstation. The number of MVNOs Mis
limited by the capability of workstation. It is reported in [48], a
permissioned blockchain with 100 participants, each equipped
with a 2.0 GHz CPU and 8 GB memory, can handle over 2000
transactions per second.
VIII. CONCLUSION
In this paper, we have proposed a decentralized blockchain-
based dynamic spectrum acquisition scheme for a wireless
downlink communication system with multiple MVNOs. It is
shown through simulation results that our proposed dynamic
spectrum acquisition scheme achieves almost the same mini-
mum sum power as the non-causal scheme that assumes the
number of active MUs in all cells and all the channels are
known non-causally for optimal dynamic spectrum allocation.
It is also illustrated that, with the help of smart contracts,
our proposed scheme is robust to the Byzantine attack. Future
works may be carried out on the decentralized blockchain-
based spectrum acquisition in other scenarios, such as grant-
free massive access in the IoT. Future works may also be
carried out on more efficient consensus protocols, which take
advantage of the broadcasting nature of wireless communica-
tions, to improve the processing efficiency for the blockchains
deployed in wireless networks.
APP EN DI X A
PROO F OF PROPOSITION 1
According to the definition of the CDF, we have
F|hmn|2(x) = Pr |gmn |2≤x(1 + Lα
mn).(47)
Since gmn is a complex Gaussian random variable with zero
mean and unit variance, |gmn|2is an exponentially distributed
random variable. Furthermore, the location of the nth MU in
the mth cell is uniformly distributed in Dmwith the PDF of
1/(πr2
m). By using polar coordinates, we obtain
F|hmn|2(x) = rm
0π
−π
1
πr2
m1−e−x(1+yα)ydθdy. (48)
After some mathematical manipulations, we obtain
F|hmn|2(x) = 1 −2
r2
m
e−xrm
0
ye−xyαdy. (49)
Let t=xyα.F|hmn |2(x)is reexpressed as
F|hmn|2(x) = 1 −2
r2
m
e−xxrα
m
0
t1
αx−1
αe−tdt1
αx−1
α
= 1 −2
αr2
m
x−2
αe−xxrα
m
0
t2
α−1e−tdt
= 1 −2
α(xrα
m)−2
αγ2
α, xrα
me−x,(50)
where γ(s, x) = x
0ts−1e−tdt denotes the lower incomplete
gamma function. Because Ψ (s, 1 + s, −x) = sx−sγ(s, x)
[16, 6.5.12], we obtain (13).
APPENDIX B
PROO F OF PROPOSITION 2
We prove Proposition 2 by contradiction. Assume that q⋆
m=
[q⋆
m1, q⋆
m2,· · · , q⋆
mNm]Tis the optimal solution to (41) such
that there exists n∈ Nmwhich satisfy
bmn log21 + qmn |hmn|2
bmnσ2>˜
Rm.(51)
We can choose a proper real scalar ∆>0such that
bmn log21 + (q⋆
mn −∆) |hmn|2
bmnσ2=˜
Rm.(52)
Note that [q⋆
m1,· · · , q⋆
m(n−1), q⋆
mn −∆, q⋆
m(n+1),··· , q⋆
mNm]T
is also feasible and has smaller objective value than q⋆
m. This
contradicts that q⋆
mis the optimal solution.
APPENDIX C
PROO F OF PROPOSITION 3
The Lagrangian of (43) is given by
˜
L=
Nm
n=1
bmnσ2
|hmn|2e
˜
Rmln 2
bmn −1+µNm
n=1
bmn −wm,
(53)
where µ≥0denotes the Lagrange multiplier associated
with the constraint Nm
n=1 bmn ≤wm. Since (43) is convex,
the Karush-Kuhn-Tucker (KKT) conditions are both necessary
and sufficient for the global optimality of (43). It can be
verified that Nm
n=1 bmn =wmmust hold for (41). From KKT
conditions, we have µo>0where µodenotes the optimal
dual solution to (43).
Taking the first-order partial derivative of ˜
Lwith respect to
bmn, we have
∂˜
L
∂bmn
=σ2
|hmn|21−˜
Rmln 2
bmn e
˜
Rmln 2
bmn −1+µ. (54)
IEEE TRANSACTIONS ON SIGNAL PROCESSING 11
From KKT conditions, we have
˜
Rmln 2
bo
mn
−1e
˜
Rmln 2
bo
mn −1=µo|hmn|2−σ2
eσ2.(55)
According to the definition of the Lambert Wfunction, we
obtain the optimal bo
mn as in (44). In (44), there exists
an unknown parameter µo. The value of µoshould satisfy
Nm
n=1 bmn =wm.
In (44), since
µo|hmn|2−σ2
eσ2≥ − 1
e,(56)
W(x)is a monotonically increasing function. Accordingly,
bo
mn is a monotonically decreasing function of |hmn|2. Thus,
we have
˜
Rmln 2
1 + Wµomaxn|hmn|2−σ2
eσ2≤bo
mn
≤˜
Rmln 2
1 + Wµominn|hmn|2−σ2
eσ2.(57)
Summing each term in (57) from n= 1 to n=Nm, we obtain
Nm˜
Rmln 2
1 + Wµomaxn|hmn|2−σ2
eσ2≤wm
≤Nm˜
Rmln 2
1 + Wµominn|hmn|2−σ2
eσ2.(58)
According to the definition of the Lambert Wfunction, we
have
µmin ≤µo≤µmax,(59)
where µmin and µmax are defined in (45).
REF ER EN CE S
[1] N. Panwar, S. Sharma, and A. K. Singh, “A survey on 5G: The next
generation of mobile communication,” Phys. Commun., vol. 18, pp. 64–
84, Mar. 2016.
[2] Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of
nonorthogonal multiple access in 5G systems with randomly deployed
users,” IEEE Signal Process. Lett., vol. 21, no. 12, pp. 1501–1505, Dec.
2014.
[3] Y. Li, M. Jiang, Q. Zhang, Q. Li, and J. Qin, “Secure beamforming in
downlink MISO nonorthogonal multiple access systems,” IEEE Trans.
Veh. Technol., vol. 66, no. 8, pp. 7563–7567, Aug. 2017.
[4] Y. Li, M. Jiang, Q. Zhang, Q. Li, and J. Qin, “Cooperative non-orthogonal
multiple access in multiple-input-multiple-output channels,” IEEE Trans.
Wireless Commun., vol. 17, no. 3, pp. 2068–2079, Mar. 2018.
[5] M. Tahir, M. H. Habaebi, M. Dabbagh, A. Mughees, A. Ahad, and K.
I. Ahmed, “A review on application of blockchain in 5G and beyond
networks: Taxonomy field-trials challenges and opportunities,” IEEE
Access, vol. 8, pp. 115876–115904, Jun. 2020.
[6] A. Y. Ding and M. Janssen, “Opportunities for applications using 5G
networks: Requirements, challenges, and outlook,” in Proc. Int. Conf.
Telecommun. and Remote Sensing, 2018, pp. 27–34.
[7] C. Liang and F. R. Yu, “Wireless network virtualization: A survey, some
research issues and challenges,” IEEE Comm. Surveys Tuts., vol. 17, no.
1, pp. 358–380, First Quart. 2015.
[8] L. Zhao, M. Li, Y. Zaki, A. Timm-Giel, and C. G¨
org, “LTE virtualization:
From theoretical gain to practical solution,” in Proc. Int. Teletraffic
Congress, 2011, pp. 71–78.
[9] 3GPP TR 22.852, “Study on radio access network (RAN) sharing
enhancements,” Jun. 2013.
[10] R. Kokku, R. Mahindra, H. Zhang, and S. Rangarajan, “NVS: A sub-
strate for virtualizing wireless resources in cellular networks,” IEEE/ACM
Trans. Netw., vol. 20, no. 5, pp. 1333–1346, Oct. 2012.
[11] X. Costa-Perez, J. Swetina, T. Guo, R. Mahindra, and S. Rangarajan,
“Radio access network virtualization for future mobile carrier networks,”
IEEE Commun. Mag., vol. 51, no. 7, pp. 27–35, Jul. 2013.
[12] M. I. Kamel, L. B. Le, and A. Girard, “LTE wireless network virtu-
alization: Dynamic slicing via flexible scheduling,” in Proc. IEEE VTC,
2014, pp. 1–5.
[13] M. Kalil, A. Moubayed, A. Shami, and A. Al-Dweik, “Efficient low-
complexity scheduler for wireless resource virtualization,” IEEE Wireless
Commun. Lett., vol. 5, no. 1, pp. 56–59, Feb. 2016.
[14] Y. Zhang, S. Bi, and Y. J. A. Zhang, “Joint spectrum reservation and
on-demand request for mobile virtual network operators,” IEEE Trans.
Commun., vol. 66, no. 7, pp. 2966–2977, Jul. 2018.
[15] J. Qiu, D. Grace, G. Ding, M. D. Zakaria, and Q. Wu, “Air-ground
heterogeneous networks for 5G and beyond via integrating high and low
altitude platforms”, IEEE Wireless Commun., vol. 26, no. 6, pp. 140–148,
Dec. 2019.
[16] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions
with Formulas, Graphs, and Mathematical Tables. New York, NY, USA:
Dover, 1972.
[17] J. S. Ball, “Half-range generalized Hermite polynomials and the related
Gaussian quadratures,” SIAM J. Numer. Anal., vol. 40, no. 6, pp. 2311–
2317, Jul. 2006.
[18] N. M. Steen, G. D. Byrne, and E. M. Gelbard, “Gaussian quadratures for
the integrals ∫∞
0e−x2f(x)dx and ∫b
0e−x2f(x)dx,” Math. Comput.,
vol. 23, no. 107, pp. 661–671, 1969.
[19] E. Chen and M. Tao, “ADMM-based fast algorithm for multi-group
multicast beamforming in large-scale wireless systems,” IEEE Trans.
Commun., vol. 65, no. 6, pp. 2685–2698, Jun. 2017.
[20] D. B. Rawat and A. Alshaikhi, “Leveraging distributed blockchain-
based scheme for wireless network virtualization with security and QoS
constraints,” in Proc. Int. Conf. Computing, Netw. and Commun., 2018,
pp. 332–336.
[21] S. Nakamoto, “Bitcoin: A peer-to-peer electronic cash system,” 2008.
[Online]. Available: https://bitcoin.org/bitcoin.pdf
[22] K. Gai, K.-K. R. Choo, and L. Zhu, “Blockchain-enabled reengineering
of cloud datacenters,” IEEE Cloud Comput., vol. 5, no. 6, pp. 21–25,
Nov. 2018.
[23] P. K. Sharma, S. Singh, Y. S. Jeong, and J. H. Park, “DistBlockNet: A
distributed blockchains-based secure SDN architecture for IoT networks,”
IEEE Commun. Mag., vol. 55, no. 9, pp. 78–85, Sept. 2017.
[24] Z. Xiong, S. Feng, W. Wang, D. Niyato, P. Wang, and Z. Han,
“Cloud/fog computing resource management and pricing for blockchain
networks,” IEEE Internet Things J., vol. 6, no. 3, pp. 4585–4600, Jun.
2019.
[25] E. M ¨
unsing, J. Mather, and S. Moura, “Blockchains for decentralized
optimization of energy resources in microgrid networks,” in Proc. IEEE
Conf. Control Technol. and Applications, 2017, pp. 2164–2171.
[26] V. Buterin, “Ethereum white paper: A next-generation smart contrac-
t and decentralized application platform,” 2013. [Online]. Available:
https://github.com/ethereum/wiki/wiki/White-Paper
[27] N. Szabo, “Formalizing and securing relationships on public networks,”
First Monday, vol. 2, no. 9, 1997.
[28] V. Buterin, “On public and private blockchains,” 2015. [Online].
Available: https://blog.ethereum.org/2015/08/07/on-public-and-private-
blockchains/
[29] M. Vukoli, “Rethinking permissioned blockchains,” in ACM Workshop
on Blockchain, Cryptocurrencies and Contracts, 2017, pp. 3–7.
[30] J. Qiu, D. Grace, G. Ding, J. Yao, and Q. Wu, “Blockchain-based secure
spectrum trading for unmanned-aerial-vehicle-assisted cellular networks:
An operator’s perspective,” IEEE Internet Things J., vol. 7, no. 1, pp.
451–466, Jan. 2020.
[31] Z. Zhou, X. Chen, Y. Zhang, and S. Mumtaz, “Blockchain-empowered
secure spectrum sharing for 5G heterogeneous networks,” IEEE Netw.,
vol. 34, no. 1, pp. 24–31, Jan. 2020.
[32] S. Zheng, T. Han, Y. Jiang, and X. Ge, “Smart contract-based spectrum
sharing transactions for multi-operators wireless communication network-
s,” IEEE Access, vol. 8, pp. 88547–88557, May 2020.
[33] M. Patnaik, G. Prabhu, C. Rebeiro, V. Matyas, and K. Veezhinathan,
“ProBLeSS: A proactive blockchain based spectrum sharing protocol
against SSDF attacks in cognitive radio IoBT networks,” IEEE Netw.
Lett., vol. 2, no. 2, pp. 67–70, Jun. 2020.
[34] X. Ling, J. Wang, Y. Le, Z. Ding, and X. Gao, “Blockchain radio access
IEEE TRANSACTIONS ON SIGNAL PROCESSING 12
network beyond 5G,” IEEE Wireless Commun., vol. 27, no. 6, pp. 160–
168, Dec. 2020.
[35] X. Xing, T. Jing, W. Cheng, Y. Huo, and X. Cheng, “Spectrum prediction
in cognitive radio networks,” IEEE Wireless Commun., vol. 20, no. 2, pp.
90–96, Apr. 2013.
[36] V.-D. Nguyen and O.-S. Shin, “Cooperative prediction-and-sensing-
based spectrum sharing in cognitive radio networks,” IEEE Trans. Cog-
nitive Commun. and Netw., vol. 4, no. 1, pp. 108–120, Mar. 2018.
[37] F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless
Networks, Volume I-Theory. NoW Publishers, 2009.
[38] R. Serfozo, Introduction to Stochastic Networks. Springer Science &
Business Media, 2012.
[39] J. G. Andrews, F. Baccelli, and R. K. Ganti, “A tractable approach to
coverage and rate in cellular networks,” IEEE Trans. Commun., vol. 59,
no. 11, pp. 3122–3134, Nov. 2011.
[40] H. S. Dhillon, R. K. Ganti, F. Baccelli, and J. G. Andrews, “Modeling
and analysis of K-tier downlink heterogeneous cellular networks,” IEEE
J. Sel. Areas Commun., vol. 30, no. 3, pp. 550–560, Apr. 2012.
[41] J. G. D. Forney and G. Ungerboeck, “Modulation and coding for linear
Gaussian channels,” IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2384–
2415, Oct. 1998.
[42] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.:
Cambridge Univ. Press, 2004.
[43] J. Duchi, S. Shalev-Shwartz, Y. Singer, and T. Chandra, “Efficient
projections onto the ℓ1-ball for learning in high dimensions,” in Proc.
Int. Conf. Machine Learning, 2008.
[44] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed
optimization and statistical learning via the alternating direction method
of multipliers,” Found. Trends in Mach. Learn., vol. 3, no. 1, pp. 1–122,
Jan. 2011.
[45] M. Castro and B. Liskov, “Practical Byzantine fault tolerance,” in Proc.
the Third Symposium on Operating Systems Design and Implementation,
1999, pp. 173–186.
[46] H. Moniz, “The Istanbul BFT Consensus Algorithm,” 2020. [Online].
Available: https://arxiv.org/abs/2002.03613
[47] D. Ongaro and J. K. Ousterhout, “In search of an understandable
consensus algorithm,” in Proc. USENIX Annual Technical Conf., 2014,
pp. 305–319.
[48] E. Androulaki, et al., “Hyperledger Fabric: A distributed operating
system for permissioned blockchains,” 2018. [Online]. Available: http-
s://arxiv.org/abs/1801.10228
[49] T. T. A. Dinh, J. Wang, G. Chen, L. Rui, K. L. Tan, and B. C.
Ooi, “Blockbench: A benchmarking framework for analyzing private
blockchains,” in Proc. ACM Int. Conf. Manag. Data, 2017, pp. 1085–
1100.
[50] R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E.
Knuth, “On the Lambert W function,” Adv. Comput. Math., vol. 5, pp.
329–359, 1996.
[51] NGMN Alliance, “NGMN 5G white paper,” 2015. [Online]. Available:
https://www.ngmn.org/wp-content/uploads/NGMN 5G White Paper V1
0.pdf
[52] 3GPP TR 36.931, “LTE; evolved universal terrestrial radio access (E-
UTRA); radio frequency (RF) requirements for LTE pico Node B,” May
2011.
[53] Quorum, “Quorum whitepaper,” 2016. [Online]. Available: http-
s://github.com/jpmorganchase/quorum
[54] P. Merriam, “Web3.py: Populus documentation,” 2020. [Online]. Avail-
able: https://web3py.readthedocs.io/en/stable/
[55] S. Diamond and S. Boyd, “CVXPY: A Python-embedded modeling
language for convex optimization,” J. Mach. Learn. Res., vol. 17, no.
83, pp. 1–5, Apr. 2016.
[56] D. A. Kruger, “GitHub: Chainhammer,” 2019. [Online]. Available:
https://github.com/drandreaskrueger/chainhammer
Miao Jiang received the B.Eng. degree in software
engineering from Sun Yat-sen University (SYSU),
Guangzhou, China, in 2015 and the Ph.D. degree
in information and communication engineering from
SYSU, Guangzhou, China, in 2020.
He is currently a Post-Doctoral Fellow with the
School of Information Engineering, Guangdong U-
niversity of Technology, Guangzhou, China. His
research interests include unmanned aerial vehicle
(UAV) communications, non-orthogonal multiple ac-
cess, physical layer security, and multiple-input-
multiple-output communications.
Yiqing Li received the B.Eng. degree in software
engineering from Sun Yat-sen University (SYSU),
Guangzhou, China, in 2015 and the Ph.D. degree
in information and communication engineering from
SYSU, Guangzhou, China, in 2020.
She is currently a Post-Doctoral Fellow with
the School of Information Engineering, Guangdong
University of Technology, Guangzhou, China. Her
research interests include reconfigurable intelligent
surfaces, wireless caching, non-orthogonal multiple
access, and multiple-input-multiple-output commu-
nications.
Qi Zhang (S’04-M’11) received the B.Eng. (Hons.)
and M.S. degrees from the University of Electronic
Science and Technology of China, Chengdu, China,
in 1999 and 2002, respectively, and the Ph.D. degree
in electrical and computer engineering from the
National University of Singapore (NUS), Singapore,
in 2007.
He is currently an Associate Professor with the
School of Electronics and Information Technology,
Sun Yat-sen University, Guangzhou, China. From
2007 to 2008, he was a Research Fellow with the
Communications Lab, Department of Electrical and Computer Engineering,
NUS. From 2008 to 2011, he was with the Center for Integrated Electronics,
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences,
Shenzhen, China. His research interests include wireless caching, unmanned
aerial vehicle (UAV) communications, non-orthogonal multiple access, and
wireless communications powered by energy harvesting.
Guangchi Zhang received the B.S. degree in elec-
tronic engineering from Nanjing University, Nan-
jing, China, in 2004, and the Ph.D. degree in com-
munication engineering from Sun Yat-Sen Universi-
ty, Guangzhou, China, in 2009.
He is currently a Professor with the School of
Information Engineering, Guangdong University of
Technology, Guangzhou, China. From 2011 to 2012,
he was a senior research associate with City U-
niversity of Hong Kong. From 2017 to 2018, he
was a visiting professor with National University of
Singapore. His research interests include reconfigurable intelligent surfaces,
unmanned aerial vehicle (UAV) communications, wireless power transfer,
physical layer security, multiple-input-multiple-output communications, and
relay wireless communications.
He was the recipient of the IEEE Communications Society Heinrich Hertz
Award for Best Communications Letter in 2014, and an Exemplary Reviewer
for the IEEE Communication Letters in 2014.
IEEE TRANSACTIONS ON SIGNAL PROCESSING 13
Jiayin Qin received the M.S. degree in radio physics
from the Huazhong Normal University, Wuhan, Chi-
na, in 1992 and the Ph.D. degree in electronics from
Sun Yat-sen University (SYSU), Guangzhou, China,
in 1997.
He is currently a Professor with the School
of Electronics and Information Technology, SYSU.
From 2002 to 2004, he was the Head of the De-
partment of Electronics and Communication Engi-
neering, SYSU. From 2003 to 2008, he was the
Vice Dean of the School of Information Science and
Technology, SYSU. His research interests include wireless communications
and submillimeter wave technology.
He was the recipient of the IEEE Communications Society Heinrich Hertz
Award for Best Communications Letter in 2014, the Second Young Teacher
Award of Higher Education Institutions, Ministry of Education (MOE), China
in 2001, the Seventh Science and Technology Award for Chinese Youth in
2001, and the New Century Excellent Talent, MOE, China in 1999.
