Performance Analysis and Optimization of Energy Harvesting Modulation for Multi-User Integrated Data and Energy Transfer

Yizhe Zhao,Yanliang Wu,Jie Hu,Kun Yang

School of Information and Communication Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China

Abstract: Integrated data and energy transfer(IDET)enables the electromagnetic waves to transmit wireless energy at the same time of data delivery for lowpower devices.In this paper,an energy harvesting modulation (EHM) assisted multi-user IDET system is studied,where all the received signals at the users are exploited for energy harvesting without the degradation of wireless data transfer (WDT) performance.The joint IDET performance is then analysed theoretically by conceiving a practical time-dependent wireless channel.With the aid of the AO based algorithm,the average effective data rate among users are maximized by ensuring the BER and the wireless energy transfer(WET)performance.Simulation results validate and evaluate the IDET performance of the EHM assisted system,which also demonstrates that the optimal number of user clusters and IDET time slots should be allocated,in order to improve the WET and WDT performance.

Keywords: energy harvesting modulation(EHM);integrated data and energy transfer(IDET);performance analysis;wireless data transfer (WDT);wireless energy transfer(WET)

I.INTRODUCTION

1.1 Background

The development of wireless technologies are requiring a larger connectivity in the upcoming 6G network,while enormous wireless devices are swarming into the smart city for providing intelligent services for human beings.Some micro devices,such as wireless sensors,are playing important roles for monitoring the surroundings and for returning feedbacks for the core networks.These bring conveniences for the further researches of many other subjects,such as geosciences [1][2].It’s becoming a great challenge to power all these micro devices with a little labour cost.Against this background,radio frequency (RF)based wireless energy transfer (WET) [3][4] enables the electromagnetic waves to deliver wireless energy for these low-power devices remotely.The controllability,stability and the convenience of WET indicate that it would be a promising technology to address the problem of power supplement in the future wireless networks.Considering the requirement of data transfer of these devices,coordinating both wireless data transfer (WDT) and WET yields the concept of integrated data and energy transfer(IDET)[5–9].

In the IDET assisted wireless systems,WDT and WET should be coordinated by allocating different resources,such as time,frequency,and antennas.Some classic approaches for separating WET and WDT have been studied,which separate the time domain,the power domain or the spatial domain for either WET or WDT.Some balance should also be achieved,in order to realize the trade-off between the WET and WDT performance.

Besides,modulation schemes in the physical layer should be studied for IDET for the sake of improving both the WET and WDT performance.In addition to the traditional modulation schemes such as M-QAM,PSK and FSK,other novel schemes should be studied by jointly considering the characteristics of information decoding and RF energy harvesting.For instance,by designing the irregular modulation schemes with a high PAPR,the WET performance can be readily improved.It would be more efficient to coordinate WET and WDT by designing appropriate modulation schemes.

1.2 Related Work

Plenty of works have focused on the joint design of an IDET system,where WDT and WET signals should be appropriately coordinated.Conventional IDET systems usually rely on two approaches to realize simultaneous transfer of wireless energy and data information,namely time switching (TS) [10,11] and power splitting (PS) [12,13].In TS,the signals are separated in the time domain,while a switcher is equipped at the receiver to forward the received signals to either energy harvester or information decoder.In PSbase IDET system,the received signals are divided into two fractions with the aid of a power splitter,one for information decoding and the other for energy harvesting.Both TS and PS schemes require additional components at the receiver end,which increases the system complexity.Based on these IDET architecture,resource allocation is further studied for improving the joint IDET performance.For instance,Yang et.al [5] developed an algorithm to jointly optimize the transmission power and the power splitting ratio in a cellular network.Li et.al [14] studied a similar network,in which the jointly allocations of subcarrier,transmit power and power splitting ratio were optimized.Hong et.al[15]studied the resource allocation in a unmanned aerial vehicles (UAVs) assisted IDET network,in which the trajectory and transmit power of the UAVs were optimized,in order to improve the WET performance in an IDET system.Sun et.al [16] proposed a novel scheme,in which time,power and spectrum are jointly and adaptively allocated,in order to achieve a higher throughput for IDET devices.Ketcham et.al [17] investigated a lowcomplexity resource allocation strategy to tackle with the power allocation and beamforming design in an OFDM-based multiuser IDET system,where a broadcast channel was conceived.The non-linear energy harvesters are considered in recent IDET works.These energy harvesters are essentially rectifiers that converts the input alternating current (AC) to direct current(DC).The conversions are always non-linear,due to the characteristics of capacities,diodes and antennas in circuits.Besides,there is always a favorable input range for practical energy harvesters,by considering the activating sensitivity and saturation effects of the circuits.For instance,Kim et.al [8] adopted a single-diode rectifier circuit as an energy harvester,which consisted of an impedance matching circuit,a diode and a smoothing circuit(low pass filter).Moon et.al [18] designed a novel heterogeneous reconfigurable device including low-power and high-power energy harvester(LP/HP-EH)blocks.Xu et.al[19]considered a general non-linear energy harvester having a classic S-shaped curve of input and output power.The relevant parameters,which were determined by circuit specifications,could be readily obtained by fitting the in/out-power-curve constructed from experimental results.This general non-linear energy harvesting model was widely used in[20,21].

Some works also focused on the modulation design in the physical layer for improving the IDET performance.Apart from some conventional modulation schemes including frequency shift keying (FSK)[22],amplitude shift keying (ASK)[23] and binary phase shift keying(BPSK)[24],some studies also focused on novel modulation techniques such as asymmetric [25] and rotation-based [26] constellation designs.In the case of that existing conventional constellation designs may not be suitable for energy delivery,these works were seeking for some specially designs of constellation for IDET purpose.Bayguzina et.al [25] considered a asymmetric phase-shift keying(PSK)modulation scheme,which can improve the IDET performance significantly.Zhao et.al [26]proposed a constellation rotation-based modulator to boost the energy delivery for WET users in a nonorthogonal-multiple-access (NOMA) system.Moreover,there have been dozens of works about irregular modulation techniques for IDET.By modulating additional bits to the indices of some communication resources,the throughput and spectrum efficiency of IDET systems is readily improved.For instance,spatial modulation schemes [27,28] implant additional bits into the indices of activated antennas,while the energy signals are transmitted on the inactivated antennas for improving the WET performance.Tone-index modulation scheme [29] was also proposed to transmit data information via the activated carrier indices for WET,while the energy harvesting efficiency can be enhanced due to a higher power-average-peak-ratio(PAPR).Cheng et.al [30] proposed a scheme based on carrier index differential chaos shift keying (CIDCSK),which exploit the inactive carriers to transmit energy signals.Cai et.al [31] proposed a code index modulated multi-carrier M-ary differential chaos shift keying(CIM-MC-M-DCSK)system,which drastically increases the data rate under a low-complexity IDET system.Moreover,some works also attempt to modulate all the information bits onto the pattern of WET signals.Kim et.al [32] proposed a novel approach,in which information bits are encoded into the positions of the energy pulses for energy delivery.Therefore,the transmitter only needs to send designated WET signals,while dedicated WDT signals are not required anymore,which can reduce the hardware complexity.

1.3 Motivation and Contribution

In the existing works,WET and WDT should be separated independently either in the time domain,power domain or others.Therefore,an improvement of the WET(or WDT)performance may result in the degradation of the other.This is the main problem on the coordination of WET and WDT.Zhou et.al [33] proposed an integrated energy harvesting and information decoder receiver (IntRx),where the received power level is used as a reference for information decoding.However,a power splitter was still required at the receiver,while trade-off between WET and WDT performance still existed.Motivated by this,we aim to study a novel irregular modulation scheme namely energy harvesting modulation (EHM),where separation between WDT and WET signals is not required.Motivated by this,we aim to study a novel irregular modulation scheme namely energy harvesting modulation(EHM),where no separation between WDT and WET signals is required.The delivered information is modulated on the different transmit power level,while a meter is equipped parallel with the energy harvesting circuit for measuring the energy harvesting power and for the following information decoding.Therefore,we do not need any signal splitters at the receiver,since there is no tradeoff between WDT and WET.The hardware complexity of the receiver can also be substantially reduced by removing the signal splitter and traditional signal processing modules,such as the passband-to-baseband converter.

Moreover,wireless channels are always time dependent in practical scenarios,which urges us to consider the channel characteristic on the joint IDET design.Meanwhile,in the multi-user scenario,channel estimation is required multi-times within a period,in order to overcome the impact of frequent channel fluctuation.Against this background,our novel contributions are summarised as follows:

• An EHM assisted multi-user IDET system is studied,while the EHM based transceiver architecture is also proposed.All the users are separated into multi clusters for overcoming the channel fluctuation impact.

• The joint IDET performance,namely the average bit error ratio (BER),the average effective data rate,as well as the average energy harvesting amount,are analysed theoretically by conceiving a time-dependent wireless channel.

• The optimal numbers of the clusters and the time slots for each receiver are obtained,in order to maximize the average effective data rate of all the users by constraining the BER and the energy harvesting performance.

• Monte Carlo based simulations validate the theoretical analysis and also evaluate the joint IDET performance of the EHM assisted system.

II.SYSTEM MODEL AND TRANSCEIVER ARCHITECTURE

The EHM assisted IDET system includes a MBS and K users (low-power devices),which are all equipped with a single antenna.The time domain is discretized into multi time slots,each of which has a duration of T.At each time slot,one EHM modulated symbol is transmitted to the targeted user,while the user is able to detect the received power for the energy harvesting demodulation and further for recovering the data information.The duration of a time slot should be larger than that of the symbol duration in 5G new radio(NR),so that the user can sample multi times for obtaining the average receive power,in order to reduce the bursty impact caused by the noise.By adopting EHM,the traditional receive signal processing modules are not required at the user,so that its hardware complexity can be largely reduced.Assume that Q time slots are required for IDET of each user.All the K users should also be allocated with different time slots for IDET,in order to avoid the inter-user interference.

2.1 Transceiver Architecture

The transceiver architecture of the EHM assisted IDET system is illustrated in Figure 1.Firstly,the normalized complex deterministic energy signal x satisfying |x|2=1 flows into the power controller for energy harvesting modulation.Various transmit power is allocated to energy signals according to the data information targeted at a specific user in the corresponding time slot.Note that in the EHM assisted IDET system,the downlink WDT modules are not required at the users.A meter is also equipped at the energy harvester to detect the harvested power level in real time.The detection results flows into the processing unit for the energy harvesting demodulation,according to the average energy harvesting power in each time slot.Generally,the meter could only detect the direct current(DC) energy harvesting power after the received signal flows through the non-linear energy harvester.It’s assumed that the non-linear energy harvesting model is known at the processing unit,so that it’s able to derive the received signal power at the receive antenna in the RF domain.Compared to the traditional TS or PS based IDET systems,EHM assisted IDET system enables the user to harvest all the energy of the received signals,since the energy consumption of the meter is negligible.Moreover,the user has a low hardware complexity,which is more suitable for the low-power devices.

Figure 1. System scenario and transceiver architecture of EHM assisted multi-user IDET system.

2.2 Channel Model

The path-loss between the MBS and the k-th user is denoted as Ωk,while the fast fading coefficient between the MBS and the k-th user in the l-th time slot is denoted as hk,l∈C.The time-dependent wireless channel in[34]is conceived in this system,where the fast fading coefficient in the current time slot is correlated to the previous time slots.The channel coefficient hk,lobeys the following recursive relationship:

where αkrepresents the temporal fading coefficient of the k-th user,while ωk,lrepresents the fading fluctuation of hk,l.It’s assumed that all the users have the same fading coefficient αk=α.According to [34],ωk,lfollows a Gaussian distribution of.Within a period,the received signal at the k-th user in the l-th time slot is expressed as

where Gaussian distributed zlrepresents the additional white Gaussian noise(AWGN)having an average power ofat the receive antenna in the l-th time slots.

2.3 Fundamental Rules of EHM

In the EHM,the data information is transmitted via the RF transmit power level.Assuming M-order EHM is conceived,the transmit power of the l-th energy signal is Pl=mk,lδ,where mk,lrepresents the label of the modulated symbolfor the k-th user in the l-th time slot,δ represents the transmit power unit.The M-order EHM actually modulates M different data information that need to be transmitted to the targeted user.

Since the user does not have any receive signal processing modules,channel estimation is also unavailable.Therefore,an reference energy signal having a transmit power of P1=uδ should be firstly transmitted in a reference time slot,so that each user can obtain the estimated value of the receive power unit(k=1,···,K),which is attenuated by the wireless channel.Note that u is a predefined value,which is known at both the MBS and all the users.In the following time slots,the users can operate energy harvesting demodulation according to the reference value ofand recover the required data information.It’s assumed that each user is allocated with successive Q time slots for WDT.If the l-th time slot is allocated for IDET of the k-th user,it can recover the modulated symbol label as

Since the wireless channel gains vary with time slots,only one reference time slot is not sufficient for estimating the accurate receive power unit,especially when the allocated time slots for a user is far from the reference time slot in the time domain.Therefore,it’s wise to separate all the K users into N clusters {K1,K2,···,KN},as shown in Figure 1.Every reference time slot is allocated for the estimation of the receive power unit for the users in each cluster Kn(n=1,···,N).The number Knof the users in each cluster is calculated as Kn=(n=1,···,mod(K,N))and Kn=(n=mod(K,N)+1,···,N).In the following context,we replace the user label k with kn(kn=1,···,Kn),which indicates the user label in Kn.Other similar operations are also required to replace hk,l,Ωk,zk,l,Pl,,respectively.

The time slot allocation of the EHM assisted IDET system is illustrated in Figure 2.Similar to the separation of all the users,the time slots should also be separated by clusters,while the time slot cluster for Knis denoted as Ln.A time circle is denotes as L={L1,···,LN},while the number of time slots in Lnis denoted as Ln.In the first time slot in Ln,the reference energy signal is broadcasted to all the users in Kn.Then,Knusers in the cluster operate IDET in their allocated times slots,while operate WET in other time slots.It’s assumed that the IDET time slots for all the users are allocated orderly according to the user labels,i.e.,the kn-th user should operate IDET ahead of the(kn+1)-th user.Further,the number of time slots required for providing IDET services for all the K users is formulated as

Figure 2. Time slot allocation for EHM assisted multi-user IDET system.

III.PERFORMANCE ANALYSIS

3.1 IDET Performance

In the time slots set Ln,the average received RF power for energy harvesting at the kn-th user in the l-th time slot is derived as

The meter of the user is able to measure the energy harvesting power multi times within a time slot.Then,the processing unit can derive the average received RF power of the signals,in order to reduce the bursty impact caused by the AWGN.

According to Eq.(1),the channel gainbetween the MBS and the kn-th user in the l-th time slot of Lncan be reformulated as

where I0(·)is the modified Bessel function of the first kind expressed as

According to the received power of the energy signal transmitted in the reference time slot,the estimated receive power unitfor energy harvesting demodulation is obtained as

If the l-th time slot in Lnis allocated for IDET for the kn-th user,when the symbolis transmitted,the symbol error probability (SEP)can be expressed as Eq.(10).

Assuming identical transmit probabilities of all the M symbols for each user,the average SEP of the kn-th user in the l-th time slot is then formulated as

In the l-th time slot in Lnwhich is allocated to the kn-th user,it’s likely to suffer from the demodulation error.The energy harvesting demodulation error usually occurs between two modulated symbols which are adjacent in the power domain.Assuming that Grey mapping rule is adopted between the symbol and the corresponding binary sequence,there is approximately only one bit error when the IDET demodulation fails.Consequently,the average bit error ratio(BER)for the kn-th user in Knwithin the duration of Lnis formulated as

where l(n,kn) represents the starting label of the IDET time slots allocated for the kn-th user.

3.2 WET Performance

In the EHM assisted IDET system,all the received power can be used for energy harvesting.The nonlinear energy harvesting model in [19] is conceived in this system.Then,the average energy harvesting power at the kn-th user in the l-th time slot in Lnis formulated as

Moreover,PMAXis the saturation energy harvesting power,PSENdenotes the energy harvesting power sensitivity,and a,b are constants related to the energy harvesting circuit.The total average energy harvesting power of the kn-th user per time slot within a time circle is further formulated as

IV.EHM ASSISTED IDET SYSTEM DESIGN

4.1 Problem Formulation

By separating all the K users into N clusters,it’s able to improve the data transmission reliability of the bad user,which is allocated with much later time slots from the reference time slot.However,when N is too large,the increased reference time slot number in a time circle hardly achieve a reliability improvement,but may increase the redundancy of the non-IDET time slots and further reduce the effective data rate.This is the same to the IDET time slots number Q.In order to achieve the total effective data rate of all the users,our optimization problem can be proposed as

where (21a) indicates the reliability constraint for all the users,(21b) provides a constraint on the energy harvesting performance,while (21c)and (21d) represent the integer constraint on N and Q.

4.2 Optimization Algorithm

Observe that(21)is an integer programming problem,while conventional optimization tools like convex optimization may not be efficient.Although exhaustive searching is able to obtain the optimal solution,the complexity of the algorithm is unaffordable.Aquila Optimizer (AO) [35] is a novel meta-heuristic technique that stimulates Aquila’s hunting behavior,which has faster converge speed for obtaining optimal solutions comparing to its peers.Therefore,AO aided algorithm is considered as a candidate for solving this complex problem.The details of the AO aided algorithm is summarised as follows.

A population of solutions is initialized asΘ(0)=,having the size of G and each individual is defined as.The populationΘ(0)is then updated asΘ(i)subsequently until reaches the maximum iteration number I.After initialization,the population of solutions is updated by one of the following four actions,where νi(i=1,2,···) are random variables following the uniform distribution within [0,1].Noted that the results after each action should be rounded to integers.•Action 1: Expanded exploration.This action mimics the soaring behavior of Aquila in order to select the best hunting area.The i-th generation of individualis updated as

where θ(i−1),∗is the optimal individual in the(i−1)-th generation,andis the average of all the individuals in the(i −1)-th generation.

•Action 2: Narrowed exploration.The optimizer narrowly explores the selected area.The i-th generation of each individualis updated as

where g′is a random integer variable selected from{1,···,G},τ1and τ2determine the spiral shape of searching,and Levy is a levy flight distribution function.The details of selection of τ1,τ2and Levy are provided in[35].

•Action 3: Expanded exploitation.The optimizer exploits the selected area and approaches optimal solutions.The i-th generation is updated as

where UB and LB are the upper and lower bound of,respectively,while κ1=κ2=0.1 are constants according to[35].

•Action 4: Narrowed exploitation.The optimizer finally seizes the optimal solution in small steps.The i-th generation is updated as

where QF(i)is a quality function defined in[35].

The details of the AO aided algorithm is summarised in Algorithm 1.

V.SIMULATION RESULTS

5.1 Parameter Settings

Monte Carlo based simulation is adopted for validating and for evaluating the IDET performance of the EHM assisted system.The modulation order is set as M=8,the number of users is K=20 and the IDET time slots number for each user is Q ∈[1,10].The transmit power unit is set to δ=0.1 W and the reference unit is u=1,while the average power of the noise and interference is set to σ2=−50 dBm [36].Line of sight (LOS) channel is conceived in the simulation [37],while the PDF of=ρ is expressed as

where 2b0=0.5 and=0.5 are the channel power gain of the LOS and NLOS component,respectively.The variance of the channel fluctuation between time slots is set to=0.01,while the path-loss Ωkfor the k-th user follows the uniform distribution Ωk～U[−35,−30]dB.The parameters related with the nonlinear energy harvesting circuit is set to a=150,b=0.014,PSEN=−40 dBm and PMAX=0.024 mW[19].

5.2 IDET Performance

We validate the theoretical analysis of average BER among all the users of the EHM assisted IDET system in Figure 3.Observe from Figure 3 that the theoretical results and the simulation results match perfectly.When we gradually increase the IDET time slots number Q for each user,the average BER increases.This is because a larger Q indicates a larger channel gain difference between the reference time slot and the IDET time slot for each user,which may cause more demodulation errors.A larger cluster number N also corresponds to a lower BER,since more reference time slots are allocated to overcome the channel fluctuation.Moreover,when the temporary fading coefficient α is larger,the wireless channel is more flatting,which results in a lower BER.

Figure 3. Average BER vs IDET time slots number Q for each user.The solid lines are theoretical results and the dots are simulation results.

Figure 4 depicts the BER versus user number per cluster.Observe from Figure 4 that more users within a cluster results in a higher BER.This is because when we have more users,there are more time slots in a time slot cluster,which causes a higher channel fluctuation and consequently reduces the demodulation accuracy.We also evaluate the BER performance with different modulation orders in Figure 5,when the average transmit power is fixed.Observe from Figure 5 that a higher modulation order always results in a higher BER,since the power distance between two adjacent EHM symbols becomes smaller.

Figure 4. Average BER vs user number per cluster.The solid lines are theoretical results and the dots are simulation results.

Figure 5. Average BER with different modulation orders.

In Figure 6,we compare our EHM scheme with traditional TS and PS approaches,in which classic MQAM modulation scheme is conceived by ensuring the same modulation order with EHM.Observe from Figure 6 that our EHM scheme outperforms the TS and the PS approaches with a lower average transmit power,since no signal splitting is required for separating WDT and WET.When the average transmit power increases,the TS and the PS approaches achieve a better BER performance.This is because the information is modulated in the power domain in our EHM scheme,while it’s modulated in the phase-amplitude domain in the TS and the PS approaches.Due to the impact of time-dependent wireless channel,the fluctuation in the power domain is higher than that in the phase-amplitude domain,since the power is equal to the square of the corresponding amplitude.When the average transmit power is higher,the power fluctuation dominates the impact on BER.Therefore,our EHM scheme is more suitable,when the average transmit power is lower than 30 dBm.Figure 7 depicts the BER versus the average pathloss Ωavrbetween the MBS and the users,where the pathloss for each MBS-user pair is randomly selected within the range of[Ωavr−2.5,Ωavr+2.5]dB.Observe from Figure 7 that a severe pathloss results in a higher BER.Moreover,when the pathloss becomes slight,the BER displays a flat trend,which has the similar reason as the curve in Figure 6.

Figure 6. Comparison among EHM,TS and PS approaches.

Figure 7. Average BER vs average pathloss between the MBS and users.

Figure 8. Average energy harvesting power per time slot vs user cluster number N.The solid lines are theoretical results and the dots are simulation results.

Figure 9. Average energy harvesting power per time slot vs IDET time slots number Q for each user.The solid lines are theoretical results and the dots are simulation results.

Figure 10. Average effective data rate vs user cluster number N.

Figure 11. Average effective data rate vs IDET time slots number Q for each user.

Figures.8 and 9 depicts the WET performance versus cluster number N and IDET time slots number Q.Observe from Figures.8 and 9 that the WET performance is concave respect to N and Q.Taking N as an example,when the cluster number is small,one reference time slot is related with more IDET time slots.However,since the temporal fading coefficient α ＜1,the mean value of the channel coefficient becomes smaller with time,which causes the energy harvesting power degradation.A large N may relief this degradation and improve the WET performance.When N is large,there are more reference time slots within a time circle.Since the reference unit is set to u=1,the energy harvesting power of the reference time slot is lower than the IDET time slot.Consequently,when we continuously increase N,the WET performance is degraded.Similar explanation is also suitable for the concave trend of Q.

We evaluate the average effective data rate in Figures.10 and 11.Similar with the WET performance,the average effective data rate also illustrates a concave trend with respect to N and Q.When the cluster number N is smaller,the increasing of N may result in a lower BER and further a higher η.However,if we continuously increase N,the reference time slots gradually dominates the whole time circle,which results in less IDET time.Therefore,the average effective data rate η is degraded.Similar explanation is also suitable for the concave trend of Q,where the increasing of a larger Q value has the same impact as the decreasing of a smaller N.Moreover,a larger α results in a higher η,since the channel is more flat and less demodulation errors occurs.

Figure 12 plots the convergence of Algorithm 1.Observe from Figure 12 that the AO aided algorithm always converges within 50 iterations by setting different values of α.Note that the convergence curves of the AO aided algorithm show the step-wise trends,since the algorithm is sometimes trapped at a local optimal solution and requires iterations to escape from it.Then,Figure 13 evaluates the optimization results of (21),where the energy harvesting constraint is set to=2×10−5W and all the users have the same BER threshold=ϵth(∀n,kn).Observe from Figure 13 that when the BER threshold increases,the optimal average effective data rate η also increases,since we are able to select a smaller N or a larger Q for reducing the redundancy of the reference signals.However,if the BER threshold is too large,the optimal value of N and Q illustrated in Figures.10 and 11 can be readily obtained.Therefore,a more relax BER constraint does not improve the optimality of the average effective data rate.

Figure 12. Convergence of Algorithm 1.

Figure 13. Optimal average effective data rate vs BER threshold.

VI.CONCLUSION

An EHM assisted multi-user IDET system is studied in this paper,while all the received signals at each user are used for energy harvesting without degrading the WDT performance.All the users are separated into clusters,in order to relief the impact of the channel fluctuation.The IDET performance are theoretically analysed by conceiving the time-dependent wireless channels.With the aid of the AO based algorithm,the average effective data rate is maximized,by ensuring the energy harvesting performance and the BER at the user.Simulation results validate our theoretical analysis,which also provide some insights for the joint IDET system design.

ACKNOWLEDGEMENT

This work is supported in part by the MOST Major Research and Development Project (Grant No.2021YFB2900204),the National Natural Science Foundation of China (NSFC) (Grant No.62201123,No.62132004,No.61971102),China Postdoctoral Science Foundation (Grant No.2022TQ0056),in part by the financial support of the Sichuan Science and Technology Program(Grant No.2022YFH0022),Sichuan Major R&D Project (Grant No.22QYCX0168) and the Municipal Government of Quzhou(Grant No.2022D031).