Harvesting–Transmission–Harvesting Mode for Cognitive Radio Networks with Energy Harvesting Maximization

This paper presents a new cognitive radio network (CRN) framework with radio frequency (RF) energy harvesting, namely, RF-powered cognitive radio networks (RF-CRNs), wherein multiple secondary users (SUs) harvest energy from the RF signals of primary users (PUs) all the time except when transmitting data in the allocated time, namely, the “harvesting– transmission–harvesting” mode. In this way, the energy harvested by each SU can be maximized until the next data transmission. Also, the total energy consumed by the SUs must be less than or equal to the total harvested energy (the energy causality constraint), while the transmit power of SUs must be restricted to protect the PUs from interference (collision constraint). Finally, under the satisfaction of quality of service of SUs (throughput constraint), our goal is to determine the optimal transmitting time and power allocation that maximize the achievable throughput in the RF-CRNs. We achieved the optimal result by transforming the optimization problem into a convex optimization problem and then applying Lagrange multiplier methods. Extensive performance evaluations showed the efficiency of the proposed algorithm.


Introduction
Nowadays, the problems of spectrum efficiency (SE) and energy efficiency (EE) in wireless networks must be solved urgently, especially in the 5G era. Cognitive radio networks (CRNs) with energy harvesting (EH) (EH-CRNs) have emerged as a promising way to address the problems of SE and EE while responding to the call for green communication at the same time. (1)(2)(3)(4)(5)(6) Through opportunistic spectrum access, a secondary CRN can opportunistically access the spectrum licensed to a primary network.
The performance of wireless networks is greatly limited by the finite capacity of the battery. Powering wireless nodes with energy scavenged from ambient sources such as heat, light, waves, and wind enables wireless nodes to run permanently without the cost of external power cables and recharging or the need to replace the battery periodically. Radio frequency (RF) EH allows a wireless node to harvest and convert electromagnetic waves from ambient RF sources (e.g., TV and radio towers, and cellular base stations) into energy, which can provide energy for many emergency scenes or remote locations that cables cannot reach. (5) Compared with ambient EH, RF EH is more flexible and sustainable as the RF signals radiated by ambient transmitters are consistently available. (5) RF energy sources can mainly be categorized into intended RF and non-intended RF. Intended RF can power nodes that require a predictable and large amount of energy due to on-demand supply and directional transmission. Non-intended RF signals include most of the radiation from nearby RF sources such as cellular base stations, primary users (PUs), and other secondary sources. Such radiation is freely available and not dedicated, and is mainly used to power low-power networks such as sensor networks. By employing EH technology, RF signals radiated by PUs no longer need be regarded as interference for secondary users (SUs) but as a continuous energy source for EH.

Related work and motivation
In the present study, SUs in RF-CRNs mainly operate in three different modes: interweave, overlay, and underlay. (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) In interweave mode, SUs first harvest energy and then opportunistically access the licensed spectrum for data transmission when PUs are detected as inactive. The SUs work in harvesting-sensing-transmitting mode, where much time and energy are spent on spectrum sensing. Once the PUs retake the channel, the SUs have to interrupt the transmission and give up the channel. (7)(8)(9)(10)(11)(12) In overlay mode, given that the SUs have knowledge of the PUs' transmit sequence and encoding scheme, the SUs harvest energy to serve both PUs and SUs. This requires excellent cooperation between PUs and SUs, which is difficult to achieve in practice. (18)(19)(20)(21) In contrast to the high energy consumption and discontinuous data transmission in interweave mode and the necessary collaboration of PU and SU in overlay mode, in underlay mode, an SU can transmit along with a PU as long as the secondary interference at the primary receiver remains below an acceptable threshold. Zheng's group presented a novel structure for underlay RF-CRNs. (13) This structure had only one SU transmitter-receiver pair in the RF-CRNs, where the SU receiver had a fixed power supply, while the SU transmitter was powered by an energy harvester that harvested green energy from the signals of the PU transmitter. The same group extended the RF-CRNs to incorporate SUs, wherein all SUs first harvested energy for a fixed duration and then transmitted data using the harvested energy to one access point for the remainder of the period using the code-division multiple access (CDMA) method. (14) Recently, a wireless-powered underlay CRN has been developed, where SUs first harvested energy in the downlink wireless power transfer phase and then used the energy for data transmission in the uplink wireless information transmission phase, adopting time-division multiple access (TDMA). To expand network coverage and reduce the transmission power of SUs in underlay mode, a new wireless EH protocol designed for an underlay cognitive relay network with multiple PU transceivers was proposed in Ref. 16. A green coexistence paradigm for underlay multi-hop EH-CRNs has been formulated in which all the secondary nodes capture energy from the PUs. (17) The authors in Ref. 17 solved the end-to-end throughput maximization problem subject to the energy causality and interference power constraints. With the recent increase in the number of hops, the time delay and outage probability will increase accordingly. (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31) In underlay RF-CRNs, SUs harvest energy and transmit data without interruption by coexisting with the PUs under an interference constraint. SUs take PUs as a stable energy source for sustainable EH through working in the harvesting-transmitting-inactive mode, in which SUs are always inactive and do nothing after transmitting data at the allocated time. (13)(14)(15)(16)(17) Since the transmitted power attenuates as the reciprocal of the distance, when the distances from the nodes to PUs are different, this mode leads to an imbalance in the harvested energy of nodes. Moreover, because the time slot is not fully utilized, the EH efficiency is low.
Motivated by the above analysis, in contrast to conventional underlay RF-CRNs, wherein SUs work in the harvesting-transmitting-inactive mode, in this paper, we propose a new energy and transmission mode for RF-CRNs with multiple SUs. In our mode, each SU harvests energy from the RF signals of each PU all the time except when transmitting data in the allocated time concurrently with the PU, namely, the "harvesting-transmission-harvesting" mode. In this way, the energy harvested by each SU can be maximized until the next data transmission. In addition, the total energy consumed by the SUs must be less than or equal to the total harvested energy, while the transmit power of SUs must be restricted to protect the PUs from interference.
Finally, quality of service (QoS) for multiple SUs is essential in many scenarios such as a wireless sensor network gathering data, monitoring events, and performing applications. To satisfy the QoS of SUs, we impose a minimum required throughput constraint on the transmitting process for each SU. In other words, our goal is to determine an optimal transmitting time and power allocation for SUs to maximize the achievable throughput of the RF-CRNs under interference, energy, and throughput constraints.

Contributions
The main contributions of this paper are summarized as follows: • First, unlike the conventional harvesting-transmission-inactive mode, we design a new harvesting-transmission-harvesting mode that enables SUs to harvest sufficient energy for the subsequent data transmission. • Second, we pay attention to guaranteeing the QoS of SUs in RF-CRNs. Given a prescribed minimum throughput threshold for each SU, we determine the optimal transmitting time and power allocation that maximize the expected throughput of RF-CRNs. • Third, we achieve the optimal result by transforming the optimization problem into a convex optimization problem and then applying Lagrange multiplier methods. • To verify the generality of the model, we investigate the impacts of typical parameters such as the transmitting power of the primary transmitter (PT), the maximum interference power of the primary receiver (PR), and the minimum throughput constraint for SUs on performance. The rest of this paper is organized as follows. The system model for the EH-CRN is described in Sect. 2. The throughput analysis and throughput maximization solution are introduced in Sect. 3 and the simulated results are presented in Sect. 4. Finally, a conclusion is given in Sect. 5.

System Model
We present a new model for RF-CRNs with multiple SUs as shown in Fig. 1. The secondary network consists of one access point (AP), N secondary users depicted as SU k (k = 1, 2, ..., N) , which coexist with one PT and one PR. The AP has a fixed power supply, whereas each SU is powered by an energy harvester, which harvests green energy from RF signals of the PT. Assuming that the PT is always actively communicating with the PR, the SUs share the licensed spectrum with the PU under the interference constraint. There are EH links, data transmission links, and interference links in the model. The links between the PT and each SU are referred to as EH links with channel power coefficients g E,k (k = 1, 2, ..., N). The links between the AP and each SU k (k = 1, 2, ..., N) are data links with channel power gain coefficients g D,k (k = 1, 2, ..., N), and the links between the SUs and the PR are referred to as interference links with channel power gain coefficients g I,k (k = 1, 2, ..., N). All SUs are equipped with a single half-duplex omnidirectional antenna and a battery with finite capacity E to store energy.
Meanwhile, as shown in Fig. 2, each frame with duration T is allocated to SU k (k = 1, 2, ..., N) for harvesting and transmission by TDMA. Unlike the conventional harvesting-transmissioninactive mode, we design a new harvesting-transmission-harvesting mode that can make SU k harvest energy after transmission rather than remain inactive. Specifically, SU k continues to harvest energy from the RF signals of the PT all the time except during the transmission subslot. The transmission sub-slot allocated to SU k is denoted as τ k and the EH time for SU k (k = 1, 2, ..., N) is calculated as (T − τ k ). Hence, the total energy harvested by SU k in frame f is calculated as ( ) , , where η k is the EH efficiency and P T is the transmission power of the PT. Note that the SUs share the spectrum with the PU in an underlay paradigm, which means that the SUs can perform concurrent transmission as long as the interference at the PR does not exceed a peak permissible threshold P I given as  (2) Since there is no sensing in an underlay paradigm, the energy required to receive and process information is negligible compared with the energy required for information transmission for convenience, and thus the SUs consume energy only for data transmission. Hence, the total energy consumption of an SU in frame f is given by ( ) , The residual energy at the end of the previous frame f − 1 can also be accumulated at the beginning of frame f as the initial energy. Hence, by considering the harvested energy and consumed energy, the residual energy at the end of frame f can be updated as By substituting Eqs. (1) and (3) into Eq. (5), we obtain To guarantee the continuous communication of each SU, ( ) , 0 f R k E ≥ must be satisfied. Supposing that the maximum capacity of the battery is E and surplus energy is discarded if

Optimal problem formulation
Given transmission power P k and the allocated time τ k , the achievable throughput of SU k for the transmission from SU k to the AP in one frame is where is the signal-to-noise ratio of the AP. We obtain the average achievable throughput of the RF-CRN as follows: where τ = [τ 1 , τ 2 , ..., τ N ] and P = [P 1 , P 2 , ..., P N ] are the vectors of time allocation and power allocation, respectively. We set a minimum required rate R out > 0 for SU k , namely, the throughput constraint, ( , ) , to satisfy the QoS of SUs. Finally, we formulate the following maximum average throughput optimization problem.
C1 indicates that the transmission power of SU k cannot exceed the tolerable inference power threshold P I at the PR, through which the PR is protected from interference, namely, the collision constraint. C2 indicates that for the allocated time τ k and transmission power P k , the energy consumed for data transmission cannot exceed the energy in the battery, namely, the energy causality constraint. C3 indicates that the total time consumed by SU k must be less than or equal to the frame duration T. C4 is the consumed time constraint for each SU k and C4 is the throughput constraint.
Obviously, Eq. (10) is a non-convex problem because of the product of the optimal variable P k and τ k in C2. From Eq. (3), we can derive ( ) , For convenience, we replace ( ) , i C k E with e k , and then we transform Eq. (8) into the following form: Here, C3′ and C4′ are equivalent to C3 and C4 in Eq. (10), respectively, and C2a′ and C2b′ are equivalent to C2. Theorem 1: The achievable throughput R(τ, e) of the RF-CRN in Eq. (13) is a joint concave function of τ and e. Proof: Please refer to Appendix A. By applying Theorem 1, the objective function R(τ, P) in Eq. (10) is converted into a concave function of R(τ, e). After introducing e, the energy causality constraint C2 is converted into affine functions as C2a′ and C2b′. Thus, Eq. (13) is a convex optimization problem that can be solved by convex optimization techniques.

Optimal resource allocation algorithm
Equation (13) is a convex optimization problem and satisfies Slater's condition, so we can solve its dual problem instead. We first introduce the partial Lagrangian function of Eq. (13) with respect to C2a′, C2b′, C3′, and C5′: where D is the set of τ, e associated with C1′. Finally, the dual problem of Eq. (13) is given by where W(•) denotes the Lambert W function, Next, we compute the dual variables λ, u, v, and w that minimize D(λ, u, v) by using the subgradient method. The sub-gradients of D(λ, u, v) at λ k , u k , v, and w k are calculated as 0 , In the nth iteration, we update λ k , u k , v, and w k as follows: where α (n−1) denotes the step size in the nth iteration. The solution method is summarized as Algorithm 1.

Simulation Results
Numerical results are shown to validate the performance of the proposed framework. The SUs are randomly placed in a circle with a radius of 10 m with the AP located at the center. The RF-CRNs coexist with a primary network that is deployed over an area with a radius of 100 m. The harvested energy and the interference in the RF-CRNs depend on the location distribution of the SUs, so we assume that the channel power gain coefficients g D,k , g E,k , and g I,k are given by g x,k = 1/|d x,k | α , where x = {D, E, I}. d x,k and α are the distance and the path loss exponent, respectively.
The simulation parameters are set as N = 5, α = 2, f = 1000, T = 100 ms, σ 2 = −140 dBm, η k = 0.5, E 0 = 0.5 J, E = 1 J, and P max = 7 W. Our model is similar to the one in Ref. 14 but with three important differences. First, the SUs work in the harvesting-transmitting mode through CDMA, as described in Ref. 14, whereas all SUs working in the harvesting-transmittingharvesting mode with TDMA can maximize the harvested energy. Second, the SUs save the energy in an infinite energy storage device, as shown in Ref. 14, whereas here, the SUs have a finite-capacity battery for storing energy, which is more realistic for practical application scenarios. Third, the RF-CRNs perform best-effort communication, and described in Ref. 14, whereas we make a minimum required throughput constraint on the transmitting process for each SU to ensure that the QoS of SUs is satisfied. Figure 3 shows the throughput of the RF-CRNs under different values of P T , P I given a prescribed minimum throughput threshold for each SU. The throughput clearly increases with increasing P I , which is because increasing P I enlarges the feasible domain of P k , further increasing R(τ, P). However, R(τ, P) decreases with increasing P T . A larger P T means more harvested energy for SUs but also more interference with the AP. Thus, when the interference is large enough or P I is too small, the SUs cannot satisfy the prescribed minimum throughput threshold, the throughput dramatically decreases to near zero, and the system is interrupted. Figures 4(a) and 4(b) show the energy status with different P I . As shown in Fig. 3, P k increases with increasing P I ; thus, more energy is required for data transmission. Since the SUs continuously harvest energy except during transmission, the harvested energy is abundant and the battery is full before each transmission of data. Figure 5 shows the relation between the throughput R(τ, P) and P I . As shown in Figs. 3 and 4, because P k increases with P I , R(τ, P) and the consumed energy increase accordingly. However, when P I is sufficiently large, R(τ, P) cannot be further enhanced. In fact, P k cannot be infinite due to the finite battery capacity and the maximum power transmission constraint P max . Figure 6 depicts the maximum throughput for R out in different scenarios. It can be seen that R(τ, P) and R out increase with P I at the same P T . This is consistent with the fact that with increasing P I , R k (τ k , P k ) and R(τ, P) also increase as shown in Fig. 3. However, R k (τ k , P k ) finally tends to be stable due to the finite battery capacity and the existence of P max . Once the maximum limit R out is exceeded, the throughput dramatically decreases to near zero and the system is interrupted due to the minimum throughput constraints.  We compare our algorithm, namely, Algorithm 1, the joint optimal time and power allocation algorithm (JOPA), with the CDMA method in Ref. 14 for different levels of interference of the PR as shown in Fig. 7. It is obvious that JOPA achieves a larger throughput than CDMA as P I increases. This is mainly due to the harvested energies of the SUs being more sufficient in JOPA than in CDMA under the same P T . With increasing P I , the SUs can enhance their transmission powers adaptively as the harvested energies are sufficient, in contrast to in CDMA. Figure 8 shows the throughput versus the number of SUs N under different R out . Indeed, when N increases, the throughput will first increase and then gradually decrease until the system interrupts. This is because the achievable throughput R(τ, P) of the RF-CRN is the sum of the throughputs R k (τ k , P k ) of SU k (k = 1, 2, …, N), as shown in Eqs. (8) and (9). Therefore, the greater the N, the greater the throughput of the RF-CRN. However, when N continues to increase, the transmission time for each SU is reduced. Thereby, the achievable throughput R k (τ k , P k ) of SU k (k = 1, 2, …, N) decreases and the QoS cannot be guaranteed, with the system interrupting.

Conclusion
In this paper, we presented a new harvesting-transmission-harvesting model for RF-CRNs. All SUs harvest energy from the RF signals of PUs all the time except when transmitting data in the allocated time. In this way, the energy harvested by each SU is always sufficient and can be maximized until the next data transmission, especially when the value of the interference constraint is large. Through the throughput constraint, we ensured transmission QoS for all SUs, which is essential in many applications, especially in wireless sensor networks performing data gathering, event monitoring, and other industrial applications. We achieved the optimal result by transforming the optimization problem into a convex optimization problem and then applying Lagrange multiplier methods. Through the maximization of harvesting energy and the minimum throughput constraint, our model can be expanded easily and used in many important applications such as large-scale CRNs, cognitive relay networks, and multi-hop CRNs.
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