Buffer-aided relaying scheme with energy harvesting in a cognitive wireless sensor network

Abstract

This article presents a practical relaying scheme that improves the outage performance of a cognitive wireless sensor network. The relays in the proposed system have finite buffers and they are self-powered by harvesting energy from the primary signal. We adopt a buffer-aided relay selection strategy that reduces overhead for exchanging the channel state information between communication nodes. In particular, a combination of the partial relay selection and the conventional max-max relay selection is proposed to obtain the benefits of both those schemes while avoiding the cases where full/empty buffers are selected to receive/forward packets with limited buffer size. The time-switching relaying protocol is exploited to harvest energy at the relays. The use of energy harvesting in the relay selection process not only prolongs the lifetime of the cognitive wireless sensor network but also improves the outage performance. A tool from Markov chain theory is implemented to model the buffer states of the relay system, which are important in determining the state transition probability. The outage probability of the secondary wireless sensor network is derived, and numerical results are provided to verify the analysis. Different relaying schemes are also compared in terms of the outage probability and average packet delay.

Introduction

Wireless sensor networks (WSNs) are considered key enablers for the Internet of Things (IoT), and these are employed over a wide range of use cases, including building management, transportation and logistics, health care, and smart grids.^1,2 In a WSN, energy efficiency is crucial because it determines the network lifetime. As such, multihop transmissions using wireless relays have been accepted as a powerful means to improve the energy efficiency of the WSNs. However, relay nodes need to consume energy to receive and forward data to other sensor nodes. Recently, wireless energy harvesting has emerged as a promising solution for sensors to obtain unlimited energy from their surrounding environment. ² Apart from the conventional renewable energy sources, such as solar and wind energy, the radio frequency (RF) energy is a viable source for energy harvesting and it has been extensively studied in recent years. ³ For multihop transmission systems, in particular, two energy harvesting protocols, namely, time-switching relaying (TSR) and power-splitting relaying (PSR) protocols, were proposed in Nasir et al. ⁴

However, the concept of a cognitive radio can be incorporated into WSNs to circumvent the limitations imposed by conventional WSNs operating in the unlicensed spectrum. ⁵ Cognitive WSN can use the spectrum of an existing system in an opportunistic manner. In particular, the cognitive WSN can access the incumbent spectrum in an underlay mode once the interference to the primary system has been limited.

Within the context of cognitive radio, wireless relaying has attracted a significant amount of attention. A max-min relay selection was proposed in Lee et al. ⁶ but without the existence of the primary source. In Yan et al., ⁷ the outage probability of the secondary system was analyzed considering the maximum power limit at the secondary transmitter. However, the impact of the primary transmitter on the secondary system was neglected. In Chen et al., ⁸ a buffer-aided relay is specifically employed in a cognitive radio system to fully exploit the spatial diversity of the channel. Nevertheless, the large amount of channel state information (CSI) overhead that is exchanged between nodes in the two subsystems for the relay selection process places a high burden on the relay system. For cognitive radio systems, relaying schemes with wireless energy harvesting were investigated in previous studies,^9,10 where the TSR protocol in Nasir et al. ⁴ was considered but without considering the interference from the primary system to the secondary system.

In this article, we consider a cognitive multihop WSN in which relay nodes have the ability to harvest energy from the primary signal. A buffer-aided relay selection scheme that incorporates full/empty buffers and the energy harvesting channel is proposed to improve the performance of the secondary WSN system. This hybrid relay selection (HRS) can alternate between the partial relay selection (PRS) scheme, which only takes the local CSI into account when selecting the best relay, and the max-max relay selection (MMRS) scheme, which allows two different relays for reception and transmission. The idea of the HRS was first proposed in Ikhlef et al., ¹¹ but only in a conventional peer-to-peer cooperative network. Note that energy harvesting would enable a self-sustained WSN, and the spatial diversity of the system is improved through the use of the energy harvesting channel in the relay selection process. With the introduction of finite buffers at the relay system, a Markov chain is used to model the state transition matrix, and the probability of being in a certain state will be obtained as a result. Then, the outage probability of the cognitive WSN will be achieved. Simulation results are provided to verify the accuracy of the analysis. The average delay of a packet due to the introduction of buffers is also discussed.

The rest of this article is organized as follows. Section “System model” describes the system model of the cognitive WSN including the energy harvesting model. Section “Relay selection” discusses the three different relay selection processes. Section “Outage probability analysis” provides an analysis of the outage probability of the cognitive WSN. Then, numerical results are presented to verify the analysis in section “Numerical results.” Finally, conclusions are drawn in section “Conclusion.”

System model

We consider a cognitive radio system model consisting of a primary system and a secondary system, as illustrated in Figure 1. The primary system comprised a primary transmitter $(T_p)$ and a primary receiver $(R_p)$ . The secondary system corresponds to a WSN which comprises a source node $(S)$ , multiple decode-and-forward (DF) relay nodes $(R_k,k=1,2,\dots ,K)$ , and a destination node $(D)$ . Each relay is equipped with a first-in first-out buffer with a size of $B$ packets. The secondary system is assumed to access the spectrum of the primary system in an underlay mode. As in Zhang et al., ¹² we assume that there is no direct link between the source and the destination nodes, which implies that the source node communicates with the destination node entirely via the relay nodes. All nodes in this system are assumed to be equipped with a single antenna and to operate in the half-duplex mode. The source node $S$ has its own power supply $P_0$ , whereas the $K$ relays harvest energy from the signal of $T_p$ using the TSR protocol. A fraction $\alpha \in [0,1]$ of the time slot $T$ is used to harvest the energy, and the remaining time slot is split into two halves. In the first half $(1-\alpha )T/2$ , the source $S$ transmits its own information to selected relays based on the chosen relay selection scheme, and a receiver node may then successfully decode the information once the signal-to-noise ratio (SNR) at the receiver node exceeds a threshold ${\gamma }_{th}$ , which can be set as ${\gamma }_{th}=2^{2R/(1-\alpha )}$ , where $R$ is the transmission rate. The best relay associated with the strongest SNR at $D$ is selected to forward the signals to $D$ , while the source $S$ remains silent in the second half period.

Figure 1.

A cognitive multihop WSN model.

All the channels between any two nodes are modeled as independent and flat Rayleigh fading channels. Accordingly, the channel gain $g_{mn}$ for the channel between node $m$ and node $n$ will follow an exponential distribution with the probability density function (PDF) given as

$$f_{g_{mn}}(g)=\frac{1}{{\lambda }_{mn}}{\exp }^{-\frac{g}{{\lambda }_{mn}}}$$ (1)

where ${\lambda }_{mn}\stackrel{\mathrm{\Delta }}{=}1/E[g_{mn}]$ . The noise at each receiver is assumed to be additive white Gaussian noise (AWGN) with distribution $\mathcal{C}\mathcal{N}(0,{\sigma }^2)$ . The amount of energy harvested at the relay $R_k$ is given as

$$E_{R_k}=\eta P{g}_{T_p{R}_k}\alpha T$$ (2)

where $P$ is the transmit power of $T_p$ and $\eta$ ( $0<\eta \le 1$ ) is the energy conversion efficiency. To avoid excessive interference to $R_p$ in the primary system, the interference power from the source $S$ to $R_p$ in the first hop, as well as the interference power from $R_k$ to $R_p$ , should be less than the interference threshold $I$ at $R_p$ . In reality, however, the amount of energy harvested from the primary signal will be quite limited due to a typically low harvesting efficiency. ³ It will result in low transmit power and hence short transmission range. Besides, the harvesting zone can be assumed to be much smaller than the transmission coverage of the primary system.^3,13 As a result, along with the path loss, we can assume that the interference from the relays to the $R_p$ can be neglected. Therefore, the maximum transmit power at the source $S$ and at the relay $R_k$ is given as $P_S=min(P_0,I/g_{S{R}_p})$ and $P_{R_k}=\rho P{g}_{T_p{R}_k}$ , respectively, where $\rho \stackrel{\mathrm{\Delta }}{=}2\eta \alpha /(1-\alpha )$ .

Relay selection

PRS

Let ${\gamma }_{S{R}_k}$ and ${\gamma }_{R_{k}D}$ $(k=1,2,\dots ,K)$ denote the SNR at $R_k$ in the first hop and the SNR at $D$ in the second hop, respectively, and then we have

$${\gamma }_{S{R}_k}=\frac{P_S{g}_{S{R}_k}}{P{g}_{T_p{R}_k}+{\sigma }^2},{\gamma }_{R_{k}D}=\frac{P_{R_k}{g}_{R_{k}D}}{P{g}_{T_{p}D}+{\sigma }^2}$$ (3)

It should be noted that the SNRs at the relays in an underlay cognitive radio are correlated due to the same interference constraint at $R_p$ . Similarly, with the same interference from $T_p$ , the received SNRs at $D$ are also correlated. Therefore, to adopt the conventional max-min selection method in Zhang et al., ¹² the global CSI between the primary and secondary systems must be obtained at all relays. This will result in a large burden and overhead in the relay selection process.

The PRS proposed in this article can be implemented without considering the common interference from the primary network. Consequently, only the local CSI is required. Note that it can be easily obtained by estimating the signal strength of the request-to-send (RTS) and clear-to-send (CTS) packets as presented in Bletsas et al. ¹⁴ A relay is selected from a set of relays that have successfully decoded the message from $S$ . In addition, the spatial diversity from the energy harvesting channel is also considered as a metric to determine the best relay. Let $\mathcal{R}(n)\subset \{R_1,R_2,\dots ,R_K\}$ be the set of relays that successfully decoded the message from $S$ , where $n=|\mathcal{R}(n)|$ denotes the cardinality of the set. The best relay $R_{k^{*}}$ is determined as

$$k^{*}=argma{x}_{k\in \mathcal{R}(n)}\left[\rho P{g}_{T_p{R}_k}{g}_{R_{k}D}\right]$$ (4)

MMRS

With the introduction of buffers at the relays, the relay selection process can choose two different relays for reception and transmission. The outage performance will benefit from the significant increase in the coding gain of this scheme. ¹¹ We assume that each buffer has contained a certain number of packets that would be dedicated to the handshake process between the nodes in the initial phase, and the best relays for reception and transmission are, respectively, determined as

$$k_r^{*}=\underset{k\in \{1,2,\dots ,K\}}{\arg \max }{\gamma }_{S{R}_k}\mathrm{and}{k}_t^{*}=\underset{k\in \{1,2,\dots ,K\}}{\arg \max }{\gamma }_{R_{k}D}$$ (5)

Nevertheless, under a practical assumption of finite buffers, ¹⁵ the scenarios with a full or empty buffer are possible for which the selected relays cannot receive or transmit data. To tackle this problem, a hybrid selection combining the benefits of the two relaying schemes mentioned above will be implemented.

HRS

Let $B_{f,k}$ denote the number of occupied elements in the buffer of the kth relay. The HRS scheme will prioritize the use of MMRS due to its advantage in coding gain. To avoid the full/empty buffer scenarios, the PRS scheme in equation (3) is utilized as an alternative to the MMRS, if

$$B_{f,k_r^{*}}=B-1\mathrm{or}{B}_{f,k_t^{*}}=0$$ (6)

To enable the capability of the alternation process, the status of buffers at the relays is considered as the criterion in the HRS scheme (in Bletsas et al., ¹⁴ short flag packets, which contain information on the estimated CSI, are exchanged among relay nodes to help relay selection. The information on the buffer state may be added to these flag packets in the proposed scheme). To ensure that relay nodes are always able to receive a data packet in the case that the PRS scheme is chosen in the next transmission interval, we need to leave one empty element in the buffer. This is the reason why the buffer is considered full when $B-1$ rather than $B$ entities are occupied in equation (6).

Outage probability analysis

Markov chain model

Due to the involvement of two different relay selection schemes, the outage probability of the secondary system is calculated by obtaining the probability of using MMRS or PRS beforehand. To do that, we first model the state transition matrix $S$ as a Markov chain, which also displays the number of possible states $N_s$ of the relay systems. Let $S_k=\{B_{f,1},B_{f,2},\dots ,B_{f,K}\}$ be the kth state, where $B_{f,k}$ $(k=1,2,\dots ,K)$ represents the number of occupied elements in the kth buffer. Note that the total number of occupied elements at the relay system will remain unchanged after the initial phase because one packet will leave the relay after another one enters a selected buffer at the selected relay for reception. Denote the total number of occupied elements as $N_t$ , and a possible state $S_k$ must satisfy the following two conditions

$$\begin{array}{c}{\displaystyle \sum }_{k=1}^K{B}_{f,k}=N_t\hfill \\ 0\le B_{f,k}\le B-1,k=1,2,\dots ,K\hfill \end{array}$$ (7)

In general, the Markov state transition matrix $S$ will be expressed as

$$S=\left[\begin{array}{cccc}\hfill p_{11}\hfill & \hfill p_{12}\hfill & \hfill \dots \hfill & \hfill p_{1N_s}\hfill \\ \multicolumn{1}{c}{⋮}& \hfill ⋮\hfill & \hfill \ddots \hfill & \hfill ⋮\hfill \\ \multicolumn{1}{c}{p_{N_{s}1}}& \hfill p_{N_{s}2}\hfill & \hfill \dots \hfill & \hfill p_{N_s{N}_s}\hfill \end{array}\right]$$

where $p_{ij}$ denotes the probability for the transition from state $S_j$ to state $S_i$ . Apparently, there are $K^2$ choices for a successful transmission from $S$ to $D$ through the relay system due to the independent and identically distributed (i.i.d.) fading channels between nodes in the secondary system. Therefore, the state transition probability for a possible transmission is equal to $1/K^2$ . Note that if there is a transition from $S_j$ to $S_i$ , the possibility of a reverse transition will exist. Besides, the state of the relay system will remain unchanged in the case of an outage transmission or of the same relay selected for both reception and transmission. Consequently, the matrix $S$ is a symmetric matrix. As a Markov chain, the state transition matrix $S$ will be a doubly stochastic matrix (a doubly stochastic matrix is a square matrix in which the sum of the elements in each of its columns and rows is equal to 1). ¹⁶ As a result, the stationary distribution of matrix $S$ is uniform, ¹⁶ meaning that the probability of being in any state of $N_s$ states will be $1/N_s$ . Besides, in a given state $S_k$ , we have $P_{\mathrm{PRS},k}=1-P_{\mathrm{MMRS},k}$ . Hence, the probabilities of using the PRS and MMRS schemes are obtained as

$$P_{\mathrm{PRS}}=\frac{1}{N_s}\sum _{k=1}^K{P}_{\mathrm{PRS},k}$$ (8)

and

$$P_{\mathrm{MMMS}}=\frac{1}{N_s}\sum _{k=1}^K(1-P_{\mathrm{MMRS},k})$$ (9)

In a given state $S_k$ , let us denote the number of full $(B_{f,k}=B-1)$ and empty buffers as $N_{F,k}$ and $N_{E,k}$ , respectively $(0\le N_{F,k},N_{E,k}\le K)$ . Over $K^2$ selections for a state transition under the MMRS scheme, there would be $N_{F,k}\times K$ choices in which the buffers of the relays for reception are full, while $(K-N_{F,k})\times N_{E,k}$ selections have empty buffers. Hence, the PRS scheme will be resorted if one of these relays is selected for reception or transmission. Consequently, the probability of using PRS in state $S_k$ is given as

$$P_{\mathrm{PRS},k}=\frac{(K-N_{F,k})N_{E,k}+K{N}_{F,k}}{K^2}$$ (10)

Remark 1

In general, for a given $K$ , $B$ , and $N_t$ , the number of possible states $N_s$ can be algorithmically achieved as the number of possible combinations of $B_{f,1}{B}_{f,2}\dots B_{f,K}$ that meet the constraints in equation (7). Then, the values of $N_{f,k}$ and $N_{E,k}$ can be easily derived. Accordingly, $P_{\mathrm{PRS},k}$ can be obtained as in equation (10). In particular, for $K=2$ and $K=3$ , the closed form of $N_s$ is, respectively, given as equation (11)

$$N_s=(\begin{array}{cc}\hfill N_t+1,\hfill & \hfill \mathrm{if}{N}_t\le B-1\hfill \\ \multicolumn{1}{c}{2B-N_t-1,}& \hfill \mathrm{otherwise}\hfill \end{array}$$ (11)

and

$$N_s=\sum _{k=(N_t-B{)}^{+}+1}^{N_t+1}(k-2(k-B{)}^{+}{)}^{+}$$ (12)

$$\mathrm{where}(x{)}^{+}\stackrel{\mathrm{\Delta }}{=}\max (0,x).$$

Outage probability of PRS scheme

$A(n)$ is defined to be an event that the strongest received SNR at $D$ , that is, ${\gamma }_{R_{k^{*}}D}$ , is less than the threshold SNR ${\gamma }_{th}$ , under the condition that the $R_{k^{*}}$ has been selected. The probability of this event is calculated as

$$\begin{array}{c}\mathrm{Pr}(A(n))=\mathrm{Pr}({\gamma }_{R_{k^{*}}D}\le {\gamma }_{th}|k^{*}=\arg \mathrm{ma}{\mathrm{x}}_{k\in \mathcal{R}(n)}({\gamma }_{R_{k}D}))\hfill \\ =\mathrm{Pr}[{\displaystyle \bigcap }_{k\in \mathcal{R}(n)}{\gamma }_{S{R}_k}\ge {\gamma }_{th},{\displaystyle \bigcap }_{k\notin \mathcal{R}(n)}{\gamma }_{S{R}_k}<{\gamma }_{th},{\gamma }_{R_{k^{*}}D}\le {\gamma }_{th}]\hfill \end{array}$$ (13)

$$\begin{array}{c}\multicolumn{1}{c}{\mathrm{Pr}(A(n))=E_z[\mathrm{Pr}\left({\displaystyle \bigcap }_{k\in \mathcal{R}(n)}(\frac{P_0{g}_{S{R}_k}}{y_k+{\sigma }^2}\ge {\gamma }_{th},\frac{\rho y_k{g}_{R_{k}D}}{z+{\sigma }^2}<{\gamma }_{th})\right)\underset{k=1,k\notin \mathcal{R}(n)}{\overset{K-n}{\Pi }}\mathrm{Pr}(\frac{P_0{g}_{S{R}_k}}{y_k+{\sigma }^2}<{\gamma }_{th})\mathrm{Pr}(P_0<\frac{I}{g_{S{R}_p}})}\\ +E_{g_{S{R}_p}}\left(\mathrm{Pr}\left({\displaystyle \bigcap }_{k\in \mathcal{R}(n)}(\frac{I{g}_{S{R}_k}}{g_{S{R}_p}(y_k+{\sigma }^2)}\ge {\gamma }_{th},\frac{\rho y_k{g}_{R_{k}D}}{z+{\sigma }^2}<{\gamma }_{th})\right)\underset{k=1,k\notin \mathcal{R}(n)}{\overset{K-n}{\Pi }}\mathrm{Pr}(\frac{I{g}_{S{R}_k}}{g_{S{R}_p}(y_k+{\sigma }^2)}<{\gamma }_{th})\right)]\hfill \end{array}$$ (14)

$$P_1(n)={\left[\frac{1}{P{\lambda }_{T_p{R}_k}}(\frac{1}{{\varphi }_1}-\sqrt{\frac{\beta }{{\varphi }_1}}{K}_1(\sqrt{\beta {\varphi }_1}))\right]}^n{[1-\frac{\theta }{{\varphi }_1}]}^{K-n}[1-{\exp }^{\frac{-I}{P_0{\lambda }_{S{R}_p}}}]$$ (15)

$$P_2(n)=E_{g_{S{R}_p}}\left[{\left[\frac{1}{P{\lambda }_{T_p{R}_k}}\right]}^K{\exp }^{\frac{-n{\gamma }_{th}{g}_{S{R}_p}{\sigma }^2}{I{\lambda }_{S{R}_k}}}{[\frac{1}{{\varphi }_2}-\sqrt{\frac{\beta }{{\varphi }_2}}{K}_1(\sqrt{\beta {\varphi }_2})]}^n{[P{\lambda }_{T_p{R}_k}-\frac{{\exp }^{\frac{-{\gamma }_{th}{g}_{S{R}_p}{\sigma }^2}{I{\lambda }_{S{R}_k}}}}{{\varphi }_2}]}^{K-n}\right]$$ (16)

Let $y_k\stackrel{\mathrm{\Delta }}{=}P{g}_{T_p{R}_k}$ and $z\stackrel{\mathrm{\Delta }}{=}P{g}_{T_{p}D}$ , then the PDF of the random variables $y_k$ and $z$ can be easily obtained. Conditioning on the common interference from $T_p$ to $D$ in $z$ , we can expand equation (13) as equation (14). Let $P_1(n)$ and $P_2(n)$ , respectively, denote the first and the second terms in equation (14). Equations (15) and (16) are the exact expressions for $P_1(n)$ and $P_2(n)$ , where $\beta \stackrel{\mathrm{\Delta }}{=}4{\gamma }_{th}(z+{\sigma }^2)/\rho {\lambda }_{R_{k}D}$ , ${\varphi }_1\stackrel{\mathrm{\Delta }}{=}{\gamma }_{th}/P_0{\lambda }_{S{R}_k}+1/P{\lambda }_{T_p{R}_k}$ , ${\varphi }_2\stackrel{\mathrm{\Delta }}{=}{\gamma }_{th}{g}_{S{R}_p}/I{\lambda }_{S{R}_k}+1/P{\lambda }_{T_p{R}_k}$ , and $\theta \stackrel{\mathrm{\Delta }}{=}(1/P{\lambda }_{T_p{R}_k}){\exp }^{-({\gamma }_{th}{\sigma }^2/P_0{\lambda }_{S{R}_k})}$ , and $K_1(·)$ is the first-order modified Bessel function of the second kind. ¹⁷ The derivations of equations (15) and (16) also use the formula ${\int }_0^{\infty }{\exp }^{-(\beta /4x)-\varphi x}dx=\sqrt{\beta /\varphi }{K}_1(\sqrt{\beta \varphi })$ . As a result, equation (13) can be expressed as Lemma 1, and the corresponding outage probability can be derived as Theorem 1.

Lemma 1

The probability in equation (13) is given as

$$\mathrm{Pr}(A(n))={\int }_0^{\infty }(P_1(n)+P_2(n))f_z(z)dz$$ (17)

Proof

Relieving the conditioning on $z$ in $P_1(n)$ and $P_2(n)$ derived in equations (15) and (16), we obtain the result in equation (17).

Theorem 1

The outage probability of the secondary system is obtained as

$$P_{out}^{\mathrm{PRS}}=\sum _{n=0}^K\left(\begin{array}{c}\hfill K\hfill \\ \multicolumn{1}{c}{n}\end{array}\right)\mathrm{Pr}(A(n))$$ (18)

Proof

Note that the outage event is the union of $K$ mutually exclusive events $A(1),A(2),\dots ,A(K)$ . Therefore, the outage probability of the secondary system can be computed using the total probability theorem as equation (18).

Outage probability of MMRS scheme

With ${\gamma }_{S{R}_{k_r^{*}}}$ and ${\gamma }_{R_{k_t^{*}}D}$ determined as in equation (5), the outage probability under the MMRS scheme in a DF relay system is given as

$$P_{out}^{\mathrm{MMRS}}=P(\min \{{\gamma }_{S{R}_{k_r^{*}}},{\gamma }_{R_{k_t^{*}}D}\}\le {\gamma }_t)$$ (19)

By conditioning on $y_k$ $(k=1,2,\dots ,K)$ , equation (19) can be expressed as

$$\begin{array}{c}{P}_{out}^{\mathrm{MMRS}}=1-E_{y_1,y_2,\dots ,y_K}[\mathrm{Pr}({\gamma }_{S{R}_{k_r^{*}}}\ge {\gamma }_t)\mathrm{Pr}({\gamma }_{R_{k_t^{*}}D}\ge {\gamma }_t)]\hfill \\ =E_{y_1,y_2,\dots ,y_K}[\mathrm{Pr}(U)+\mathrm{Pr}(V)-\mathrm{Pr}(U)\mathrm{Pr}(V)]\hfill \end{array}$$ (20)

where $U\stackrel{\mathrm{\Delta }}{=}\{{\gamma }_{S{R}_{k_r^{*}}}<{\gamma }_t\}$ and $V\stackrel{\mathrm{\Delta }}{=}\{\mathrm{Pr}[{\gamma }_{R_{k_r^{*}}D}<{\gamma }_t]\}$ . We have

$$\begin{array}{c}\multicolumn{1}{c}{\mathrm{Pr}(U)=\mathrm{Pr}[\frac{\min [\frac{I}{g_{S{R}_{k_r^{*}}}},P_0]g_{S{R}_{k_r^{*}}}}{y_{k_r^{*}}+{\sigma }^2}<{\gamma }_t]}\\ =\mathrm{Pr}[\frac{I}{g_{S{R}_{k_r^{*}}}}\ge P_0]\mathrm{Pr}(\frac{P_0{g}_{S{R}_{k_r^{*}}}}{y_k+{\sigma }^2}<{\gamma }_t)\hfill \\ +\underset{\frac{I}{P_0}}{\overset{\infty }{\int }}\mathrm{Pr}(\frac{I{g}_{S{R}_{k_r^{*}}}}{g_{S{R}_{k_r^{*}}}(y_k+{\sigma }^2)}<{\gamma }_t)f_{g_{S{R}_p}}(g_{S{R}_p})d{g}_{S{R}_p}\hfill \end{array}$$ (21)

Note that if the channel of the best relay for reception fails, that is, ${\gamma }_{S{R}_{k_r^{*}}}\le {\gamma }_t$ , the other channels from $S$ to any relay will also be in an outage. Therefore, relieving the condition on $y_1,y_2,\dots ,y_K$ , we obtain

$$\begin{array}{c}\multicolumn{1}{c}{E_{y_1,y_2,\dots ,y_K}[\mathrm{Pr}(U)]={[1-\frac{\theta }{{\varphi }_1}]}^K[1-{\exp }^{\frac{-I}{P_0{\lambda }_{S{R}_p}}}]}\\ +\underset{\frac{I}{P_0}}{\overset{\infty }{\int }}{[1-\frac{{\theta }_2}{{\varphi }_2}]}^K{f}_{g_{S{R}_p}}(g_{S{R}_p})d{g}_{S{R}_p}\hfill \end{array}$$ (22)

where ${\theta }_2\stackrel{\mathrm{\Delta }}{=}(1/P{\lambda }_{T_p{R}_k}){\exp }^{(-{\gamma }_{th}{g}_{S{R}_p}{\sigma }^2/I{\lambda }_{S{R}_k})}$

Similarly, we also have

$$\mathrm{Pr}(V)=\frac{\rho y_{k_r^{*}}{g}_{R_{k_t^{*}}D}}{z+{\sigma }^2}$$ (23)

By relieving on $y_1,y_2,\dots ,y_K$ and conditioning on the interference channel gain $z$ from the primary transmitter $T_p$ , we obtain the second part of equation (20) as

$$E_{y_1,y_2,\dots ,y_K}[\mathrm{Pr}(V)]=\underset{\frac{I}{P_0}}{\overset{\infty }{\int }}{(1-\frac{1}{{\varphi }_3}\sqrt{\frac{\beta }{{\varphi }_3}}{K}_1\sqrt{\beta {\varphi }_3})}^K{f}_z(z)dz$$ (24)

where ${\varphi }_3\stackrel{\mathrm{\Delta }}{=}1/{\lambda }_{T_p{R}_k}$ . Following similar derivations as above, the third part of equation (20) is achieved as in equation (25). Then, substituting above results into equation (20), we will obtain $P_{out}^{\mathrm{MMRS}}$

$$\begin{array}{c}{E}_{y_1,y_2,\dots ,y_K}[\mathrm{Pr}(U)\mathrm{Pr}(V)]=E_z[(1-{\varphi }_3\sqrt{\frac{\beta }{{\varphi }_3}}{K}_1\sqrt{\beta {\varphi }_3}-\frac{\theta }{{\varphi }_1}+\theta \sqrt{\frac{\beta }{{\varphi }_1}}{K}_1\sqrt{\beta {\varphi }_1}{)}^K[1-{\exp }^{\frac{-I}{P_0{\lambda }_{S{R}_p}}}]\hfill \\ +\underset{\frac{I}{P_0}}{\overset{\infty }{\int }}{(1-{\varphi }_3\sqrt{\frac{\beta }{{\varphi }_3}}{K}_1\sqrt{\beta {\varphi }_3}-\frac{{\theta }_2}{{\varphi }_2}+{\theta }_2\sqrt{\frac{\beta }{{\varphi }_2}}{K}_1\sqrt{\beta {\varphi }_2})}^K\times f_{g_{S{R}_p}}(g_{S{R}_p})d{g}_{S{R}_p}]\hfill \end{array}$$ (25)

Outage probability of the secondary system

With the probabilities of using PRS and MMRS schemes given in equations (8) and (9) along with the corresponding outage probabilities in equations (18) and (19), the outage probability of the secondary system is given in Lemma 2.

Lemma 2

The outage probability of the secondary network is given as

$$P_{out}=P_{\mathrm{MMRS}}{P}_{out}^{\mathrm{MMRS}}+P_{\mathrm{PRS}}{P}_{out}^{\mathrm{PRS}}$$ (26)

Numerical results

In this section, we investigate the impact of the energy harvesting process as well as that of the hybrid buffer-aided relay scheme on the outage performance of the cognitive sensor network. Both analytical results and simulation results are presented to verify the analysis, and a comparison of the performance of the secondary network under the HRS scheme to that under MMRS and PRS schemes is also presented. The nodes $S$ , $R_k(k=1,2,\dots ,K)$ , $D$ , $R_p$ , and $T_p$ are assumed to be located at $(0,0)$ , $(0,1)$ , $(0,2)$ , $(0,1.5)$ , and $(1,1.5)$ , respectively, on the xy-plane. The path loss effect with a path loss exponent of 4 will also be taken into account. The transmission rate of the secondary system is set as $R=0.5\mathrm{bps}/\mathrm{Hz}$ , and the noise variance and the energy harvesting efficiency are assumed to be ${\sigma }^2=0.1$ and $\eta =0.6$ , respectively. The interference threshold $I$ at the primary receiver is assumed to be 1.5 dB. We assume that half of each buffer at the relay is occupied by data packets, that is, $B_k=\lfloor B/2\rfloor$ , where $\lfloor x\rfloor$ denotes the largest integer less than or equal to $x$ .

In Figure 2, the influence of the energy harvesting period $\alpha$ on the outage probability of the secondary system is considered with the PRS and HRS schemes. The value of $\alpha$ is varied within the range $[0.1,0.7]$ . The transmit power at the source $S$ is fixed to 2.5 dB. Let the buffer size $B$ of each relay be equal to 20 and investigate the outage performance with $K=3$ and $8$ . Looking at Figure 2, we can see that more energy is harvested at the relays as $\alpha$ increases. Therefore, the transmit power at $R_{k^{*}}$ becomes higher, and as a result, $P_{out}$ is shown to decrease. However, we also observe from Figure 2 that $P_{out}$ only decreases as $\alpha$ increases until a certain point, and after that point, $P_{out}$ begins to increase. This can be explained by the trade-off between the energy harvesting period and the data transmission period. To be more specific, if the relays spend more time on the energy harvesting process, which leads to more energy being harvested, the time for the data transmission will be shortened. In contrast, if less power is harvested at the relays with less time for energy harvesting, more time will be used to transmit data. From Figure 2, we can also confirm that the outage probability decreases as the number of relays increases. Besides, the performance of the secondary system with the HRS scheme is notably superior to that with the PRS scheme.

Figure 2.

Outage probability versus the time fraction for energy harvesting $(\alpha )$ .

Figure 3 illustrates how the outage probability varies with the secondary transmit power $P_0$ at the source. The outage performance is seen to improve as the secondary transmit power $P_0$ increases. The floors in the high $P_0$ regime can be explained as follows. Due to the interference constraint at the primary system, the secondary transmit power $P_S$ has to satisfy $P_S=min(P_0,(I/g_{S{R}_p}))$ , as discussed in section “System model.” It may restrict the actual transmit power, resulting in the floors in Figure 3.

Figure 3.

Outage probability versus $P_0$ .

Figure 4 shows the impact of the primary transmit power $P$ on the outage probability of the secondary sensor network. An increase in $P$ will increase the amount of energy harvested at the relays and also increase the interference from the primary transmitter to the secondary receiver. In Figure 4, we can see the trade-off between the two conflicting effects on the outage probability.

Figure 4.

Outage probability versus $P$ .

In Figure 5, we investigate the relationship between the outage probability of the WSN and the buffer size with $K=3$ . Figure 5 shows that the outage performance of the network with the HRS scheme gradually approaches that with the MMRS scheme, which is equipped with an infinite buffer size. In particular, for the buffers with a size larger than 30, the outage probability with HRS is closely matched by that with the MMRS scheme. In addition, at $B=1$ , the HRS will stick to the PRS scheme, and therefore, the outage probability is the same as that of the PRS scheme. We also observe that the analytical results for the HRS outage probability are in exact agreement with the simulation results.

Figure 5.

Outage probability versus buffer size $B$ .

Figure 6 presents the average delay of the data packets die to the intrinsic use of the buffer-aided relaying scheme. Note that a packet is considered as a delayed packet if it cannot be transmitted in the next period of $((1-\alpha )T)/2$ after entering the buffer of the relay selected for reception. In this case, the average delay will be calculated as the number of necessary transmission time intervals for a packet to reach its destination. Figure 5 shows that the average delay increases as the number of relays increases. This could be explained by the increase in the number of options for relaying, which results in a longer period for which a packet is stored in the relay. Additionally, the average delay is also seen to grow as the buffer size increases. Note that the order of the information can be added to the preamble of each packet for destination $D$ to reconstruct the original signals transmitted by $S$ . It is important to mention that for a low-power WSN with $K=3$ or $4$ , a buffer size of 30 will result in an average delay of roughly 50 to 100 transmission time intervals.

Figure 6.

Average delay of a data packet.

Conclusion

This article presented a hybrid relaying scheme to exploit the benefits of the buffer-aided relay to improve the performance of a cognitive WSN with energy harvesting capabilities. Apart from the advantage of a longer lifetime as a result of the energy harvesting, the burden of information exchange among the nodes in the relay selection of the conventional cognitive network was also relaxed with the introduction of a PRS scheme. An increase in the coding gain of the HRS scheme due to the MMRS resulted in a significant improvement in the outage performance of the system compared to the conventional PRS scheme. The analytical expression for the outage probability of the secondary WSN was also derived and verified through simulations. It was shown that the average delay would be kept under an acceptable level with appropriate buffer size and order information appended to each data packet.