How Many Hops are Needed in Multi-hop Energy
Harvesting Wireless Networks
XiangliLiu,ZanLi
∗
, Senior Member, IEEE, Jianhuan Wang
State Key Lab of ISN, Xidian University, Xi’an Peoples R China
Email: xlliu@mail.xidian.edu.cn, zanli@xidian.edu.cn, 18710840003@163.com
∗
corresponding author
Abstract—Energyharvestinggivesapromisingwaytodeal
with the power constrained problem by harvesting energy from
the external environment. In this paper, the multi-hop wireless
network is considered where the relays with energy storage
equipments are random scattered in several d iscs. T he chosen
relay nodes are used to decode-and-forward(DF) the received
signals to the next terminal. The other active nodes in the
discs harvest energy from the received signal. With the aim to
achieve the minimum system outage probability, the close-form
expressions are proposed about the optimal disc locations and
about the optimal number of hops, respectively.
Index Terms—Energy harvesting, decode-and-forward(DF),
multi-hop network.
I. INTRODUCTION
T
He wireless sensor networks are widely used in practical
occasions, such as target tracking, environment monitor-
ing and temperature control[1,2]. But the power constraint is
rather stringent. Normally, local sensors are powered by small
batteries and it is difficult or not economic to replace those
batteries once they are used up. How to prolong the sensor’s
lifetime? One is by optimizing power allocation algorithms
aimed to reduce power consumption of the total system or the
sensor node. The other is to find external charging power, such
as the energy harvesting (EH) [3,4]. EH is usually to harvest
energy from nature environment, such as solar[5,7], thermo-
electric Energy Sources [6-8], vibration[7,9,10], and elec-
tromagnetic Radiation[11,12]. et.al. For the Electromagnetic
Radiation method, according to the transmission distance, it
can be divided into two kinds, far-field and near-field. In the
near-field case, Inductive coupling[13] and magnetic resonance
method [14] are always used to provide the controllable energy
source. Radio Frequency (RF) EH is used in far-field to harvest
energy from RF signals[15]. RF energy transfer is suitable for
powering a larger number of devices distributed in a wide
area. Simultaneous wireless information and power transfer
(SWIPT) is the dual use of RF [16-20].The papers [16,17]
firstly proposed the SWIPT concept, where the node has the
ability of energy harvesting and information decoding at the
same time from the receive signal. The harvested energy can
be used directly for the following data transmission. The work
This work was supported by the National Natural Science Founda-
tion of China under Grant 61401338, the Science Foundation of Shaanxi
Provience under Grant 2016JQ6012,and China Postdoctoral Science Founda-
tion 2016M592756.
in [18] proposed two relay protocols for power splitting-based
relaying (PSR) and time switching-based relaying (TSR). And
they gave the optimal ratio between energy harvesting and
information forwarding at the relay. The works in [19] consid-
ered the SWIPT in nonorthogonal multiple access cooperative
networks. The users are divided in two categories, the near
user and the far users. Besides the direct communication with
the source, the near user can also act as the relay nodes
of the far users. The works in [20] considered the multi-
user SWIPT cooperative networks with only one relay node.
They showed that the traditional Max-Min criterion is not
suitable for SWIPT system, further gave the user scheduling
approaches in some special cases.
Most of the above energy harvesting networks are based
on two-hop network. In this paper, we consider the multi-hop
networks. The sensors harvest energy from the received signal,
which belongs to the RF EH. Our main contributions are the
following two aspects:
1) Assuming the hops number is fixed, the optimal distances
among the source, the relays and the destination are given.
2) Under the equispaced relay system, the closed-form
expression of the optimal number of hops are obtained.
II. S
YSTEM MODEL
We consider a multi-hop wireless network where a source,
S, communicates with a destination, D. There is no direct link
from the source to the destination. The location of the relay
follows the Poisson Point Process (PPP). The relay is chosen
randomly to decode-and-forward (DF) the signal to the next
location.
Fig. 1. system model
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