- 1 -
Capacity Enhanced Resource Allocation Algorithm for
Device-to-Device Uplink Underlaying Cellular Networks#
Sun Ke, Xu Quansheng, Li Xi
**
5
(School of Information and Communication Engineering, Beijing University of Posts and
Telecommunicaitons, Beijing 100876, China)
Abstract: In this paper, we investigate the resource allocation problem among multiple cellular users
and multiple D2D pairs to optimize the system capacity performance. We study the resource allocation
involving resource block (RB) assignment and power allocation, which is difficult to tackle 10
simultaneously. A two-phase resource allocation scheme is proposed to solve the problem. Firstly, an
interference graph based heuristic clustering algorithm and a heuristic RB assignment algorithm are
performed to realize the RB assignment. The multi-user interference is properly coordinated by
clustering and appreciable system capacity is achieved by the RB assignment. Secondly, we assign
different powers for all the users to explore a further capacity enhancement. We prove the concavities 15
of the lower and upper bound of the optimization function, thus the power allocation problem becomes
a convex optimization problem and we solve it with a low complexity gradient method. Finally, we
present simulation results to verify the proposed scheme. It is shown that, with remarkably reduced
complexity, our proposed two-phase scheme achieves a near-optimal performance in terms of the
system
Key words: capacity enhancement; D2D; interference graph; resource allocation
0 Introduction
The recent socio-technological trend in proximity-based applications and services, and the
increasing market interest in short-range communications have triggered the research and 25
standardization communities to explore the potential of device-to-device (D2D) communications
[1]
. D2D communication underlaying cellular networks has brought much attention worldwide due
to its potential to improve the spectrum efficiency, offload the cellular system, enhance the cell
throughput and save the energy of user equipment (UE)
[2]
. However, D2D communication can
cause serious interference problems due to sharing cellular resources. Therefore, effective resource 30
allocation needs to be performed to achieve improved overall network performance.
There are several existing works that considered resource allocation issues in D2D
underlaying cellular networks
[3]–[6]
. The goal is to reduce the interference from D2D
communication to the cellular networks and to guarantee the performance of D2D communication
at the same time. Doppler et al in [3], proposed a centralized interference aware resource 35
allocation scheme to minimize the interference thus improve the network performance. The
authors in [4] provided analysis on optimum resource allocation and power control between the
cellular and D2D connections that share the same resources for different resource sharing modes.
A capacity enhancement method using interference limited area was proposed in [5] to solve the
resource sharing problem with a strict power constraint of D2D pairs. In [6], a fair resource 40
allocation for the cellular users and D2D pairs was proposed with max-min fairness and the D2D
pairs must not generate intolerable interference to the cellular users.
However, the aforementioned mechanisms in [3], [4], [5] focus on how D2D pairs sharing the
resources of cellular users, resource sharing between D2D pairs has not been studied. Besides, the
authors in [5] only take one D2D pair into consideration and the interference to the cellular users 45
- 2 -
was not included. The resource sharing scheme in [6] treats the cellular users and D2D pairs as the
primary and secondary users in cognitive network, which put emphasis on the QoS protection for
cellular users and set harsh criterion for the D2D pairs. Note that when resource allocation
schemes are performed at the BS, the computational complexity is of great significance, especially 50
when allowing multiple D2D pairs share the same spectrum with cellular users. This increases the
scheduling delay and imposes a heavy processing burden on the BS.
In this paper, we investigate the resource allocation which involves RB assignment and
power allocation among multiple cellular users and multiple D2D pairs. Inter-user interference
between cellular and D2D links is explicitly considered. Since solving the RB assignment and 55
power allocation simultaneously is very difficult, many works decompose the problem into two
sub-problems to reduce the complexity while maintaining good performance [7], [8]. So we
propose a two-phase resource allocation scheme to obtain the capacity enhancement and assure
QoS requirements for all the users including the D2D pairs. Firstly, we formulate the interference
graph based on the interference relations between cellular users and D2D pairs. An interference 60
graph based heuristic clustering algorithm and a heuristic RB assignment algorithm are performed
to solve the RB sharing problem. The interference graph based clustering takes advantage of
user’s location and the transmitting power to form the interference relations. The strong interferers
are separated by clustering and an appreciable system capacity is achieved by the RB assignment.
The heuristic algorithms in phase one can achieve a sub-optimal performance in terms of system 65
capacity, but comes at much lower computational complexity than the exhaustive search.
Secondly, we assign different powers for all the users to explore a further capacity enhancement.
We prove the concavities of the lower and upper bound of the optimization function. Then the
power allocation problem becomes a convex optimization problem and we solve the problem
based on a gradient method which also has a low complexity. 70
The remaining of this paper is organized as follows. In Section II, the D2D underlaying
cellular system model is presented and the corresponding resource sharing problem is formulated.
In Section III, we develop the interference graph based heuristic clustering algorithm, heuristic RB
assignment algorithm and the sub-optimal power allocation scheme. Simulation results are
presented in Section IV followed by the conclusion in Section V. 75
BS
Communication
on RB1
Communication
on RB2
D3,t
C2
D2,t
D2,r
D3,r
D1,r
D1,t
C1
Communication link Interference link
System model for D2D communications underlying cellular network when sharing uplink resource.
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1 System model and problem formulation
System description 80
In this paper, we consider a single cellular network. As depicted in , there exist two
types of communications, namely the traditional cellular communication between BS and a
cellular user and the directed D2D communication, which is treated as an underlay to the
traditional cellular communication. For simplicity, we emphasize on the intra-cell interference due
to the resource sharing of the D2D pairs and the traditional cellular users, and all the UEs are 85
equipped with a single omnidirectional antenna. We assume that both the cellular users and the
D2D pairs are uniformly distributed in the cell. Each D2D pair consists of one transmitter and one
receiver which satisfy the distance constraint. The sets of cellular users and D2D pairs are denoted
by 1,2, , L L and 1,2, ,M M , respectively, where lC denotes a traditional cellular
user, ,m tD and ,m rD denote a potential D2D pair. There are total N RBs denoted by set 90
1,2, , N N for data transmission, where nRB is the n-th RB. The sets of cellular users and
D2D pairs are denoted by A and D, respectively.
We assume that any channel occupied by a cellular user can be shared with D2D pairs and
multiple D2D pairs can share the same channel. However, resource sharing between the cellular
users is forbidden. Considering fairness for different communication links to acquire efficient 95
communication service, each communication link can be allocated at most one RB for its data
transmission through every scheduling process. In the uplink interference scenario described in
, cellular users and D2D pairs which share the same RB form a cluster. There is no
interference between users in different clusters and there is at most one cellular user in each
cluster. 100
If
nRB is allocated to cellular user l and reused by D2D pair m, mathematically, for D2D
pair m the received signal at the receiver ,m rD on nRB is expressed as:
, , ,
, , , ,
, ,
m r m r m r
m m t m t l l l i i t i t
i
D D Dn
m D D D C C C D D D
i i m D
y P h s P h s P h s n
nM S
(1)
where
mD
P is the transmission power of the transmitter at the D2D pair m,
lC
P is the transmission
power of cellular user
lC ,
y
xh is the channel gain of the x-y link, xs is the transmitted signal, n is 105
the noise with one-sided power spectral density, 2 . Here,
nS represents the cluster which
traditional cellular user and D2D pairs reuse the same
nRB for individual data transmission and
iD denotes the D2D pair , ,,i t i rD D .
The signal to interference plus noise ratio (SINR) achieved at the D2D receiver ,m rD on
nRB can be given as: 110
,
,
, ,
,
2
2 2 2
, ,
| |
| | | |
m r
m m t
m m r m r
l l i i t
i
D
D Dn
D D D
C C D D
i i m D
P h
P h P h
nM S
(2)
On the cellular side, similarly, the SINR achieved at the BS from cellular user
lC in the
uplink period is:
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,
2
2 2
,
| |
| |
l l
l
i i t
i
BS
C Cn
C BS
D D
i D
P h
P h
nM S
(3)
Resource allocation problems 115
Note that in this paper, we focus on assigning appropriate resource blocks and power for all
the users in order to minimize interference and achieve a higher system capacity. We define the
capacity of the cellular network as the sum of the channel capacity for all the communication links
including the traditional communication links and D2D links.
Let
, ,([ ],[ ])n l n m
T
Q = be the RB assignment matrix for cellular users and D2D pairs, 120
where
, ,, {0,1}n l n m , with , ,l m n L M N . , 1n l denotes that nRB is allocated to
cellular user
lC and , 0n l otherwise. Similarly, , 1n m denotes that nRB is allocated to
D2D pair
mD and , 0n m otherwise. Let ( , )C DP = P P be the power allocation vector for cellular
users and D2D pairs, where
1 2
[ , ,..., ]
LC C C C
P P PP = ,
1 2
[ , ,..., ]
MD D D D
P P PP . Note that in this paper
we aim to maximize the total channel capacity. Therefore, we can obtain the optimal RB 125
assignment and power allocation by solving the optimization problem as:
, ,
1 1 1
max R ( ) ( )
N L M
n n
l n l m n m
n l m
W
R
N
P P (4)
2( ) log (1. ). . l
n n
l l C l
W
s t R R
N
P (5)
2( ) log (1 ). mm
n n
m D mR R
W
N
P (6)
,
1
1
L
n l
l
(7) 130
, ,m
1 1
1, 1
N N
n l n
n n
(8)
, ,m, | 1, 1n l m n l nC D S (9)
max max0 ,0l mC C D DP P P P (10)
where ( )nlR P is the achievable data rate for cellular user lC on nRB and it has a minimum
requirement of
lR , ( )
n
mR P is the achievable data rate for D2D pair mD on nRB and it has a 135
minimum requirement of mR . is a constant SINR gap to the Shannon capacity. According to
[9]，it is related to the required bit error rate and approximately as 3 / 2ln(5 )l lBER .The
constraint in (7) ensures that two or more traditional cellular users occupy the same RB for data
transmission is not allowed, while (8) guarantees that each time a cellular user or D2D pair can
obtain at most one RB through every RB assignment.
nS is the cluster previously mentioned. Due 140
to the data rate constraint, we can get
,
l m
n n
C l D m (11)
where l and m are the SINR threshold of (2) and (3), which is determined by the minimum
required data rate and the PHY-specific relation between the rate and SINR.
To solve this problem, we need to find the optimal RB assignment matrix Q and the power 145
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allocation vector P . According to [10], the computational complexity of the optimal RB
assignment without power allocation is
1
0
( 1)
( . )
( 1)!
NN
n
optimal L
n
M
C O J
N
(12)
where ( )!x denotes the factorial computation of a nonnegative integer x and n
LJ represents the
permutation operation which is defined as 150
!
,
( )!
0,
y
x
x
J x y
when x y
otherwise
(13)
where x and y are both nonnegative integer and we further define (0)! 1 .
Due to the resource sharing between cellular users and D2D pairs, it is difficult to coordinate
the multi-user interference. Since (6) is non-concave to the binary variable
,n l and ,n m , it is a
mixed integer linear programming (MILP) problem and it is hard to get a relaxed solution. Note 155
that from (12), the RB assignment is NP-hard with nonlinear constraints, let alone the power
allocation and rate requirement for all the users. There is no polynomial-time algorithm to obtain
the optimal solution for (6). Therefore we propose a two-phase resource allocation scheme: (i)
interference graph based clustering algorithm and heuristic RB assignment algorithm are proposed
to decide how to allocate RBs to all users, (ii) power allocation for all the users to explore a 160
further capacity enhancement. We decompose the problem into two sub-problems and then can get
a near-optimal solution with much lower complexity.
C1 C2
D1 D2 D3
1 1,C D
1 2,C C
2 3,C D
2 3,D D
2 2,C D
A sample interference graph corresponding to . 165
2 Two-phase resource allocation
In this section, we propose a two-phase resource allocation scheme. First an interference
graph based clustering algorithm and heuristic RB assignment algorithm are applied to solve the
RB assignment. Then we settle the power allocation problem for all the users based on the
concavity of the objective function through a gradient method. 170
Graph-based clustering and RB assignment
Consider an illustrative example with two cellular users and three D2D pairs as illustrated in
. We can infer the interference intensity from user’s geographic location and construct a
corresponding interference graph in . In this graph which is denoted by ( , )G V E , each node
(from set V) represents a cellular user or D2D pair and each edge (from set E) contains “cost” or 175
weight that characterize the potential interference between two nodes. The weight between two
node i and node j, is denoted by ,i j , the higher the value of ,i j , the stronger the potential
interference between the two nodes. Since reusing same RB between two cellular users is
forbidden, so the weight between the cellular nodes is very large.
To get all the edge weight, we need to know all the interference relations between node i and 180
node j. If the BS is the aware of the location of all the users, we can get the estimated interference
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and save some signaling overhead. In the first phase, we use an average power for cellular and
D2D users. Note that the interference from node i to node j and node j to node i is not necessary
the same, so we use the total interference as the edge weight. Then ,i j can be calculated as
, , ,
, ,
,
,
,
. .
. .
i j C i j D j BS
D i j D j i
node i j
node i j
node i j
P d P d
P d P d
A
A D
D
(14) 185
where
CP and DP are the average transmission power of cellular and D2D pairs respectively,
,x yd is the distance between transmitter x and receiver y, α is the path loss exponent.
The RB assignment problem then becomes a clustering problem, where a cluster represents a
RB. Our proposed clustering scheme aims at minimizing the interference in the system to improve
user’s throughput. Since the inter-cluster weight is maximized, the result will tend to separate the 190
strong interferers into different RBs, thus achieving interference coordination. The clustering
problem is actually the MAX-K-CUT problem in the graph theory. In other words, how to
partition vertexes set V into N disjoint sets
1 2{ , ,..., }nR R R R to maximize the weight between
the disjoint sets in graph ( , )G V E should be studied. It can be formulated as:
1
,
1 1 ,
max
i j
N N
u v
i j i u R v R
(15) 195
To solve (15) and consider the SINR constraint in (11), a heuristic algorithm I is presented to
solve the problem.
Algorithm I graph based heuristic clustering algorithm
Initialize: construct the interference graph based on L, M and ,i j . Let ,, kk u vu v R
W
be the 200
intra cluster weight of cluster
kR , initially the cluster is empty, 0kW .
if L M N then
assign the L M nodes in L M clusters, one in each.
else if L N L M
assign the L cellular nodes to the L clusters, one in each. 205
end if
for the remaining M nodes, sorting them by their degree in descending order. Let *V be the sorted
set of the nodes.
while
*V then
Take a node i from the front of *V 210
if
kR then
assign node i to cluster
kR
else
for k = 1 to N do
Calculate the increased intra-cluster weight if node i is assigned to
kR , ,
k
k m uu R
W
. 215
end for
end if
if argmink ki W then
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assume that node i is to be assigned to
kR ,calculate the SINR threshold for every node
in
kR by the rate constraint in (11). 220
if ,
l m
k k
C l D m then
assign node i to
kR , break the tie randomly.
update intra-cluster weight,
k k kW W W
end if
end if 225
k k iR R V ,
* *
iV V V
end while
All the accessed D2D pairs can be assigned a RB, or the set *V may never be empty. The
idea of the algorithm is to iteratively assign nodes to the cluster such that the increased 230
intra-cluster weight is minimized. However, first we need to assign the cellular nodes to different
clusters to avoid interference between cellular users. The scenario of N L is out of scope of this
paper.
When the clustering is done, all the users are grouped into N clusters for RB allocation. Note
that there are !N possible ways, we should decide which RB is assigned to which cluster to 235
maximize the capacity. Our aim is to find the optimal RB assignment matrix which maximizes (6).
Assume that the BS can acquire the instantaneous channel state of each communication link.
Exhaustive search for this problem is infeasible if N is a very large number. So we employ a
heuristic algorithm that iteratively assigns RB to clusters generated in section A and we can get a
low complexity while maintain the capacity performance. 240
Algorithm II heuristic algorithm for RB assignment
Initialize: N={1,2,…,N} is the RB pool. Sort the N clusters in size from the smallest to the largest
(break the tie arbitrarily).
for i = 1 to N do 245
while N
jN , calculate log2(1 . )
i
j
i uu R
T
if argmax ij T then
assign
jRB to iR , jN = N -
end if 250
end while
end for
Power allocation for all users
After the first phase assignment, cellular and D2D users are grouped into N different clusters 255
and every user has a fixed power. In this phase, we consider allocating different transmission
power for all the users to achieve a further capacity enhancement. Since we already obtain the RB
assignment matrix Q in the first phase, the optimization problem in (6) can be rewritten as:
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1 1
max ( ) ( ) ( )
L M
l m
l m
W
Z R R
N
P P P (16)
where )C DP = (P ,P is the transmission power vector for all users. The problem in (16) still has the 260
constraints (5), (6), (10) and (11), and it is not monotonically increasing or decreasing for the
power constraint in (10). ( )xR P is the achievable data rate, which is a function of P . According to
[11],
2( ) log (1 . ( ))x yR P P is a quasi-concave function of P . The classic method to solve the
power allocation is water-filling. Here we propose an alternate optimization algorithm based on
the concavities of the lower and upper bound of (16) to solve the maximization problem. The 265
lower and upper bound of (16) can be derived, respectively as:
2 2
1 1
log ( . ( )) log ( . ( ))
l m
L M
C D
l m
l
W
N
Z
P P (17)
2 2
1 1
1 1
log ( . ( )) log ( . ( ))
l m
L M
l m
C D
l
u
l m m
W
N
Z
P P (18)
We can get the lower bound (17) by replacing 1 with . From the constraint in equation
(11), we obtain the inequality / 1 . Then the upper bound (18) can be obtained by replacing 1 270
with / .
Note that
2log ( ( ))W P is a (log, x)-concave function of P proved in [11]. Since the
summation of concave functions is also concave function, so (17) and (18) are both concave
functions. The concavity of the function guarantees that there is a unique convergent point and the
convergent point is global optimal. We assume that the optimal power vectors of the lower and 275
upper bound are *
lP and
*
uP respectively. Then the global maximum value of (16) exists
between *( )lZ P and
*( )uZ P . The smaller between the two values
*( )lZ P and
*( )uZ P , the closer they
approach the global maximum of (16). We can get the suboptimal power allocation from
* argmax( )l lZP (19)
* argmax( )u uZP (20) 280
* *argmin( )( ) ( )u lZ ZP P (21)
* *
min ,
i l j u
j
P P
iP P
P P
P (22)
Note that solving (17) and (18) is a convex optimization problem, we employ the
optimization algorithm based on gradient method in [12] to get the optimal power vector *
lP and
*
uP .
Then, based on (21) and (22), we can choose the power allocation vector for (16). Considering the 285
power consumption, the vector with smaller total power consumption is chosen as our power
allocation vector for (16). Compared with the first phase allocation, we can achieve a further
capacity enhancement, because the multi-user interference is further coordinated through power
allocation. According to [12], the gradient method has a low computational complexity of ( )O N
and it just needs a few iterations to reach the optimal solution. 290
Complexity analysis
The complexity of the proposed interference graph based heuristic clustering algorithm is
related to the following tasks: assign the cellular users to L clusters; find the D2D pair which can
minimize the increased intra-weight of each cluster meanwhile maintaining the SINR constraint.
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This heuristic algorithm has complexity ( )O L MN . The heuristic RB assignment algorithm 295
which iteratively assigns RB to clusters obviously has a complexity of 2( )O N . Therefore, the
overall complexity of phase one is 2(( ) )O L MN N . Compared with the complexity of the optimal
RB assignment calculated in (12), our proposed RB assignment scheme can achieve a much lower
computational complexity. The power allocation scheme has a complexity of ( )O N . Hence, the
two-phase resource allocation for cellular and D2D pairs can achieve a polynomial-time 300
complexity, which is feasible to apply to the real-time system.
3 Simulation results
In this section, we evaluate the performance of the proposed resource allocation scheme for
the D2D communication underlaying cellular network when D2D pairs sharing uplink resources.
The main simulation parameters are listed in table 1. Some of the parameters are referred from 305
[13]. The proposed resource allocation scheme is compared with random resource allocation in
which D2D pairs share cellular users’ resources randomly. As shown in , simulations are
carried out in a single cell, where the cellular and D2D users are distributed randomly in the
network and the distance between D2D transmitter and receiver is under the maximum distance
constraint. 310
Tab. 1 Simulation Parameters and Values
Parameters I/mA
Cell Radius 500m
Bandwidth for Each RB
Max D2D Communication Distance
Max Cellular User Tx Power
Max D2D Tx Power
Path Loss Factor
Small Scale Fading
Noise Power Spectral Density
Noise Figure
BER Requirement
180kHz
25m
23dBm
23dBm
4
Rayleigh
-174dBm/Hz
9 dB
10-4
The total channel capacity with different numbers of D2D pairs and different numbers of
resource blocks using different resource sharing schemes are illustrated in and . We can
see that the total capacity goes up with both the number of D2D pairs and the number of resource 315
blocks increasing. On the one hand, when the amount of resources is fixed, more D2D users
contribute to a higher system capacity. On the other hand, as the amount of resource increases, the
probability of resources with less interference to D2D links assigned to them enhances, this can
lead to the increased capacity of the system. This phenomenon is similar to the effect of multiuser
diversity. Definitely, cellular users can also contribute to the performance. 320
In the first phase, after the interference graph based clustering and the heuristic RB
assignment, we can get the system capacity with the average power as shown in and .
Though it is not as good as the two-phase scheme, it can obviously achieve a better performance
than the randomly resource sharing scheme in which the cellular user and D2D pairs share the
resource blocks randomly (resource sharing between two cellular users is still forbidden). Note 325
that the proposed two-phase resource allocation scheme can achieve an approaching performance
compared with the optimal resource sharing scheme with an exhaustive search. However, the
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proposed scheme has much lower computational complexity than the exhaustive search as proved.
This is a great advantage when the number of the cellular and D2D users is very large.
8 9 10 11 12 13 14 15 16
3
4
Total Number of Cellular users and D2D pairs
T
o
ta
l
C
h
a
n
n
e
l
C
a
p
a
c
it
y
(M
b
p
s
)
Optimal
Proposed One-phase
Proposed Two-Phase
Random
330
System capacity with different resource sharing schemes (L=8, N=10)
10 11 12 13 14 15 16
3
4
5
Number of RBs
T
o
ta
l
C
h
a
n
n
e
l
C
a
p
a
c
it
y
(M
b
p
s
)
Optimal
Proposed One-phase
Proposed Two-Phase
Random
System capacity with different resource sharing schemes (L=8, M=8)
0 200 400 600 800 1000 1200 1400 1600 1800 2000
0
1
The Minimum Required Rate(Kbps)
A
v
e
ra
g
e
O
u
tr
a
g
e
P
ro
b
a
b
ili
ty
D2D - Proposed Power Allocation
D2D - Fixed Power
Cellular - Proposed Power Allocation
Cellular - Fixed Power
335
The average outage probability for cellular and D2D users (L=8, M=8, N=10)
In , we obtain the average outage probability of cellular and D2D users when they can’t
reach the minimum required data rate. The two-phase resource sharing with a power allocation
scheme can reach a lower outage probability than the first phase resource sharing scheme which 340
has fixed power. We can see that the D2D users are much easier to meet the minimum data rate
requirement, since the average communication distance of D2D pair is much smaller than the
cellular users. This is the good virtue of D2D communication.
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4 Conclusion 345
We have investigated the resource allocation problem involving RB assignment and power
allocation to optimize the system capacity performance in D2D communications underlaying
cellular networks. We have proposed a two-phase resource allocation scheme to solve the problem.
Simulation results have proved the fact that a near-optimal performance in terms of the system
capacity is achieved, but with much lower complexity than the exhaustive search. The proposed 350
scheme could be an effective method for D2D communication systems.
References
[1] Astely, D.; Dahlman, E.; Fodor, G.; Parkvall, S.; Sachs, J., "LTE release 12 and beyond," Communications
Magazine, IEEE, , , ,160, July 2013. 355
[2] Doppler, K.; Rinne, M.; Wijting, C.; Ribeiro, .; Hugl, K., "Device-to-device communication as an underlay
to LTE-advanced networks," Communications Magazine, IEEE, , , ,49, Dec. 2009.
[3] Janis, P.; Koivunen, V.; Ribeiro, C.; Korhonen, J.; Doppler, K.; Hugl, K., "Interference-Aware Resource
Allocation for Device-to-Device Radio Underlaying Cellular Networks," Vehicular Technology Conference, 2009.
VTC Spring 2009. IEEE 69th , vol., no., ,5, 26-29 April 2009. 360
[4] Chia-Hao Yu; Doppler, K.; Ribeiro, .; Tirkkonen, O., "Resource Sharing Optimization for
Device-to-Device Communication Underlaying Cellular Networks," Wireless Communications, IEEE
Transactions on, , , ,2763, August 2011.
[5] Hyunkee Min; Jemin Lee; Sungsoo Park; Daesik Hong, "Capacity Enhancement Using an Interference Limited
Area for Device-to-Device Uplink Underlaying Cellular Networks," Wireless Communications, IEEE Transactions 365
on , , , ,4000, December 2011
[6] Long Bao Le, "Fair resource allocation for device-to-device communications in wireless cellular networks,"
Global Communications Conference (GLOBECOM), 2012 IEEE, vol., no., ,5456, 3-7 Dec. 2012.
[7] Zhicai Zhang; Haijun Zhang; Hui Liu; Wenpeng Jing; Xiangming Wen, "Energy-efficient resource
optimization in spectrum sharing two-tier femtocell networks," Communications Workshops (ICC), 2013 IEEE 370
International Conference on , vol., no., ,575, 9-13 June 2013.
[8] Kosta, C.; Hunt, B.; Quddus, .; Tafazolli, R., "A Distributed Method of Inter-Cell Interference
Coordination (ICIC) Based on Dual Decomposition for Interference-Limited Cellular Networks," Communications
Letters, IEEE , , , ,1147, June 2013.
[9] Goldsmith, .; Soon-Ghee Chua, "Variable-rate variable-power MQAM for fading channels," 375
Communications, IEEE Transactions on, , , ,1230, Oct 1997.
[10] Rongqing Zhang; Xiang Cheng; Qi Yao; Cheng-Xiang Wang; Yang Yang; Bingli Jiao, "Interference
Graph-Based Resource-Sharing Schemes for Vehicular Networks," Vehicular Technology, IEEE Transactions on ,
, ,,4039, Oct. 2013.
[11] Papandriopoulos, J.; Dey, S.; Evans, J., "Optimal and Distributed Protocols for Cross-Layer Design of 380
Physical and Transport Layers in MANETs," Networking, IEEE/ACM Transactions on, , ,
,1405, Dec. 2008.
[12] Wei-Chen Pao; Yung-Fang Chen, "Adaptive Gradient-Based Methods for Adaptive Power Allocation in
OFDM-Based Cognitive Radio Networks," Vehicular Technology, IEEE Transactions on , , ,
,848, Feb. 2013. 385
[13] Feiran Wang; Lingyang Song; Zhu Han; Qun Zhao; Xiaoli Wang, "Joint scheduling and resource allocation
for device-to-device underlay communication," Wireless Communications and Networking Conference (WCNC),
2013 IEEE , vol., no., ,139, 7-10 April 2013.
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D2D 通信中基于容量增强的上行复用
资源分配算法
孙科，徐全盛，李曦
（北京邮电大学信息与通信工程学院，北京 100876）
摘要：针对蜂窝和 D2D 混合通信网络中的容量优化问题，提出了一种无线资源分配策略。395
该策略包含了资源块的分配以及功率分配，并且分为两个阶段进行。首先，对干扰图采用启
发式分簇算法，将会产生较大干扰的用户分离，并提出一种启发式资源块分配算法，通过分
簇，多用户之间的干扰得到协调，资源块分配后也得到了较高的系统容量。然后，考虑各用
户的功率分配问题，根据最优化目标函数的凸凹性质提出一种基于梯度算法的功率分配机
- 12 -
中国科技论文在线
制，进一步优化了系统容量性能。仿真结果表明，所提的两阶段机制具有较低的算法复杂度，400
并能够接近最优的系统容量。
关键词：容量增强；终端直通；干扰图；资源分配
中图分类号：TN911
