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Resource Allocation for Underlaid Device-to-Device Communication by
Incorporating Both Channel Assignment and Power Control
Rui Tang1, Jiaojiao Dong2, Zhengcang Zhu1, Jun Liu1, Jihong Zhao1, 2 and Hua Qu1
1- School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, Sh aanxi, P. R. China;
2- School of Telecommunication and Information Engineering, Xi’an University of Posts & Telecommunications, Xi’an
710061, Shaan xi, P. R. China
Abstract—Device-to-Device (D2D) communication can greatly
enhance the system throughput (ST) and individual quality-of-
service (Q oS) experience by reusing the spectrum of cellular
network. But due to dense spectrum sharing, severe co-channel
interference may be imposed between cellular links (C-links)
and D2D links (D-links). So, to fully utilize the gain of D2D
communication, we attempt to maximize the ST of D -links with
guaranteed individual Q oS requirement for both types of links
by joint consideration of channel assignment (CA) and power
control (PC). Specifically, particle swarm optimizati on (PSO)
is explicitly adopted to optimize CA, but when deriving the
fitness value for each CA particle, underlaid PC optimization
will be implicitly performed for throughput maximization on
each channel , together with a gradual removal (GR) scheme to
maintain individual Q oS requirement and admit the maximum
number of D-links into the syste m. Thanks to the numerical
results, we demonstrate the superiority of our scheme in terms
of ST and system capacity (SC), i.e., the number of admitte d D-
li nks, when comparing with the on es in lite rature .
Keywords-D2D communication, channel assignment, power
control, particle swarm optimization, gradual removal, geometry
programming
I. INTRODUCTION
Recently, with the increasing demands for high data-rate
transmission in proximity, D2D communication has received
great attentions [1-2]. It is a novel communication paradigm
where the communication link in vicinity is built up between
the user equipments instead of being relayed via base station
(BS). It can substantially improve spectral efficiency, reduce
energy/power consumption and shorten transmission latency.
Besides, it can extend cell coverage, offload the burden of
BS and enable new types of services, e.g., local gaming.
We consider non-orthogonal spectral sharing mode [1]
for the underlaid D2D communication where C- and D-links
reuse the same channels due to spectral shortage, so mutual
interference is imposed between above two types of links. As
radio resource allocation has been proved to be effective in
managing co-channel interference and optimizing system
performance, several schemes have been studied in the prior
works [3-8] . In [3 ], a jo int spectral reuse mode selection and
PC scheme was raised to maximize overall throughput, but
only one channel was included and the QoS protection for
the secondary D-links was neglected. Multi-channel scenario
was considered in [4-5], where ST was stressed in [4] while
user fairness was highlighted in [5], i.e., to maximize the
minimu m individual data-rate among D-links. But individual
QoS requirement was omitted and only CA was designed.
Taking the above drawbacks into account, a joint admission
control, PC and CA scheme was proposed in [6] to optimize
the overall throughput. But the works in [3-6] restricted that
one channel could only be reused by at most one D-link,
which greatly limited the e xploitation of spectral efficiency.
So, the authors in [7-8] eliminated the above constraint and
maximized the ST for D-links with guaranteed individual
QoS requirement by either PC [7] or CA [8], but the gain of
joint resource allocation was miss ed compared to [6].
Inspire from the preceding works [3-8], we focus on the
same scenario as in [7-8] and attempt to maximize the ST for
D-links with individual QoS protection for the sake of user
fairness by joint consideration of CA and PC as in [6]. Due
to the high complexity of original problem, we decompose it
into two pa rts, namely CA an d PC, where PSO is e xplicit ly
adopted in CA by defining the fitness function as the ST of
all admitted D-links, but when deriving the fitness value for
each particle, PC optimization is performed for throughput
maximization on each orthogonal channel, including a GR to
achieve individual QoS requirement with maximu m number
of D-links being admitted. Finally, we elucidate the efficacy
of our scheme in terms of ST and SC via simulation.
The rest of this paper is organized as follows. Section 2
describes the system model and formulates our optimization
problem. Section 3 amply illustrates our joint optimization
scheme. Simulations are conducted to show the performance
of our scheme in Section 4. Finally, the conclusion is drawn
in Section 5.
II. SYST EM MODEL AND PROBL EM FORMULAT ION
A single cell scenario is studied in the following analysis.
We assume that D-links could only reuse the uplink channels
with C-links due to the asymmetry of the network load in
cellular system, and each D-link could reuse at most one
channel for the sake of user fairness while one channel could
be reused by multiple D-links for the exploitation of spectral
efficiency as in [7-8]. We assume that there are N channels
in the system, and each of them has been pre-assigned to a
C-lin ks with the same label, but the scheduling of C-links is
out the scope of our paper. Besides,
M
D-links are trying to
access into the cellular system in non-orthogonal spectral
sharing mode. We define the sets of C-lin ks and D-links as
{1, 2, ..., }CN
and
{1, 2, ..., }DM
. For the i-th channel,
we denote the set of D-links reusing it by
i
S
, and we assume
,
ii
SjS
. For simplicity, QoS e xperience is abstracted
by signal to interference plus noise ratio (SINR), and the
SINRs of the i-th C-lin k an d j-th D-link are defined in (1).
2015 Fifth International Conference on Communication Systems and Network Technologies
978-1-4799-1797-6/15 $31.00 © 2015 IEEE
DOI 10.1109/CSNT.2015.33
432
Figur e 1 . The structure of our joint optimization scheme
,,
,
,
,
,,,
()
()
i
i
CC
Cii
iCD D C
Bk ki i
kS
DD
jji
D
ji DC C DD D D
lj
ji i jl li j
lS
Gp a
Gp
Gp b
Gp Gp
(1)
whe re C
i
G and
,
CD
Bk
G
are the pathgain from the transmitters
of the i-th C-lin k an d the k-th D-lin k to BS , an d
D
j
G
is th e
pathgain of the j-th desired D-link, while
,
DC
ji
G
is the pathgain
from the transmitter of the i-th C-link to the receiver of the j-
th D-link, and
,
DD
jl
G
is the pathgain from the transmitter of
the l-th D-link to the receiver of the j-th D-link. Besides,
,
CD
ij
are the background noises at their receivers, while
,
,
CD
iji
pp
are their transmit powers, and
C
i
p
is fixed and ,
D
ji
p
is upper bounded by
,maxD
j
p
. Moreover,
,
0,
D
ti i
tS
. Each
channel is seen as a Gaussian channel with Shannon capacity,
and the normalized data-rate (with respect to bandwidth) of
the above two links are given below in (2).
2
,2,
log (1 ) ( )
log (1 ) ( )
CC
ii
DD
ji ji
Ra
Rb
(2)
In addition, we denote the SINR thresholds of above two
types of links as
,
CD
ij
which must be attained to meet the
individual QoS requirement. To evaluate the performance of
our scheme, the ST and SC of D-links are defined in (3) as
and
respectively, where
||
is to derive the cardinality
of the corresponding set, while
,
()|
D
mn M N
x
X
is CA re late d
binary variable matrix, and if the n-th channel is as s igned to
the m-th D-link,
,1
D
mn
x
, otherwise
,
0
D
mn
x
. And
,
()
D
njn
Sx
indicates that
n
S
is a function of
,
,
D
jn
xiD
, and if
,
1
D
jn
x
,
n
jS
, otherwise
n
jS
.
,
,
()
,
()
|( )| ()
D
njn
D
mn
nC mS x
D
njn
nC
Ra
Sx b
(3)
Finally, the optimization model in this paper is expressed
in (4), where (4-b) is local power budget at each D-link, and
(4-c) is the definition of the CA related binary variable and
th e reus e res trictio n for the sake o f us er fairness, wh ile 4(d -e)
are the individual QoS protection for each admitted links.
,, ,
,
,
,()
,max
,
,,
,
()
:0 , , ( )
{0,1}, 1, ( )
()
,(
,
)
DD D
ji ji njn
D
mn
px nC mS x
DD
ji j
DD
ji ji
iC
DD
jji
CC
ii
C
D
ij
Ci
i
maximize R a
subject to p p j D i C b
xxjDc
iC d
xjDe
(4)
III. OUR PSO BASED JOINT OPT IMIZATION SCHEME
The optimization problem formulated in (4) is a mixed
integer non-linear programming, which turns out to be NP-
hard. So we put forward a joint optimization structure shown
in Fig. 1 to si mplify t he s olu tio n and gain some in sigh ts into
related evaluation. In CA part, we adopt PSO to approximate
to the optimal CA particle for ST maximization by the nature
of birds’ foraging, but when deriving the fitness value for
each CA particle, i.e., all CA binary variable are known, PC
part will be imp licitly involved. In essence, the optimization
of CA is performed upon the optimality of PC part, and due
to the consistency between the fitness function in CA part
and the optimization target in PC part, CA and PC are thus
tightly coordinated and jointly optimized, and the design for
each part will be giv en below in details.
A. PC part
PC part is to determine the optimal transmit powers of all
D-links for ST maximization under any given particle from
CA part, i.e., all binary variables
,
,,
D
ji
xjDiC
are known.
Besides, due to the orthogonality among different channels,
the global PC optimization can be decomposed into multiple
sub-problems on each channel. Without loss of generality,
we consider the i-th channel, which is reused by the D-links
s pecified in
,
{|1}
D
iki
SkDx
, and the PC optimization
model can be reduced to (5). As only one channel is involved,
the label of the channel is reduced in denotations for brevity.
,max
()
:0 ,
()
()
,()
i
D
j
p
DD
jj i
D
j
D
j
jS
CC
D
ji
maxmize a
subject to p p j S
d
R
b
S
c
j
(5)
Before optimizing the problem in (5), we have to make
sure if the feasible set is nonempty, namely if all individual
SINR requirements could be maintained simultaneously, and
if the feasibility is violated, it is plausible to remove the least
numbe r of D-links while ma int ain th e QoS requiremen t for
the rema ining ones, especially for the priorit ized C-link. By
433
the results in [9], we put forward a two-step feasibility check
and a further GR scheme in our hybrid cellular system before
th e fina l p erfo rmanc e maximizat ion .
1) Step one: check if the maximum e igenvalue of matrix
i
D
S
D(Γ )Z
is les s tha n 1, where
i
D
S
D(Γ )
is a diagonal matrix
with the j-th diagonal element being the SINR requirement
of the j-th D-lin k in
i
S
, and Z is the normalized pathgain
matrix with all diagonal elements being 0, while the rest are
calculated through
,,
/,
DD D
mn mn m
ZGGmn
, where the index
of a D -lin k is its s eq uen ce order in
i
S
rather than its actual
lin k lable in
D
. And by Perron-Frobenious theorem in [9], if
the condition above is satisfied, there exists a positive
Pareto-optimal transmit power vector, so that all individual
SINR requirement of D-links in
i
S
can be maintained at the
same time, then we continue to step two; otherwise the
system is infeasible and further user removal is required.
2) Step two: we derive the positive Pareto-optimal
transmit power vector from (6), where
E
is an identity
matrix of the same size with Z. Then we proceed to check
if the local power budget of each D-links, i.e., constraint (5-
b), and the SINR requirement of the prioritized C-link, i.e.,
(5-c), are both satisfied, and if the above condition is
fulfi lled , the s ys tem is feasib le; otherw ise, t he syst em is
infeasible, and further user removal is also required.
*{}|
D
jj
p
ii
D-1 D
SS
(E - D(Γ )Z) D(Γ )η
(6)
If the feasibility could not be maintained, we are trying to
admit the most number of D-links as the original problem
has been proved to be NP-complete [10]. Specifically, we
iteratively remove a D-link according to its influence to the
cu rrent syste m un ti l th e fea sibil ity is attained . A met ric is
defined in (7) to evaluate the above influence, where two
parts are involved : the first term is the effective interferen ce
at its own receiver, showing the condition of its desired link;
while the se con d te rm is th e sum of its incurred effect ive
interference, indicating its impact on the rest system. So, the
D-link with the largest metric, i.e.,
**
arg max ( )
DD
jj j
jp
,
will be can ce lled at each time.
**
,,
()
ii
DD DDDD DDDD
kS lS
jj jkkj lljj
kj lj
Zp Zp
(7)
Unfortunately, even aft er the feas ibilit y is maintain ed, th e
ST maximization problem for feasible D-links on a channel
s till re mains a n o pen issue [11], an d optimal ity can only b e
achieved when no more than two D-lin ks are involved [12].
To weight the tradeoff between performance and complexity,
we make a reasonable approximation by assuming that all D-
links pose high SINR requirement, i.e.,
1,
D
j
jD
, so
that
22
log (1 ) log ( )
DDD
jjj
R
, wh ich is valid du e t o t he
contents in D2D communication, e.g., multimedia or large
files. In this way, the revised problem for ST maximization
in feasible system could be resolved as concluded in the
following proposition.
Proposition 1: The revised ST maximization problem is (log,
x)-concave in
D
j
p
under the approximation above.
Proof. In (5), the objective function could be switched into
22
log ( ) log ( )
ii
DD
jSj
Sj
j
under the approximation
above, and due to the strict monotonicity of log-function, it
could be further changed into minimizing
1
()
i
D
jS j
. Then,
the revised problem is shown in (8), which is to minimize a
posynomial [13] under upper bounds on posynomials, thus is
the standard form of geometry programming (GP). With the
help of [13], the standard from of GP can be turned into a
convex optimization via logarithmic change of variable, i.e.,
the ST maximization problem is (log, x) concave in
D
j
p
. Ƶ
1
,max
,
() ()
:0 , ( )
/
/1, ()
()
Di
j
i
D
jS j
p
DD
jj i
CD D C C C
D
j
C
Bk k i i i i
kS
D
ji
minmize a
subject to p p j S
c
b
Gp Gp
jS d
(8)
Re mark . To solve the constrained convex optimization, we
can resort to the barrier method [14]. Upon the optimality of
ST ma ximization for feasible D-links, PC part feeds back
the optimal ST value to CA part for the rest PSO operations .
B. CA part
We adopt PSO to find the optimal CA particle with the
feedback from PC part. PSO is a stochastic and evolutionary
optimization algorithm [15] with good performance and low
computational complexity, thus has been widely applied in
resource allocation. In PSO, a number of particles form a
swarm and move around in the search space looking for the
optima. The position of each particle represents a candidate
solution to an optimization problem, and a fitness function is
defined to evaluate the quality/fitness of each solution. Every
particle will memorizes the personal and global best position
discovered so far in order to guide them to the best solution
after certain iteratio ns in th e fo rm of ve lo city. As illust rat ed
in Fig. 1, the specified implementation of PSO in our CA
part will b e sequentially explained at len gth b elo w.
1) the definition of variables and fitness function: There
are three key components associated with each particle: the
position, the velocity and the fitness value. (i) with interger
coding, the position of the s-th particle is coded into a vector
consisting of
M
interger elements as shown in (9) with
,
j
s
yCjD
indicating the label of the specified channel
assigned to the j-th D- lin k, i.e., the variab les in CA part. As
the standard PSO is suited to a continuous solution space,
we first convert our original interger solution space into a
continuous one to fit in with above constraint by the
introduction of continuous velocity below; (ii) the velocity
of the s-th particle is coded into a vector consisting of
M
real elements as shown in (10) with
[0, ],
j
s
vNjD
, and
used to update the current position as will be described in 3);
(iii) to comply with our optimization target, the fitness value
of the s-th p art icle is defin ed as the ST of all D -lin ks and
denoted as
s
F
.
12
[ , ,..., ]
M
sss s
yy yy
(9)
12
[ , ,..., ]
M
sss s
yy yv
(10)
434
TABLE I. THE MAIN SIMULATION PARAMETERS AND SETTINGS
Parame ters Se ttings
Ant enna
t ype an d gain
Omni
-directional
, 14/0 dBi for BS/UEs
Maximum transmit power of
all D-lin ks
2
3dBm
SI NR
t hr eshol d of all C -
links
10dB
Power spect ral density of
background noise
-
174dBm/Hz
The
number of
c
hannels
4
Bandwidth
of each c
ha nnel
180kHz
No ise F igure
5
/9 dB for BS/UEs
Pa thloss Model fo r C
-
links
10
128.1 37.6 log ( [ ])dkm
[2]
Pa thloss Model fo r D
-
links
10
148.0 40.0log ( [ ])dkm
[2]
Figur e 2 . Perfor mance comparison with the change in the total number of
D-links
Figur e 3 . Perfor mance comparison with the change in SINR requirement
of D-links
2) the initiation of the particle swarm: the PSO begins
with a group of particles known as the in itial particle swarm.
It is a
(2 1)
pso
NM
matrix with the s-th row being the
s-th p art icle , i.e.,
[, , ]
sss
Fyv
, where
pso
N
is the total number
of partic les in the init ial partic le s wa rm. The fitnes s value of
each particle is determined via the interface between CA
and PC part as shown in Fig. 1: CA part passes to PC part
with the position of a particle, i.e.,
s
y
, then PC part decodes
it into the CA binary variables
,,,
D
mn
xmDnC
, i.e., if
,,
,1,0,
mD D
smnml
ynx x ln
, and delivers corresponding
fitness value back to CA part by solving the underlaid PC
optimization as specified in Section III-A.
3) the updating of the position and velocity for each
particle: the velocity and position of a particle are updated
according to (11) and (12) respectively, and evolve to the
optima with the local stored and e xchanged information, i.e.,
the personal best and global best position.
1
12
()()
tt tt tt
ss ps gs
wc c
vv p-y p-y
(11)
11ttt
sss
y=y+v
(12)
where the superscript
t
or
1t
represents the time iteration;
w
is an inertia weight, and can be interpreted as the fluidity
of the medium in which a particle moves.
t
p
p
and
t
g
p
denote
the personal best and global best position of the s-th particle
at iteration
t
.
1
c
and
2
c
are the acceleration coefficients that
determine the magnitude of random forces in the direction
of personal best
t
p
p
and global best
t
g
p
.
and
are two
independent random coefficients between 0 and 1, which are
generated at each iteration for each particle, and they ensure
the convergence of the particle and allow an elegant and
well-explained method for preventing explosion.
4) the decoding and convergence check: as mentioned
in 1), the standard PSO is suited for continuous solution
space, and we convert our interger solution into continuous
one stored in the position of the particles in order to utilize
the nature when a flock of birds collectively forage for food.
But to derive the fitness value of each pos ition with the help
of PC part, we have to reverse above process as in (13) and
recover the CA related interger variables, where
()round
opertion rounds the elements of
s
Y
to the nearest integers.
12
([ , , ..., ])
M
ssss
round y y yy
(13)
With the definition of position in 1), all elements in the
updated
s
y
are real numbers ranging from 0 and N, so each
decoded element
{0},
j
s
yC jD
, and when
0
j
s
y
, it
indicates that no channel is allocated to the j-th D-link.
Besides, the number of generations that evolve depends on
whether an acceptable solution is reached or a pre-defined
iteration limitation is exceeded, i.e.,
T
. We adopt a fixed
ite rat ion limita tio n for s implicity.
IV. NUMERICAL RESULTS
We consider a circular isolated cell with radius being
150m, where BS is at cell center, and all transmitters of C-
435
and D-links are uniformly distributed in the cell area, while
the receiver of any D-link is uniformly distributed in the
circular area of its corresponding transmitter with the radius
being 20m. The transmit powers of all C-links are set with
th e s ame le ve l for s imp lic ity , i.e .,
23 ,
C
i
pdBmiC
, and
the PSO related parameters are set as follows:
20
pso
N
,
12
0.79, 2, 2, 50wccT
, and the rest are listed and set
in Table I, where
d
is the link distance. It’s noteworthy that
our joint optimization structure can be readily extended to
the multiple-input and multiple-output antenna system [16],
which leads to a different optimization model in underlaid
PC part. Five algorithms are compared in this section: (i) PC
optimization with random CA (Alg-1), e.g., [3, 7]; (ii) CA
optimization with fixed power settings raised in [8] (Alg-2),
besides, to make it comparable with ours, we set all admitted
D-links with the same transmit power so that the SINR
requirement of the prioritized C-link is maintained; (iii)
random CA with fixed power settings (Alg-3), and the
transmit powers of D-links are set in the same manner as in
Alg-2; (iv) the joint CA and PC optimization scheme in [6]
(Alg-4) which is superior than the CA optimization in [4-5];
(v) ours. We observe the variations in ST and SC of all
algorithms with the change in
M
and
,
D
j
jD
, and the
fin al res ult s are av era ged ov er 1000 ra ndom topologies.
Shown in Fig. 2(a-b), with the increase in
M
by s ett ing
12
D
j
dB
, the ST and SC of all algorithms are raised as
more mu lt ius er div ers it y is utili zed . Revealed in F ig. 3(a -b),
with the increase in
D
j
by setting
10M
, the SC of all
algorithm decreases as the system load level is heightened,
and more D-links are like ly to be removed to benefit the QoS
maintenance of the rema ining system. But the change in ST
is not monotonic and depends on the following two factors:
(i) the g ain o f GR, i .e., more room is left for the rema ining
D- links after th e re mov al o f some; (ii) the loss o f GR, i.e.,
the ST lost along with the removed D-links. Besides,
delineated in Fig. 2 and Fig. 3, co mpared to Alg-4, the rest
enable one channel to be reused by multiple D-links, thus
fully explore the spatial gain among different D-links and
results in higher ST and SC; compared to Alg-1-Alg-3, our
scheme further utilizes the gain when CA and PC are in
elaborate cooperation and reaps a better performance ; by
comparing Alg-1 and Alg-2, we find PC is more essential to
improve the ST on each channel as Alg-1 outweighs Alg-2 in
ST uncovered in Fig. 2(a), while CA is more effective to
admit D-links into the system among multiple channels even
under fixed power settings, thus contributes to a higher SC as
indicated in Fig. 2(b).
V. CONCLUSIONS
In this paper, we attempt to maximize the ST of underlaid
D2D communication under individual QoS requirement by
considering both CA and PC. A novel PSO based resource
allocation structure is proposed where CA and PC are tightly
cooperated for global optimality. With the help of numerical
results, we elucidate the efficacy of our joint optimization
scheme in term of ST and SC when compared with the ones
in literature.
ACKNOWLEDGMENT
This work has been partly supported by the National
High Technology Research and Development Program of
Chin a (863 Prog ram) 2014A A01A 701 a nd 2014AA 01A707.
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