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# Power allocation and relay selection for energy efficient cooperation in wireless sensor networks with energy harvesting

- Yin Wu
^{1}Email author, - Wenbo Liu
^{2}and - Kaiyu Li
^{2}

**2017**:26

https://doi.org/10.1186/s13638-017-0811-9

© The Author(s). 2017

**Received:**8 September 2016**Accepted:**25 January 2017**Published:**6 February 2017

## Abstract

In this paper, we investigate a joint power allocation and relay selection scheme for energy efficient cooperation in energy harvesting-wireless sensor networks (EH-WSN). We mainly propose a simple heuristic algorithm to improve the energy efficiency of each node in a clustering based EH-WSN. First, the effect of cooperative communication is evaluated, and then, the energy sustainability of every node is taken into account, finally, we formulate an online optimization problem which can be solved near optimally with low computational complexity. Extensive simulation results are presented to show the outstanding performance of our proposed scheme in nodes’ transmitting power allocation and average working utility. Therefore, this joint optimization algorithm has a promising future in real applications.

## Keywords

- Cooperative communication
- Energy harvesting
- Wireless sensor network
- Transmitting power control
- Relay selection

## 1 Introduction

Nowadays, a new class of wireless sensor network that harvest energy from the environment (solar, wind, vibration, etc.) is emerging. Because of its intrinsic capability of self-sustainability, a lot of researches have been done on it; many of them focus on the high-efficient energy utilization [1–3]. As for this energy harvesting-wireless sensor networks (EH-WSN), the main challenge is to maximize its working performance under energy harvesting constraints, so studies on the MAC protocol, routing protocol, and cross layer optimization also obtain lots of achievements [4–10].

Recently, the use of cooperative communication in EH-WSN has attracted some interest [11, 12]. For example, Kuang-Hao Liu has investigated a battery-aware relay selection scheme, which is called BARS, for energy harvesting (EH) relays with finite energy storage [13]. It takes into account both channel state information and battery status in choosing the cooperating relay. The analysis result shows that the number of potential relays and the overhead for collecting required information have significant effects on the system outage probability. Songtao Guo et al. [14] have considered applying a simultaneous wireless information and power transfer technique to cooperative clustered wireless sensor networks, they develop a distributed iteration algorithm of power allocation, power splitting, and relay selection to maximize the system energy efficiency, and they find that power splitting ratio plays an imperative role in the relay selection. Weikai Xu et al. [15] have proposed a power splitting-based relaying and a time switching-based relaying protocols to enable wireless information transferring and energy harvesting in a denoise and forward two-way relay network, they analyze the two proposed protocols and obtain the optimal results for power of sources, power splitting ratio, and time switching factor. Zhe Wang et al. [16] have considered an energy harvesting relay station to improve the service quality of a cellular network. The goal is to assign each mobile station a relay station to minimize the probability of relay service outage. C. Huang et al. [17] proposed a deterministic EH model for the Gaussian relay channel and studied delay & nondelay constrained traffics. H. Li et al. [18] addressed the problem of transmission scheduling in EH-WSN when only partial information is available. I. Krikidis et al. [19] researched the interaction between data and energy queues when only knowledge of the arrival rates was available. Especially, K. Singh et al. [20] studied a joint source and relay transmitting power allocation scheme to maximize the system throughput. However, to the best of authors’ knowledge, joint relay selection and power allocation for a cooperative communication clustering EH-WSN has not been addressed in the literature.

- (1)
Based on the cooperative communication protocol in clustering EH-WSN, we propose a simplified cooperative relay model and analysis node’s transmission power, bit error rate, and energy harvesting evolution procedure.

- (2)
To maximizing the energy utilization efficiency, we deduce a joint power allocation and relay selection algorithm. Then, we analyze the changes of energy saving efficiency and average network energy when different relays are chosen. These derivations provide practical design insights into the effect of various parameters on the system performance.

- (3)
The numerical results show that locating the relay node closer to the middle of source node and destination node yields more energy savings. It also demonstrates that the proposed cooperative protocol can improve the balance of cluster nodes’ residual energy, since it intelligently track the node’s energy sustainability in an online fashion.

The remainder of this paper is organized as follows. Section 2 presents the overview of system communication model; Section 3 analyzes the energy model; Section 4 introduces our joint optimization algorithm; Section 5 presents the experimental results including several key metrics; and Section 6 concludes the paper with drawback and future work.

## 2 System communication model and analysis

*R*

_{ i }represents the optimum relay,

*S*is the source cluster head, and

*D*is the destination cluster head. All nodes in the network have EH ability and have only one antenna.

*S*broadcasts its data as byte

*x*, all the relay node

*R*

_{ i }and destination cluster head

*D*can hear this message, and their received signals are shown as follow, respectively:

*P*
_{
S
} just represents the transmission power of *S*; \( {h}_{S, D}\sim C N\left(0,{\sigma}_{S, D}^2\right) \), and \( {h}_{S,{R}_i}\sim C N\left(0,{\sigma}_{S,{R}_i}^2\right) \) are zero mean circularly symmetric complex Gaussian random variables, represent the independent identically distributed fading channel gains of *S* to *D* and *S* to *R*
_{
i
}. (p.s. all channels are orthogonal and irrelevant, its fading gain from node *i* to node *j* is *h*
_{
i,j
} which follows Rayleigh distribution), and *n*
_{
S,D
}, and \( {n}_{S,{R}_i} \) represent the additive Gaussian noise of *S* to *D* and *S* to *R*
_{
i
}, which also follows *CN*(0, *N*
_{0}).

*P*

_{ R }if the decoding program is successful, or otherwise, it should keep silence. So in the end,

*D*should receive two signals: one direct from

*S*and the other from

*R*

_{ i }. After a maximal ratio combining procedure, the recovered signal should be

_{coop}, may be expressed as the weighted sum of the BERs of these two cooperative cases:

where BLER_{SR} is the block error rate (BLER) of *S* to *R*
_{
i
}, BER_{non ‐ coop} is the BER of noncooperative transmission which directs from *S* to *D*, and BER_{full ‐ coop} is the BER of the cooperative diversity transmission which from *S* and *R*
_{
i
} to *D*.

## 3 Energy model and analysis

*E*
_{
i
}(*τ*) is the residual energy of node *i* at the end of time slot *τ*, *P*
_{EH,i
}(*τ*) is the harvested energy of node *i* during slot *τ*, *I*(⋅) is the binary indicator function and *a*
_{
i
}(*j*) is the event that node *i* receives and transmits packets, and *E*
_{
TX
}, *E*
_{
RX
} just represent the energy consumption of data transmission and reception.

*P*

_{PA}and the total power consumption of all other transceiver circuit blocks

*P*

_{CCT}. In which

*P*

_{PA}could be calculated by the node’s transmission power

*P*

_{out}:

*E*

_{ b }is the required energy per bit at the receiver for a target BER

*P*

_{ b };

*R*

_{ b }is the bit rate; and

*L*represents the channel path loss and may be calculated according to \( L={d}_{i, j}^k{L}_{\mathrm{ref}} \):

*d*

_{ i,j }is the distance between node

*i*and

*j*,

*k*is the path loss index, and

*L*

_{ref}is the reference path loss when distance is 1 m. So

*P*

_{PA}could be written as

*η* is the drain efficiency of RF amplifier; *ξ* is the peak to average power ratio decided by modulation scheme.

As for *P*
_{CCT}, it consists of the transmission circuit power consumption *P*
_{CCT − tx
} and reception circuit power consumption *P*
_{CCT − rx
}, exact values to be decided by detailed hardware components.

*P*
_{PA − source − non ‐ coop} is just the transmission power of source cluster head *S*.

*S*is

*P*

_{PA − source − coop}and

*P*

_{PA − relay − coop}are the transmission power of

*S*and

*R*

_{ i }, respectively. So, the total transmission energy consumption per bit under cooperative diversity is

When comparing formulas 8 and 11, it is apparently that the energy saving brings by cooperative communication must be greater than the energy cost increment in the meantime, only this can make *ε*
_{saving} be positive. In addition, the transmission energy consumption is proportional to the communication distance, so only the distance between *S* and *D* exceeds a certain threshold, the cooperative communication can be applicable. As for our EH-WSN, cluster heads are usually quite distant. Hence, the cooperative technique fits perfectly.

## 4 Joint optimization algorithm design

*α*is a proportionality coefficient, aiming at balancing the proportion of above two items in the objective function.

*ST*(

*i*) is a representation of energy sustainability for EH node

*i*[21]:

*σ*and

*μ*are the appropriately chosen constants,

*P*

_{EH,i }is the harvesting power rate for each node

*i*,

*E*

_{ S,i }and

*E*

_{ M,i }are the stored energy in the node

*i*’s battery and the maximum battery capacity, respectively.

*ST*(

*i*) and

*ε*

_{saving}(

*i*) are the normalization results of

*ST*(

*i*) and

*ε*

_{saving}.

*i*is the optional relay node in the cluster.

*E*

_{ S − TX }and

*E*

_{ R − TX }are the transmit energies per information bit of the nodes

*S*and

*R*, respectively.

Through the analysis of formula 14, we can figure that *ST*(*i*) is generating by nodes in the cluster automatically, which varies with the environment’s energy. As for the *ε*
_{saving}, from formula 12, we could know, when node *S* and node *D* are chosen; *ε*
_{saving} is in inverse proportion to *E*
_{coop}. Hence, in order to maximize *ε*
_{saving}, we just need to minimize *E*
_{coop}. So, the next paragraphs describe the optimization of *E*
_{coop}:

*E*

_{ S − TX }and

*E*

_{ R − TX }to represent the constraints in formula 13. Firstly, we use (SNR

_{ SR }and SNR

_{ RD }) to calculate (BER

_{non ‐ coop}and BER

_{full ‐ coop}) [23]:

where SNR_{
SR
} and SNR_{
RD
} are the signal noise ratio of communication channel from node *S* to relay *R* and from *R* to *D*.

_{ SR }as follow:

*K*is a scaling factor. And according to formula 6, 15, and 16, we can infer that

*L*

_{ SR },

*L*

_{ SD }, and

*L*

_{ RD }show the communication channel path loss for node

*S*to relay

*R*, node

*S*to

*D*, and node

*R*to

*D*. For convenience of analysis, we take these three as given parameters which could be calculated by each node.

*E*

_{coop}can be expressed as

*E*

_{coop}minimization into a single variable optimization algorithm with

*E*

_{ S − TX }:

Obviously, the above formula is a nonlinear function of *E*
_{
S − TX
}; we can use an exhaustion method to compute the optimal result, but at the same time, it must cause a heavy computation burden to the sensor node, in order to avoid this, we make a further analysis on formula 26: when node *S* and *D* have been chosen already, *L*
_{
SD
} should be seen as a constant value; thus, we only have to deal with *L*
_{
SR
} and *L*
_{
RD
}. So, the optimization problem can be approximately decomposed as a combination of these two parameters’ independent actions.

*L*

_{ SR }as zero, formula 26 is shown as

*L*

_{ RD }as zero, it is shown as

So far, we have worked out the transmitting power allocation equations for every distributed feasible relay node. Each candidate relay node in the clusters could calculate its corresponding transmitting power based on the *L*
_{
SR
} and *L*
_{
RD
} according to formulas 29 and 30; also the energy saving efficiency *ε*
_{saving} could be figured out.

*ε*

_{saving}(

*i*) and

*ST*(

*i*) automatically and independently; hence, a relay index

*T*

_{ RE }can be defined as

*ε*

_{saving}(

*i*) and

*ST*(

*i*) and computing the

*T*

_{ RE }(

*i*). The one with maximal value just become the cooperative relay. But also it should be noted that if a node’s current energy status cannot afford the cooperative communication, it would not be selected into the candidate set. The diagram of this joint optimization algorithm is shown below.

## 5 Results and analysis of simulation

Simulation parameters

Parameter | Value | Parameter | Value |
---|---|---|---|

Target end-to-end BER | 10 | Bit rate | 10 kb/s |

Target source-relay BER | 10 | Transmission power | 98.2 mW |

Path loss exponent | 3.5 | Noise power spectral density | −171 dBm/Hz |

Peak average ratio | 1 | Reception power | 109.5 mW |

Drain efficiency of RF | 0.35 | Energy harvesting rate | 1 mW |

| 0.1, 5 | Reference path loss | 10 |

*S*, relay

*R*, and destination node

*D*lie in a straight line, in which

*S*’ location is regarded as original point, and the distance from

*D*to

*S*is 30 m; by readjusting the location of

*R*gradually, we can obtain the numerical changes of optimal power allocation. Simulation result is shown in Fig. 3.

_{ RD }is just the distance from

*R*to

*D*, when it becomes zero means

*R*coincides with

*D*. From the above result, we can see that the total transmission energy (

*E*

_{ S − TX − OPT}plus

*E*

_{ R − TX − OPT}) falls to minimum when

*R*is placed in the middle of

*S*and

*D*(Dist

_{ RD }/Dist

_{ SD }≈ 0.5); otherwise, it rises up rapidly. In addition, Fig. 4 shows the effective operation distance threshold of relay node (− 2.5 < Dist

_{ RD }/Dist

_{ SD }< 3.5), and the transmitting energy of

*S*takes a greater proportion. P.S. the minus sign means

*R*is located on the other side of

*S*opposite direction with

*D*.

Furthermore, the numerical value variation of BLER_{
SR
} at the relay node is also recorded in Fig. 4: it represents the data reception success rate from *S* to *R*. We can see that *R* cannot decode data correctly when Dist_{
RD
}/Dist_{
SD
} < − 2.5.

*S*and

*D*. Here,

*D*is placed on the original point with

*S*30 m away. The corresponding energy saving efficiency

*ε*

_{saving}is calculated and shown in Fig. 5. Five contour lines represent different energy saving levels when

*R*is located inside. In macroscale,

*R*’s position seems nearly a circle under the same

*ε*

_{saving}; but in microscale, the closer to the middle of

*S*and

*D*, the more efficient working of

*R*.

*α*= 0.6.

*ε*

_{saving}of each scenario, as shown in Fig. 8. We can see that the network with bigger total number has higher efficiency

*ε*

_{saving}. The reason is the more nodes in a cluster, the higher probability of a bigger

*T*

_{ RE }(

*i*).

*E*

_{ S − TX − OPT}plus

*E*

_{ R − TX − OPT}) between them is shown in Table 2.

Comparison between the suboptimal results and the optimal results

Dist | −2.0 | −1.5 | −1.0 | −0.5 | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Difference (μJ) | 10.1 | 7.8 | 6.4 | 4.3 | 2.5 | 1.3 | 2.6 | 4.4 | 6.4 | 7.9 | 10 | 12.3 |

We could see that the difference falls to the minimum also when relay *R* is placed in the middle of *S* and *D*, and the corresponding relative error is almost less than 5%. So, the proposed optimization computing method is really available and has enough precision.

## 6 Conclusions

In this paper, we have investigated an optimal relay selection for energy efficient cooperation in a clustering based EH-WSN. We have formulated a novel and computationally efficient relay selection heuristics for sensor nodes based on both local path loss values and energy harvesting rates. Extensive simulation results are presented to demonstrate that the proposed algorithm achieves near optimally relay node selection and transmitting power allocation. Therefore, this scheme forms the basis of a simple and practical cooperation strategy for EH-WSN and can be directly deployed in real applications (such as solar power monitoring system). It also can be integrated with other optimization protocols to achieve energy efficient network-wide cooperation.

Future work will focus on the proposal of a multi-objective algorithm for node placement and coverage of cooperative EH-WSN. Moreover, we will consider different application cases, including energy harvester-sharing networks and structural health monitoring scene.

## Declarations

### Acknowledgements

This work was supported by the Natural Science Foundation of Jiangsu Province, China (BK20150880). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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