An Energy-Efficient Transmission Protocol for RNC-Based Cooperative WSNs with Partial Energy Harvesting Nodes

Abstract

This paper addresses the energy-efficient transmission for the scenario of cooperative wireless sensor networks with partial energy harvesting (EH) nodes. A new EH decoding-recoding policy is proposed by regarding the EH constraints and the characteristics of random network coding. We develop an energy efficiency model to investigate the tradeoff mechanism between the saved energy and the waiting time of the EH node, through which the corresponding parameters in the policy are also optimized. Moreover, we propose a novel transmission protocol by embedding the considered policy in the opportunistic reception algorithm. The decoding failure probability is then derived to examine its transmission reliability. The obtained theoretical and simulation results indicate that the proposed protocol achieves superiority in energy efficiency; meanwhile, it can also provide similar transmission reliability under specific conditions, as compared to the conventional algorithms in the two-hop model.

1. Introduction

Wireless sensor networks (WSNs) have attracted numerous research interests in recent years for their economical deployment and wide applications. In most cases, the sensor nodes in WSNs are equipped with low-complexity hardware and single antenna, which restrain the transmission reliability in wireless fading channels. Besides, in many typical applications such as volcano monitoring [1], structural monitoring [2, 3], and vehicle tracking [4], the sensor nodes are usually powered by the battery with limited capacity, which restrain the lifetime of the network. Therefore, transmission reliability and energy consumption are two major challenges for WSNs [5].

Several solution techniques have been developed to handle the two issues, such as cooperative communication (CC) [6] and network coding (NC) [7]. CC is a very promising approach to improve transmission reliability of single-antenna devices. A transmitting node that uses CC can share its packet with neighboring nodes, and, then, these nodes can transmit the packet to the intended receiver cooperatively, thereby creating virtual multiple-input-multiple-output (MIMO) system. The intended receiver can obtain diversity gains by combining the received signals, which bring a signal-to-noise ratio advantage over the single-antenna case. Besides, CC in WSNs (cooperative WSNs) [8] enables long distance transmission to be divided into several short segments, which reduce the transmitting power.

The drawback of CC is the low transmission efficiency. Fortunately, NC brings a breakthrough to this issue by combining the incoming packets at intermediate nodes, and it shows that the throughput can achieve the max-flow-min-cut bound. From then on, many NC schemes have been proposed to improve cooperative WSNs [9–11].

Conventional NC schemes in cooperative WSNs usually make the assumption that the batteries of the nodes can provide stable energy supplies. Recently, energy harvesting (EH) [12, 13] technique has been proposed as a promising approach to address the energy issue of WSNs. EH refers to harnessing and converting energy from the environment to electrical energy periodically, so that the limitation of the battery capacity can be conquered. Hence, it is desirable to employ EH to handle the energy issue of NC-based cooperative WSNs. However, different from the conventional constant energy supplies, the node powered by EH is restricted by a new class of constraints; that is, the consumed energy up to any time is bounded by the harvested energy until this point [14, 15]. Meanwhile, the energy supplies of EH are periodical and random. Therefore, these characteristics of the energy supplies should be carefully taken into consideration when employing EH in the NC-based cooperative WSNs.

1.1. Related Work

For the cooperative WSNs, Li et al. [16] developed a space time block code-based scheme, in which energy efficiency is analyzed as a tradeoff between the reduced transmission and overhead energy consumption. In [17], Cui et al. employed CC to reduce energy consumption of the sensor nodes. In this scheme, the best modulation and transmission strategy are analyzed to minimize the total energy consumption. However, all these cooperative schemes require strict synchronization between the nodes, which is difficult to be realized in WSNs.

The birth of NC technology looses the above synchronization requirement. As a class of NC, Li et al. [18] demonstrated that the optimal network throughput can be achieved through linear NC. Furthermore, Koetter and Médard [19] presented an algebraic framework to construct the coding coefficient for linear NC. On the basis of that, random NC (RNC) [20–22] was proposed to reduce the complexity and enable linear NC to be deployed by the distributed manner. Hence, RNC provides a simple, yet effective, approach to improve the latency and transmission efficiency, which makes it very suitable to be deployed in cooperative WSNs.

Recent work [23] has employed RNC to improve the transmission reliability in cooperative WSNs. However, in this scheme, the intermediate node has to receive all the incoming packets to construct the coding vector (CV), which is energy inefficiency from the perspective of popular sensor transceiver today, because the receiving circuit energy consumption of a packet is even larger than the transmitting one [24]. An opportunistic reception (OR) algorithm has been proposed in [25] by considering the above energy consumption characteristic. In OR, the intermediate node generates the CV through forwarding or decoding-recoding manners adaptively, so that the received packets can be reduced. To sum up, RNC provides a superior tradeoff between energy efficiency and transmission reliability in cooperative WSNs [23, 25]. Nevertheless, these schemes are designed under conventional energy assumption, without involving the EH constraints.

On the other hand, in related work on EH, some contributions have been made for the point-to-point wireless systems. For example, the authors in [14, 26] investigated the throughput optimization over the finite horizon for both the cases where the harvested energy information is noncausally and causally known to the transmitter. In [15], the authors extended the results to the three-node Gaussian relay channel with EH source and relay nodes. In [27], the authors developed a more practical circuit model by considering the half-duplex constraint of the battery. For the wireless networks with EH constraints, the authors in [28] evaluated some standard medium access control protocols in WSNs. In [29], the authors analyzed the reliability of broadcast transmission in erasure-based networks with EH nodes. For the related work in NC-based and EH-enabled schemes, the authors in [30] studied the performance of NC-aided CC in two-way networks, where the relays were able to harvest energy emitted by wireless transmissions. In [31], a NC-based protocol is developed by taking into account the assumption that the sink is responsible for harvesting and transferring wireless energy to the sources. In [32], the authors proposed an EH-aided scheme for the node which was responsible for transmitting messages in a timely manner while being prudent about energy consumption. However, all these works focus on the networks which only consisted of the EH nodes, without considering the hybrid case.

1.2. Summary of Main Contributions

This paper focuses on the energy-efficient transmission for the RNC-based cooperative WSNs with partial EH nodes. Compared to the former works [23, 25], in our setup, the network consists of two types of nodes; one is powered by normal batteries, while the others are powered by EH constraints. Moreover, different from the single metric in the point-to-point EH schemes [14, 26], in the proposed protocol, both the energy efficiency and transmission reliability are considered. Besides, some technologies, such as RNC and CC, are also involved. Compared to the work in [29], although RNC is similar to the erasure code, the evaluated metric and network setup are different. The main contributions of this paper are summarized as follows:

• (i)

The energy efficiency for the cooperative WSNs with partial EH nodes is investigated. Firstly, a novel EH decoding-recoding policy is proposed to utilize the EH node, so as to save the energy of the rest nodes in the network. An energy efficiency model is established by computing the saved energy per round. And then, the policy parameters are selected through the optimization of the model. Moreover, the impacts of some parameters, such as the EH rate and transmission error probability, are also analyzed.

(ii)

A new transmission protocol is proposed by embedding the designed policy into the OR algorithm. The decoding failure probability is theoretically derived to evaluate the transmission reliability of the proposed protocol. On the basis of that, the appropriate application conditions of the protocol are obtained.

The remainder of this paper is organized as follows. Section 2 describes the system model. In Section 3, the EH decoding-recoding policy and the energy efficiency model are developed, and then the proposed protocol is presented. In Section 4, the decoding failure probability of the protocol is derived. Simulation results are presented in Section 5. Finally, Section 6 concludes the paper.

2. System Model

2.1. Cooperative WSNs

We consider multihop clustered WSNs, in which a source node in the source cluster sends data to a sink with the aid of several intermediate clusters, as depicted in Figure 1. Each cluster is composed of n sensor nodes and one EH node. (The model can also describe the case that n sensor nodes and one EH node are alive while the others are asleep. In fact, each cluster may have arbitrary sensor and EH nodes, and the assumption here is only made to declare the scope of this paper.) The sensor and EH nodes are powered by the nonrechargeable and rechargeable batteries, respectively. The operation of the system is broken into rounds, and it is assumed that the source node has data to send in each round.

Figure 1

System model of RNC-based cooperative WSNs.

One transmission round consists of four phases, as shown in Figure 2. Phase I is the intrasource cluster broadcasting, as shown in Figure 2(a); the source node splits the original data into m packets as $\mathit{P}=(P_1,\dots ,P_k,\dots ,P_m{)}^T$ and then broadcasts them to the other nodes in the source cluster, named as $r_{Si}$ , $i=\mathrm{1},\dots ,n$ . The intracluster communication is assumed to be error-free. $r_{Si}$ randomly selects a $\mathrm{1}\times m$ CV ${\mathit{V}}_{Si}=(V_{Si}^{(1)},\dots ,V_{Si}^{(k)},\dots ,V_{Si}^{(m)})$ to combine all the incoming packets as $$\begin{array}{cc}& P_{Si}={\mathit{V}}_{Si}·\mathit{P}.\end{array}$$ (1) Note that $P_k$ , $V_{Si}^{(k)}$ , and $P_{Si}$ are the elements over Galois field of size q, and each $V_{Si}^{\left(k\right)}$ is randomly selected with probability $1/q$ .

Figure 2

Transmission procedure of cooperative WSNs.

Phase II is the source-intermediate cluster transmission, as depicted in Figure 2(b). In this phase, each $r_{Si}$ transmits its outgoing packet to the intermediate cluster in the next hop. The outgoing packet encapsulates both ${\mathbf{V}}_{Si}$ and $P_{Si}$ . Each sensor node in the intermediate cluster, named as $r_{Ii}$ , tries to receive all the packets [23] from the source cluster. And then, $r_{Ii}$ recodes all the successfully received data as $$\begin{array}{cc}& P_{Ii}={\mathit{A}}_{Ii}·{\left[\dots ,P_{Sj},\dots ,P_{Sk}\right]}^T.\end{array}$$ (2) ${\mathit{A}}_{Ii}=(\dots ,A_{Ii}^{(j)},\dots ,A_{Ii}^{(k)})$ is also a randomly selected L length vector over Galois field, where L is the number of successfully received packets at $r_{Ii}$ . With (1), we rewrite the coded data $P_{Ii}$ as the product of a CV and P : $$\begin{array}{cc}& P_{Ii}={\mathit{V}}_{Ii}·\mathit{P},\end{array}$$ (3) where ${\mathit{V}}_{Ii}={\mathit{A}}_{Ii}·[\dots ,{\mathit{V}}_{Sj}^T,\dots ,{\mathit{V}}_{Sk}^T{]}^T$ . After that, $r_{Ii}$ reencapsulates ${\mathit{V}}_{Ii}$ and $P_{Ii}$ into its outgoing packet.

Phase III is the interintermediate clusters communications, as shown in Figure 2(c). In this phase, if $r_{Ii}$ fails to receive all the incoming packets in Phase II, it keeps silent. Otherwise, $r_{Ii}$ sends its recapsulated packet to the next cluster. The rest of intermediate clusters perform the operation in the same manner as the one in Figure 2(b), so the coded packets are delivered one by one, until the last cluster near the sink.

Phase IV is the decoding phase, in which the sink tries to receive all the packets from the last cluster nearby, as shown in Figure 2(d). We assume that $$\begin{array}{cc}& {\mathit{P}}_D={\left(P_{I^{\prime }1},\dots ,P_{I^{\prime }k},\dots ,P_{I^{\prime }w}\right)}^T\end{array}$$ (4) is the w received data, and $$\begin{array}{cc}& {\mathit{V}}_D={\left[{\mathit{V}}_{I^{\prime }1}^T,\dots ,{\mathit{V}}_{I^{\prime }k}^T,\dots ,{\mathit{V}}_{I^{\prime }w}^T\right]}^T\end{array}$$ (5) is the w received CVs, in which $P_{I^{\prime }k}$ and ${\mathit{V}}_{I^{\prime }k}$ are extracted from the outgoing packet of $r_{I^{\prime }k}$ . Thus, (4) can be rewritten as $$\begin{array}{cc}& {\mathit{P}}_D={\mathit{V}}_D·\mathit{P},\end{array}$$ (6) and if not less than m out of the CVs in ${\mathbf{V}}_D$ are linearly independent, P can be recovered through Gaussian elimination [20]. Otherwise, the decoding failure occurs at sink. Additionally, since transmission error may occur due to wireless channel fading, it is assumed that the transmission error follows a Bernoulli process with a probability p at each node.

2.2. Energy Harvesting Model

In this study, to meet the practical situation, it is assumed that the harvested energy information is causally unknown to the EH node, and we employ a Bernoulli process as the EH model. In this model, the EH node can harvest one unit of energy with probability μ at the beginning of each round. With probability $\mathrm{1}-\mu$ no energy is harvested. Note that only the EH node is capable of harvesting energy in the considered network.

3. The Proposed Protocol

3.1. EH Decoding-Recoding Policy

We propose a framework to utilize the EH node $r_{\mathrm{E}\mathrm{H}}$ in the intermediate cluster, whose current energy level is denoted as $E_{\mathrm{E}\mathrm{H}}$ . If $r_{\mathrm{E}\mathrm{H}}$ has harvested sufficient energy, $$\begin{array}{cc}& E_{\mathrm{E}\mathrm{H}}\ge m{E}_R+x{E}_T,\hspace{1em}\mathrm{1}\le x\le n,\end{array}$$ (7) in which $E_R$ and $E_T$ are the receiving and transmitting circuit energy consumption of one packet, respectively. Constraint (7) indicates that $r_{\mathrm{E}\mathrm{H}}$ is capable of receiving and transmitting m and x packets without being exhausted. Thus, $r_{\mathrm{E}\mathrm{H}}$ will be permitted to receive packets in phase II of the next transmission round. Meanwhile, x selected sensor nodes are turned off, so as to save energy. In the next round, if $r_{\mathrm{E}\mathrm{H}}$ successfully receive m packets, the received data can be written as $$\begin{array}{cc}& {\mathbf{P}}_{\mathrm{E}\mathrm{H}}={\mathbf{V}}_S·\mathbf{P},\end{array}$$ (8) in which $$\begin{array}{cc}& {\mathit{P}}_{\mathrm{E}\mathrm{H}}={\left(P_{I1},\dots ,P_{Ik},\dots ,P_{Im}\right)}^T,\\ {\mathit{V}}_S={\left[{\mathit{V}}_{S1}^T,\dots ,{\mathit{V}}_{Sk}^T,\dots ,{\mathit{V}}_{Sm}^T\right]}^T.\end{array}$$ (9) $r_{\mathrm{E}\mathrm{H}}$ obtains P by solving (8), and, then, it locally generates x linear independent packets as $$\begin{array}{cc}& P_{Ii}={\mathit{A}}_{Ii}·\mathit{P},\hspace{1em}i=1,\dots ,x.\end{array}$$ (10) By doing this, x sensor nodes avoid energy consumption in this round. On the other hand, if (7) is not satisfied, $r_{\mathrm{E}\mathrm{H}}$ will only keep on harvesting energy in the next round.

Here, we propose an example to illustrate the positive significance of the policy to the energy consumption. Figure 3 depicts some transmission manners of the EH node. In Figure 3(a), $x=2$ , so two nodes are turned off and avoid energy consumption in the current transmission while the EH node transmits two packets. Figure 3(b) shows an extreme case, in which the whole network is turned off, and all the packets are forwarded by the EH node. Overall, the employing of the EH node is beneficial for the energy saving of the network.

Figure 3

Transmission manners of the EH node.

3.2. Energy Efficiency Analysis and Parameter Optimization

$r_{\mathrm{E}\mathrm{H}}$ is capable of decoding and recoding only when m packets are successfully received; however, if the transmission error is taken into account, constraint (7) is not sufficient anymore to ensure that m packets can be successfully received by $r_{\mathrm{E}\mathrm{H}}$ . In fact, it only offers the lower bound of the required energy. Moreover, the value of x should also be given. In this part, these issues are investigated in detail.

3.2.1. How Much Energy Should Be Harvested?

To harvest sufficient energy so that m packets can be received by $r_{\mathrm{E}\mathrm{H}}$ , (7) should be rewritten as $$\begin{array}{cc}& E_{\mathrm{E}\mathrm{H}}\ge E\left(R\right)E_R+x{E}_T.\end{array}$$ (11) R refers to the number of received packets at $r_{\mathrm{E}\mathrm{H}}$ to insure that m packets can be successfully received in one round, and $E(R)$ is denoted as its mathematical expectation. Since the transmission error process follows the Bernoulli process, R is a Pascal ( $m,1-p$ ) random variable, so $E(R)$ can be written as $$\begin{array}{cc}& E\left(R\right)=\frac{m}{1-p}.\end{array}$$ (12) Substituting (12) into (11), the EH constraint can be expressed as $$\begin{array}{cc}& E_{\mathrm{E}\mathrm{H}}\ge ⌈\frac{m{E}_R}{1-p}+x{E}_T⌉.\end{array}$$ (13) Hence, we employ (13) as the threshold to decide if $r_{\mathrm{E}\mathrm{H}}$ will be permitted to receive in the next round.

3.2.2. How to Select x?

We select x by establishing an energy efficiency model. Firstly, the energy efficiency G is defined.

Definition 1 (energy efficiency).

Energy efficiency G is defined as the ratio of the saved energy and the corresponding cost, which is evaluated by the waiting time. It can be expressed as $$\begin{array}{cc}& G\left(x\right)=\frac{E_G\left(x\right)}{N_P\left(x\right)}.\end{array}$$ (14)

In (14), $E_G(x)$ is the saved energy if x sensor nodes are turned off. It can be written as $$\begin{array}{cc}& E_G\left(x\right)=\frac{x}{n}{E}_C,\end{array}$$ (15) where $E_C$ is the average energy consumption of n sensor nodes. Quantitatively, $E_C$ equals the sum of the energy consumption from both the receiving and transmitting circuits by the n sensor nodes. $N_P(x)$ is the waiting time $r_{\mathrm{E}\mathrm{H}}$ spends to meet EH constraint (13), and it can be expressed in terms of round as $$\begin{array}{cc}& N_P\left(x\right)=⌈\frac{⌈m{E}_{\mathrm{R}}/\left(\mathrm{1}-p\right)+x{E}_T⌉}{\mu }⌉.\end{array}$$ (16) Substituting (15) and (16) into (14), G can be rewritten as $$\begin{array}{cc}& G\left(x\right)=\frac{\mu x{E}_C}{n\left(m{E}_R/\left(1-p\right)+x{E}_T\right)},\hspace{1em}0\le x\le n.\end{array}$$ (17) With (17), it can be derived that $$\begin{array}{cc}& \frac{\partial G}{\partial x}=\frac{\mu mn{E}_R{E}_C/\left(1-p\right)}{n^2{\left(m{E}_R/\left(1-p\right)+x{E}_T\right)}^2}>0,\\ \frac{\partial G}{\partial \mu }=\frac{x{E}_C}{n\left(m{E}_R/\left(1-p\right)+x{E}_T\right)}>0,\\ \frac{\partial G}{\partial p}=-\frac{\mu xm{E}_R{E}_C}{n{\left(m{E}_R+x{E}_T\left(1-p\right)\right)}^2}<0.\end{array}$$ (18) According to (18), the following analysis can be made:

• (1)

Energy efficiency G is the monotonically increasing function with the growth of x, so x should be maximized in the policy to achieve the optimal energy efficiency. Therefore, we set $x=n$ in the proposed policy.

(2)

G is the monotonically increasing function with the growth of EH rate μ, which means that sufficient energy environment is profitable for energy efficiency.

(3)

G is the monotonically decreasing function when p increases, which indicates that the poor transmission reliability is harmful for energy efficiency.

With the above results, the pseudocode of the proposed policy can be described as Algorithm 1. In the description, $E_{\mu }$ is the harvested energy in each round and is modeled as a 0-1 random integer variable with probability μ. S is the number of successfully received packets by $r_{\mathrm{E}\mathrm{H}}$ . ${\Phi }_S$ and ${\Phi }_r$ are the index sets of the sensor nodes in the source and intermediate clusters, respectively.

Algorithm 1: EH decoding-recoding policy.

Initialization: S = 0, ${\mathrm{\Phi }}_S={\mathrm{\Phi }}_r=\{\mathrm{1},\dots ,n\}$ .

Input: $E_{\mathrm{E}\mathrm{H}}$ , $E_{\mu }$ .

(1)    $E_{\mathrm{E}\mathrm{H}}=E_{\mathrm{E}\mathrm{H}}+E_{\mu }$

(2)    $r_{Sj}$ transmits its outgoing packet, $\forall j\in {\mathrm{\Phi }}_S$

(3)   if    $E_{\mathrm{E}\mathrm{H}}\ge ⌈m{E}_R/(\mathrm{1}-p)+n{E}_T⌉$

(4)    $r_{Ii}$ is turned off, $\forall i\in {\mathrm{\Phi }}_r$

(5)    $r_{\mathrm{E}\mathrm{H}}$ receives $⌈m/(\mathrm{1}-p)⌉$ packets form source cluster in Phase II and update S

(6)    $E_{\mathrm{E}\mathrm{H}}=E_{\mathrm{E}\mathrm{H}}-⌈m{E}_R/(\mathrm{1}-p)⌉$

(7)   if  S == m

(8)     $r_{\mathrm{E}\mathrm{H}}$ decodes and recodes by (8) and (10)

(9)     $r_{\mathrm{E}\mathrm{H}}$ transmits n packets in Phase III

(10)     $E_{\mathrm{E}\mathrm{H}}=E_{\mathrm{E}\mathrm{H}}-n{E}_T$

(11)     else

(12)      transmission failure occurs

(13)     end if

(14) else

(15)      $r_{\mathrm{E}\mathrm{H}}$ only harvests energy in this round

(16) end if

The EH decoding-recoding policy can be embedded into conventional RNC-based algorithm to improve the energy efficiency. In this study, we embed it into the OR algorithm [25] and propose a new protocol, which is described in Figure 4.

Figure 4

Procedure of the proposed protocol.

4. Transmission Reliability Analysis

We evaluate the transmission reliability of the proposed protocol by deriving its decoding failure probability. To facilitate the analysis, we simplify the model to a two-hop one, which is also employed in [23, 25]. Besides, it is assumed that all the incoming links at sink exhibit the same transmission error probability $P_{rd}$ . S and $S_D$ are denoted as the number of successfully received packets in $r_{\mathrm{E}\mathrm{H}}$ and sink, respectively.

The decoding failure probability of the proposed protocol can be expressed as $$\begin{array}{cc}& P_f=P_{\mathrm{E}\mathrm{H}}\mathrm{P}\mathrm{r}\left(E_{\mathrm{E}\mathrm{H}}\ge ⌈\frac{m{E}_R}{1-p}+n{E}_T⌉\right)+P_{\mathrm{O}\mathrm{R}}\mathrm{P}\mathrm{r}\left(E_{\mathrm{E}\mathrm{H}}<⌈\frac{m{E}_R}{1-p}+n{E}_T⌉\right),\end{array}$$ (19) in which $P_{\mathrm{E}\mathrm{H}}$ and $P_{\mathrm{O}\mathrm{R}}$ are the decoding failure probabilities when EH decoding-recoding and OR algorithms are triggered, respectively. According to the description of Algorithm 1, $P_{\mathrm{E}\mathrm{H}}$ can be written as $$\begin{array}{cc}& P_{\mathrm{E}\mathrm{H}}=\mathrm{P}\mathrm{r}\left(S\ge m\right)\mathrm{P}\mathrm{r}\left(S_D<m\hspace{0.17em}|\hspace{0.17em}S\ge m\right)+\mathrm{P}\mathrm{r}\left(S<m\right)\mathrm{P}\mathrm{r}\left(S_D<m\hspace{0.17em}|\hspace{0.17em}S<m\right).\end{array}$$ (20) With the transmission error probability p, $\mathrm{P}\mathrm{r}(S\ge m)$ can be expressed as $$\begin{array}{cc}& \mathrm{P}\mathrm{r}\left(S\ge m\right)={\displaystyle \sum }_{i=m}^{⌈m/\left(\mathrm{1}-p\right)⌉}\left(\begin{array}{c}⌈\frac{m}{\left(\mathrm{1}-p\right)}⌉\\ i\end{array}\right){\left(\mathrm{1}-p\right)}^i{p}^{⌈m/\left(\mathrm{1}-p\right)⌉-i}.\end{array}$$ (21) $\mathrm{P}\mathrm{r}\left(S_D<m\hspace{0.17em}|\hspace{0.17em}S\ge m\right)$ can be written as $$\begin{array}{cc}& \mathrm{Pr}\left(S_D<m\hspace{0.17em}|\hspace{0.17em}S\ge m\right)={\displaystyle \sum }_{i=\mathrm{0}}^{m-\mathrm{1}}\left(\begin{array}{c}n\\ i\end{array}\right){\left(\mathrm{1}-P_{rd}\right)}^i{P}_{rd}^{n-i}.\end{array}$$ (22) On the other hand, $\mathrm{P}\mathrm{r}(S<m)$ can be expressed as $$\begin{array}{cc}& \mathrm{P}\mathrm{r}\left(S<m\right)=\mathrm{1}-\mathrm{P}\mathrm{r}\left(S\ge m\right)={\displaystyle \sum }_{i=\mathrm{0}}^{m-\mathrm{1}}\left(\begin{array}{c}⌈\frac{m}{\left(\mathrm{1}-p\right)}⌉\\ i\end{array}\right){\left(\mathrm{1}-p\right)}^i{p}^{⌈m/\left(\mathrm{1}-p\right)⌉-i};\end{array}$$ (23) $\begin{array}{cc}& \mathrm{P}\mathrm{r}\left(S_{\mathrm{D}}<m\hspace{0.17em}|\hspace{0.17em}S<m\right)=\mathrm{1}.\end{array}$ (24) Substituting (21)–(24) into (20), $P_{\mathrm{E}\mathrm{H}}$ can be obtained as $$\begin{array}{cc}& P_{\mathrm{E}\mathrm{H}}={\displaystyle \sum }_{i=m}^{⌈m/\left(\mathrm{1}-p\right)⌉}\left(\begin{array}{c}⌈\frac{m}{\left(\mathrm{1}-p\right)}⌉\\ i\end{array}\right){\left(\mathrm{1}-p\right)}^i{p}^{⌈m/\left(\mathrm{1}-p\right)⌉-i}{\displaystyle \sum }_{i=\mathrm{0}}^{m-\mathrm{1}}\left(\begin{array}{c}n\\ i\end{array}\right){\left(\mathrm{1}-P_{rd}\right)}^i{P}_{rd}^{n-i}+{\displaystyle \sum }_{i=\mathrm{0}}^{m-\mathrm{1}}\left(\begin{array}{c}⌈\frac{m}{\left(\mathrm{1}-p\right)}⌉\\ i\end{array}\right){\left(\mathrm{1}-p\right)}^i{p}^{⌈m/\left(\mathrm{1}-p\right)⌉-i}.\end{array}$$ (25)

To derive $\mathrm{P}\mathrm{r}(E_{\mathrm{E}\mathrm{H}}\ge ⌈m{E}_R/(\mathrm{1}-p)+n{E}_T⌉)$ , we denote L as the number of required rounds when (13) is satisfied. According to the energy balance law [12], the harvested energy is equal to the consumed one; that is, $$\begin{array}{cc}& E\left(L\right)\mu =⌈\frac{m{E}_R}{\left(\mathrm{1}-p\right)}+n{E}_T⌉.\end{array}$$ (26) On the other hand, $\mathrm{P}\mathrm{r}(E_{\mathrm{E}\mathrm{H}}\ge ⌈m{E}_R/(\mathrm{1}-p)+n{E}_T⌉)$ can be written as $$\begin{array}{cc}& \mathrm{P}\mathrm{r}\left(E_{\mathrm{E}\mathrm{H}}\ge ⌈\frac{m{E}_R}{\left(\mathrm{1}-p\right)}+n{E}_T⌉\right)=\frac{\mathrm{1}}{E\left(L\right)}.\end{array}$$ (27) Substituting (26) into (27), it can be obtained as $$\begin{array}{cc}& \mathrm{P}\mathrm{r}\left(E_{\mathrm{E}\mathrm{H}}\ge ⌈\frac{m{E}_R}{\left(\mathrm{1}-p\right)}+n{E}_T⌉\right)=\frac{\mu }{⌈m{E}_R/\left(\mathrm{1}-p\right)+n{E}_T⌉}.\end{array}$$ (28) With (28), $\mathrm{P}\mathrm{r}(E_{\mathrm{E}\mathrm{H}}<⌈m{E}_R/(\mathrm{1}-p)+n{E}_T⌉)$ can be also obtained as $$\begin{array}{cc}& \mathrm{P}\mathrm{r}\left(E_{\mathrm{E}\mathrm{H}}<⌈\frac{m{E}_R}{\left(\mathrm{1}-p\right)}+n{E}_T⌉\right)=\mathrm{1}-\frac{\mu }{⌈m{E}_R/\left(\mathrm{1}-p\right)+n{E}_T⌉}.\end{array}$$ (29) The expression of $P_{\mathrm{O}\mathrm{R}}$ is derived in [25], and by substituting it and (25), (28), and (29) into (19), $P_f$ can be expressed as $$\begin{array}{cc}& P_f=\left(\frac{\mu }{⌈m{E}_R/\left(\mathrm{1}-p\right)+n{E}_T⌉}\right){\displaystyle \sum }_{i=m}^{⌈m/\left(\mathrm{1}-p\right)⌉}\left(\begin{array}{c}⌈\frac{m}{\left(\mathrm{1}-p\right)}⌉\\ i\end{array}\right){\left(\mathrm{1}-p\right)}^i{p}^{⌈m/\left(\mathrm{1}-p\right)⌉-i}{\displaystyle \sum }_{i=\mathrm{0}}^{m-\mathrm{1}}\left(\begin{array}{c}n\\ i\end{array}\right){\left(\mathrm{1}-P_{rd}\right)}^i{P}_{rd}^{n-i}+{\displaystyle \sum }_{i=\mathrm{0}}^{m-\mathrm{1}}\left(\begin{array}{c}⌈\frac{m}{\left(\mathrm{1}-p\right)}⌉\\ i\end{array}\right){\left(\mathrm{1}-p\right)}^i{p}^{⌈m/\left(\mathrm{1}-p\right)⌉-i}+P_{\mathrm{O}\mathrm{R}}\left(\mathrm{1}-\frac{\mu }{⌈m{E}_R/\left(\mathrm{1}-p\right)+n{E}_T⌉}\right).\end{array}$$ (30)

5. Simulation Results

In this section, we examine the energy efficiency and transmission reliability of the proposed protocol through simulations. Firstly, we examine the effectiveness of the proposed energy efficiency model in Section 3. And then, we compare the proposed protocol with OR [25] and RNC-based cooperative communication (NCCC) [23], in terms of lifetime and decoding failure probability $P_f$ .

The simulation model follows the simplified two-hop one in Section 2, with $m=2$ , $n=4$ . The lifetime is defined as the round when the first node exhausts its energy in intermediate cluster, which is widely used in the literatures [12, 17]. An energy model similar to [17] is utilized, which has receiving energy consumption $E_R=3$  mJ/packet and transmitting energy consumption $E_T=1$  mJ/packet. All the sensor nodes have the initial energy $E_i=6000$  mJ, $i\in \{\mathrm{1,2},\mathrm{3,4}\}$ , and the EH node has the initial energy $E_{\mathrm{E}\mathrm{H}}=0$  mJ. We employ the minimal residual energy at the end of each round, denoted as $E_{\mathrm{m}\mathrm{i}\mathrm{n}}$ , to present the lifetime of the network, which is defined as $$\begin{array}{cc}& E_{\mathrm{m}\mathrm{i}\mathrm{n}}=\left\{\begin{array}{cc}\min \left(E_i,E_{\mathrm{E}\mathrm{H}}\right),\hfill & \text{when\hspace{0.17em}\hspace{0.17em}the\hspace{0.17em}\hspace{0.17em}proposed\hspace{0.17em}\hspace{0.17em}policy\hspace{0.17em}\hspace{0.17em}is\hspace{0.17em}\hspace{0.17em}triggered}\hfill \\ \min \left(E_i\right),\hfill & \text{otherwise.}\hfill \end{array}\right.\end{array}$$ (31)

5.1. Effectiveness of the Proposed Energy Efficiency Model

Figure 5 depicts a simulation trail of the EH decoding-recoding policy under different values of x. In the figure, each severe fall of $E_{\mathrm{m}\mathrm{i}\mathrm{n}}$ indicates that the proposed policy is triggered. It can be observed that the lifetime is monotonically increased as the value of x grows. From the interval of the severe fall of $E_{\mathrm{m}\mathrm{i}\mathrm{n}}$ , we see that although the proposed policy is triggered less frequently when $x=n=4$ , the lifetime reaches the maximum, which means that the optimal energy efficiency is obtained. These results coincide well with the analytical ones from the proposed model in Section 3.

Figure 5

Minimal residual energy of the proposed policy with varieties of x when $\mu =p=\mathrm{0.1}.$

Figure 6 shows a simulation trail of the minimal residual energy of the policy with varieties of EH rate μ when $p=0.1$ . It can be observed that the growth of μ prolongs the lifetime of the proposed policy. Figure 7 presents the average lifetime comparisons of the policy under different EH rate μ, in which each metric is averaged by 20 simulation trails. It also shows that the growth of μ increases the lifetime of the proposed policy for each value of x. Moreover, the figure indicates that it yields optimal lifetime by setting $x=n$ .

Figure 6

Minimal residual energy of the proposed policy with varieties of μ when $p=0.1$ .

Figure 7

Average lifetime of the proposed policy with varieties of EH rate when $p=\mathrm{0.1}$ .

Figure 8 presents a trail of the minimal residual energy of the policy with varieties of p when $x=4$ and $\mu =0.3$ . It shows that the growth of p deteriorates the lifetime. Figure 9 depicts the average lifetime when $x=4$ and $\mu =0.3$ . In the figure, the dash line represents each trail while the red line represents the average value. Similarly, it shows that the bad transmission quality is harmful to the lifetime of the proposed policy. These results also correspond well with the analytical ones in Section 3.

Figure 8

Average lifetime of the proposed policy with varieties of p when $\mu =0.3$ .

Figure 9

Average lifetime of the proposed policy when $x=4$ and $\mu =0.3$ .

To sum up, the effectiveness of the proposed energy efficiency model is verified through the above results.

5.2. Lifetime

We compare the energy efficiency of the proposed protocol to OR algorithm [25] and NCCC [23], in terms of average lifetime, which is calculated by 20 simulation trails. In Figure 10, the dash line is the simulation trail while the red line is the average value. The result shows that the proposed protocol is superior to the other compared schemes under the same transmission error probability. Besides, when μ increases, the performance gain can be further improved. In fact, the proposed protocol is able to utilize the EH node and consume the harvested energy in a high efficient manner, thus yielding better performance. The results indicate that it is beneficial for the energy efficiency to optimize the parameters of the policy.

Figure 10

Average lifetime comparisons.

5.3. Transmission Reliability

Figure 11 shows the decoding failure probability of the proposed policy. In the figure, the theoretical results are calculated by (25). It can be observed that the theoretical results match the simulations very well. The curve experiences a severe fall when transmission error probability $p=1/3$ , which is caused by the variety of the term $⌈m/(\mathrm{1}-p)⌉$ in (21) and (23). In our studied case, $m=2$ , so $⌈m/(\mathrm{1}-p)⌉$ varies from 3 to 4 before and after the point $p=1/3$ , respectively. In general, the growth of p yields poor transmission reliability for the proposed policy.

Figure 11

Decoding failure probability of EH decoding-recoding policy when $P_{rd}=0.1$ .

The comparisons of the decoding failure probabilities are given in Figure 12. Compared to OR and NCCC, although the proposed policy always performs the worst, it can be seen that when p is in small value or $P_{rd}$ is in large value, the performance gap is not obvious. Thus, the above results reveal the appropriate scenario when the proposed policy can be applied, that is, when the wireless links between the clusters are in good quality or the ones between the intermediate cluster and sink are in bad quality.

Figure 12

Comparisons of decoding failure probability of the proposed policy.

Figure 13 depicts the decoding probability of the proposed protocol. Compared to the results in Figure 13(b), it can be observed that the performance gap between the compared schemes is less obvious in Figure 13(a). This result coincides well with the one in Figure 12, because, in Figure 13(a), $p=0.1$ is smaller than 0.2 in Figure 13(b), and, in such scenario, the EH decoding-recoding policy embeded in the proposed protocol can achieve similar transmission reliability comparing with OR and NCCC. On the other hand, in both Figures 13(a) and 13(b), when $P_{rd}$ is in large value, the performance gap is reduced, which is also corresponding with the results in Figure 12. Moreover, Figure 13 shows that the growth of μ deterates the transmission reliability of the proposed protocol, because the EH decoding-recoding policy is triggered more frequently.

Figure 13

Decoding failure probability of the proposed protocol.

Figure 14 is the deocding failure probability of the proposed protocol, in terms of μ and p. The results are theoretically calculated by (30). It shows that, in Figures 14(a), 14(b), and 14(c), when p is with small value, the proposed protocol yields superior transmission reliability, while the influences of the varieties of μ and $P_{rd}$ are not obvious. However, when p is with large values, the growth of μ will deteriorate the performance obviously. This comparison also verifies the appropriate scenario for the proposed protocol, that is, when p is in small value, the proposed protocol can achieve superior performance in both energy efficiency and transmission reliability.

Figure 14

Decoding failure probability of the proposed protocol.

6. Conclusion

In this paper, we proposed an energy-efficient transmission protocol for the scenario of cooperative WSNs with partial EH nodes. An EH decoding-recoding policy was proposed, and we established an energy efficiency model to design and optimize the corresponding parameter, so as to improve the lifetime of the investigated network. Moreover, we examined the transmission reliability of the proposed protocol by deriving the metric of decoding failure probability. Theoretical and simulation results indicate that, in the two-hop model, the proposed protocol outperforms the compared schemes in lifetime, while it also obtains similar transmission reliability when the wireless links between the clusters are in good quality or the ones between the intermediate cluster and sink are in bad quality.