Signal and System Design for Wireless Power Transfer : Prototype, Experiment and Validation
aa r X i v : . [ c s . I T ] A ug Signal and System Design for Wireless PowerTransfer : Prototype, Experiment and Validation
Junghoon Kim, Bruno Clerckx, and Paul D. Mitcheson
Abstract —A new line of research on communications andsignals design for Wireless Power Transfer (WPT) has recentlyemerged in the communication literature. Promising signal strate-gies to maximize the power transfer efficiency of WPT relyon (energy) beamforming, waveform, modulation and transmitdiversity, and a combination thereof. To a great extent, thestudy of those strategies has so far been limited to theoreticalperformance analysis. In this paper, we study the real over-the-airperformance of all the aforementioned signal strategies for WPT.To that end, we have designed, prototyped and experimented aninnovative radiative WPT architecture based on Software-DefinedRadio (SDR) that can operate in open-loop and closed-loop (withchannel acquisition at the transmitter) modes. The prototypeconsists of three important blocks, namely the channel estimator,the signal generator, and the energy harvester. The experimentshave been conducted in a variety of deployments, includingfrequency flat and frequency selective channels, under staticand mobility conditions. Experiments highlight that a channel-adaptive WPT architecture based on joint beamforming andwaveform design offers significant performance improvementsin harvested DC power over conventional single-antenna/multi-antenna continuous wave systems. The experimental results fullyvalidate the observations predicted from the theoretical signaldesigns and confirm the crucial and beneficial role played by theenergy harvester nonlinearity.
Index Terms —Energy harvesting, Wireless Power Transfer(WPT), Waveform, Beamforming, WPT Prototype, Nonlinearity
I. I
NTRODUCTION I NTERESTS in radiative (far-field) Wireless Power Transfer(WPT) have been growing recently because WPT is aninvaluable technology to energize a large number of low-power autonomous devices. It is viewed as an enabler for manyemerging applications such as the Internet of Things, WirelessSensor Networks, and for innovative wireless networks whereradiowaves are used for the dual purpose of communicatingand energizing [1]. In particular, radiative WPT is attractivesince it enables long-distance power delivery and small re-ceiver form factors, in comparison with other technologies.A crucial challenge of radiative WPT system design is tomaximize the harvested DC power subject to a transmitpower constraint, or equivalently to enhance the end-to-endpower transfer efficiency. To that end, the traditional line ofresearch in the RF literature has been devoted to the design ofefficient rectennas so as to increase the RF-to-DC conversion
The authors are with the Department of Electrical and Electronic En-gineering, Imperial College London, London SW7 2AZ, U.K. (e-mail:junghoon.kim15, b.clerckx, [email protected]). This paper is anexpanded version from the IEEE MTT-S Wireless Power Transfer Conference,Taipei, Taiwan, May 10-12, 2017. This work has been partially supported bythe EPSRC of UK, under grant EP/P003885/1. efficiency. It is well-established that a variety of technologies(e.g. CMOS, Diode) and topologies (e.g. single shunt, voltagemultiplier) can be considered for rectenna designs [2]–[4].Aside rectenna design, a new and complementary line ofresearch on communications and signal design for WPT hasemerged recently in the communication and signal processingliterature [5]. Indeed the amount of DC power that can beharvested is not only a function of the rectenna design but alsoof the transmit signal strategy and of the wireless propagationchannel condition. In other words, the transmit signal designhas a major impact on the end-to-end power transfer efficiencyas it influences the signal strength at the input of the rectennabut also the RF-to-DC conversion efficiency of the rectifier.Four different kinds of transmit signal design strategies havebeen proposed, specifically for WPT purposes, to boost thereceived DC power.A first strategy is to design (energy) waveforms in orderto exploit the rectenna nonlinearity and boost the RF-to-DCconversion efficiency e rf − dc . Previous studies have observedthat multisine waveforms can increase e rf − dc [6], [7], andthat high Peak-to-Average Power Ratio (PAPR) waveforms en-hance e rf − dc [8]. A systematic waveform design methodologyfor WPT was first proposed in [9]. Waveforms can be designedwith and without Channel State Information at the Transmitter(CSIT) depending on the frequency selectivity of the channel.The optimal design of channel-adaptive waveform in [9] re-sults from a tradeoff between exploiting the channel frequencyselectivity (so as to maximize the RF-to-RF transmissionefficiency e rf − rf ) and the energy harvester (EH) nonlinearity(so as to boost the RF-to-DC conversion efficiency e rf − dc ).Due to the rectifier nonlinearity, the optimal waveform designcan be obtained as the solution of a non-convex optimizationproblem, which is not easily implemented in a real-timesystem. Strategies for reducing waveform design complexityhave therefore been introduced in [10]–[12]. Moreover, sinceCSI needs to be acquired to the transmitter, a proper jointdesign of the waveform and the channel acquisition strategyneeds to be considered, and a possible solution is to designthe waveform for WPT based on a limited number of feedbackbits [13].A second strategy is to design multi-antenna (energy) beamforming in order to increase the RF input power ofthe energy harvester and therefore enhance the RF-to-RFtransmission efficiency e rf − rf . This strategy also requires anappropriate CSIT acquisition scheme for WPT [14]. Similarlyto wireless communications, the simplest form of beamform-ing is Maximum Ratio Transmission (MRT) [15]. Alternativetechniques to multi-antenna beamforming, also enabling direc- tional/energy focusing transmission, consist in retrodirectiveand time-modulated arrays [16] and time-reversal techniques[17]. Waveform and multi-antenna beamforming can be com-bined so as to optimally exploit the beamforming gain, thechannel frequency diversity gain and the nonlinearity of therectifier [9], [11].A third strategy is to design (energy) modulation forsingle-carrier transmission. In contrast to the energy wave-form that commonly relies on an optimized deterministicmultisine/multi-carrier, the energy modulation induces ran-dom fluctuations of a single-carrier. Similarly to the energywaveform, the design of the energy modulation aims at ex-ploiting the nonlinearity of the rectifier to boost the RF-to-DC conversion efficiency e rf − dc . Indeed, as a consequenceof the energy harvester nonlinearity, the RF-to-DC conversionefficiency e rf − dc differs depending on whether the rectifierinput signal is modulated or not [18]. For instance, a realGaussian modulation offers a higher harvested DC power thana circularly symmetric complex Gaussian modulation [19].A new modulation scheme based on flash signaling (a formof on-off keying distribution with low probability of highamplitude signals) has recently been introduced in [20]. Itexploits the rectifier nonlinearity by transmitting signals ofvery high amplitudes with low probability. Flash signalingwas shown to outperform a real Gaussian modulation andmaximize the amount of harvested DC power. Flash signaling-based energy modulation can also be combined with multi-antenna so as to additionally exploit a beamforming gain.A fourth strategy is to use phase sweeping transmit di-versity in a multi-antenna WPT setup to boost the RF-to-DC conversion efficiency [21]. Transmit diversity aims atartificially inducing fast fluctuations of the wireless channel atthe input of the rectifier using dumb transmit antennas. Thosefluctuations are shown to improve the RF-to-DC conversionefficiency thanks to the rectifier nonlinearity. Interestingly,transmit diversity does not rely on CSIT and demonstratesthat multiple transmit antennas can be beneficial to WPT evenin the absence of CSIT.The theoretical performance benefits of the aforementionedfour signal strategies have been studied in the literature, basedon simplified linear and nonlinear energy harvester models.Since the theoretical analysis relies on numerous assumptions,commonly made to simplify the signal and system design, itremains to be seen whether those emerging signal designs forWPT still deliver the expected benefits in a realistic setup.In particular, aside the crucial nonlinearity and nonidealitiesof the energy harvester, real-world experimentation of WPTis subject to numerous impairments such as amplifier nonlin-earity and gain/phase offset, that are neglected, and can beoverlooked, in any theoretical analysis. This calls for proto-typing and experimenting those emerging signal strategies toassess their real-world performance and validate the feasibilityof the underlying signal theory for WPT.There have been studies on WPT prototyping, in both theRF and the communication literature. In the RF literature,multisine waveforms have been experimented in [6], [22], [23]and the corresponding e rf − dc has been measured. These exper-iments were performed using open-loop based prototypes with static and heuristic waveforms fed directly into the rectifier,not using closed-loop based architecture with channel-adaptive(relying on CSIT so as adjust the transmission strategy dy-namically as a function of the wireless frequency-selectivepropagation channel) and optimized waveforms transmittedover-the-air. In the communication literature, emphasis hasbeen put on closed-loop based adaptive beamforming with amulti-antenna transmitter, as shown in e.g. [24]–[28]. Theseworks studied channel acquisition techniques, and over-the-airfeedback, for WPT and focused on increasing e rf − rf throughadaptive beamforming.Recall nevertheless that maximizing the end-to-end powertransfer efficiency is not achieved by maximizing e rf − rf and e rf − dc independently [5], [29]. This is because e rf − rf and e rf − dc are coupled due to the rectifier nonlinearity. This callsfor systematic signal strategies that maximize the overallpower transfer efficiency e rf − rf × e rf − dc by jointly accountingfor the effect of the wireless channel and the harvester non-linearity [5], [9], [29], and therefore completely bridge the RFand communication approaches. The first prototype to demon-strate the feasibility and over-the-air performance of waveformstrategies that are adaptive to the wireless channel, accountfor the harvester nonlinearity and maximize e rf − rf × e rf − dc appeared in [30].In this paper, we build upon the prototype of [30], andimplement all the four recently developed signal design strate-gies, namely waveform, beamforming, modulation, transmitdiversity. The performance gain and feasibility of all thosefour strategies, and combination thereof, in real-world environ-ments is assessed and verified experimentally for the first time in the literature. In particular, we ask ourselves the followingquestions: Can we establish an experimental environment ofopen-loop and closed-loop WPT and verify the advantagesof systematic signal design for WPT (including waveform,beamforming, modulation, transmit diversity) through experi-mentation? Can we confirm theory from measurements? Canwe validate or invalidate the linear and nonlinear energyharvester models used in the WPT and Wireless Informationand Power Transfer (WIPT) literature? The contributions ofthe paper are summarized as follows. First , we design, prototype and experiment a WPT systemthat can operate in both open-loop and closed-loop modes.The setup consists of three important blocks, namely thechannel acquisition, the signal optimization and generation,and the energy harvester(s). Software Defined Radio (SDR) isused to implement a wireless power transmitter and a channelestimator, and various rectennas with single-diode and voltagedoubler rectifiers are designed to work as energy harvesters.Leveraging the flexibility and reconfigurability of the SDR, itis possible to implement various transmission signal designand CSI acquisition strategies in one set of experimentalequipment. In its open-loop WPT mode, the architecture does Recall that [24], [25], [26], [27], and [28] focus on beamforming-onlytechniques where beamforming is optimized/designed for WPT. None ofthem focuses on energy modulation (designed to maximize the harvested DCpower), waveform (designed to maximize harvested DC power), or transmitdiversity. Any modulation or waveform used in those papers are conventionalcommunication modulation/waveform, not signals designed/optimized forWPT. not rely on any CSIT (and therefore the channel acquisitionmodule), though still increases the harvested DC power byusing energy modulation and transmit diversity. In its closed-loop WPT mode, the architecture relies on a frame structureswitching between a channel estimation/acquisition phase andwireless power transmission phase. Channel acquisition isperformed every second and transmit signal is generatedaccording to a joint waveform and beamforming design tomaximize e rf − rf × e rf − dc . Second , we implement the four signal design strategiesmentioned above, namely waveform, beamforming, transmitdiversity and energy modulation, in the prototype. The realover-the-air performance are assessed experimentally for eachof the strategies and for a combination thereof. This contrastswith other WPT prototyping works that focus on the adap-tive beamforming approach only, e.g. [24]–[28], or on test-ing conventional/non-adaptive (not WPT-optimized) waveform[6], [8], [22], [23].
Third , the performance (in terms of harvested DC power)of the WPT architecture is investigated in a variety of de-ployments, including frequency flat (FF) and frequency selec-tive (FS) channels, and under static and mobility conditions.Experiments highlight the suitability of each signal designunder various propagation conditions and the role played byvarious parameters such as the channel frequency selectivity,the velocity, the number of tones, the number of transmitantennas, the signal bandwidth and the rectenna design.
Fourth , and importantly, the experimental results of thevarious signal strategies confirm and validate the observationmade from the theory of the rectifier nonlinearity and thesignal designs proposed and developed in [9], [10], [18]–[21]. In particular, the following observations made fromthe theory are fully confirmed in the experiments: 1) Thediode nonlinearity is fundamental and beneficial to WPTperformance and is to be exploited in any systematic transmitsignal design for WPT and WIPT; 2) The linear model ofthe EH, obtained by ignoring the rectifier nonlinearity, isnot validated by experiments and measurements and leads topoor signal designs; 3) The wireless propagation channel andfading has a significant impact on WPT signal design andsystem performance; 4) A systematic WPT signal and systemdesign has a big influence on the energy transfer efficiencywith and without CSIT; 5) CSI acquisition and channel-adaptive waveforms are essential to boost the performance infrequency-selective channels; 6) Multiple antennas can be usedin conjunction with transmit diversity to improve the energytransfer efficiency without CSIT; 7) Energy waveform andmodulation can be used in conjunction with beamforming tomaximize e rf − rf × e rf − dc and achieve a combined gain. Organization : Section II introduces the system model andSection III presents theoretical performance analysis. SectionIV introduces the prototype design. Section V offers all ex-perimental results and observations and Section VI concludesthe work and discusses future works.
Notations : Bold letters stand for vectors or matrices whereasa symbol not in bold font represents a scalar. | . | and k . k referto the absolute value of a scalar and the 2-norm of a vector. E { . } refers to the averaging/expectation operator. II. T HE S YSTEM AND THE S IGNAL M ODELS
We consider a Multiple Input-Single Output (MISO) WPTsystem based on the four signal design strategies mentionedin the introduction. The general system model, along withthe mathematical model of each signal design technique, arepresented in this section.
A. MISO WPT System Model
The transmitter is equipped with M transmit antennas anduses N subbands, while the receiver is equipped with a singleantenna. The transmit signal at time t on antenna m is writtenas x m ( t ) = N − X n =0 s n,m ( t ) cos (2 πf n t + φ n,m ( t ))= ℜ ( N − X n =0 ω n,m ( t ) e j πf n t ) (1)with ω n,m ( t ) = s n,m ( t ) e jφ n,m ( t ) where s n,m ( t ) and φ n,m ( t ) refer to the amplitude and phase of the subband signal onfrequeny f n and transmit antenna m at time t . Quantities S and Φ are N × M dimensional matrices of the amplitudesand phases of the sinewaves with their ( n, m ) entry denotedas s n,m ( t ) and φ n,m ( t ) . The average transmit power constraintis given by P Mm =1 E {| x m | } = k S k F ≤ P . Vector-wise, thetransmit signal vector x ( t ) can be written as x ( t ) = ℜ ( N − X n =0 w n e j πf n t ) (2)where w n = [ ω n, ( t ) · · · ω n,M ( t )] T .The transmit signal propagates through a multipath channel.We assume that the (frequency-domain) channel coefficient h n,m ( t ) changes at a rate slower than the transmission signaland that the channel is effectively stationary within a singletime frame (i.e., we drop the time dependency of the channelcoefficients). The received signal from transmit antenna m iswritten as y m ( t ) = N − X n =0 s n,m ( t ) A n,m cos (2 πf n t + ψ n,m ( t )) (3)where the amplitude and phase A n,m and ψ n,m are such that A n,m e jψ n,m ( t ) = A n,m e j ( φ n,m ( t )+ ¯ ψ n,m ) = e jφ n,m ( t ) h n,m (4)and the frequency response of the multipath channel is givenby h n,m = A n,m e j ¯ ψ n,m . The channel vector h n can bewritten as h n = [ h n, · · · h n,M ] .The total received signal is the sum of (3) over all transmitantennas, namely y ( t ) = M X m =1 N − X n =0 s n,m ( t ) A n,m cos (2 πf n t + ψ n,m ( t ))= ℜ ( N − X n =0 h n w n e j πf n t ) . (5) At the receiver, the signal y ( t ) impinges on the receiveantenna and is absorbed by the rectifier. A simple and tractablemodel of the rectenna, introduced in [9], is used in this paperfor the analysis. The model expresses the output DC currentas a function of the input signal y ( t ) and relies on a Taylorexpansion of the diode characteristic function. Following [9],the rectenna output DC power under perfect matching andideal low pass filter is related to the quantity z DC = k R ant E { y ( t ) } + k R E { y ( t ) } (6)with R ant the antenna impedance and k i = i s i !( nv t ) i for i =2 , , where i s is the reverse bias saturation current, v t is thethermal voltage, n is the ideality factor. The fourth order term E { y ( t ) } accounts for the rectifier nonlinearity. As a reference,following [9], k = 0 . and k = 0 . . Considering R ant = 50Ω , the coefficient of the fourth order term is 5630times larger that the second order coefficient, and explains whynonlinearity is non-negligible. B. (Energy) Waveform and Beamforming
Various channel non-adaptive (not relying on CSIT) andadaptive (relying on CSIT) multisine waveform strategies forWPT have been proposed in the past few years and can beused in single-antenna as well as multi-antenna setup [9], [10].Since those waveforms are deterministic, i.e. not modulated,we can drop the time dependency such that ω n ( t ) = ω n .In Table I, we highlight various waveform design methodsand the mathematical representations of the waveform coeffi-cients ω n for single antenna and w n for multi antenna system,assuming the CSI (in the form of the frequency-domainresponse h n for all frequency component n ) is available at thetransmitter. All those waveforms can be expressed in closed-form and can therefore be implemented and tested in real-time over-the-air transmission. We do not consider the optimalwaveform design of [9], [11], [12] because they result from aconvex/non-convex optimization problem that cannot be easilysolved and implemented in real-time. C. (Energy) Modulation
Energy modulation is another strategy for WPT to inducefluctuations of the transmit signal amplitude of a singlecarrier and boost the harvested DC power. In contrast to themultisine waveform that is deterministic, energy modulationcarries information due to the randomness inherent from themodulation. However the modulation is designed in such a waythat it maximizes the harvested DC power [20]. In its simplestform, M = 1 , N = 1 , and the transmit signal ω n,m ( t ) at time t on carrier frequency f can be written as ω n,m ( t ) = ω ( t ) = s ( t ) e jφ ( t ) (7)where s ( t ) = √ P p m I ( t ) + m Q ( t ) and φ ( t ) =tan − (cid:16) m Q ( t ) m I ( t ) (cid:17) . The message signal can be expressed incomplex form as m ( t ) = m I ( t ) + jm Q ( t ) and m ( t ) is anormalized ( E {| m ( t ) | } = 1 ) complex baseband equivalentsignal that represents the (energy) modulation symbol at time t . The coefficient √ P is used to guarantee the averagetransmit power constraint P .We consider conventional modulation schemes (commonlyused and designed for communication purposes) such as PSK,QAM and Circularly Symmetric Complex Gaussian - CSCG(equally distributing power between the real and the imaginarydimensions, i.e., ℜ { ω } ∼ N (0 , P ) and ℑ { ω } ∼ N (0 , P ) ) andcompare with modulations specifically designed for wirelesspower delivery, such as Real Gaussian (allocating the transmitpower to only one dimension e.g. ℜ { ω } ∼ N (0 , P ) ) [19],and the recently proposed flash signaling [20] characterizedby a uniformly distributed phase φ over [0 , π ) and theamplitude distributed according to the following probabilitymass function p s ( s ) = ( − l , s = 0 , l , s = l √ P , (8)with l ≥ . We can easily verify that E (cid:2) | ω | (cid:3) = E (cid:2) s (cid:3) = 2 P ,hence satisfying the average power constraint. By increasing l , s = l √ P increases and p s ( l √ P ) decreases, thereforeexhibiting a low probability of high amplitude signals. D. Transmit Diversity
In contrast to (energy) waveform and modulation that in-duces amplitude fluctuations of the transmit signal, transmitdiversity is designed to generate amplitude fluctuations ofthe wireless channel [21]. Those fluctuations of the wirelesschannel are beneficial to the energy harvester thanks to therectifier nonlinearity. To induce fluctuations of the wirelesschannel, transmit diversity relies in its simplest form onmultiple dumb antennas fed with a low PAPR continuous waveand antenna-dependent time varying phases. In this case, thewaveform design factor ω n,m ( t ) at the antenna m at time t oncarrier frequency f is expressed as follows ω n,m ( t ) = ω m ( t ) = se jφ m ( t ) , (9)where s = q PM is the amplitude of the continuous wave oneach transmit antenna (with uniform power allocation), and φ m ( t ) is an antenna dependent time varying phase (whoserate of change can be predefined). The total transmit powerover all antennas is fixed to P .Transmit diversity can also be implemented in combinationwith the aforementioned energy modulation and waveformstrategies. Transmit diversity with energy modulation can bedesigned by transmitting the same energy symbol on allantennas but applying an additional antenna-dependent randomphase φ m, td ( t ) , such that ω n,m ( t ) = ω m ( t ) = s ( t ) e jφ m ( t ) , (10)where s ( t ) = q PM p m I ( t ) + m Q ( t ) and φ m ( t ) =tan − (cid:16) m Q ( t ) m I ( t ) (cid:17) + φ m, td ( t ) . The normalized complex modula-tion symbol m ( t ) = m I ( t ) + jm Q ( t ) is the same for all an-tennas. Similarly, transmit diversity with multisine waveformtransmits the same waveform on all antennas and applies anantenna dependent time varying phase before being launched TABLE I. Various Waveform Design Methods and Descriptions
Antennas CSIT WaveformDesignMethod Expression Description ReferenceSISO no CSIT UP ω n = √ P √ N The uniform power allocation (UP) simply assigns the same powerto all frequencies components, with a zero phase. [9]CSIT ASS ω n = (cid:26) √ P e − j ¯ ψ n n = ¯ n n = ¯ n. The adaptive single sinewave (ASS) allocates power to theone frequency corresponding to the strongest channel ¯ n =arg max i | h i | . This is the optimal solution for the linear EHmodel (2nd order term-only in (6)), and therefore aims at maxi-mizing e rf − rf . [9]CSIT UPMF ω n = √ P √ N e − j ¯ ψ n The uniform power allocation and matched fiter (UPMF) allocatesthe same amplitude for all frequencies components, but thechannel phase is matched on each sinewave based on the CSIT. [9]CSIT MF ω n = A n r P P N − n =0 A n e − j ¯ ψ n The matched filter (MF) allocates power to all sinewaves pro-portionally to the frequency domain channel strengths. It is aparticular case of SMF with β = 1 . [9]CSIT MAXPAPR ω n = A n r P P N − n =0 1 A n e − j ¯ ψ n The maximize PAPR (MAX PAPR) allocates power inverselyproportional to the channel strength to maximize the PAPR atthe rectifier input. [9]CSIT SMF ω n = A βn r P P N − n =0 A βn e − j ¯ ψ n The scaled matched filter (SMF) is a low-complexity multisinewaveform design strategy motivated by observations of the op-timized signal. β is a scaling factor, whose choice results froma compromise between exploiting the EH nonlinearity and thechannel frequency selectivity, and therefore aims at maximizing e rf − rf × e rf − dc . [10]MISO no CSIT UP w n = √ P √ NM The uniform power allocation (UP) in MISO also simply assignsthe same power to all frequencies and spacial components, witha zero phase. [9]CSIT UPMF w n = √ P √ N h Hn k h n k The uniform power allocation (UP) is applied in the frequencydomain, and the matched (or maximum ratio transmission) beam-forming (MF) is applied in the spatial domain. [9]CSIT SMF w n = h Hn k h n k k h n k β r P P N − n =0 k h n k β The single antenna channel gain A n and optimal phase e − j ¯ ψ n are substituted by the multi-antenna effective channel gain k h n k and the MRT beamforming vector h Hn / k h n k , respectively. MISOversionof [10] over the air. Considering a channel non-adaptive in-phase mul-tisine waveform with uniform power allocation in frequencyand space (denoted as UP in Table I), ω n,m ( t ) on antenna m at time t on frequency f n is expressed as follows ω n,m ( t ) = ω n,m ( t ) = se jφ m ( t ) , (11)where s = q PNM and φ m ( t ) is the antenna dependent timevarying phase of transmit diversity.III. T HEORETICAL P ERFORMANCE A NALYSIS
The scaling laws of (6) have been introduced in [9] as a wayto predict the theoretical performance benefits of WPT signaldesigns and the key role played by the rectifier nonlinearityand the signal parameters (e.g. N , M ). The behavior predictedfrom the scaling laws will be contrasted with the measurementresults. To that end, this section summarizes some of thoseexisting theoretical scaling laws for waveform designs [9] andfor transmit diversity [21], and extends them to account formobility conditions and to (energy) modulation. A. (Energy) Waveform and Beamforming
The scaling laws for waveform designs under perfect CSITare provided in [9]. We here extend them to account fordelayed CSIT due to mobility and time varying channels.To represent the delayed CSIT in a mobility condition andaccount for the differences between the CSI acquired at thetime of channel estimation and the actual channel at the time of transmission, we have added a channel instance factor k to the transmit and receive signal. The evolution of h k,n ismodeled by a first-order Gauss-Markov process h k,n = ǫ h k − ,n + p − ǫ g k,n , (12)where g k,n ∈ C × M has i.i.d. entries distributed accordingto CN (0 , and E h h ∗ k − ,n g k,n i = M , where M denotes M × M zero matrix. We assume g k,n is i.i.d for all frequencycomponets n in FS channel, and g k,n = g k ∀ n in FF channel. h ,n is independent of g k,n for all k ≥ . The coefficient ǫ (0 ≤ ǫ < quantifies the amount of the correlation betweenelements h k − ,n,m and h k,n,m , and we assume all the elementsof h k,n have the same ǫ . The time correlation coefficient ǫ follows Jakes’ model for fading channel [31] ǫ = J (2 πf D T ) where J ( . ) is the zeroth order Bessel function, T denotes thechannel instantiation interval, and f D = vf c c is the maximumDoppler frequency where v is the terminal velocity, f c iscarrier frequency, and c = 3 × m/s . The time correlationcoefficient ǫ is therefore a measure of the channel timevariation, and it is related to the velocity of the mobile terminal( ≤ ǫ ≤ ).Following the same approach as in [9], we calculated thescaling laws of UP and UPMF techniques with the abovedelayed CSIT model in single and multi-antenna systems withfrequency flat and selective channels. To that end, we assumedthat the transmitter at time k does not know h k,n , but has onlyaccess to the channel at time k − to design the transmit signal TABLE II. Scaling Laws of Energy Waveforms z DC N,M No CSIT CSIT z DC , UP z DC , UPMF
FF Channel N ≫
1, M = 1 k R ant P + 2 k R P N k R ant P + 2 k R P N N ≫
1, M ≫ k R ant P + 2 k R P N ǫ k R ant P M + (1 − ǫ ) k R ant P + ǫ k R P NM + 2(1 − ǫ ) k R P N FS Channel N ≫
1, M = 1 k R ant P + 3 k R P k R ant P + 3 k R P + ǫ π / k R P N N ≫
1, M ≫ k R ant P + 3 k R P ǫ k R ant P M + (1 − ǫ ) k R ant P + ǫ k R P NM + 3(1 − ǫ ) k R P (i.e. a delayed version of the CSI). The scaling laws are shownin Table II.Since the UP strategy is non-adaptive to the CSI, the timecorrelation coefficient ǫ does not affect its performance. Theresults of z DC , UP in Table II is indeed not a function of ǫ . Awaveform gain proportional to N is achieved in FF channels,but not in FS channels. No beamforming gain is achievedeither. However, with the channel-adaptive UPMF strategy, ǫ has a significant effect on the z DC performance. When ǫ = 1 ,the scaling laws z DC , UPMF boil down to those provided in [9],and a gain proportional to N and M is observed in both FF andFS channel conditions. On the other hand, as ǫ decreases andapproaches 0, z DC , UPMF converges to z DC , UP . As ǫ decreases,the beamforming gain vanishes in FS and FF channels, whilethe waveform gain vanishes in FS channels but remains in FFchannels. In other words, velocity and delayed CSIT incurs abigger hit in FS channels than in FF channels. B. (Energy) Modulation
This subsection derives the theoretical scaling laws of z DC for each modulated signal. The transmission is assumednarrowband and the channel assumed frequency flat. We canwrite z DC = k R ant E {| m ( t ) | } P + 32 k R E {| m ( t ) | } P = k R ant P + 32 k R E {| m ( t ) | } P (13)where m ( t ) is the normalized complex modulation symbolmentioned in section II-C. Since all modulations are normal-ized to have the same average transmit power, the differencebetween modulations can only be explained by the high-ordermoments, namely E {| m ( t ) | } . Table III displayed z DC of sev-eral modulation schemes such as PSK, QAM, Gaussians, andflash signaling and compare with the unmodulated ContinuousWave (CW). TABLE III. Scaling Laws of Energy Modulation z DC Continuous Wave (CW) k R ant P + 1 . k R P BPSK k R ant P + 1 . k R P k R ant P + 1 . k R P Complex Gaussian k R ant P + 3 k R P Real Gaussian k R ant P + 4 . k R P Flash Signaling (with l ) k R ant P + l k R P A first observation is that the second order term of z DC and (6), i.e. the linear model of the EH [5], [9], is thesame for all modulation schemes, cannot motivate the designof energy modulation and cannot predict the performanceof energy modulation. A second observation is that there isa large performance gap between conventional modulationsand those designed for WPT. This is due to the rectifiernonlinearity that favours modulations with large high- ordermoments E {| m ( t ) | } . Among the conventional modulationmethods, the complex gaussian (CSCG) signal shows thelargest fourth order term compared to BPSK or 16QAM. A realGaussian, though suboptimal for communication purposes, ismore suitable for WPT since it leads to a higher fourth ordermoment than its complex counterpart. Flash signaling furtherboosts the fourth order term as l increases. For l > √ , flashsignaling is expected to lead to a higher DC power than a realGaussian. C. Transmit Diversity
The performance of transmit diversity was analyzed in [21].It was shown that by randomly changing the phase of acontinuous wave on each transmit antenna, we achieve a gainproportional to the number of antennas M in the fourth orderterm of z DC , despite the lack of CSIT. Additional benefitsare obtained by combining transmit diversity with (energy)modulation and waveform. The scaling laws of z DC for trans-mit diversity with continuous wave and modulation/multisinewaveform versus the single antenna continuous wave aredisplayed in Table IV. TABLE IV. Scaling Laws of Transmit Diversity [21] z DC GainCW k R ant P + k R P TD-CW k R ant P + k R P G td G td = 1 + M − M TD-Modulation k R ant P + k R P G td G mod G mod = E {| m ( t ) | } TD-Multisine k R ant P + k R P G td G mt G mt N ր ≈ N IV. P
ROTOTYPING AND T ESTBED S ETUP
In order to verify that the proposed transmit signal designmethods are feasible and improve the performance in a realworld setting, a point-to-point WPT system prototype is re-quired. This section discusses the implementation of a WPT
Antenna 1 Block
CE BlockLO2.45 GHzPowerAmpBaseband Waveform Generation
OFDM Modulator for Pilot Transmission
PowerOptimization
Pilot IFFT
Energy Harvester
OFDM Demodulator for Channel Estimation
FFT
PowerSplitter
Transmitter
EH Block
Tx 1 RxAnt.Antenna 2 Block ExternalPowerAmps Coaxial Cable
Receiver
PCI Express Bus
ChannelEstimation
Antenna 3 BlockAntenna 4 Block Tx 2Tx 3Tx 4
Fig. 1. System architecture with equipment and a peripherals connection. system consisting of a transmitter capable of generating andtransmitting various types of signals, and a receiver capableof channel estimation and energy harvesting. This systemenables performance evaluation and validation of varioussignal generation techniques under various wireless channelenvironments . A. Overall System Architecture and Hardware Setup
The system operates in the 2.4 GHz ISM band. The targetoperating range is to achieve an average received power of theorder of -20 dBm at a distance of 5 meters. This is motivatedby the fact that 10-100 µW is enough to power modernwireless sensors and low-power devices [29]. In compliancewith the Code of Federal Regulations, Title 47, Part15 (FCCPart15) regulation, the system is designed to operate with aneffective isotropic radiated power (EIRP) of less than 4 watt(36dBm) [32]. The system consists of up to four transmitantennas and one receive antenna and can be operated inMISO or SISO mode depending on the transmit signal strategyconsidered. Fig.1 displays the system block diagram whichincludes the equipment and the peripheral connections. Fig.2illustrates the complete prototype.We chose National Instrument (NI) software-defined radioprototyping equipment to implement the transmitter that isable to generate and transmit various types of WPT and pilotsignals. The transmitter hardware has been configured with aNI PXI platform and USRPs. Four pairs of RF transceiverswere used to implement the four transmit antennas. Thefunctions of signal design, optimization and generation on onehand and pilot transmission/channel acquisition on the otherhand are combined within the transmitter, and these functionsare programmed and controlled using LabView.The receiver is divided into two large functional blocks.One is a channel estimation block (CE block) that receivesthe pilot signal, estimates the channel, and feeds back tothe transmitter. The other is an energy harvesting block (EHblock), made of a rectifier, that converts the received RFsignal to DC power. The RF signal received by the antenna It can also be used to perform simultaneous wireless information andpower transfer (SWIPT) in the future. (a) (b)
Fig. 2. WPT prototype (a) two antenna configuration (b) four antenna transmit antennas. passes through the power splitter and delivers power to eachblock. For the single antenna system, the CE block is alsoimplemented on the NI SDR platform by using independentRF transceiver and FPGA module. For the multi-antennasystem, one of the FPGA and RF transceiver modules operateas a transmitter and a receiver’s CE block at the same time.The transmit and receive signal paths in the same module areoperated completely independent and do not affect each other.We installed the hardware (a pair of FPGA module and RFtransceiver) responsible for the CE block in the same PCIexpress chassis as the transmitter. This configuration enablesCSI feedback from the receiver to the transmitter via thePCI express bus, which allows the transmitter to recognizethe changes of CSI in real time . The cables connecting the We use a power splitter for measurement convenience, such as monitoringan RF input power to the energy harvester. An RF switch could have beenused instead of the power splitter and may be a better choice to maximizethe received power at the energy harvester. Unlike a power splitter thatdistributes power by 50% to each block, it can send 100% of power to theenergy harvester during the wireless power transmission phase. However, theobjective of this paper is to compare the energy harvesting performance ofvarious signal design techniques. Therefore, using a power splitter does notaffect the performance comparison, but makes the system easier to implement. A final WPT system would require an over-the-air CSI feedback. We hereuse a wired (instead of wireless) feedback of the CSI as this experimental setupis sufficient to answer the main questions and objectives raised in the paper,namely to assess experimentally the advantages of closed-loop and open-loop systematic signal designs for WPT (including waveform, beamforming,modulation, transmit diversity), confirm theory from measurement, and vali-date the crucial role played by the rectifier nonlinearity. Replacing the wiredfeedback of the CSI by a wireless counterpart, and accordingly implementingand validating the design of optimized WPT signals (joint waveform andbeamforming) under limited feedback, is an important issue that is left forfuture works. equipment and the antenna are long enough so that variouswireless channel environments can also be measured.
B. Channel Estimation and WPT Signal Transmission
The architecture of Fig. 1 requires the design of a suitableframe structure to enable channel acquisition and WPT signaltransmission, as per Fig. 3. The transmission signal includestwo different types of signals, namely an OFDM signal formulti-frequency channel estimation and an optimized WPTsignal (unmodulated multisine waveform or energy modulatedcontinuous wave) for power delivery. The frame structure hastherefore been designed to accommodate two different signalsin the time domain. The length of the time frame T frame hasbeen set by default to one second. One second was believedto be sufficient for deployments where the wireless channeldoes not change rapidly, such as in a static office environmentand where there is no moving object during the measurements.Nevertheless, T frame can be adjusted and shortened to 200msfor deployments with moving objects. OFDM-based pilotsignals are transmitted at the beginning of each frame forchannel estimation and synchronization purposes. The duration T pilot has been fixed to 512 µ s for single antenna transmissionand includes therein a frame synchronization and pilot signals.In the case of multi-antenna transmission, the duration T pilot is extended depending on the number of transmit antennas.To estimate multi-antenna channels, each antenna transmitsa pilot in a different time slot. Therefore, T pilot in the 2-antenna MISO experiment is 1 ms, and 4 ms for 4-antenna. Atthe receiver, the CE block receives the pilot signal, estimatesthe channel, and feeds back the CSI to the transmitter. Thetransmitter then computes and generates an optimized WPTsignal based on the calculated CSI. The time required for thecomputation and generation of the new signal (based on thenewly acquired CSI) is T prev (approximately 30 to 40ms),and the signal optimized based on the CSI from the precedingframe is transmitted during this processing time. During theremainder of the frame, the wireless power signal optimizedfor the current frame (based on the current CSI) is transmittedand T current is usually within the range 960-970 ms. Convert RF signal to DC IdleReceive Pilot / Channel EstimationPilot WPT signal from previous frame
Wireless Power Transfer (WPT) based on CSI of current frame
ContinuousTransmissionTransmit SignalFrame StructureReceiver (CE) (cid:127) (cid:129)(cid:141)(cid:143)(cid:144)(cid:157)
Receiver (EH) (cid:127) !" (cid:127) (cid:141)(cid:157)% (cid:127) &'(cid:141)(cid:141)(cid:157)($
Fig. 3. Frame structure and operations at the transmitter and receiver.
The system uses a pilot-based channel estimation method.The pilot signal is generated based on OFDM signal for theestimation of the channel on a various number of frequencies.We use a block-type pilot that assigns a reference signal to allfrequency components of interest. No interpolation is thereforeneeded. The Least-Square (LS) method is chosen as a chan-nel estimation technique because of its low-complexity. The OFDM channel estimation block operates at 2.45 GHz centerfrequency with 20MHz bandwidth and subcarriers spacing of78.125KHz. The upper and lower 5MHz bands are used asguard bands, thus the effective region that can actually beused to estimate the channel is the 10MHz in the middle andcomposed of 128 subcarriers. In other words, we can generatea maximum 128-tone signal and acquire the CSI on those128 tones. The CSI is nevertheless commonly estimated on asmaller number of subcarriers, since the WPT optimized signalis transmitted on typically up to 16 tones because of the PAPRlimits of the transmitter (that clips the signal when more than16 in-phase sinewaves are transmitted).WPT signals are generated based on the various signaldesign techniques introduced in Section II. The channel adap-tive multisine waveforms are applied to single and multi-antenna setups. The modulation signal is tested on a singleantenna setup, and the transmit diversity signal is generatedusing two antennas. In order to illustrate the effect of thewaveform designs of Table I, Fig. 4 displays the magnitudeof a measured channel frequency response (for single antennasetup) and compares the allocated amplitudes for the differenttypes of multisine waveform strategies. It can be seen thatSMF allocates power to all frequencies (so as to exploit therectifier nonlinearity), but emphasizes (more or less dependingon the choice of β ) the strong frequency components andattenuates the weakest ones (so as to benefit from the channelfrequency diversity). This contrasts with MAX PAPR thatinverts the channel (and allocates more power to the weakestcomponents) so as to maximize the PAPR of the signal at therectifier input. C S I M a gn i t ud e -5 -4 -3 -2 -1 0 1 2 3 4 5 Frequency [MHz] W P T W ave f o r m A m p li t ud e non-adaptive UPadaptive MAX PAPRadaptive MF Fig. 4. Frequency response (magnitude) of the wireless channel and WPT waveformmagnitudes ( N = 16 ) for 10MHz bandwidth. Remark 1:
Note that the proposed closed-loop architecturecontrasts with conventional open-loop approaches in the RFliterature with waveform being static/non-adaptive [6]–[8],[33], and beamforming relying on tags localization, not on thechannel state [16]. Indeed, the waveform adaptation, channelestimation and frame structure are not present in those works,therefore preventing the signal at the input of the rectennato be truly optimized. The proposed closed-loop architecturealso differs from those of [24]–[28] in the communicationliterature, where emphasis was on adaptive beamforming (to maximize e rf − rf ), rather than joint waveform and beamform-ing design (to maximize e rf − rf × e rf − dc ). C. Rectifier Design
To construct the receiver’s EH block, we first considereda single-diode rectifier circuit. It consists of an impedancematching circuit, a diode and a smoothing circuit (low passfilter). The rectifier printed circuit board (PCB) is fabricatedwith a λ /4 length of microstrip, L-matching network, andfollowed by a Schottky diode rectifier circuit. The diode andthe low pass filter implemented in the prototype are the sameas in the rectenna used for circuit simulations in [21]. Thevalues of the matching network components have howeverbeen modified to fit the fabricated PCB and have been designedunder the assumption of a 4-tone in-phase multisine inputwaveform as mentioned in [10] under -20 dBm input powercondition. The assumption of 4-tone input is chosen because itis a middle ground for all those test conditions (ranging from1 tone to 16 tones). Also, though the input waveform can have16 sinewaves, power allocation across all sinewaves is unlikelyto be uniform due to the potential frequency selectivity. Thisimplies that a subset of the sinewaves will be allocated power.Considering these cases, we have chosen the 4-tone as a robustbaseline to design the rectifier. The reflection coefficient S11of the rectifier is less than -10dB between 2.38 GHz and 2.5GHz, and bandwidth is 120 MHz. We use Taoglas GW.15antenna for the experiment. It is a universal 2.4 GHz bandWiFi antenna, and the characteristics of the antenna are asfollows: frequency 2.4-2.5 GHz, peak gain in free space <=2dbi, efficiency <= 80%, VSWR <=1.8.In addition, a rectifier with a voltage doubler structure wasalso built to verify the effectiveness of the nonlinear rectennamodel and signal designs in other types of rectifier. Thestructure is the same as a single diode rectifier, but the outputvoltage is doubled using one rectifier for positive signals andone for negative signals, added via a series ouput. Circuitdiagrams and photograph of the both rectifiers are shown inFig. 5. RL10 kΩD1SMS7630-079LFL12.4 nHC10.3 pF C21 nFRF In (a) RL12 kΩD2SMS7630-079LFL10.3 nHC11.5 pF C20.3 pF C32.7 nFC42.7 nFRF IN D1SMS7630-079LF (b)(c) (d)
Fig. 5. Fabricated rectifiers and circuit schematics, Single-diode rectifier (a) schematic,(c) photo, and Voltage-doubler rectifier (b) schematic, (d) photo.
V. E
XPERIMENTS AND V ALIDATION
The WPT testbed introduced in Section IV has been experi-mented in various indoor propagation conditions. This sectionreports the measured harvested DC power for the varioustypes of WPT signals. We compare the measured results withthe observations made from the theoretical results of SectionIII. We confirm experimentally the benefits of the systematicsignal designs and the importance of modeling the rectifiernonlinearity in order to explain the measured results.
A. Waveforms in SISO System
The harvested DC power has been measured in variouspropagation environments with the objective to assess theimpact of the multisine waveform design, the number ofsinewaves and the bandwidth. Measurements were carried outin a normal office environment in static conditions. Test loca-tions involve LoS and NLoS conditions, and exhibit frequency-flat (FF) channels and frequency-selective (FS) channels, re-spectively.The transmit waveforms are designed according to eachwaveform design schemes such as UP, MAX PAPR, ASS,MF, and SMF ( β =3) with 1 to 16 tones of uniformly spacedsinewaves in 10MHz and 2.5MHz bandwidth. The inter-frequency spacing is given by B/N with B = 10 , . MHzand N = 2 , .., . In all test cases, the transmit power was setto 33dBm and the RF power measured at the receiver based onthe CW signal was around -20dBm. The single-diode rectifierof Fig. 5(a) was used.The harvested DC power was measured for 60 seconds foreach test case and measurements were carried out five times ,with a 5min interval, at each location while maintaining staticconditions, before taking the average.Fig.6 displays the received DC power measurement resultsas a function of N under various bandwidths (2.5 and 10MHz) and channel conditions (frequency flat and frequencyselective). Since the test locations are different for FF and FSchannel, the absolute value of the received power is different,but the relative performance gain according to different wave-form design schemes in different channel characteristics canbe observed. We make some important observations from themeasurements. First , not all of the channel adaptive waveforms achievebetter performance than the non-channel adaptive waveforms.The results of Adaptive SS (ASS) and MAX PAPR are indeedworse than UP in frequency-flat (FF) and frequency-selective(FS) channel, respectively. ASS allocates the full power to onlyone (though the strongest one) sinewave to maximize e rf − rf ,but at the cost of achieving a low e rf − dc , and provides verylittle gain in FF channels because the waveform cannot benefitfrom any frequency diversity gain and does not exploit therectifier nonlinearity. On the other hand, MAX PAPR schemeis inefficient in FS channel. MAX PAPR scheme inverts thechannel to make the input waveform to the rectifier look likean in-phase multisine with uniform power allocation at the Splitting the total time duration into a number of short snapshots (60 sec-onds in this setup) is often used in channel characterization and measurement,e.g. [34]. Number of Sinewaves N (a) FF channel, 10 MHz
Number of Sinewaves N (b) FS channel, 10 MHz
Number of Sinewaves N (c) FS channel, 2.5 MHz
Fig. 6. Received DC power as a function of N under various bandwidths and channelconditions: (a) Frequency flat channel and 10 MHz, (b) Frequency selective channel and10 MHz, (c) Frequency selective channel and 2.5 MHz. rectifier input. Therefore, MAX PAPR maximizes the PAPRof the input signal to maximize e rf − dc at the cost of wastingan excessive amount of power in inverting the channel andachieving a poor e rf − rf . This confirms experimentally thatfocusing on maximizing PAPR in multisine waveform design(with the hope to maximize e rf − dc ), and allocating all powerto the strongest sinewave (with the hope to maximize e rf − rf )are not suitable strategies in general settings, as highlighted in [9]. Second , increasing the number of sinewaves N boosts theperformance in FF and FS channels. By increasing N , aproperly designed waveform can exploit the nonlinearity ofthe rectifier to boost e rf − dc , but also exploits the frequencydiversity of the channel to boost e rf − rf . This confirms re-sults in [9] that the diode nonlinearity is beneficial to WPTperformance and is to be exploited in systematic waveform.If N increases continuously and the peak voltage increasesabove the breakdown voltage of the diode, the efficiency maydecrease sharply. However, since N is limited to 16 in thecurrent prototype, the diode breakdown voltage is not reached. Third , significant performance gain with a channel-adaptivewaveform strategy such as SMF can be obtained in FSchannel. Recall that an optimized waveform for WPT, in-cluding SMF, allocates power in a non-uniform manner tomultiple sinewaves, with more power allocated to the strongestfrequency components, so as to maximize e rf − rf × e rf − dc [5],[9], [10]. The gain of SMF with β = 3 over non-adaptive UPwith 16-tone on FF channel is 9.27% but it reaches 90.85%on the FS channel. Compared to conventional continuous wave(single tone), the gain is as high as 150%. This confirms resultsin [9] that CSI acquisition and systematic channel-adaptivewaveforms that maximize e rf − rf × e rf − dc are essential to boostthe performance in frequency-selective channels (as in NLoSscenarios). In a SISO frequency-flat channel, the result alsoconfirms that CSI is not essential to the transmitter to designefficient waveforms since there is no frequency selectivity tobe exploited to further boost e rf − rf . Fourth , comparing 2.5MHz and 10MHz bandwidth signals,we note that spreading the frequencies across a larger band-width is beneficial as the waveform design, if adaptive to theCSI, can benefit from a channel frequency diversity gain. Thisalso confirms results in [9] that larger bandwidths can boostthe output DC power.Overall, those observations are inline with the observationsin the prior theoretical works [9], [10], and with the theoreticalgain of the waveform design that scales with N (in the fourth-order term of (6)) according to Table II. It is worth to recall thatall those four observations were already made in [9] and [10]based on analysis and circuit simulations. All experimentalresults fully match with the theory and therefore validatethe rectifier nonlinear model and the systematic waveformdesign methodology introduced in [9], [10] and subsequentworks [11], [13]. Results also confirm experimentally thefeasibility and the promising gains offered by a closed-loopWPT architecture. Remark 2:
The above results and observations also confirmexperimentally the inaccuracy of the linear model, obtainedby ignoring the fourth order term in (6), and its inefficiencyin designing multisine waveforms [9]. Recall that the ASSwaveform is motivated by the linear model, as it results fromallocating all power to the strongest frequency component [9].Clearly, the fact that the ASS performance is poor and evensometimes worse than non-adaptive waveforms demonstratethat the linear model does not capture the essence of theenergy harvester, is inefficient for WPT signal designs, and is inaccurate to predict the waveform performance . B. Waveforms with Voltage Doubler Rectifier
In the previous subsection, we considered a rectifier com-posed of a single diode followed by a low-pass filter with aload R L , as illustrated in Fig. 5(a). This is the simplest rectifierconfiguration. In this subsection, the experiment is extendedto other types of rectifiers with multiple diodes.The nonlinear rectenna model was originally derived andmotivated by a single diode rectifier circuit in [9]. The modelwas then shown (analytically and through circuit simulations)to hold for more general rectifiers with many diodes in[10]. In order to verify experimentally that the model andthe corresponding signal designs are valid for other typesof rectifier circuits with more diodes, the same test as inprevious subsection has been performed using the voltagedoubler circuit using two diodes of Fig. 5(b). Number of Sinewaves N (a) FF channel
Number of Sinewaves N (b) FS channel
Fig. 7. Received DC power using voltage doubler rectifier as a function of N with 10MHz bandwidth under two different channel conditions (a) Frequency flat channel (b)Frequency selective channel. It appears that the observations made from Fig. 6 with thesingle diode rectifier also hold for the voltage doubler rectifierin Fig. 7. The increase and decrease trend of the harvested ASS should achieve the highest performance according to the linear model,which is clearly not the case. Moreover the benefits of the other waveformscannot be explained from the linear model.
DC power as a function of the waveform designs remains thesame for both rectifiers. The tests were performed in the samelocations as the single diode rectifier experiment of Fig. 6, andthe overall received power increased by 30% when using thevoltage doubler. The SMF signal has a maximum gain overCW of 170%, which is higher than that achieved in the singlediode experiment.Results confirm that the nonlinear rectenna model (6), usedfor the design of systematic waveforms and for the predictionof the harvested DC power performance with various signaldesign techniques, is valid not only for a single diode rectifiercircuit but also for a rectifier circuit using multiple diodes.
C. Waveforms in Mobility Conditions
WPT technology is expected to be predominantly embeddedin low-power tiny and portable devices such as IoT devices.In the presence of mobility, CSI needs to be acquired on aregular basis. In the event where the channel changes rapidlybetween two successive CSI acquisition at the transmitter, theCSIT is delayed and the harvested DC power z DC , UPMF dropsdue to a loss in waveform and beamforming gains, as shownin Section III-A. In this section, we investigate experimentallythe sensitivity of channel-adaptive waveform to mobility.We designed the experiment to check the relations betweenthe channel state information acquisition period and the ter-minal velocity. In previous subsections, the time frame wasfixed to one second, i.e. the CSI was acquired every second.In static channel conditions, such a time frame is sufficientbut in mobility conditions, it may not be enough to guaranteea gain of channel-adaptive over non-adaptive waveforms. Wehere consider and compare two different frame structures, with1 second and 200ms period, under various mobility profiles,with the objective to shed some light on the sensitivity of WPTsignals to mobility. Different frame structures imply differentchannel acquisition periods. Since the period influences thetime correlation coefficient ǫ mentioned in Section III-A, bothframe structures experience different ǫ under the same velocitycondition. We set four different velocity of moving antenna,namely 0.01, 0.05, 0.5, and 1 m/s, and investigate the gainsover channel non-adaptive WPT. 1 m/s is approximately 4km/hwhich corresponds to pedestrian speed. Linear Slider0.5 mRxTx
Velocity : 0.01, 0.05, 0.5, and 1 m/s
Fig. 8. Mobility Experiment Setup.
To generate controllable and reproducible mobility condi-tions, we used a linear slider of 50cm length, illustrated in Fig. 8, to move the transmitter while the receiver remains fixed.We compare the performance of a channel-adaptive SMF (with β = 3 ) and a non-adaptive UP waveform, both consisting of 16sinewaves uniformly spaced in a 10 MHz bandwidth. For eachtest case, measurements are carried out five times, each timetaken for a duration of 5-minutes. Results are then averagedover all measurements. Velocity (m/s) (a) 1s frame
Velocity (m/s) (b) 200ms frame
Fig. 9. Received DC power as a function of terminal velocity with different signal framestructures.
Fig. 9 shows the experimental results with the 1-second timeframe and 200 ms time frame. The graph first shows that theharvested DC power level with the non-adaptive UP waveformis nearly constant regardless of the velocity of mobile antenna.As shown in Section III-A the scaling law of the non-adaptiveUP signal is not affected by the time correlation coefficient ǫ ,which is the same in the measurement results. The graph alsoshows in both frame structure cases that the adaptive SMFsignal exhibits some gain over non-adaptive UP signal in alow-velocity condition but the gain decreases as the velocityof the mobile antenna increases (i.e. as ǫ decreases). Since ǫ is related not only to the velocity but also to the channelestimation period, the gain reduction rate of the SMF signaldue to the increase in velocity is different in the two framestructures. In a low-velocity test case such as 0.01m/s, adaptiveSMF signals have a similar gain of about 40% over non-adaptive UP for both 1s and 200ms frame structure. On the other hand, at 1m/s pedestrian velocity, the gain of the SMFsignal is almost zero when using the 1s frame, but a gain of12% is still observed when using the 200ms frame.These observations show the relation between the veloc-ity of a mobile antenna, CSIT acquisition period, the timecorrelation coefficient ǫ , and the harvested DC power. Theinfluence of ǫ on DC power harvesting performance shown inSection III-A was confirmed in this experiment. The designof an appropriate frame structure is important to cope withvarious mobility conditions. D. Joint Beamforming and Waveform in MISO System
The prototype system is equipped with two antennas, andperformance can therefore benefit from a beamforming gainon top of the waveform gain already highlighted in previoussubsections. According to the scaling laws in Table II, thebeamforming and waveform gains are cumulative as bothappear in the fourth order term of (6) through the term
N M .As discussed in [9], this highlights that the number of transmitantennas and number of sinewaves can be traded off to achievea given target performance. In this subsection, we assess theperformance benefits of conducting a joint beamforming andwaveform design over the single-antenna waveform designand over conventional multi-antenna energy beamforming withcontinuous wave [5].In other words, we assess the performance benefits ofexploiting jointly the spatial (beamforming) and frequency(waveform) domains of the transmit signal, and investigatehow one could leverage the frequency domain of the waveformto decrease the complexity of the spatial domain beamformer(number of transmit antennas).The experiments were performed in FF (LoS position)and FS (NLoS position) channel conditions as in the singleantenna system. UPMF and SMF signals on two antennasand UP, UPMF, and SMF signal on one antenna are used forperformance comparison for various N . Recall that UPMF insingle-antenna setting relies on CSIT for channel phase com-pensation on each sub-carrier (in contrast to UP) and allocatespower uniformly over all sub-carriers (similarly to UP). Theexperiments were carried out at five different locations for eachFF and FS channel condition. Test locations were chosen tohave FF channel on LoS position and FS channel on NLoSposition with received RF power of about -20dBm based onCW signal. The harvested DC power was measured for 60seconds, repeated five times, and results were averaged over allmeasurement for each test case. Fig. 10 displays the harvestedDC power for each signal design and number of tones. Wemake the following observations. First , we observe that spatial domain and frequency domainprocessing can be traded off. Comparing 2-antenna SMF withCW ( N = 1 ) and 1-antenna SMF with N ≥ , we notethat the 1-antenna waveform outperforms the 2-antenna beam-forming in FS channel. This significant gain can be obtainedin FS channel where the 1-antenna SMF with N ≥ canjointly exploit the nonlinearity of the rectifier and the channelfrequency diversity. This shows that the hardware complexityincrease in the spatial domain (having two antennas rather than Number of Sinewaves N (a) FF channel
Number of Sinewaves N (b) FS channel
Output DC Power (uW) CD F ( % ) CW1ant 8tone SMF2ant 1tone MRT2ant 8tone SMF4ant 1tone MRT4ant 8tone SMF (c) CDF
Fig. 10. (a), (b)Received DC power as a function of N with 10 MHz bandwidth undertwo different channel conditions (FF and FS) with one and two transmit antennas. (c)Measured CDF of DC output power in different locations one) can be decreased by adopting a more efficient waveform.In other words, the use of SMF multisine waveform candecrease the need for multiple transmit antennas for a givenperformance target. Second , we observe that the gains from the spatial (beam-forming) and frequency (waveform) domains are cumulative.For UPMF and SMF, the 2-antenna setting leads to about100% gain over the SISO setting for all N in both channels.Remarkably, the 2-antenna SMF with N = 16 achieves a gain of about 110% over the 2-antenna conventional beamformingwith CW ( N = 1 ) and close to 350% over the 1-antennaCW, in FS channel conditions. Interestingly, the sharp increasein DC power with N achieved by the 1-antenna SMF isstill observed in the 2-antenna setting. This highlights thatSMF jointly exploits the multi-antenna beamforming gain, thechannel frequency diversity gain and the rectenna nonlinearity.Those results also show that various performance enhancementfactors can be superimposed and applied in WPT, which canlead to significant performance improvements.Additional MISO joint beamforming and waveform exper-iments were carried out using the four antenna prototypeto verify the performance of multi-antenna with multi-toneWPT under many different wireless environments. Cumulativedistribution function (CDF) of measured DC output powerwith various numbers of antennas and tones is presented inFig. 10(c). One tone MRT and eight tone SMF signals for eachnumber of antennas were used and performance compared.The measurement are taken at 100 different locations in theoffice and the distance between the transmitter and the receivervaries between 3 and 5.5 meters. Each measurement was taken1 second and repeated ten times with one minute of time in-terval at each location. The graph clearly shows multi-antennawith multi-tone SMF signals outperform multi-antenna withsingle-tone MRT signals, and the gain is significant. Besides,the 4-antenna 1-tone waveform shows similar performance thatof the 2-antenna 8-tone waveform. In the same manner, 2-antenna single-tone and 1-antenna 8-tone show similar per-formance. Such behavior reaffirms the two observations weidentified earlier regarding the joint beamforming and wave-form gain. Those observations are inline with the observationsmade from the theoretical gain of the joint waveform andbeamforming design that scales with N M (in the fourthorder term of (6)) according to Table II. This indicates that thetheoretical analysis and simulation results provided in SectionIII-A are consistent with the experimental results in the actualwireless environment. Remark 3:
The key observation of this subsection is thatdifferent types of gains can be accumulated by jointly usingwaveform and beamforming, such as a beamforming gain, afrequency diversity gain and the gain from the rectifier non-linearity. This contrasts with beamforming-only approaches,e.g., [24]–[26], that provide a beamforming gain-only. Recallthat results of the beamforming-only approach (and thereforesomewhat equivalent to [24]–[26]) is obtained by looking at1-tone results in Fig. 10. Results here show that the gain ofthe joint beamforming and waveform design scheme leadsto significantly larger harvested DC power compared to theconventional beamforming-only schemes of [24]–[26]. .
E. Modulations
According to the scaling laws of Table III, conventionalmodulations used for communications such as BPSK, QAMand complex Gaussian (simply denoted as CG) should be out-performed by energy modulations such as real Gaussian (RG)and flash signaling. We carried out a modulated waveformexperiment in order to confirm the theoretical predictions of Table III. The signal was generated with a modulation rateof 2.5 MHz for all modulation types. To rigorously observethe differences due to the modulation schemes (rather thanmeasuring the effect induced by the fluctuations of the chan-nel), the experiment was conducted by feeding the transmittedsignal directly into the rectifier through cable connections(in contrast to the over-the-air radiation used in the othersubsections). The rectenna received input RF power was set at-20dBm, and the harvested DC power was measured for fiveminutes and five times for each modulation type, before beingaveraged. Fig. 11 displays the measurement results.
CW BPSK 16QAM CG RG l=2 l=3 l=4 l=5
Modulation types
Fig. 11. Received DC power vs. Modulation types.
We observe that the general trend of Fig. 11 matcheswell the theoretical results of Table III. Namely, the PSKmodulations does not perform any better than CW becausePSK does not induce any amplitude fluctuation and does notaffect the fourth order term E { y ( t ) } of z DC . 16QAM andCG exhibit a respective 13% and 26% gain compared to CWbecause of the amplitude fluctuation that increases E { y ( t ) } .Similarly, RG achieves a 42% gain thanks to the larger fourthmoment of a RG distribution compared to a CG distribution.Flash signaling provides even higher DC power as it increasesthe fourth moment E { y ( t ) } as l increases by enabling a smallprobability of very large amplitude signals. Nevertheless, thebehavior does not match exactly what was predicted fromTable III. The highest DC power is achieved at l = 3 withan overall gain of 95% over CW, but decreases when l isfurther increased. This behavior is due to the peak voltageof the received signal that exceeds the breakdown voltage ofthe diode. Such breakdown voltage is not modeled in z DC .A similar trend, though less severe, has been observed inthe circuit simulations provided in Appendix A, though thebreakdown voltage of the diode was found to be lower in theactual circuit than in the circuit simulations. Note that theperformance could be improved by designing a circuit that isrobust to diode breakdown and copes with high peak voltages(see discussions in [18], [29] and references therein). Remark 4:
It is important to recall that observations madefrom Fig. 11 cannot be explained from the linear model of therectenna. All those modulations achieve the same second orderterm E { y ( t ) } , and according to the linear model, they shouldall achieve the same performance. Obviously this is incorrect and only accounting for the rectifier nonlinearity through thefourth order term E { y ( t ) } can explain the difference betweenthe modulations. This further demonstrates that the inaccuracyof the linear model highlighted in Remark 2 carries on to othertypes of signals such as modulation. Remark 5:
Energy modulation is not only important for im-proving WPT efficiency but plays a major role in simultaneouswireless information and power transmission (SWIPT) systems[19], [20]. Conventional PSK/QAM modulations have beenused in SWIPT [35], [36], and measurement results here showand confirm that we should depart from such modulation if onewants to make the best use of the radiowaves. Results showhere that energy modulations based on flash signaling, whoserandomness has been optimized to maximize the amountof DC power with no consideration for information trans-fer, significantly outperform other modulations/distribution interms of harvested DC power. It is left as future work toexperimentally show how such modulations perform in termsof information transfer and what is the tradeoff between rateand power.
F. Transmit Diversity
The transmit diversity experiment was performed using twotransmit antennas at six different LoS test locations locatedat a distance of 2.5 to 4m in a normal office environment.At each test location, the transmitter generates different typesof signals such as single antenna continuous wave/complexGaussian/multisine waveform ( N = 8 ) and their two-antennatransmit diversity counterparts. The phase changing rate fortransmit diversity signals and modulation rate for the complexGaussian signal is set to 2.5MHz. The DC power measure-ments were conducted for one minute and repeated five timeswith some time intervals, before being averaged to obtain thefinal measurements. Fig. 12 displays the measurement resultsat the six different test locations. Loc.1 Loc.2 Loc.3 Loc.4 Loc.5 Loc.6
Test Locations
Continuous Wave (CW)Transmit Diversity - CWComplex Gaussian (CG)Transmit Diversity - CGMulti-Tone (N=8) (MT)Transmit Diversity - MT
Fig. 12. Transmit Diversity performance measurement in six different locations
The experimental results show that the TD with CW signalhas an average gain of about 28% compared to the CW signalalthough there is some difference in each test position. TD withCG and TD with multisine/multitone ( N = 8 ) signal show a31% and a 66% gain respectively over the CW signal. Thoseresults are inline with the observations from the theoretical analysis of TD signals provided in Table IV. This indicatesthat the theoretical model that shows the energy harvestingperformance improvement by using TD in subsection III-Cis consistent with the actual experimental results over real-world wireless channels. Recall that those gains are achievedwithout any CSIT. Transmit diversity is appealing for low-complexity applications with a massive number of low-powerdevices because the transmitter is equipped with cheap/dumbantennas, the receivers do not need power-consuming signalprocessing block such as channel estimation and feedback, andthe energy harvesting performance can be improved simultane-ously for all receivers. Though the prototype was designed andmeasurements were conducted with two transmit antennas, asmentioned in the theoretical model, the gain can be improvedby increasing the number of transmit antennas.VI. C ONCLUSIONS AND F UTURE W ORKS
A WPT testbed with and without CSIT acquisition and var-ious signal transmission strategies (beamforming, waveform,modulation and transmit diversity) was designed, prototypedand experimented. The harvested DC power achieved by thosestrategies and combination thereof was analyzed as a functionof various parameters such as the propagation conditions,CSIT quality, bandwidth, rectenna design and experimentalresults were contrasted with the theoretical analysis.It has been shown that the design of an appropriate signalgeneration method (such as SMF) that adapts as a functionof the channel condition can significantly boost the harvestedDC power performance. Large gains are obtained when usinga combination of waveform and beamforming. The larger thenumber of tones in the waveform and the wider the bandwidth,the larger the gains. Significant performance improvementswere possible through signal design based on CSIT underfrequency-selective channel, so as to jointly benefit from abeamforming gain, a waveform gain, the rectenna nonlinearityand the frequency selectivity of the channel. In the casewhere CSIT is not available, the power transmission efficiencycan be greatly improved by using proper energy modulationsor by generating artificial fading through a multi-antennatransmit diversity strategy. Widely used modulations for datacommunication have also been shown to improve the powertransfer efficiency depending on the modulation type, but areoutperformed by modulation designed specifically for WPT.This work demonstrates experimentally the importance andbenefits of modelling and exploiting the harvester nonlineari-ties originating from the convexity of the I-V characteristics ofthe diodes. On the other hand, it is also verified that the linearmodel of the harvester obtained by ignoring the nonlinearityleads to poor signal design.There are many interesting research avenues to pursue.Beyond the MISO system, a large-scale multisine multiantennaWPT with jointly optimized beamforming and waveform,applicable to both single-user and multi-user deployments, isa promising architecture [11]. It is also worth to implementand investigate a larger number of transmit antennas in thetransmit diversity experiment. When it comes to channelacquisition, the wired feedback of CSI needs to be replaced by a wireless counterpart. To that end, a low-power simplemethod to feedback CSI from receiver to transmitter andaccordingly design the joint waveform and beamforming, asstudied in [13], would be an interesting avenue that has notbeen experimented yet. Moreover, another interesting areawill be to consider a WPT architecture where the transmitsignals and the rectennas adapt themselves dynamically as afunction of the channel state [29], which requires the design ofrectennas adaptive to their input waveforms (shape and power)[37]. These will be considered in future enhancements of ourtestbed system. Moving beyond WPT, it is also interesting tostudy how the prototype could be expanded to a real SWIPTsystem so as to assess the performance of SWIPT waveformand the corresponding rate-energy tradeoff. Some preliminaryresults are available in [38].VII. A
CKNOWLEDGMENTS
We thank B. Lavasani and National Instruments for provid-ing some of the equipments needed to conduct the experiment.A
PPENDIX AC IRCUIT S IMULATIONS
Beamforming, waveform, modulation and transmit diversityperformance have been analyzed using circuit simulations andresults have been contrasted with the theory (using z DC scalinglaws). Readers are referred to [9] and [10] for waveformand beamforming, to [20] for modulation and to [21] fortransmit diversity. In all cases, circuit simulations confirmthe benefits of the four signal strategies. In the sequel, weprovide some more PSPICE circuit simulations for modulationto complement the ones obtained in [20]. The rectifier circuitfor the simulation is the same as the one used in [21] and wegenerate modulation signals with 2.5MHz symbol rate and -20dBm of RF Power in Matlab. The simulations were repeated300 times using randomly generated modulation signals foreach modulation format, and the results were then averaged.Fig. 13 illustrates the received DC power simulation results ofdifferent modulations. CW BPSK 16QAM CG RG l=2 l=3 l=4 l=5
Modulation types
Fig. 13. Simulated received DC power with several modulation schemes and flashsignaling l = 2 , , , . The results show that some of the conventional modulationsare effective to boost the DC power. For instance, CG signals exhibit higher efficiency than other conventional modulationschemes. PSK modulation has no performance advantagecompared to the continuous wave because all symbols havethe same magnitude. 16QAM signal leads to a performanceimprovement of about 17% because of the amplitude fluc-tuations among symbols. On the other hand, with energymodulation, the performance improvement is more significant.RG leads to a 60% gain compared to a continuous wave.Flash signaling exhibits significantly better performance. Themaximum delivered power occurs at l = 4 . The gain observedon circuit simulations with flash signaling also appear largerthan in the measurements of Fig. 11. The results also showthat the simulations are inline with the scaling laws calculatedin Table III. R EFERENCES[1] B. Clerckx, R. Zhang, R. Schober, D. W. K. Ng, D. I. Kim, and H. V.Poor, “Fundamentals of wireless information and power transfer: Fromrf energy harvester models to signal and system designs,”
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