J. Cent. South Univ. (2018) 25: 2626-2640

DOI: https://doi.org/10.1007/s11771-018-3941-2

Bidirectional secondary transmissions with energy harvesting in cognitive wireless sensor networks

TANG Kun(唐锟)¹, SHI Rong-hua(施荣华)¹, ZHANG Ming-ying(张明英)²,SHI He-yuan(施鹤远)³, LEI Wen-tai(雷文太)¹

1. School of Information Science and Engineering, Central South University, Changsha 410083, China;

2. China Electronics Standardization Institute, Beijing 100007, China;

3. School of Software, Tsinghua University, Beijing 100084, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: To the existing spectrum sharing schemes in wireless-powered cognitive wireless sensor networks, the protocols are limited to either separate the primary and the secondary transmission or allow the secondary user to transmit signals in a time slot when it forwards the primary signal. In order to address this limitation, a novel cooperative spectrum sharing scheme is proposed, where the secondary transmission is multiplexed with both the primary transmission and the relay transmission. Specifically, the process of transmission is on a three-phase time-switching relaying basis. In the first phase, a cognitive sensor node SU₁ scavenges energy from the primary transmission. In the second phase, another sensor node SU₂ and primary transmitter simultaneously transmit signals to the SU₁. In the third phase, the node SU₁ can assist the primary transmission to acquire the opportunity of spectrum sharing. Joint decoding and interference cancellation technique is adopted at the receivers to retrieve the desired signals. We further derive the closed-form expressions for the outage probabilities of both the primary and secondary systems. Moreover, we address optimization of energy harvesting duration and power allocation coefficient strategy under performance criteria. An effective algorithm is then presented to solve the optimization problem. Simulation results demonstrate that with the optimized solutions, the sensor nodes with the proposed cooperative spectrum sharing scheme can utilize the spectrum in a more efficient manner without deteriorating the performance of the primary transmission, as compared with the existing one-directional scheme in the literature.

Key words: cooperative transmission; cognitive wireless sensor network; time-switching relaying; wireless energy harvesting; joint optimization

Cite this article as: TANG Kun, SHI Rong-hua, ZHANG Ming-ying, SHI He-yuan, LEI Wen-tai. Bidirectional secondary transmissions with energy harvesting in cognitive wireless sensor networks [J]. Journal of Central South University, 2018, 25(11): 2626–2640. DOI: https://doi.org/10.1007/s11771-018-3941-2.

1 Introduction

With the rapid development of the Internet of Things (IoT), wireless sensor networks (WSN) are considered one of the most important facilitators, which is widely employed in healthcare, agriculture, and environmental monitoring [1–5]. However, a serious problem of overwhelming demand on radio spectrum has occurred with the increasing use of IoT devices and the assigned spectrums are often under-utilized due to the inflexible spectrum policy [6–9]. In order to efficiently utilize the spectrum resources, cognitive radio (CR) techniques have been adopted into WSNs to overcome the limitations of conventional WSNs operating in unlicensed spectrum [10–13]. Furthermore, in some certain extreme circumstances, wireless sensor nodes are difficult to be equipped with a continuous power supply or not easy to replace the battery. Wireless energy harvesting (WEH) techniques have been widely considered promising solutions to significantly prolong the lifecycle of WSNs [14–16]. In particular, energy can be replenished from the environmental resources, such as solar, wind or radio frequency (RF) signals. For the majority of wireless transmission scenarios, the energy harvesting based on RF signal is more attractive due to its wireless, readily available, low cost, and small form factor implementation [17, 18]. Thus, combining CR with WEH techniques can effectively improve spectral efficiency while realizing green communication.

1.1 Related works

Although the amount of energy for non-intended RF energy harvesting is in milli-watts, it is sufficient for powering the low-energy wireless nodes, such as short-range sensor networks [19]. For high-energy requirement networks, the dedicated power beacons are intended to provide RF energy signal for WSNs [20]. Furthermore, a distinct advantage of RF energy harvesting is that both the information and energy can be carried simultaneously by the RF signals. Thus, simultaneous wireless information and power transfer (SWIPT) scheme has been paid much attention in the field of wireless-powered WSNs [21, 22].

Considering the cognitive WSNs with the SWIPT scheme, the radiated RF signals from the primary users (PUs) can be treated as sources not only for transmitting data but also for supplying energy to secondary users (SUs)/sensors, and then, the SUs/sensors utilize the harvested energy to perform cognitive transmissions. In Refs. [23, 24], two optimal spectrum sensing and access policies were respectively proposed to maximize the total throughput under the energy causality and collision constraints. In Ref. [25], an optimal mode selection strategy was presented for RF energy harvesting cognitive WSNs to improve the system performance. The authors in Ref. [26] proposed a 2-D spectrum sensing and harvested energy estimating scheme to improve the performance of wireless-powered cognitive WSNs. A continuous- time energy harvesting scheme was proposed in Ref. [27] for a wireless sensor network, where an energy-constrained sensor node as a relay employed time-switching relaying protocol or power-splitting relaying protocol to achieve cooperative cognitive transmission.

In contrast to the previous works [23–27], where the SUs can access the licensed spectrum for the primary transmission in an opportunistic manner, it was investigated that the SUs can be act as relays to achieve spectrum sharing in wireless-powered CR networks in Refs. [28–31]. The throughput maximization of the system was studied in Refs. [28, 29], where an energy harvesting-enabled SU serves as a relay to scavenge energy from the primary transmission, while forwarding primary information together with its own transmission. In Ref. [30], the authors considered the relay equipped with multiple antennas to harvest energy from two PUs. Then it utilized the harvested energy to facilitate cognitive transmission. In a wireless- powered cooperative CR network, where the SUs were the potential eavesdroppers, the authors jointly designed a power splitting coefficient and secure beamforming to guarantee the security of the primary confidential information [31].

1.2 Motivation and contribution

In all above mentioned literatures, a common characteristic is that the SUs/sensors only can be allowed to access the primary spectrum during the cognitive transmission phase. However, for some applications of combining the CR networks with sensors in Internet of Things (IoT), the sensors intend to exchange data with each other. Therefore, we develop a novel cooperative spectrum sharing scheme for wireless-powered cooperative cognitive WSNs. In this scheme, an energy-constraint sensor SU₁ harvests energy from the transmission of primary transmitter (PT) firstly, then it assists the PT to forward information while the sensors SU₁ and SU₂ are intended to exchange information, namely, the sensors not only scavenge energy but also effectively utilize the spectrum opportunities in both the primary and cognitive transmission phases. The main contributions are summarized as follows:

1) We develop a cooperative spectrum sharing scheme with bidirectional secondary transmissions for wireless-powered cooperative cognitive WSNs. Specifically, the time-switching relaying (TSR) protocol is adopted and the transmission process can be divided into three stages. In the first stage, a dedicated time-slot is used for WEH at the sensor SU₁. In the second stage, the PT and the sensor SU₂ are allowed to simultaneously transmit data. Meanwhile, the primary receiver (PR) can also receive data from SU₂ for interference cancellation. In the third stage, the SU₁ forwards the PT’s information and its own data together when the signal of SU₂ is decoded correctly by the SU₁ in the second stage. Otherwise, only the primary signal will be retransmitted by treating the SU₂’s data as interference which will be removed at the PR.

2) We present exact closed-form expressions for the outage probabilities of both the primary and secondary systems by analyzing three possible scenarios for data transmission in the third phase. Derived outage probabilities reveal that a suitable energy harvesting duration and a power allocation coefficient enable the proposed scheme achieving a better throughput performance of the secondary system compared with other scheme.

3) We formulate an optimization problem with the purpose of minimizing the outage probability of the secondary system while guaranteeing the primary outage performance. A corresponding optimal algorithm is designed to derive the sub-optimal WEH duration and power allocation factor.

The rest of this paper is organized as follows. Section 2 describes the system model and introduces the spectrum sharing scheme. In Section 3, we analyze the outage probabilities of both the primary and secondary systems. A jointly optimizing algorithm based on minimizing the outage probability of the secondary system is proposed in Section 4. Section 5 presents the numerical and simulation results. The conclusion of this paper is provided in Section 6.

2 Spectrum sharing scheme

2.1 System model

Consider a wireless-powered cooperative cognitive WSN with bidirectional secondary transmission as shown in Figure 1, where a pair of primary users coexist with a pair of secondary users/sensors. For the primary system, a PT intends to deliver signals to other PR with target rate r_p. We assume that the direct path between the PT and PR does not exist due to large propagation loss and shadowing, thus the PT communicates with the PR assisted by a nearby sensor node SU₁. In return, sensor nodes SU₁ and SU₂ are allowed to utilize the licensed primary spectrum to communicate in a bidirectional manner. However, the cooperation is infeasible when the SU₁ is an energy-constrained node. Thus, the SU₁ should have the capability to harvest RF energy. All terminals are assumed to have a single omnidirectional antenna and a half-duplex operation is applied here.

We assume that the PT and SU₂ have constant power supplying with P_p and P₂, respectively, whereas the node SU₁ does not, and it thus needs to harvest energy from the PT’s RF signals. Assume that all channels undergo quasi-static Rayleigh block fading, that is, the channel coefficients remain unchanged over a time slot T, and independent and identically distributed between different time slots. Let h₁, h₂, h₃ and h₄ denote the channel coefficients between PT and SU₁, SU₁and SU₂, SU₁ and PR, and SU₂ and PR, respectively. The channel coefficient gains |h₁|², |h₂|², |h₃|² and |h₄|² are exponentially distributed with mean v₁, v₂, v₃, and v₄, respectively.

Figure 1 Wireless-powered cooperative cognitive WSN with bidirectional secondary transmissions

2.2 Energy harvesting and information transmission

By adopting the time-splitting relaying (TSR) scheme, the relay spends part of time for WEH and the remaining time is used for information processing. Thus, the whole operation includes three stages.

In the first stage, the PT transmits the dedicated energy signal x_e to the SU₁ during αT time slot, where α (0<α<1) is the fraction of the time slot used by the SU₁ for WEH. The received signal at the SU₁ can be formulated as

                      (1)

wheredenotes the received additive white Gaussian noise (AWGN) at the SU₁. In this paper, the amount of harvested energy from the noise is ignored since the noise power is small enough. Thus, the amount of harvested energy at the SU₁ during αT is given by

                       (2)

wheredenotes the energy harvesting efficiency. Thus, the transmission power of the SU₁ is

                (3)

In the second stage, both the PT and SU₂ simultaneously transmit their signals x_p and x₂ with power P_p and P₂ during the first (1–α)T/2 phase, respectively. Meanwhile, the PR also receives the signal x₂ due to the wireless broadcast nature. Since the SU₁ intends to communicate bidirectionally with SU₂, the SU₁ always decodes x₂ at first by treating the primary signal x_p as interference, and then processes the primary signal x_p by utilizing amplify-and-forward (AF) method. Therefore, the corresponding received signal at the SU₁ can be expressed as

               (4)

where is the received AWGN at the SU₁.

As shown in Figure 2, in the third stage, there are three cases for the data transmission and reception regarding to whether both the SU₁ and PR can correctly receive the signal x₂ or not in the second stage.

Figure 2 Block diagram illustrating operation process of information transmission for primary and secondary systems

Case 1: If SU₁ correctly decodes the signal x₂ in the second stage, the x₂ will be removed. Then, the SU₁ will feed back the acknowledgement (ACK) frame to the SU₂ and PR. After receiving the ACK frame, the PR will drop decoding the signal x₂. In the third stage, the SU₁ uses a fraction λ of its harvested energy to relay the primary signal to the PR while employing a fraction (1–λ) of harvested energy to serve its own transmission by superposition coding scheme. Thus, the resulting achievable rate of the link from SU₂ to SU₁ is given by

           (5)

Then, the broadcasted information at the SU₁ can be expressed as

      (6)

where β₁ denotes the power normalization factor of the SU₁ and it can be expressed as

                        (7)

Correspondingly, the received signal at the PR in the third stage is given by

        (8)

where is the received AWGN at the PR. The received signal-to-interference and noise ratio (SINR) is then written as

         (9)

and the achievable rate at the PR is At the SU₂, the corresponding received signal is then given by

      (10)

where is the received AWGN at the SU₂. The resulting SINR at the SU₂ can be written as

                     (11)

and the achievable rate from SU₁ to SU₂ is . The sum rate of the bidirectionally secondary transmissions is therefore given by

                           (12)

Case 2: If the SU₁ erroneously receives the signal x₂ during the second stage, an outage event occurs for the secondary system as stated in Ref. [10], then SU₁ releases a negative acknowledgement (NACK) frame to other terminals. Therefore, spectrum sharing is not activated and all harvested energy in the first stage is used to relay the primary signal by treating the signal x₂ as interference. If the PR fails to decode the signal x₂, the primary signal is decoded directly at the PR by treating the secondary signal x₂ as interference. In this scenario, the broadcasted signal at the SU₁ is given by

        (13)

where β₂ is the power normalization factor of the SU₁, and it is given by

                (14)

Correspondingly, the received signal at the PR in the third stage is given by

       (15)

The received SINR at the PR is then expressed as

              (16)

and the achievable rate is

Case 3: If the SU₁ erroneously receives the signal x₂ but the PR correctly decodes x₂, the interference signal x₂ will be canceled from the received signal at the PR. In this case, the transmit signal at the SU₁ is the same as case 2. After canceling the x₂, the residual signal at the PR is given by

     (17)

Thus, the received SINR at the PR can be expressed as

              (18)

The corresponding achievable rate is

3 System outage probabilities

In this section, we analyze the outage probabilities of the primary and secondary systems to evaluate the system performance of the proposed spectrum sharing scheme. As previously mentioned, the SU₁ processes the received signal in the second stage with different power normalization factors depending on whether the SU₁ receives the x₂ correctly or not. Let E_s denote the event of the SU₁ correctly detecting the secondary signal x₂. In this case, x₂ will be canceled firstly from the received signal at the SU₁, then the spectrum sharing is performed; otherwise, an outage even occurs for the secondary system and the received signal at the SU₁ is processed with AF-based operation by treating the signal x₂ as interference. In this situation, we assume that the all harvested energy is used to relay the primary signal while the SU₂ keeps silent. Let E_p denote the event of PR correctly detecting the secondary signal x₂ after hearing a NACK frame from the SU₁. In this scenario, the interference signal x₂ can be eliminated from the received signal at the PR.

Let and denote the outage probabilities of the primary and secondary systems, respectively. Thus, we have

               (19)

           (20)

whereandrespectively denote the outage probabilities of the primary and secondary systems when the spectrum sharing is performed; and represent the outage probabilities of the primary system when the signal x₂ is correctly and erroneously decoded at the PR, respectively; denotes the outage probability of the secondary system when the spectrum sharing is not activated, that is,

3.1 Spectrum sharing probability and interference cancellation probability

As previous mentioned, since the SU₂ is intended to exchange information with the SU₁, the node SU₁ always decodes the signal x₂ firstly in the second stage. To detect the x₂ correctly, the target secondary rate r_s should be not great than the achievable rate R₂₁. Without loss of generality, we assume the block time T=1. From Eq. (5), the spectrum sharing probability, that is, the probability of the signal x₂ being decoded, can be derived as

                 (21)

whereand

Proof: Please refer to Appendix A.

Consistently, the probability of successfully decoding the secondary signal x₂ at the PR is expressed as

                    (22)

Remark 1: From Eq. (21), we can obtain the following observations: 1) With the increase of P_p and/or ω_s, Pr{E_s} turns small since the SU₁ is more difficult to decode the signal x₂. 2) With the shorter distance between the SU₁ and SU₂, the v₂ becomes larger. As a result, more interference generated from the PT can be tolerated and Pr{E_s} turns larger. 3) With P₂ tending to infinite, l and m approach to zero, so that Pr{E_s}≈1.

3.2 Primary outage probability of Case 1

When the SU₁ correctly decodes the signal x₂, the spectrum sharing is activated and the superposition coding scheme is utilized for simultaneously transmitting the primary and secondary signals. To detect the primary signal correctly, the target primary rate r_p must be no larger than the achievable rate R_PR,1. Thus, the outage probability of the primary system is given by

                      (23)

Proposition 1: Let and When the SU₁ correctly receives the signal x₂, the outage probability of the primary system is given by

1) If ,

                                (24)

2) If ,

                 (25)

where

                  (26)

and

      (27)

with denoting the first-order modified Bessel function of the second kind [32].

Proof: Please refer to Appendix B.

3.3 Primary outage probability of Case 2

In this case, the secondary signal x₂ from the SU₂ is erroneously received by both the SU₁ and PR. The resulting primary signal is transmitted by SU₁ with overall harvested energy, while the SU₂ maintains silent. From Eq. (16), the outage probability of the primary system is defined as

                      (28)

Proposition 2: Let and When the signal x₂ is erroneously decoded at both the SU₁ and PR, the outage probability of the primary system is given by

                    (29)

where

              (30)

and

(31)

From Eq. (29), the closed-form solution of I₂ is difficult to derive. However, it is relatively easy to obtain the upper bound of I₂ with the given system parameters, which is denoted as

     (32)

where and Thus, the lower bound of the primary outage probability is given by

                     (33)

Proof: Please refer to Appendix C.

3.4 Primary outage probability of Case 3

In case 3, the secondary signal x₂ is erroneously decoded by the SU₁ but is correctly received by the PR in the second stage. Thus, the interference signal x₂ can be removed from the received signal at the PR. The outage probability of the primary system can be expressed as

                      (34)

Therefore, the outage probability of the primary system can be derived as

                    (35)

where

                        (36)

and

 (37)

We can also obtain the lower bound of as follows:

                     (38)

where

          (39)

The proof is omitted because it is similar to the proof of the Proposition 2.

3.5 Secondary outage probability

Based on the proposed spectrum sharing scheme, the SU₁ and SU₂ are intended to communicate in a bidirectional manner, which occurs only when x₂ is decoded correctly at the SU₁ in the second stage. Thus, the outage probability of the secondary system is given by

                       (40)

Proposition 3: LetWhen the spectrum sharing is activated, the secondary outage probability can be expressed as

1) If

                                (41)

2) If

 (42)

Proof: It is similar to Appendix B.

Remark 2: From Eqs. (9) and (11), we can observe that and Asandthe outage event occurs ifand which match perfectly with Eqs. (24) and (41). It also illustrates that how to choose the power allocation factor λ and the energy harvesting time ratio α is critical to the information transmission.

4 Optimization problem analysis

For each time slot, the occurrence of spectrum sharing is determined by whether the SU₁ can correctly decode the secondary signal x₂ in the second stage. When x₂ is received correctly at the SU₁, the spectrum sharing is activated, then SU₁ sends its signal to the SU₂ while acting as a relay to transfer the primary signal to the PR. In this case, the SU₁ can adjust its transmission power and data rate to achieve win-win results for both the primary and secondary systems.

According to formulate (21), (22), (25), (29), (35) and (42), the energy harvesting time ratio α and the power allocation factor λ can be jointly optimized by minimizing the outage probability of the secondary system while protecting the outage performance of the primary system. Due to the lack of direct transmission between the PT and PR, it is typically difficult to formulate an optimal constraint for primary transmission. Instead, a sub-optimal constraint is devised as follows. The outage probability of the primary system with the opportunistic spectrum sharing should not be less than the outage probability of Case 2. Therefore, the optimization problem is formulated as (P1)

       (43)

Based on the previous analyses, the optimal power allocation factor λ can be derived only when spectrum sharing is activated. In this case, the outage event occurs when for the primary system and/orfor the secondary system. In order to guarantee the efficient transmission for both systems, the relationship between the power allocation factor λ and energy harvesting time ratio α is then expressed as

                        (44)

whereandThus, problem (P1) can be rewritten as problem (P2)

       (45)

In the following, we propose a computationally effective optimization algorithm to obtain the optimal parameters of λ and α based on a three-stage procedure.

Step 1): Analyzing the monotonicity of the optimization problem (P2). For any given energy harvesting time ratio α₀, if more power is allocated to relay the primary signal, the outage probability of the primary system will be decreased, and the secondary system may be subject to more

interference. As a result, is a monotonic increasing function, while is a monotonic decreasing function in respect of λ. Therefore, if is true with the given α₀, the exact critical point λ₀ can be obtained by letting otherwise, the outage event occurs.

Step 2): Determining the optimal value of λ. If the optimal power allocation coefficient is ; If the optimal power allocation coefficient can be chosen as to minimize the objective function, where △λ denotes a small positive real number; otherwise, if , we select the optimal power allocation coefficient asto protect the primary transmission.

Step 3): Select the optimal value α. One- dimension search over available scope of α is performed to obtain the globally optimal solution of problem (P2).

The detailed procedure is described in Algorithm 1.

Algorithm 1 The proposed optimal algorithm for (P2)

Define △α as the search step, △λ>0 as a small positive real number, and Initialize α=α₀.

1.For the given

if do S1-S2

S1: Solvingby Monte Carlo simulation to obtain critical point λ;

S2: Do the following procedures to obtain the optimal value λ^* of (P2),

if

The optimal value of problem (P2) is λ^*=λ;

else if

The optimal λ of problem (P2) is

else if

The optimal of problem (P2) is

end if

else

An outage event occurs.

end if

Update

end for

2.Choose the globally optimal solution from the following equation

5 Numerical results

In this section, we provide numerical results to demonstrate the accuracy of the derived expressions and illustrate the performance of the proposed transmission scheme with variable system parameters. In the simulations, the distance between PT and PR is normalized to 1. Let D₁, D₂, D₃ and D₄ represent the distance between PT and SU₁, SU₂ and SU₁, SU₁ and PR, SU₂ and PR, respectively. Thus, we have and for h₁, h₂, h₃ and h₄, respectively, where –3 is the path loss exponent. To simplify the analysis process, we assume the noise power The energy harvesting efficiency is set as η=0.5. The algorithm proposed in the Section 4 is adopted for simulations.

5.1 Comparison with other scheme

In the following section, the proposed spectrum sharing scheme is compared with other one-way spectrum sharing scheme [29], where each transmission block can be divided into three phases by introducing a parameter ρ. The scheme of Ref. [29] can be modified as follows:

In the first phase, the PT spends a part of time ρT to broadcast dedicated energy signal for ST performing energy harvesting operation. In the first duration , the PT transmits its signal to the ST.In the remaining duration, the ST relays AF-processed primary signal together with its own signal by superposition coding scheme.

Figure 3 reveals the achievable throughput of the primary system with respect to primary transmission power for different secondary transmission powers P_s. From the figure, the primary throughput is improved with the increase of the primary transmission power. Moreover, the proposed scheme always outperforms the scheme in Ref. [29] due to adopt interference cancellation scheme for the PR. However, the primary throughput with the proposed scheme is decreased with higher secondary transmission power because more interference is introduced when the SU₁ cannot be able to decode a secondary signal. In Figure 4, the primary throughput is deteriorated with the increase of distance between the PT and SU₁ since the longer the distance, the lower the amount of harvested energy at the SU₁. With the low primary transmission power, the primary throughput with proposed scheme is lower than the scheme in Ref. [29] when D₁=0.8, because the secondary transmission from the SU₂ may bring a significantly interference to the primary transmission. Consistently, in the high power range, the primary throughput with the proposed scheme is higher to the scheme in Ref. [29].

Figure 3 Throughput of primary system versus primary transmission power for different secondary transmission power P₂ (D₁=0.5, D₂=0.25 and D₃=1–D₁)

Figure 4 Throughput of primary system versus primary transmission power for different transmission distance D₁ (D₂=0.25 and D₃=1–D₁, P₂=20 dB)

5.2 Outage probability with primary transmission power

Figures 5 and 6 testify that the outage probability analyses of both the primary and secondary systems are valid because the simulation results coincide exactly with the theoretical analysis.

Figure 5 reveals the outage performance of both the primary and secondary systems in respect of primary transmission power for different primary and secondary target rates. In this figure, the primary outage probability is decreased with the increase of the primary transmission power. Moreover, the outage performance becomes better with lower target transmission rate because the channel is easier to support a lower transmission rate. Besides, the lower bounds of the primary outage probabilities show a remarkable agreement with the analytical results. The secondary outage performance becomes better with the lower primary transmission power because the SU₁ can easier to decode its desired signal, and thus the occurrence probability of the spectrum sharing gets higher. Nevertheless, the occurrence probability of the spectrum sharing becomes lower due to the fact that there is more interference coming from the PT with the higher primary transmission power. Consistently, the outage probabilities of both the systems get worse with the decrease of the target transmission rates.

Figure 5 Outage probabilities of both primary and secondary systems versus transmission power of primary system for different primary target transmission rates (D₁=0.5, D₂=0.25 and D₃=1–D₁, P₂=20 dB, r_s=r_p–0.3 bit/(s·Hz^–1))

Figure 6 Outage probabilities of both primary and secondary systems versus transmission power of primary system for different distance D₁ (D₂=0.25 and D₃=1–D₁, P₂=20 dB, r_p=0.75 bit/(s·Hz^–1), r_s=r_p–0.3 bit/(s·Hz^–1))

Figure 6 demonstrates the outage probabilities of both the systems with respect of primary transmission power for different distances D₁. With the increase of the primary transmission power, the primary outage performance is improved. The primary outage probability is decreased with smaller distance D₁ since the SU₁ can harvest more RF energy from the primary transmission. The outage performance of the secondary system first gets better and then gets worse with the increase of the primary transmission power. When the primary transmission power is less, the secondary outage probability is improved with shorter distance D₁ because more RF power can be harvested at the SU₁. However, higher primary transmission power can bring more interference to the SU₁ in the second phase. Furthermore, with the decrease of the distance D₁, the secondary outage performance is deteriorated due to the fact that the smaller the distance D₁, the lower the spectrum sharing probability.

5.3 Outage probability with secondary transmission power

Figure 7 illustrates the outage probabilities of both the primary and secondary systems against the secondary transmission power for different target transmission rates. The primary outage performance is deteriorated with the increase of the secondary transmission power. In the lower secondary transmission power, the spectrum sharing probability becomes lower because the channel between the SU₁ and SU₂ cannot withstand the interference from the PT. However, the spectrum sharing probability is nearly close to one with the high secondary transmission power, and thus the primary outage probability tends to be constant. The outage performance of the secondary system gets better with the increase of the secondary transmission power due to the improved spectrum sharing probability. Similarly, the outage performance of both primary and secondary systems becomes better with the decrease of the target transmission rates.

Figure 8 depicts the outage probability of both the primary and secondary systems in respect of secondary transmission power for different distance D₁. In this figure, the primary outage performance is deteriorated with the increase of the secondary transmission power. Furthermore, we can also find that the shorter the distance D₁, the better the primary outage performance because more power can be harvested for relaying transmission. The outage performance of the secondary system is improved in the whole range of the secondary power. With the lower secondary transmission power, the larger the distance D₁, the better the outage performance for the secondary system. However, the shorter the distance D₁, the better the outage performance with high power range since the primary signal is non-dominant and SU₁ can also harvest more energy with smaller D₁. The theoretical results also agree well with the simulation results.

Figure 7 Outage probabilities of both primary and secondary systems versus transmission power of secondary system for different target transmission rates (D₁=0.5, D₂=0.25 and D₃=1–D₁, P_p=20 dB. r_s=r_p–0.3 bit/(s·Hz^–1))

Figure 8 Outage probabilities of both primary and secondary systems versus transmission power of secondary system for different distance D₁ (D₂=0.25 and D₃=1–D₁, P_p=20 dB. r_p=0.75 bit/(s·Hz^–1), r_s=r_p–0.3 bit/(s·Hz^–1))

6 Conclusions

This paper developed a novel cooperative spectrum sharing scheme based on bidirectional secondary transmissions, where an energy- constrained sensor node SU₁ spends a part of time to harvest energy from the primary RF signal. Utilizing the harvested energy, the SU₁ helps the primary data transmission and in return, it can be allowed to exchange information with another sensor node SU₂ in a bidirectional manner for the opportunity of spectrum access. The exact expressions of outage probabilities for both primary and secondary systems were derived. To maximize the secondary outage probability while protecting the outage performance of the primary system, a joint algorithm was proposed to obtain the optimal energy harvesting time and power allocation coefficient. The extensive simulation results illustrated that the achievable rate of the secondary system can be significantly enhanced by adopting the proposed cooperative spectrum sharing scheme.

Appendix

A. Proof for derivation of Eq. (21)

Let and . We can see that X and Y are both exponentially distributed with mean v₁ and v₂, respectively. Then, Eq. (21) can be expressed as

        (A1)

where and After some mathematical manipulations, Eq. (21) can be obtained.

B. Proof for derivation of Proposition 1

Substituting Eqs. (3) into (9), we can find that the term in denominator is much smaller than other terms. For simplicity, we assume that the Let andThus, we define

               (B1)

where the c, d, f of W₁ is

(B2)

1) If ,

                            (B3)

2) If ,

                (B4)

Now, we have

(B5)

Defining a new integration variable Eq. (B5) can be rewritten as

     (B6)

Let the first and second terms of (B6) be H₁ and H₂, respectively, i.e.,

                 (B7)

and

                 (B8)

where K₁{·} is defined in Eq. (27). Besides, we can obtain

 (B9)

 (B10)

Thus, we have

                 (B11)

C. Proof for derivation of Proposition 2

Assuming and substituting Eq. (3) into (16), we can rewrite (16) as

 (C1)

Let and define

             (C2)

Then, the c.d.f. of W₂ can be derived as

              (C3)

Now, we further have

                             (C4)

where I₁ and I₂ are expressed in Eqs. (30) and (31), respectively. Similarly, we can obtain

                (C5)

             (C6)

Thus, the exact expression for is given by

                     (C7)

Let and , I₂ can be rewritten as

     (C8)

and we can finally derive the result of Eq. (33).

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(Edited by YANG Hua)

中文导读

基于能量收割的认识无线传感网络中次用户双向传输方案的研究

摘要：在目前基于能量收割的认知无线传感网络中频谱共享方案中，大多数方案限制了次用户系统仅能在主用户空闲时或者进行协作传输时才能共享频谱。为了解决这一问题，本文提出了一种新的协作频谱共享方案。在此方案中，次用户系统可以在主用户传输信息时和协作认知传输时均能共享频谱。具体来说，整个传输过程按时间切换中继方案可以分为三个阶段。在第一阶段，一个认知的传感节点SU₁通过接收主用户发送的能量信号进行能量收割；在第二阶段，另一个认知的传感节点SU₂和主用户发送端同时发送信息给SU₁；在第三阶段，传感节点SU₁可以通过协助主用户信息传输从而获得频谱共享的机会。在所有的接收端均采用联合的解码和干扰消除技术来获得所需的信息。通过数学分析，本文得到主用户系统和次用户系统的中断概率的闭式解。进一步来说，本文还分析了基于能量收割时间和功率分配比例的优化问题，同时相应地提出了一种有效的算法获取优化值。仿真结果表明，将提出的优化算法和频谱共享方案结合，系统的频谱效率较传统的方案有了极大的提高，同时主用户系统的传输速率也有了较大的提升。

关键词：协作传输；认知无线传感网络；时间切换的中继；无线能量收割；联合优化

Foundation item: Project(61201086) supported by the National Natural Science Foundation of China; Project(201506375060) supported by the China Scholarship Council; Project(2013B090500007) supported by Guangdong Provincial Science and Technology Project, China; Project(2014509102205) supported by the Dongguan Municipal Project on the Integration of Industry, Education and Research, China; Project(2017GK5019) supported by 2017 Hunan-Tech & Innovation Investment Project, China

Received date: 2017-07-05; Accepted date: 2018-03-01

Corresponding author: LEI Wen-tai, PhD, Associated Professor; Tel: +86-18108425818; E-mail: leiwentai@csu.edu.cn; ORCID: 0000- 0002-3916-0533