Two-Stage Matching for Energy-Efficient Resource
Management in D2D Cooperative Relay
Communications
Chen Xu
∗
, Junhao Feng
∗
, Zhenyu Zhou
∗
, Zheng Chang
†
,ZhuHan
‡
, and Shahid Mumtaz
§
∗
School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, China.
†
Department of Mathematical Information Technology, University of Jyv
¨
askyl
¨
a, Jyv
¨
askyl
¨
a, Finland.
‡
Department of Electrical and Computer Engineering, University of Houston, Houston, USA.
§
Instituto de Telecomunicac¸˜𝑜es, 1049-001 Aveiro, Portugal.
Abstract—Device-to-device (D2D) cooperative relay can assist
users with inferior channel conditions to implement multi-hop
transmissions, improving network coverage and throughput.
However, energy efficiency is an important issue to be optimized
because of the limited battery capacity of handheld equipments.
Considering a two-hop D2D relay communication scenario, this
paper proposes a resource management approach that jointly
optimizes relay selection, spectrum allocation, and power control,
so that the total energy efficiency of D2D links is maximized while
guaranteeing the quality of service (QoS) requirements of D2D
and cellular links at the same time. Since the formulated joint
optimization problem involves a four-dimensional matching that
is NP-hard, we propose a pricing-based two-stage matching algo-
rithm to reduce dimensionality and provide a tractable solution.
In the first stage, the spectrum resources reused by relay-to-
receiver links are determined by a two-dimensional matching.
Then, a three-dimensional matching is conducted to match users,
relays, and the spectrum resources reused by transmitter-to-relay
links. The optimal transmit power is solved during the preference
establishment process in the second stage. As shown in simulation
results, the proposed algorithm not only performs good on energy
efficiency, but also enhances the average number of served users
in comparison to the case without any relay.
Index Terms—D2D, energy efficiency, resource management,
cooperative relay, matching theory.
I. INTRODUCTION
As the demand for wireless data services grows dramatical-
ly, revolutionary technologies that focus on improving network
coverage and throughput within the limited system resources
have been constantly emerging. Device-to-device (D2D) com-
munication that allows user equipments (UEs) to communicate
with each other through direct links without the base station
(BS) relaying [1], [2], is considered to be one of the key tech-
nologies in future 5G wireless system [3], [4]. In the underlay
mode, D2D links and traditional cellular UEs (CUEs) share
the same spectrum resources, providing significant increases
in spectrum efficiency and system throughput [1]. However,
there exists a possibility that the channel condition between
two potential D2D UEs cannot support a direct single-hop link.
For this reason, D2D cooperative relay has naturally become
an important application that can assist two UEs with inferior
direct link to communicate [5].
Due to its low cost and few modifications to current
infrastructures, D2D relays may work more efficiently than
fixed relays. There have already been some works that focus
on relay selection [6], [7] and resource allocation [8], [9]
to optimize the performance of D2D relay communications.
However, few works above have covered the power control
problem, which is closely related to energy efficiency ( EE). As
the UEs are handheld equipments with limited battery capacity
and consumed by booming wireless services, one key issue is
to reduce the energy consumption [10]. An iterative Hungarian
method was proposed to solve the relay and spectrum alloca-
tion problem with optimal transmit power at each nodes in
[11]. Nevertheless, EE has not been considered in this work,
and the cellular spectrum resources were allocated to only one
of the two hops in D2D relay link.
Therefore, we put emphasis on energy-efficient resource
management in D2D cooperative relay communications, then
formulate the problem as the joint relay selection, spectrum
allocation and power control optimization for two-hop D2D
relay transmissions underlay cellular networks. Both the first
hop from D2D TX to D2D RS and the second hop from D2D
RS to D2D receiver (RX) are allowed to reuse the spectrum
of CUEs to improve spectrum efficiency. Our objective is to
find an approach to determine the optimal relay, spectrum and
transmit power of TXs and RSs, which maximizes the EE of
D2D links and simultaneously guarantees the QoS of all the
links.
The problem is difficult to solve as it not only includes
continuous and discrete variables, but also involves four-
dimensional resource allocation indicators. Noting that D2D
TX-RX pairs (TRs), RSs, the first-hop spectrum and the
second-hop spectrum, should be matched effectively, we em-
ploy matching theory [12], [13] to solve the joint allocation
problem. As the four-dimensional matching is of great com-
plexity, we first simplify the matching problem as one two-
dimensional and one three-dimensional matching problems.
For each matching, we utilize a pricing strategy to approximate
the optimal solution. The power control process is coupled
with the three-dimensional matching, and the optimal transmit
power maximizes the total EE of the two-hop link.
The rest of this paper is organized as follows. In Section II,
we describe the system model. The formulation of the four-
dimensional matching problem is introduced in Section III. In
Section IV, we present the proposed two-stage matching algo-
rithm. We show the simulation results with related discussions
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