Network-coding-based two-way relay cooperation with energy harvesting

Abstract

For the relay cooperation systems or networks, in some scenarios, the relay is deployed in the hard-to-reach areas, such as on the remote mountains or in the sea. It is impractical for the relay to be powered by grid energy. And if the relay is powered by battery, it is difficult and high cost to replace the depleted battery. To overcome the power dependence of the relay, this article proposes the network-coding-based two-way relay cooperation with energy harvesting, where the relay is equipped with multiple antennas for information decoding and energy harvesting. Network coding is adopted at the relay to reduce the time slots, and low-density parity check codes are employed at the sources to improve the reliability. We introduce a maximal ratio combining–based decoding algorithm for the proposed system to achieve coding gain and diversity gain. Furthermore, we analyze the outage probability and bit error rate of the system when the optimal antenna selection algorithm is adopted at the relay to transmit data. Theoretical analysis and numerical simulation results show that the proposed system outperforms the corresponding point-to-point system under the same condition. The result also demonstrates that the relay should be deployed closer to the user whose outage probability is required to be lower.

Keywords

Relay cooperation energy harvesting network coding maximal ratio combining low-density parity check codes

Introduction

Energy harvesting from ambient environment can potentially reduce the dependence on the supply of battery or grid energy. Recently, energy-harvesting communications and networks^1–5 have attracted great attention from both academic and industrial communities. Based on the energy-harvesting technology, the communication nodes can benefit the energy saving and lower the carbon footprint. What is more important, because the nodes are powered by harvested energy, their lifetime is not limited by the battery or grid energy, and they can be deployed in hard-to-reach areas to enlarge the coverage and reduce the communication blind zones. Traditional energy-harvesting techniques rely on natural energy sources such as solar or wind. The energy harvested level is influenced by many factors, such as the time of the sunshine and the seasonal weather patterns. Since ambient radio frequency (RF) signals are widely available in the world, a promising harvesting technology is to use the RF energy. RF-based energy-harvesting communications can realize simultaneous information and power transfer (SWIPT),^6–8 which generates great interest in the research of this area.

RF-based energy harvesting is extensively investigated in various communication scenarios, such as multiple-input multiple-output (MIMO) systems,^9,10 cognitive radio networks,^11,12 and relay cooperation.^13–15 Relay cooperation^16,17 enables single-antenna nodes to share the use of their antennas to form a virtual MIMO, which exploits the spatial diversity and improve the performance of wireless communication systems. Hence, relay cooperation with energy harvesting can not only achieve high performance but also break through the power limitation. Li et al.⁴ considered a cooperative communication in sensor networks with energy harvesting. In order to maximize the long-term utility of the network, energy efficient scheduling strategies are developed by a Markov decision process (MDP). Ku et al.¹⁸ investigated a cooperative system where one source transmits data to one destination with the assistance of an energy-harvesting decode-and-forward relay. The average symbol error rate performance is minimized through the MDP framework. Minasian et al.¹⁹ studied an energy-harvesting amplify-and-forward relay cooperative network. In offline and online settings, optimal policies for transmission are obtained via maximizing the throughput.

Some researchers extended the one-way cooperative systems or networks with energy harvesting^4,18,19 to two-way relay cooperation scenarios. For a non-regenerative two-way multi-antenna relay network with energy harvesting, Li et al.²⁰ considered a non-convex energy-harvesting-constrained relay beam-forming optimization problem. Based on semi-definite programming and rank-one decomposition theorem, an iterative algorithm is proposed to find the global optimal solution. Shah et al.²¹ proposed a two-way multiplicative relay with energy harvesting, where the relay node uses power splitting–based relaying protocol for energy harvesting and information processing. Du et al.²² presented a time switching–based network-coding relaying (TSNCR) protocol for the two-way relay system with energy harvesting. The outage probability for the proposed TSNCR protocol is derived and further minimized by a genetic optimization algorithm. All the scenarios considered in Li et al.,²⁰ Shah et al.,²¹ and Du et al.²² ignore the direct link between the sources which may be blocked due to obstacles. However, when there are no obstacles between the sources, the direct link should be taken into account.

In this article, we investigate the network-coding-based two-way relay cooperation with energy harvesting. There are direct links between the sources and the relay is equipped with multiple antennas which are able to harvest energy. The main contributions of this article are summarized as follows:

Network-coding-based two-way relay cooperation with energy harvesting is proposed. At the sources, low-density parity check (LDPC) codes are employed to improve the reliability, and at the relay, network coding is adopted to reduce the time slots and improve the average throughput.

Maximal ratio combining (MRC)-based decoding algorithm for the network-coding-based two-way relay cooperation is introduced, via which coding gain and diversity gain are achieved.

When the relay adopts the optimal antenna selection algorithm to transmit data, the outage probability and bit error rate (BER) of the network-coding-based two-way relay cooperation with energy harvesting are studied by theoretical analysis and numerical simulations.

The rest of this article is organized as follows. In section “System description,” the system description of the network-coding-based two-way relay cooperation with energy harvesting is presented. Section “MRC-based decoding algorithm for the proposed system” introduces the MRC-based decoding algorithm for the proposed system. Section “Performance analysis of the proposed system” analyzes the outage probability of the system. Simulation results are provided in section “Simulation results.” Finally, in section “Conclusion,” we conclude the whole paper.

System description

Network-coding-based two-way relay cooperation with energy harvesting is described as follows. Two users S₁ and S₂ exchange information with the help of relay R. S₁ and S₂ are equipped with single antenna with battery or grid power supply. The relay R is equipped with K antennas without external power supply, and it is powered by the energy harvested from the RF signals from S₁ and S₂. At the relay, some antennas are used to decode the incoming signal, and the rest antennas are used to harvest energy, which is used to broadcast the information to the users. To further improve the reliability of the system, LDPC codes²³ are adopted at S₁ and S₂.

Figure 1 shows the three time slots of the network-coding-based two-way relay cooperation with energy harvesting, which is designed as follows:

In time slot 1, the information bits at S₁ are encoded into a codeword $c_{1} = (c_{1}^{(1)}, \dots, c_{N}^{(1)})$ by LDPC-1. $c_{1}$ is sent to R and S₂ over a broadcast channel.

In time slot 2, the information bits at S₂ are encoded into a codeword $c_{2} = (c_{1}^{(2)}, \dots, c_{N}^{(2)})$ by LDPC-2. $c_{2}$ is sent to R and S₁ over a broadcast channel.

At the relay R, some antennas are used to decode the signals, and the rest antennas are used to harvest energy from the RF signals from S₁ and S₂. The relay combines the recovered $c_{1}$ and $c_{2}$ by network coding which is denoted as bitwise exclusive OR (XOR) operation in the Galois field (GF) (2). XOR is indicated by ⊕, and the new corresponding codeword $c_{R}$ is achieved by

\begin{array}{l} c_{R} = c_{1} \oplus c_{2} = (c_{1}^{(1)} \oplus c_{1}^{(2)}, \dots, c_{N}^{(1)} \oplus c_{N}^{(2)}) \\ = (c_{1}^{(R)}, \dots, c_{N}^{(R)}) \end{array}

(1)

Figure 1.

Network-coding-based two-way relay cooperation with energy harvesting.

In time slot 3, R broadcasts $c_{R}$ to S₁ and S₂ simultaneously using the harvested energy. In practical communication systems, it should be noted that not all the harvested energy can be used for transmission. The energy utilization ratio is much less than 100% due to the variety of operations at the relay.

If the relay transmits the recovered $c_{1}$ and $c_{2}$ to S₂ and S₁ separately in two time slots, totally, four time slots are needed for one transmission period. By network coding at the relay, the time slots are reduced to three. It sharply increases the average throughput of the system.

MRC-based decoding algorithm for the proposed system

An MRC-based decoding algorithm for the network-coding-based two-way relay cooperation with energy harvesting is introduced. Because S₁ and S₂ are reciprocal, here, we just describe the decoding algorithm for S₁. Binary phase-shift keying (BPSK) modulation is adopted. According to equation (1), the relationship between $c_{i}^{(R)}$ and $c_{i}^{(1)}$ , $c_{i}^{(2)}$ , is shown in Table 1.

Table 1.

Relationship between $c_{i}^{(R)}$ and $c_{i}^{(1)}$ , $c_{i}^{(2)}$ .

$c_{i}^{(1)}$	$c_{i}^{(2)}$	$c_{i}^{(R)}$
0	0	0
0	1	1
1	0	1
1	1	0

At S₁, there are two received signals: $r_{2} = (r_{1}^{(2)}, \dots, r_{N}^{(2)})$ from S₂ and $r_{R} = (r_{1}^{(R)}, \dots, r_{N}^{(R)})$ from R. S₁ decodes $c_{2}$ based on $r_{2}$ and $r_{R}$ .

However, $r_{R}$ corresponds to $c_{R}$ . It is not the same as $r_{2}$ which corresponds to $c_{2}$ directly. It is illustrated that

c_{i}^{(R)} = {\begin{matrix} c_{i}^{(2)}, if c_{i}^{(1)} = 0 \\ {\bar{c}}_{i}^{(2)}, if c_{i}^{(1)} = 1 \end{matrix}, i = 1, \dots, N

(2)

where ${\bar{c}}_{i}^{(2)}$ is the inversion of $c_{i}^{(2)}$ .

We assume $r_{3} = (r_{1}^{(3)}, \dots, r_{N}^{(3)})$ . Since $c_{1}$ is known to S₁, according to equation (2) and the property of BPSK modulation, we assign $r_{i}^{(3)}$ as below

r_{i}^{(3)} = {\begin{matrix} r_{i}^{(R)}, if c_{i}^{(1)} = 0 \\ - r_{i}^{(R)}, if c_{i}^{(1)} = 1 \end{matrix}, i = 1, \dots, N

(3)

Based on $r_{R}$ and $c_{1}$ , $r_{3}$ is achieved by equation (3), which corresponds to $c_{2}$ directly.

Because $r_{2}$ and $r_{3}$ are from S₂ and R, respectively, they are over independent fading channels. Using MRC combination,²⁴ we combine $r_{2}$ and $r_{3}$ which both correspond to $c_{2}$ , and then put the combined signals into the LDPC-2 decoder at S₁. Finally, information from S₂ is decoded efficiently. This decoding scheme is called as MRC-based decoding algorithm, which can achieve coding gain and diversity gain.

Performance analysis of the proposed system

In this section, we investigate the outage probability performance of the network-coding-based two-way relay cooperation with energy harvesting. Suppose $h_{12}$ and $h_{21}$ represent S₁-S₂ channel in time slot 1 and S₂-S₁ channels in time slot 2, respectively. $h_{1 R}^{(k)} (k = 1, \dots, K)$ and $h_{2 R}^{(k)}$ represent S₁-R channel in time slot 1 and S₂-R channel in time slot 2, respectively. $h_{R 1}^{(k)} (k = 1, \dots, K)$ and $h_{R 2}^{(k)}$ represent R-S₁ channel and R-S₂ channel in time slot 3, respectively. All channels suffer from independent Rayleigh fading. $h_{12}$ , $h_{21}$ , $h_{1 R}^{(k)}$ , $h_{2 R}^{(k)}$ , $h_{R 1}^{(k)}$ , and $h_{R 2}^{(k)}$ are zero-mean complex Gaussian random variables with unit variance. $d_{1 R}^{2}$ , $d_{2 R}^{2}$ , and $d_{12}^{2}$ are the power attenuation factors of S₁-R, S₂-R, and S₁-S₂ channels due to different distances. Assume the transmission power at S₁ and S₂ is P.

Energy harvested at the relay

At the relay, for the RF signals from S₁, the number of energy-harvesting antennas is $K_{1}$ , where $K - K_{1}$ antennas are applied for information decoding to recover the codewords. The energy harvested from S₁ is calculated as

P_{1} = \frac{P \sum_{k = 1}^{K_{1}} {| h_{1 R}^{(k)} |}^{2}}{d_{1 R}^{2}}

(4)

For the RF signals from S₂, the number of energy-harvesting antennas is $K_{2}$ . Similarly, the energy harvested from S₂ is calculated as

P_{2} = \frac{P \sum_{k = 1}^{K_{2}} {| h_{2 R}^{(k)} |}^{2}}{d_{2 R}^{2}}

(5)

Assuming the energy utilization ratio at the relay is $η (0 \leq η \leq 1)$ , the total transmission energy at the relay is

\tilde{P} = η (P_{1} + P_{2}) = \frac{η P \sum_{k = 1}^{K_{1}} {| h_{1 R}^{(k)} |}^{2}}{d_{1 R}^{2}} + \frac{η P \sum_{k = 1}^{K_{2}} {| h_{2 R}^{(k)} |}^{2}}{d_{2 R}^{2}}

(6)

Signals received at the sources

We investigate only the outage probability of S₁ due to the reciprocal of S₁ and S₂.

At S₁, the received signals from S₂ is

r_{2} = \frac{\sqrt{P} h_{21}}{d_{12}} x + n_{2}

(7)

where $x$ is the BPSK modulation of codeword $c_{2}$ . $n_{2} = (n_{1}^{(2)}, \dots, n_{N}^{(2)})$ is the additional noise. $n_{i}^{(2)} (i = 1, \dots, N)$ are zero-mean complex Gaussian random variables with variance $σ^{2}$ .

Assume the optimal antenna selection algorithm²⁵ is adopted at the relay to select the optimal antenna $h_{R 1}^{(o)}$ from $h_{R 1}^{(1)}, \dots, h_{R 1}^{(K)}$

{| h_{R 1}^{(o)} |}^{2} = max {{| h_{R 1}^{(1)} |}^{2}, \dots, {| h_{R 1}^{(K)} |}^{2}}

(8)

where $h_{R 1}^{(k)} (k = 1, \dots, K)$ represents R-S₁ channel and $\max {\cdot}$ is the maximum function. The relay sends $\tilde{x}$ over the antenna $h_{R 1}^{(o)}$ with transmission power $\tilde{P}$ . $\tilde{x}$ is the BPSK modulation of codeword $c_{R}$ .

At S₁, the received signals from R is

r_{R} = \frac{\sqrt{\tilde{P}}}{d_{1 R}} h_{R 1}^{(o)} \tilde{x} + n_{R}

(9)

where $n_{R}$ is defined the same as $n_{2}$ . Substituting equation (6) into equation (9), we have

\begin{matrix} r_{R} & = \frac{\sqrt{\frac{η P \sum_{k = 1}^{K_{1}} {| h_{1 R}^{(k)} |}^{2}}{d_{1 R}^{2}} + \frac{η P \sum_{k = 1}^{K_{2}} {| h_{2 R}^{(k)} |}^{2}}{d_{2 R}^{2}}}}{d_{1 R}} h_{R 1}^{(o)} \tilde{x} + n_{R} \\ = \frac{\sqrt{d_{2 R}^{2} η P \sum_{k = 1}^{K_{1}} {| h_{1 R}^{(k)} |}^{2} + d_{1 R}^{2} η P \sum_{k = 1}^{K_{2}} {| h_{2 R}^{(k)} |}^{2}}}{d_{1 R}^{2} d_{2 R}} h_{R 1}^{(o)} \tilde{x} + n_{R} \end{matrix}

(10)

According to equation (3), we achieve $r_{3} = (r_{1}^{(3)}, \dots, r_{N}^{(3)})$ as below

r_{i}^{(3)} = {\begin{matrix} \frac{\sqrt{d_{2 R}^{2} η P \sum_{k = 1}^{K_{1}} {| h_{1 R}^{(k)} |}^{2} + d_{1 R}^{2} η P \sum_{k = 1}^{K_{2}} {| h_{2 R}^{(k)} |}^{2}}}{d_{1 R}^{2} d_{2 R}} h_{R 1}^{(o)} {\tilde{x}}_{i} + n_{i}^{(R)}, if c_{i}^{(1)} = 0 \\ - \frac{\sqrt{d_{2 R}^{2} η P \sum_{k = 1}^{K_{1}} {| h_{1 R}^{(k)} |}^{2} + d_{1 R}^{2} η P \sum_{k = 1}^{K_{2}} {| h_{2 R}^{(k)} |}^{2}}}{d_{1 R}^{2} d_{2 R}} h_{R 1}^{(o)} {\tilde{x}}_{i} - n_{i}^{(R)}, if c_{i}^{(1)} = 1 \end{matrix}, i = 1, \dots, N

(11)

By MRC combination, we have

\begin{matrix} y & = [(h_{21})^{*} (h_{R 1}^{(o)})^{*}] [\begin{matrix} r_{2} \\ r_{3} \end{matrix}] \\ = (h_{21})^{*} r_{2} + (h_{R 1}^{(o)})^{*} r_{3} \end{matrix}

(12)

where $(\cdot)^{*}$ denotes the conjugate transpose. At S₁, information from S₂ is achieved by decoding $y$ via LDPC-2 decoder.

Outage probability of the sources

An outage event occurs when the instantaneous channel capacity falls below the data transmission rate. The probability of the outage event occurring is defined as the outage probability.¹⁷

At S₁, the instantaneous channel capacity is

C = \log_{2} (1 + γ)

(13)

where $γ$ is the effective instantaneous signal-to-noise ratio (SNR). Based on equations (7), (11), and (12)

γ = \frac{P {| h_{21} |}^{2}}{d_{12}^{2} σ^{2}} + \frac{η P {| h_{R 1}^{(o)} |}^{2} (d_{2 R}^{2} \sum_{k = 1}^{K_{1}} {| h_{1 R}^{(k)} |}^{2} + d_{1 R}^{2} \sum_{k = 1}^{K_{2}} {| h_{2 R}^{(k)} |}^{2})}{d_{1 R}^{4} d_{2 R}^{2} σ^{2}}

(14)

Hence, the outage probability can be calculated as

\begin{matrix} P_{out} & = \Pr {C < R_{c}} \\ = \Pr {\log_{2} (1 + \frac{P {| h_{21} |}^{2}}{d_{12}^{2} σ^{2}} + \frac{η P {| h_{R 1}^{(o)} |}^{2} (d_{2 R}^{2} \sum_{k = 1}^{K_{1}} {| h_{1 R}^{(k)} |}^{2} + d_{1 R}^{2} \sum_{k = 1}^{K_{2}} {| h_{2 R}^{(k)} |}^{2})}{d_{1 R}^{4} d_{2 R}^{2} σ^{2}}) < R_{c}} \end{matrix}

(15)

where $R_{c}$ is the data transmission rate, which is regarded as the code rate of LDPC-2. For Rayleigh fading channels as described at the beginning of section “Performance analysis of the proposed system,” $| h_{21} |$ , $| h_{1 R}^{(k)} |$ , $| h_{2 R}^{(k)} |$ , and $| h_{R 1}^{(k)} |$ follow the Rayleigh distribution. Hence, ${| h_{21} |}^{2}$ , ${| h_{1 R}^{(k)} |}^{2}$ , ${| h_{2 R}^{(k)} |}^{2}$ , and ${| h_{R 1}^{(k)} |}^{2}$ follow the exponential distribution $ε (1)$ , whose common distribution function $F_{X} (x)$ and density function $f_{X} (x)$ are

F_{X} (x) = {\begin{matrix} 1 - e^{- x}, & x \geq 0 \\ 0, & x < 0 \end{matrix}, f_{X} (x) = {\begin{matrix} e^{- x}, & x \geq 0 \\ 0, & x < 0 \end{matrix}

(16)

The density function of $Y = {| h_{R 1}^{(o)} |}^{2} = max {{| h_{R 1}^{(1)} |}^{2}, \dots, {| h_{R 1}^{(K)} |}^{2}}$ follows²⁶

f_{Y} (y) = K f_{X} (y) {(F_{X} (y))}^{K - 1} = {\begin{matrix} K e^{- y} {(1 - e^{- y})}^{K - 1}, & y \geq 0 \\ 0, & y < 0 \end{matrix}

(17)

The outage probability will be further analyzed by simulations.

Simulation results

In this section, we investigate the outage probability and BER performance of the network-coding-based two-way relay cooperation with energy harvesting by numerical simulations. S₁-R, S₂-R, S₂-S₁, and R-S₁ are Rayleigh block fading channels with perfect channel state information. The average SNRs per bit per antenna of the signals are defined as the ratio of transmission power P and the noise power $σ^{2}$ at the sources. BPSK modulation and MRC-based decoding algorithm are adopted. Without loss of generality, we assume $d_{12} = 4$ and $d_{1 R} = d_{2 R} = d_{12} / 2 = 2$ in the simulations.

Outage probability comparison of the proposed system and the point-to-point system

In this part, we present the outage probability performance of the proposed system with various numbers of antennas at the relay. Assume that the numbers of antennas K = 2 or 3, where the number of information decoding antennas is 1, and the number of energy-harvesting antennas K₁ = K₂ = 1 or 2. The energy utilization ratio at the relay $η = 1, 0.8, 0.6$ . The data transmission rate is referred to as the overall code rate $R_{c} = 1 / 2$ .

Figure 2 compares the outage probabilities of the proposed system and the point-to-point system. It is shown that the outage probability of the proposed system is much lower than that of the point-to-point system, and the diversity order is higher. This states that the proposed system can improve the performance without increasing the total power consumption. It is also demonstrated that the outage probability performance of the proposed system with K = 3 clearly outperforms that of the system with K = 2 under the same conditions. This can be contributed to the following fact: the more the antennas are equipped at the relay, the more the energy is harvested and the higher diversity gain is achieved with the optimal antenna selection algorithm. Figure 2 also depicts that the higher the energy utilization ratio $η$ , the lower the outage probability.

Figure 2.

Outage probability comparison of the proposed system with two or three antennas and various energy utilization ratios at the relay.

Outage probability of the proposed system with various $d_{1 R}$ , $d_{2 R}$

We investigate the effect of the relay location on the outage probability of the proposed system. Assume K = 3, K₁ = K₂ = 2, $η = 1$ , $d_{12} = 4$ , and $d_{1 R} + d_{2 R} = d_{12} (d_{1 R} \geq 1, d_{2 R} \geq 1)$ . Figure 3 shows the outage probability of the proposed system versus $d_{1 R}$ with various SNRs. It is seen that when $d_{1 R}$ is small which means the relay is close to S₁, the outage probability of the proposed system (S₁ is considered) is low. For instance, at SNR = 20 dB, when $d_{1 R}$ decreases from 2 to 1, the outage probability drops from $10^{- 5}$ to $3 \times 10^{- 7}$ . However, the relay is closer to S₁. It means the relay is further to S₂, whose outage probability will be increased. Hence, we need to decide the relay location based on the required outage probability of S₁ or S₂. The relay should be deployed closer to the user whose outage probability requires to be lower on the premise that the outage probability of the other user is satisfied.

Figure 3.

Outage probability of the proposed system versus $d_{1 R}$ with SNR = 10, 15, or 20 dB.

Outage probability of the proposed system with various antenna selection algorithms

Assuming K = 3, K₁ = K₂ = 2, and $η = 1$ , we compare the outage probability of the proposed system with the optimal antenna selection, equal power allocation algorithm,²⁷ and random antenna selection algorithm. It is shown in Figure 4 that the diversity orders of both optimal antenna selection algorithm and equal power allocation are higher than that of random antenna selection algorithm. Figure 4 also demonstrates that the outage probability of the system with the optimal antenna selection algorithm is lowest. However, these merits of the optimal antenna selection are at the cost of high implementation complexity and long time-delay. To select the optimal antenna from K antennas using optimal antenna selection algorithm, K−1 comparison times is needed. Hence, for a practical system, we should consider the trade-off between reliability performance and complexity or time-delay.

Figure 4.

Outage probability of the proposed system with the optimal antenna selection, equal power allocation algorithm, or random antenna selection algorithm at the relay.

BER of the proposed system with LDPC codes at the sources

In this part, we investigate the BER performance of the proposed system with LDPC codes. Assume K = 2 or 3, K₁ = K₂ = 1 or 2, and $η = 1$ . Random LDPC codes employed by S₁ and S₂ are with code rate $R_{c} = 1 / 2$ , code length $N = 1000$ , d_v = 3, and d_c = 6. Min-sum iterative decoding²⁸ is adopted. For fair comparison, in the point-to-point system, the same LDPC code is adopted by the node. Figure 5 shows that the BER performance of the proposed system clearly outperforms that of the point-to-point system in various decoding iterations. This significant superiority owes to the following two facts. (1) At the user, MRC-based decoding algorithm combines the two signals from S₂ and R, which are through independent fading S₂-S₁ and R-S₁ channels. (2) At the relay, multiple antennas are equipped and the optimal antenna selection is adopted. Hence, high spatial diversity gain and coding gain are achieved.

Figure 5.

BER performance of the proposed system with LDPC codes, where two or three antennas are deployed at the relay, and one or ten decoding iterations are implemented at the user.

Comparison of the proposed system and the power splitting–based system

In the proposed system, the relay adopts the antenna switching–based protocol for information decoding and energy harvesting, where some antennas are used to decode the incoming signal, and the rest antennas are used to harvest energy. In this part, we compare it with the system where the power splitting–based protocol is adopted by the relay as described in Ding et al.⁸ Random LDPC codes employed by S₁ and S₂ are the same as given in section “BER of the proposed system with LDPC codes at the sources.” Assume K = 2 and K₁ = K₂ = 1. For a fair comparison, because half of the antennas are used to harvested energy in the proposed system, we assume that half of the power for each antenna is used to harvested energy in the power splitting–based system.

Figure 6 compares the BER of the proposed system with that of the power splitting–based system with various energy utilization ratios $η$ . It is shown that BER performance of the proposed system with $η = 1$ is inferior to that of the power splitting–based system with $η = 1$ , however, superior to that of the system with $η = 0.6$ or 0.3. Actually, for the power splitting–based system, the relay needs to first split the power for information decoding and energy harvesting at each antenna and then combine the harvested energy from all antennas. Hence, compared with the proposed system, its implementation complexity is much higher and the time-delay is longer. Furthermore, it is inevitable to decrease the energy utilization ratio.

Figure 6.

BER comparison of the proposed system and the power splitting–based system with various energy utilization ratios $η$ .

Conclusion

In this article, we have studied the network-coding-based two-way relay cooperation with energy harvesting, which combines coded cooperation, network coding, and energy-harvesting technologies. It can achieve high diversity and coding gain, reduce the time slots, and overcome the dependence on the supply of battery or grid energy. An MRC-based decoding algorithm is introduced for the proposed system to combine signals from independent channels and combat the fading. When the optimal antenna selection algorithm is adopted at the relay to transmit data, the outage probability and BER of the proposed system are investigated by theoretical analysis and numerical simulations. The results show the superiority of the proposed system compared with the point-to-point system. For the relay, simulation result also shows that the performance of the scheme employing the optimal antenna selection algorithm is better than that of the random antenna selection algorithm or equal power allocation algorithm.

Footnotes

Academic Editor: Danilo De Donno

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (nos 61501256, 61271234, and 61302102), the Natural Science Foundation of Jiangsu Province (no. BK20150857), the China Postdoctoral Science Foundation (no. 2014M561694), and NUPTSF (no. 214007).

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Network-coding-based two-way relay cooperation with energy harvesting

Abstract

Keywords

Introduction

System description

MRC-based decoding algorithm for the proposed system

Performance analysis of the proposed system

Energy harvested at the relay

Signals received at the sources

Outage probability of the sources

Simulation results

Outage probability comparison of the proposed system and the point-to-point system

Outage probability of the proposed system with various d 1 R , d 2 R

Outage probability of the proposed system with various antenna selection algorithms

BER of the proposed system with LDPC codes at the sources

Comparison of the proposed system and the power splitting–based system

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References

Outage probability of the proposed system with various $d_{1 R}$ , $d_{2 R}$