Multi-User Wireless Information and Power Transfer in FBMC-Based IoT Networks

In order to address the shortcomings of orthogonal frequency division multiplexing (OFDM) and extend the lifetime of energy-constrained Internet-of-Things (IoT) devices, the combination of filter bank multi-carrier (FBMC) and simultaneous wireless information and power transfer (SWIPT) is investigated in this paper. Specifically, a multi-user FBMC-based SWIPT system is proposed in which user nodes (UNs) have the capability for both energy harvesting (EH) and information decoding (ID) with the aid of separate antennas. A practical non-linear EH model, which considers the saturation effects of the EH circuit, is considered. The information receiver at both the UNs and base station (BS) adopts an iterative interference cancellation (IIC) receiver to cancel the intrinsic interference in the demodulated FBMC signal. A sum-rate maximization problem is solved to jointly optimize parameters such as time, power, and weight allocations. Sub-optimal schemes are proposed for comparison. Numerical results show that the optimal solution significantly outperforms the sub-optimal methods in terms of achievable sum-rate and amount of harvested energy. Moreover, the results show that the proposed algorithm converges within a few iterations.

from poor out-of-band (OOB) emissions due to the use of rectangular filters, which can cause severe interference in asynchronous scenarios [3].
As a result, waveforms that are suitable for asynchronous access, such as filter bank multicarrier (FBMC), have been investigated for future wireless applications [4], [5]. FBMC employs well-localized prototype filters to improve the poor OOB leakage of OFDM, which reduces its sensitivity to asynchronous transmissions compared to OFDM. This makes FBMC a suitable alternative to OFDM in applications that require grant-free transmissions. By adopting FBMC, the strict synchronization procedure can be relaxed and CP overhead can be significantly reduced. Thus, improving the spectral efficiency compared to OFDM. In [1], the authors investigated the compatibility of FBMC with OFDM in a scenario where cellular users employing OFDM for synchronous communication coexist with mMTC users operating asynchronously using FBMC. The results showed that it is possible for OFDM-based cellular users to coexist with FBMC-based mMTC devices in future wireless networks.
A key challenge of FBMC systems is the lack of subcarrier orthogonality which causes intrinsic interference, i.e., intersymbol interference (ISI) and intercarrier interference (ICI). To eliminate ISI and ICI, offset QAM has been used in FBMC systems [6]. However, in FBMC-OQAM systems, orthogonality is achieved only in the real domain. The imaginary part of the signal causes intrinsic interference, which limits the direct implementation of conventional LTE-based schemes such as channel estimation and space-time block code (STBC) [7]. To resolve the problems in FBMC-OQAM, the transmission of complex QAM symbols in FBMC systems has been proposed [8], [9]. However, FBMC-QAM systems cannot guarantee complex domain orthogonality, resulting in high intrinsic interference.
Apart from the need for asynchronous access, it is essential for future mMTC networks to be self-sustaining [10]. In recent years, simultaneous wireless information and power transfer (SWIPT) has been recognized as a promising approach to provide device self-sustainability and prolong the battery life of energy-constrained wireless nodes [11], [12]. In SWIPT, a receiver node can harvest energy and decode information from the received radio frequency (RF) signal by employing either the separated receiver mode or co-located receiver mode [13]. In the separated receiver mode, separate receivers are used for information decoding (ID) and energy harvesting (EH). Thus, each receiver can have a dedicated antenna without the need to split the received signal. In the co-located receiver mode, on the other hand, a single receiver simultaneously performs ID and EH. The received signal is split into two portions for ID and EH by either time switching (TS) or power splitting (PS) [14]. Most early works in SWIPT assumed a linear EH model. However, practical EH devices consist of a rectifier circuit with diodes and transistors which imposes a non-linear behavior on the EH circuit. Thus, non-linear EH models have been implemented for SWIPT recently [13], [15].
Dealing with the intrinsic interference caused by the loss of orthogonality is a key design requirement in FBMC-QAM systems. Unlike traditional wireless communications, in which the interference is treated as an undesired signal, it can be exploited as a useful signal for wireless EH in SWIPT systems [16]. By harnessing the benefits of FBMC-QAM and SWIPT, billions of IoT devices can be effectively connected and powered anywhere, any time.

A. RELATED WORK
In recent years, a lot of research has been conducted to evaluate the performance of SWIPT in IoT networks. Most of the research at the physical layer has considered the combination of SWIPT with techniques such as cooperative communications, full-duplex and multicarrier waveforms. Asiedu et al. [12] studied a multi-hop decode-and-forward (DF) SWIPT system for IoT networks, and investigated two optimization problems with the aim of finding the optimal PS ratio to optimize the source transmit power and the achievable rate. Reference [17] studied SWIPT for IoT sensor networks in which multiple transmitter-receiver pairs exchange information and energy by employing PS at the receiver node. The objective of [17] is to minimize the total transmit power by optimizing the message configurations, hybrid beamforming vectors, and PS ratio at the receiver nodes.
The performance of SWIPT in multicarrier waveforms has also been investigated in the literature [18]- [20]. In [18] a multi-user OFDM-based SWIPT system is investigated, in which two multiple access and EH schemes are implemented: (i) time division multiple access (TDMA) transmission with a TS-based receiver and (ii) orthogonal frequency division multiple access (OFDMA) transmission with a PS-based receiver. Reference [19] proposed an OFDM-based SWIPT system in which the received signal is partitioned into two subcarriers groups: one group for ID and the other group for EH. Moreover, a joint subcarrier and power allocation problem is derived to maximize the harvested energy. A similar model is presented in [20], where the goal is to maximize the users' sum-rate by optimizing the channel allocation and power allocation. Because the received signal is separated into two groups for ID and EH, neither PS nor TS is needed at the receiver.
Majority of the existing work on SWIPT in multicarrier waveforms are based on OFDM. However, as mentioned above, OFDM does not meet all the requirements of future IoT applications, especially the need for a huge connection density and asynchronous access [1]. For such applications, non-orthogonal waveforms have been shown to perform better than OFDM [5]. To harness the advantages of SWIPT and non-orthogonal waveforms, the combination of generalized frequency division multiplexing (GFDM) and SWIPT has been investigated recently [21]- [23]. In [21], a GFDM-based cooperative relay system is proposed to improve the quality of experience and extend users' battery life at the edge of a cell. A joint subcarrier and subsymbol allocation for a multiuser SWIPT GFDM system is studied in [22], in which a sum-rate maximization problem is solved to optimize the sub-block allocation, power allocation, and PS ratio. The authors in [23] extended the SWIPT model in [21] to a GFDM-based amplify-and-forward (AF) system and derived an analytical expression for the bit error rate (BER).

B. CONTRIBUTION
Motivated by the advantages of FBMC 1 systems over conventional OFDM, i.e., high spectral efficiency and suitability for asynchronous access, this paper focuses on the combination of FBMC and SWIPT for future IoT applications by exploiting the intrinsic interference in FBMC as a source of RF energy. The suitability of FBMC for asynchronous transmissions will enable the implementation of grant-free random access at the UNs, which can reduce the synchronization overhead and delay incurred in a typical OFDM-based system. Furthermore, in future wireless networks, an FBMC-based IoT network can coexist 2 with an OFDM-based cellular network to increase the overall system throughput and avoid the leakage interference involved in asynchronous communication in OFDM [1].
Specifically, a multi-user FBMC-based IoT network is considered, in which a single antenna base station (BS) transmits signals to multiple UNs in the downlink (DL) and receives signals from the UNs in the uplink (UL). Each UN can decode information and harvest energy from the received. For the SWIPT implementation, the separate receiver model with separate antennas for the energy and information receivers is considered. Thus, there is no need for TS or PS. The energy receiver is a combination of the antenna for RF energy reception and a rectifier to convert the received RF signal to DC. Moreover, unlike [22], a non-linear energy harvesting model, which is more practical, is adopted in this paper. In order to remove the intrinsic interference in FBMC an iterative interference cancellation (IIC) receiver is employed for the information decoding at both the BS and UN [24]- [26].
It was shown in [27] that because the prototype filters used in FBMC systems are well-localized in frequency domain, even-numbered subcarriers causes negligible interference to other even-numbered subcarriers, i.e., only adjacent (even and odd-numbered) subcarriers interfere with each other. Therefore, following the work in [19], the DL signal is partitioned into even and odd-numbered groups where modulated data is transmitted only on even-numbered sub-carriers. 3 The advantage of this is twofold: (i) by sampling only evennumbered sub-carriers for ID, the ICI level at the UN is significantly reduced, (ii) with reduced ICI, the complexity 1. In the sequel, we refer to FBMC-QAM simply as FBMC 2. The coexist of FBMC-based SWIPT UNs with OFDM-based cellular users is an interesting future topic which is beyond the scope of this paper.
3. This assumption follows from the fact that in many IoT applications the amount of downlink data received is very small compared to the uplink transmission. of the iterative receiver at the UN can also be reduced, which reduces the amount of power consumed by the IIC processing at each UN. Moreover, with a dedicated antenna, the energy receiver can harvest energy from both even and oddnumbered subcarriers. The harvested energy in the DL is then either used to support the UL transmission of the UNs or stored in a battery for the operations of the information receiver. Since the BS has a constant power supply and higher processing capacity for information processing, both even and odd-numbered subcarriers carry modulated data in the UL phase. The main contributions of this work are highlighted as follows.
• This paper investigates a multi-user FBMC-based SWIPT system in which no TS or PS is needed at the SWIPT receiver. A non-linear EH model is adopted to verify the practicality of the proposed model. The proposed system can provide network self-sustainability, improved spectral efficiency and suitability for asynchronous transmissions. • An IIC receiver is implemented to cancel the intrinsic interference at the information receiver of both the UN and the BS. • A weighted sum-rate (WSR) maximization problem is formulated with the aim of optimizing the weight allocation, time allocation, and power allocation of each UN under the total DL transmit power and EH constraints. To effectively solve the WSR problem, it is converted to an equivalent weighted minimum mean squared error (WMMSE) problem, which is then converted to two subproblems: (i) time and weight resource allocation problem and (ii) power resource allocation problem. • The power allocation problem is found to be nonconvex. Thus, an iterative optimization algorithm is proposed using closed-form solutions derived for the DL and UL power allocation. The time and weight allocation problem, on the other hand, is shown to be a convex problem. Therefore, closed-form expressions are derived for time and weight allocations in both DL and UL. The results show that equal time and weight allocations are optimal in the proposed model. • A joint resource allocation algorithm is proposed to combine the solutions of the time and weight allocation problem and the power allocation problem. This algorithm is used to find the maximum WSR using the optimal resources from the two subproblems. • A centralized approach is adopted such that the resource allocation computation is implemented at the BS. This is because the BS can obtain a global channel state information (CSI), has a bigger processing capacity and is supplied by a constant power source. Adopting a centralized approach reduces the computational burden and power consumption at the UN.

C. ORGANIZATION
The remainder of the paper is organized as follows: In Section II, the proposed FBMC-based SWIPT system model and the problem formulation are described. The optimization solutions and algorithms are presented in Section III. Simulation results and complexity analysis of the proposed model are presented in Section IV. Finally, concluding remarks are provided in Section V.

II. SYSTEM MODEL AND PROBLEM FORMULATION
In this section, the details of the proposed multi-user FBMCbased SWIPT system is discussed. The proposed system, shown in Fig. 1, consists of a single antenna BS and K UNs. Each UN has two antennas: one dedicated to information reception and transmission, and the other dedicated to energy reception. The UNs are scheduled to transmit and receive via TDMA.

A. DOWNLINK PHASE
In the DL phase, all UNs undertake EH and ID as shown in Fig. 1. It is shown in [27] that data on even-numbered subcarriers causes negligible interference to other even-numbered subcarriers. This is because FBMC systems employ prototype filters that are well-localized in the frequency domain which limits OOB leakage to adjacent subcarriers. Therefore, in order to reduce the level of intrinsic interference at the UN, QAM modulated data is inserted only on even-numbered subcarriers in the DL. With reduced interference at the UN, the complexity and power consumption of the information receiver can also be reduced. Under this setup, the n-th transmitted symbol vector from the BS to the k-th UN during its assigned time slot τ k is given as G n,k represents the L×M prototype filter matrix whose entry on the l-th diagonal is given as where g[i] is the prototype filter coefficient [27]. Note that the PHYDYAS prototype filter presented in [28] is used for the per subcarrier filtering in this paper.

1) INFORMATION RECEIVER
At the information receiver, the received signal is first filtered, down-sampled and then passed through the FFT block. The resulting signal after the filtering operation is represented as whereH dl k = G H n,k H dl k G n,k , z dl k is the L × 1 additive white Gaussian noise (AWGN) vector at UN k and H dl k is the L × L multipath fading channel matrix between the BS and UN k . The entry on the l-th diagonal of H dl k represents the complex channel gain of the l-th subchannel of UN k and can be modeled as [29] where d k is the distance between the BS and UN k ,d is the reference distance for the path loss, A is the attenuation at the reference distance, κ is the path loss exponent, g t is the BS antenna gain and g r is the UN antenna gain. Also, λ represents the wavelength of the RF signal with frequency f c . The frequency domain signal vector after down-sampling and FFT is given as whereĤ dl k = HHdl k is the M × M down-sampled effective channel matrix andz dl k = H G H n,k z dl k is the M × 1 effective noise vector. As mentioned above, modulated data is inserted only on even-numbered subcarriers in the DL phase. Therefore, the sampled received signal on even-numbered subcarriers of the k-th UN can be expressed as y e,dl n,k =Ĥ e,dl k a e,dl n,k +z dl k , where a e,dl n,k = [a e,dl n,0 , a e,dl n,2 , . . . , a e,dl n,M−2 ] represents the data on even-numbered subcarriers andĤ e,dl k is the corresponding M/2 × M/2 effective channel matrix. By getting rid of the odd-numbered subcarriers, we can assume negligible ICI between subcarriers due to the low OOB emission performance of FBMC. This implies that UN k is only affected by ISI. Thus, the even-numbered demodulated signal associated to the m-th subcarrier and the n-th symbol for UN k is given as  (8) whereĥ e,dl m,n,k is the m-th diagonal element ofĤ e,dl k . To eliminate the ISI term in (8), an IIC receiver is implemented as shown in Algorithm 1 in Section III. Without loss of generality, it is assumed that the receiver undergoes enough IIC iterations to completely remove the ISI term in (8). This assumption has been made in order to obtain insight regarding the optimization of the resource allocation in the energy harvesting and data transmission of the proposed scheme. Moreover, with the reduced intrinsic interference at the UN, fewer number of IIC iterations are required to remove the ISI term in (8). As shown in [3], the IIC algorithm is capable of removing the intrinsic interference with a few iterations. We note that the extension to the case with residual interference after IIC is an important direction for future research. 4 Thus, the demodulated signal after the last IIC iteration can be expressed aŝ r dl m,n,k =ĥ dl m,n,k a e,dl m,n,k +z dl k .
The effective signal-to-noise ratio (SNR) of UN k is calculated as the ratio of the signal power and the effective noise power. From (7), the power of the processed noise can be calculated as where G = G H n,k G n,k and σ 2 z dl k represents the noise variance. Therefore, for the n-th symbol and m-th subcarrier of UN k the effective noise power, σ 2 k = g m,n,k σ 2 z dl k is Gaussian. The 4. Please refer to our work in [3] for an analysis of how many iterations is required to remove the interference below the error floor.
corresponding SNR for UN k is defined as where P dl m,n,k is the power allocated to UN k in the DL. Therefore, the DL data rate of UN k for the time period τ k is given by where N represents the number of FBMC symbols, T denote the total transmission time, and α is the time allocated for DL communication.

2) ENERGY RECEIVER
As mentioned above, each UN is equipped with a separate antenna for EH, which implies that each UN can harvest energy from all sub-carriers in every DL time slot. At the EH receiver, the contribution of noise is assumed to be negligible. Therefore, the received signal at the EH receiver of UN k is given as whereH dl k = H dl k G n,k . Considering the linear EH model, the total harvested power by UN k is given as where β k denotes the energy conversion efficiency in the linear region of the EH circuit, ψ k is the UL transmission time of UN k ,h m,n,j represents the diagonal entries ofH dl k and γ dl m,n,j = K j=1 τ j N n=1 M m=1 |h dl m,n,j | 2 P dl m,n,j . The linear EH model is employed in the literature due to its relatively simple implementation. However, it does not capture the non-linear behavior of the rectifier circuit. To tackle the problem with the linear EH model, the practical EH model in [15] and [30], which uses a non-linear function to model the harvested power, is considered in this paper. By adopting this model, the non-linear harvested power of UN k can be expressed as γ dl m,n,j > P th (15) where k = αβ k (1−α)ψ k and P th is the saturation threshold power of the EH receiver. During the UL time slot of UN k , ψ k , the UL transmit power is P ul k = P k . Furthermore, each user is capable of harvesting energy during all time slots due to their dedicated energy antenna. The energy harvested in other time slots is stored in a battery and the information receiver draws power from the battery for its processing, e.g., IIC algorithm. While the additional processing required for IIC may consume some of the power harvested, there are many applications of IoT networks where the downlink data required to be detected at a UN is very small, and hence negligible compared to the total energy harvested.

B. UPLINK PHASE
Now, consider the multiple access UL communication between the BS and UNs. Since the BS has a higher processing capacity, it is assumed that modulated data is transmitted on both even and odd subcarriers in the UL. This is a practical assumption because in most IoT applications UNs will collect data and transmit to a BS, resulting in a higher data rate requirement on the UL compared to the DL. During time slot ψ k , the n-th transmit symbol vector of UN k is given as Similar to the DL phase, the received signal at the BS is filtered, down-sampled and converted to the frequency domain using the FFT operation. The signal at the output of the receive filter is expressed as whereH ul k = G H n,k H ul k G n,k , z ul is the L × 1 AWGN vector and H ul k is the L × L multipath fading channel matrix between UN k and the BS. After down-sampling and FFT the frequency domain signal vector for UN k is given as whereĤ ul k = HHul k andz ul = H G H n,k z ul . Note that, unlike the UNs, the BS suffer from both ICI and ISI. Therefore, the demodulated signal associated with the m-th subcarrier and the n-th symbol of UN k is given as whereĥ ul m,n,k is the m-th diagonal element ofĤ ul k . As in the DL case, the ICI and ISI terms are estimated and removed by applying a fixed number of IIC iterations at the BS.
Assuming perfect cancellation of the intrinsic interference after IIC, the resulting processed signal is given aŝ r ul m,n,k =ĥ ul m,n,k a ul m,n,k +z ul .
The effective noise power, σ 2 , is calculated as shown in (10) respectively.

C. PROBLEM FORMULATION
Consider the fact that, at each transmit node (UNs or BS), a maximum power threshold is set on the transmit power and that each node's transmission is restricted to its allocated time slot. Under these constraints, we aim to maximize the UL-DL WSR of each UN. Mathematically, the UL-DL WSR maximization problem for the proposed FBMC-based SWIPT system is formulated as where P dl 0,max is the maximum transmit power at the BS and P c is the power consumed by UN k for information processing. ω dl k and ω ul k are the DL and UL weights for To reduce the complexity involved in solving problem P(1), it is converted to an equivalent WMMSE minimization problem [31]. The WSR to WMMSE conversion steps are presented in Appendix A. The WMMSE problem is expressed as represent the MMSE for the DL and UL of UN k (see Appendix A). Problem P(2) can be split into the time and weight resource (TRS) allocation problem and the power resource (PRS) allocation problem as shown in Appendix A. This is expressed as respectively. Here, T RS and P RS are defined as and .

III. INTERFERENCE CANCELLATION AND OPTIMIZATION SOLUTIONS
In this section, the IIC algorithm and the detailed solution for WMMSE problem, P (2), are presented. The optimized parameters obtained from solving P(2) are used in a joint resource allocation algorithm to solve P(1).

A. ITERATIVE INTERFERENCE CANCELLATION
In this subsection, we present the IIC algorithm used in this paper. As mentioned above, FBMC systems achieve improved frequency confinement compared to OFDM. However, this comes with the loss of complex orthogonality between subcarriers, resulting in high intrinsic interference. To remove the interference terms in (8) and (19), an IIC receiver is proposed in this paper. Notice from (8) and (19) that the interference terms are determined by the type of prototype filter, FFT/IFFT, and the fading channel effect. Unless a different prototype filter is selected, the interference terms vary mainly with the fading channel. After the initial decoding iteration, the receiver node (UN or BS), estimates the multipath channel responses (H dl k and H ul k ) and compute the effective channel matricesĤ dl k andĤ ul k using the filter response matrix G n,k and the IFFT matrix . In each iteration, the detected signal is remodulated to obtain estimates of the transmitted data symbols (a dl n,k or a ul n,k ). To obtain the ICI term in (19) the current estimated data symbol is multiplied by the estimated channel and filter responses. On the other hand, the ISI terms in (8) and (19) are obtained by multiplying the previous estimated data symbols by the estimated channel and filter responses. The calculated ICI and ISI terms are then subtracted from the received signal in order to achieve a better version of the demodulated signal in the next iteration. Detailed discussion on the IIC algorithm can be found in [3] and [25], and are shown in Algorithm 1.

B. OPTIMAL RESOURCE ALLOCATION (ORA)
The scheme for solving problem P(1) is presented in this subsection. As shown in the previous section, P(1) can be Algorithm 3 WSR: Joint Resource Allocation Algorithm Run line search to find x for the TRS optimization Set time resource allocation to equal allocation Calculate the weight using ω k = 2x K log (2) T 2 Perform UL and DL IIC using Algorithm 1 Find P dl m,n,k and P ul m,n,k , using Algorithm 2 Calculate sum-rate using the objective function in (23) converted to a WMMSE problem, P(2), which is further split into the TRS and PRS allocation problems. The solutions for the TRS and PRS problems are presented as follows:

1) TRS OPTIMIZATION
The solution for the TRS allocation problem is presented in Theorem 1.
Theorem 1: The optimal time and weight allocation for the WSR maximization problem is equal time and weights allocation, that is, Proof: See Appendix C.

2) PRS OPTIMIZATION
The closed-form solutions for P dl m,n,k and P ul m,n,k are derived by differentiating the Lagrangian of (28) with respect to P dl m,n,k and P ul m,n,k , respectively, and equating the differential to zero. Thus, the optimal DL and UL power allocation for UN k can be express as and . Note that λ dl can be found using the bisection method and λ ul k is given as M m=1 |ĥ dl m,n,j | 2 P dl m,n,j . Proof: See Appendix D. As shown in Appendix D, the PRS problem is non-convex considering all variables jointly. Hence, an iterative algorithm is used to find the local optimum solutions of the DL and UL power allocations as shown in Algorithm 2.

3) WSR: JOINT RESOURCE ALLOCATION
The optimal solutions of the TRS and PRS allocation problems in addition to the IIC algorithm are used in a joint resource allocation algorithm to find the maximum WSR as described in Algorithm 3. The performance of the optimal joint resource allocation algorithm is compared with five suboptimal schemes in the next section.

IV. SIMULATION RESULTS
In this section, numerical results are presented for the proposed multi-user FBMC-based SWIPT system. A set up with 1.4MHz channel bandwidth and 4-QAM modulation is considered in the simulation. The noise spectral density is set as N 0 = −174 dBm/Hz. The UNs are assumed to be randomly distributed within a 10m radius around the BS. For the channel model, the Friis model is assumed for the path loss with κ = 2, A = 1 andd = λ/4π [29]. Here, the energy conversion efficiency in the linear region of the EH receiver is set to 0.5 [32]. Unless otherwise stated, each plot assumes K = 4 UNs.
The optimal scheme is compared to five suboptimal schemes. The list of schemes presented in this section are OOOA, FEFA, FEOA, FOOA, EEOA and EEFA. The labeling of the various schemes use 'O' to represent optimal allocation, 'F' to represent fixed allocation, and 'E' to represent equal allocation. Also, each of the first three letters in the scheme names represent the type of allocation for a particular resource. The first letter represents the time allocation type, the second letter represents the power allocation type, the third letter represents the weight allocation type, and the last letter stands for 'allocation', that is, 'time', 'power', 'weight', 'allocation'. For example, OOOA means optimal time, optimal power, and optimal weights allocations. The various schemes' names and descriptions are described in Table 1. Note that the fixed weight for each UN is set as 5 in the simulation. In addition, the fixed time allocation is achieved by randomly choosing the time allocated for each UN.

A. PROOF AND CONVERGENCE SIMULATIONS
In this subsection, simulation results on Theorem 1, and the convergence of Algorithm 2 are discussed.

1) TRS ALLOCATION RESULTS
For the time resource allocation, simulation results are presented to affirm Theorem 1. Fig. 2 shows plots for the T RS of two UNs for DL (top half) and UL (bottom half)   communications. It can be observed from these plots that the T RS allocations of both UNs are similar for both UL and DL. This is consistent with Theorem 1, which states that the x value in (29) is the same for all UNs in both UL and DL. Also, time and weight allocations are the same. A similar deduction on the x value can be inferred from Fig. 3. From Fig. 3 it is shown that both the x and z functions in (29) for DL and UL communications are the same and possess the same optimal value. This implies that, the BS only has to determine x once, and this can be done by using a simple line search method. In this paper, the Golden Section Search method is used [33]. Fig. 4 shows the convergence curve for the Golden Section Search method. From Fig. 4, it can be observed that the line search method converges after 10 iterations. This implies that determining the value of x and the time and weight allocations would not be computationally intensive. . 5 contains the convergence plot for the DL and UL power resource allocation algorithm. From the figure, it can be observed that 10 iterations is enough to achieve convergence in Algorithm 2. Hence, Algorithm 2 will also not result in a huge computational burden at the BS.

B. HARVESTED POWER SIMULATIONS
In this subsection, simulation results on the energy harvested in the proposed system considering a non-linear EH model are presented. With the antenna threshold effect, the maximum amount of energy harvested by each UN can not exceed k P th , due to the non-linear behavior of the EH receiver circuit. The saturation threshold power is set as 7 dBm [31]. Fig. 6 shows a plot of the amount of power harvested against the BS transmit power. From the figure, it can be observed that as the transmit power increases, the amount of power harvested by each UN increases. There is a constant increase until the EH threshold is reached, which occurs around P dl 0,max = 35 dBm in Fig. 6. At this point, the power harvested cannot exceed the threshold due to the non-linear behavior of the energy harvester. It can be seen from Fig. 6 that, in the range of BS transmit power considered in the simulation, the EH receiver operates predominantly in the linear region for P th = 7 dBm. If a different value of P th is selected, the linear and non-linear regions of the EH receiver will be shifted accordingly. In addition, Fig. 6 shows that all the schemes with equal power allocation (i.e., FEFA, FEOA, EEOA, and EEFA) show a completely linear behavior over the range BS transmit powers.
From Fig. 6(a) it is shown that the available power at each UN is the same for the OOOA scheme because of the equal time allocation for the DL and UL communication. A similar behavior is observed for the EEOA and the EEFA schemes. Also, in the FEFA scheme, UNs have equal power because of the equal power allocation in the DL. However, for the FOOA and FEOA schemes, since there are different time allocations for the DL and UL, the power harvested by each UN is different. Fig. 6(a) shows that for a BS transmit power of 30 dBm, each UN can harvest power of 0 dBm (1 mW) using the proposed optimal scheme. Assuming a typical IoT device that transmits data for a time duration of 450 ms with a maximum peak power of 200 mW and a duty cycle of 10%, it is shown in [34] that if the data transmission occurs every minute the average power transmitted over the period is 0.15 mW. This implies that the amount of energy harvested by the proposed scheme is more than six times the average transmit power required in the UL transmission of such an IoT device. Unlike Fig. 6(a), which shows the amount of power harvested by each UN, Fig. 6(b) shows a plot of the total power harvested by 4 UNs. It can be observed from Fig. 6(b) that the OOOA harvests the most energy and therefore has the highest power available for its UL communication. The order of decreasing amount of power harvested is as follows: OOOA, FOOA, FEFA, EEOA, EEFA, and FEFA. Fig. 7 shows the total amount of power harvested for each scheme with an increasing number of UNs. From the figure, it can be observed that the amount of energy harvested increases with an increasing number of UNs. For the schemes with equal power allocation, increasing the number of UNs beyond K = 6 does not significantly improve the amount of power harvested. This implies that optimizing the power allocated to each UN is necessary to maximize the amount of harvested energy. Fig. 8(a) shows a plot of the weighted sum-rate against BS transmit power. From the plot the descending order of performance is as follows: OOOA, FOOA, EEOA, FEOA, EEFA and FEFA. It can be observed from the figure that the schemes with optimized resource allocations performed better compared to the schemes with fixed resource allocations. Also, it can be seen that the optimal scheme (OOOA) attains the best performance as expected. Note, however, that the scheme with fixed time allocation is only slightly poorer than the fully optimal scheme. This affirms the deductions made in the previous section that the fixed time allocation coincides with the optimal time allocation.

C. WEIGHTED SUM-RATE AND BIT-ERROR-PROBABILITY SIMULATIONS 1) WEIGHTED SUM-RATE
A plot showing the effect of increasing number of UNs on the weighted sum-rate is presented in Fig. 8(b). As expected, with an increasing number of UNs the weighted sum-rate increases for all schemes except FEFA and EEFA. The weighted sum-rate for the FEFA and EEFA schemes remains constant as the number of UNs increases. This is due to the equal/fixed time, power and weight allocations. However, the schemes with either time, power or weight allocations being optimized compensates for the poor performance of the other equally allocated resources, as shown for the EEOA and FEOA curves.

2) BIT-ERROR-PROBABILITY
The bit-error-probability (BEP) expression for the k-th UN can be obtained as in [35], and is given by where Q(·) denotes the Q-function and i is the transmission phase, i.e., DL or UL. Figs. 9(a) and 9(b) show the average BEP for the DL and the UL communications, respectively. From Fig. 9(a), all schemes with equal power allocations have the same BEP values. In addition, the OOOA has a similar BEP when compared to the FOOA scheme due to the use of the DL optimal power and weight allocations for both schemes. Fig. 9(b) considers the UL BEP for the various schemes. The UL depends on the UL power for each UN, which in turn depends on the amount of power harvested during the DL communication phase (i.e., the power available depends on both the DL and UL time allocations). As expected, OOOA and FOOA have better performance compared to the other schemes. In addition, the UL BEP of EEFA, EEOA, FEFA and FEOA schemes are different due to both the time (i.e., equal DL and UL time allocations) and the optimal UL power allocation in each scheme. As can be seen from Fig. 9(b), a BEP of 10 −4 can be achieved by the OOOA scheme on the uplink when the BS transmits with a power of 10 dBm.

D. IMPLEMENTATION AND COMPLEXITY ANALYSIS
Here, the complexity analysis for each proposed SWIPT protocol (i.e., OOOA, FEFA, FEOA, FOOA, EEOA and EEFA) is presented. A centralized processing approach is utilized for the optimal resource allocation, in which all the processing involved in solving problem P(1) are implemented at the BS. This is because the BS has a larger processing capacity, can obtain the global CSI and has a constant power supply.  Table 2.
Note that the centralized approach reduces the processing complexity and power consumption at the UN. However, each UN must perform IIC at the information receiver, which requires local CSI. A detailed complexity analysis of the IIC algorithm is given in [3], including a discussion on alternative approaches to reducing this complexity. It is shown in [3] that only a few IIC iterations are sufficient to remove the intrinsic interference in FBMC. Furthermore, the batteries at the UNs are recharged continuously, while the IIC processing is only needed when the node receives a downlink packet. In most IoT applications, e.g., wireless sensor networks, the amount of downlink data received is very small compared to the uplink transmission. As such the IIC processing will be implemented periodically and can therefore be supported by the harvested power in the batteries. A full analysis of the power consumption of the signal processing at the UNs is beyond the scope of this paper.

V. CONCLUSION
In a multi-user IoT network with energy-constrained devices, SWIPT can serve as a source of power for UNs and provide network self-sustainability. In addition, FBMC is a promising waveform for future IoT applications due to its high spectral efficiency and suitability for asynchronous transmissions. This paper investigated the combination of SWIPT with FBMC systems for IoT networks. Specifically, a multi-user FBMC-based SWIPT system is considered where each UN has two antennas, one for EH and the other for ID. A practical non-linear model is considered at the energy receiver, whereas an IIC receiver is employed at the information receiver. A WMMSE problem is solved to optimize the time, weight and power allocations. Five sub-optimal schemes are proposed for comparison. The complexity analysis of the proposed optimal and sub-optimal schemes is also presented. The results show that the optimal time and weight allocations coincide with equal time and weight allocation. In terms of average sum-rate at BS transmit power of 20 dBm, the optimal scheme outperforms the scheme with equal time, equal power, and optimal weight allocation by about 40%. In summary, the proposed FBMC-based SWIPT system is a promising technique for future IoT applications due to the capability of achieving network self-sustainability, high spectral efficiency and suitability for asynchronous transmissions simultaneously. Future work will investigate a model in which FBMC-based SWIPT IoT devices coexist with OFDM-based cellular devices.

APPENDIX A WSR AND WMMSE RELATIONSHIP
From equations (8) and (19) Substituting v dl m,n,k and v ul m,n,k into (35)     Similarly, the Lagrangian and KKT conditions for the WSR problem with respect to P dl m,n,k and P ul m,n,k are deduced as and Comparing (42) and (43) to (45) and (46), respectively, the WMMSE weights can be estimated as making the WSR and WMMSE problems equivalent. Now, inserting (47) into (41) results in From (48), the WMMSE problem can be split into the time and weight resource allocation problem and the power resource allocation problem as where T RS and P RS are defined in (29) and (30), respectively. Therefore, the weights and time allocation can be determined from (49), while the power allocation can be determined from (50).

APPENDIX B CONVEXITY PROOF OF TIME AND WEIGHT RESOURCE ALLOCATION PROBLEM
The time and weight resource problem can be split into two sub problems, the DL time and weight allocation problem and the UL time and weight allocation problem. The Lagrangian of the individual problems are defined respectively as Concentrating on (51), the first derivatives of L dl RS with respect to the time and weight variables α, τ k , and ω dl k are respectively given as and The Second derivatives of L dl RS with respect to the time variables α, τ k , and ω dl k are respectively derived as . (58) The Hermitian matrix for the DL time and weight resource allocation problem Lagrangian is represented as ⎡ From the Hermitian matrix all the second derivatives have positive values. Therefore, the DL time and weight allocation problem is convex with respect to all its variables. Next, the convexity of the UL time and weight allocation problem is checked. The first derivatives of L ul RS with respect to the time and weight variables α, ψ k , and ω ul k are respectively given as The Second derivatives of L ul RS with respect to the time variables α, ψ k , and ω ul k are respectively derived as , The Hermitian matrix for the UL time and weight resource allocation problem Lagrangian is represented as ⎡ From the Hermitian matrix, L ul RS is non-convex with respect to all variables but convex with respect to individual variables. However, the differentials presented considered α and not (1 − α) as a variable. If (1 − α) is made a variable, then the total problem becomes a concave problem.
From the analysis presented above, both the DL and UL time and weight resource problems are concave problems. 5 Hence, the overall time and weight resource allocation problem is concave.

APPENDIX C OPTIMAL TIME AND WEIGHT RESOURCE ALLOCATION PROOF
From (29), let x k =α k ω dl k T log (2) and z k =α k ω ul k T log(2) , whereα k = ατ k andα k = (1 − α)ψ k . Thus, the optimization problem in (49) can be rewritten as FromT RS the optimal values of x k and z k can be found individually by a line search method usinḡ andT ul RS,k = MN z k − log 2 (z k ) .
This implies that the optimum solution of each UN can be found separately. However, by observingT dl RS,k andT ul RS,k , it can be deduced that the optimal values of x k and z k are the same for all UNs, i.e., x 1 = x 2 = . . . = x K = z 1 = z 2 = . . . = z K = x . Therefore, the line search will be performed once. Based on this deduction, the optimalα k , ω dl k ,α k , and ω ul k should satisfy Note that different combinations of values (i.e.,α k and ω dl k , andα k and ω ul k ) can result in x log (2) T . Therefore, there is 5. The objective functions are individually concave with respect to all the variables. However, the time constraint is linear with respect to all variables. The power constraint is also linear with respect to τ k and ψ k , but concave with respect to α. Since the objective function is concave with respect to all variables, both optimization problems are concave problems. Therefore, the total time and weight allocation problem is concave. a need to find the optimal values ofα k , ω dl k ,α k , and ω ul k . First, let the optimal DL and UL weights be defined as x log (2) α 1 T = ω dl 1 , x log(2) α 2 T = ω dl 2 , . . .
x log(2) α K T = ω dl K , x log(2) α 1 T = ω ul 1 , x log(2) α 2 T = ω ul 2 , . . . , x log(2) α K T = ω ul K . (77) Next, we find the optimal values ofα k andα k . The differential of the optimization problem with respect toα k andα k are given as   λ ul j β ĵ α k > 0, ∀k, which implies thatα k +α k = 0. Therefore,α k = −α k . Moreover, since bothα k andα k are positive valued variables,α k =α k . This implies that the optimal time allocation coincides with equal time allocation, i.e.,α k =α k = 1/K. This also leads to equal weight allocations for all UNs according to (77), i.e., ω dl k = ω ul k = ω k . Therefore, the weight of UN k can be found as ω k = 2x K log(2) Furthermore, the second derivatives of L RS with respect to P dl m,n,k and P ul m,n,k are given as (1−α)ψ j ). An iterative algorithm is used to obtain the optimal P dl m,n,k and P ul m,n,k which minimizes problem (50). The optimal λ dl can be found using the bisection method, while the optimal λ ul k is acquired as