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Transfer communication Power the in Wireless emerged for design signals WT,Wvfr,Bafrig P rttp,Nonlinearit Prototype, WPT Beamforming, Waveform, (WPT), fcetrcenss st nraeteR-oD conversio RF-to-DC the o increase design the to to as devoted line so been rectennas has traditional transmit efficient literature the RF a end-to-en end, the in the that to research To to enhance efficiency. subject to is transfer equivalently power design power or system DC constraint, WPT harvested power radiative technologies the other of re- maximize with challenge small comparison crucial and in A delivery factors, attract power form is long-distance WPT ceiver enables communicating radiative it of particular, In purpose since dual [1]. energizing the and for wher used networks are wireless innovative radiowaves Wirel for Things, low- and of Networks, Internet of Sensor the many for as number enabler such an applications large as emerging viewed a is It devices. energize autonomous power to technology invaluable I h PR fU,udrgatEP/P003885/1. grant partiall under been UK, has (e of work This EPSRC U.K. 2017. the 10-12, Transfe 2AZ, Power May Wireless Taiwan, MTT-S Taipei, SW7 IEEE the from London version expanded London, [email protected] b.clerckx, College junghoon.kim15, Imperial gineering, h uhr r ihteDprmn fEetia n Electr and Electrical of Department the with are authors The ne Terms Index Abstract WT aebe rwn eetybcueWTi an is WPT because recently growing been have Transfer (WPT) Power Wireless (far-field) radiative in NTERESTS rnfr:Pooye xeietadValidation and Experiment Prototype, : Transfer inladSse einfrWrls Power Wireless for Design System and Signal Anwln frsac ncmuiain and communications on research of line new —A Eeg avsig ieesPwrTransfer Power Wireless harvesting, —Energy .I I. 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WPT and communication for literature the design in signal recently and emerged communications on research utpir a ecniee o etnadsgs[2]–[4] designs rectenna for volta considered shunt, be single can (e.g. technol topologies multiplier) of and variety Diode) a CMOS, that (e.g. well-established is It efficiency. h nryhretradteeoeehneteRF-to-RF the enhance therefore and efficiency transmission harvester energy the beamforming ehiust ut-nen emomn,as nbigdi enabling Alternative also beamforming, [15]. multi-antenna (MRT) to Transmission beamform- techniques Ratio of Maximum form is simplest ing the Similarl communications, [14]. WPT wireless for to scheme acquisition CSIT appropriate ed ob osdrd n osbeslto st design feedback to of is number limited solution [13]. a possible on bits joint based a strategy WPT proper for and acquisition waveform a considered, the channel transmitter, be the the to and waveform needs to the acquired of be real-time sin design to Moreover, a [10]–[12]. needs in in complexit CSI introduced design been implemented waveform therefore reducing easily have for optimization not non-convex Strategies a is system. of which solution the problem, desi as waveform obtained optimal be the nonlinearity, can rectifier the to Due oepottercen olnaiyadbotteRF-to-DC the boost and nonlinearity efficiency rectenna conversion the exploit to htmliiewvfrscnincrease can waveforms multisine that s st os h Ft-Ccneso efficiency conversion RF-to-DC the boost to as (so hthg ekt-vrg oe ai PP)wvfrsen- waveforms hance (PAPR) Ratio Power Peak-to-Average high that eetvt s st aiieteR-oR transmission RF-to-RF the maximize to efficiency as freque re- channel (so [9] the exploiting selectivity in between waveform tradeoff a channel-adaptive from channe of sults the design of optimal selectivity frequency The Transmitt the the on at depending Information designed (CSIT) State be Channel can without Waveforms [9]. and in with proposed first was WPT for A of line complementary and new a design, rectenna Aside A first second e rf − taeyi odsg (energy) design to is strategy e dc rf − 8.Asseai aeomdsg methodology design waveform systematic A [8]. taeyi odsg ut-nen (energy) multi-antenna design to is strategy nodrt nraeteR nu oe of power input RF the increase to order in rf n h nryhretr(H nonlinearity (EH) harvester energy the and ) e rf e − rf dc − rf rvossuishv observed have studies Previous . hssrtg lorqie an requires also strategy This . e waveforms rf − dc 6,[] and [7], [6], norder in e rf ogies − rec- dc . ncy ave ion gn gn ge na ce so er ). l. y y g y 1 2 tional/energy focusing transmission, consist in retrodirective static and heuristic waveforms fed directly into the rectifier, and time-modulated arrays [16] and time-reversal techniques not using closed-loop based architecture with channel-adaptive [17]. Waveform and multi-antenna beamforming can be com- (relying on CSIT so as adjust the transmission strategy dy- bined so as to optimally exploit the beamforming gain, the namically as a function of the wireless frequency-selective channel frequency diversity gain and the nonlinearity of the propagation channel) and optimized waveforms transmitted rectifier [9], [11]. over-the-air. In the communication literature, emphasis has A third strategy is to design (energy) modulation for been put on closed-loop based adaptive beamforming with a single-carrier transmission. In contrast to the energy wave- multi-antenna transmitter, as shown in e.g. [24]–[28]. These form that commonly relies on an optimized deterministic works studied channel acquisition techniques, and over-the-air multisine/multi-carrier, the energy modulation induces ran- feedback, for WPT and focused on increasing erf−rf through dom fluctuations of a single-carrier. Similarly to the energy adaptive beamforming. waveform, the design of the energy modulation aims at ex- Recall nevertheless that maximizing the end-to-end power ploiting the nonlinearity of the rectifier to boost the RF-to- transfer efficiency is not achieved by maximizing erf−rf and DC conversion efficiency erf−dc. Indeed, as a consequence erf−dc independently [5], [29]. This is because erf−rf and of the energy harvester nonlinearity, the RF-to-DC conversion erf−dc are coupled due to the rectifier nonlinearity. This calls efficiency erf−dc differs depending on whether the rectifier for systematic signal strategies that maximize the overall input signal is modulated or not [18]. For instance, a real power transfer efficiency erf−rf erf−dc by jointly accounting Gaussian modulation offers a higher harvested DC power than for the effect of the wireless channel× and the harvester non- a circularly symmetric complex Gaussian modulation [19]. linearity [5], [9], [29], and therefore completely bridge the RF A new modulation scheme based on flash signaling (a form and communication approaches. The first prototype to demon- of on-off keying distribution with low probability of high strate the feasibility and over-the-air performance of waveform amplitude signals) has recently been introduced in [20]. It strategies that are adaptive to the wireless channel, account exploits the rectifier nonlinearity by transmitting signals of for the harvester nonlinearity and maximize erf−rf erf−dc very high amplitudes with low probability. Flash signaling appeared in [30]. × was shown to outperform a real Gaussian modulation and In this paper, we build upon the prototype of [30], and maximize the amount of harvested DC power. Flash signaling- implement all the four recently developed signal design strate- based energy modulation can also be combined with multi- gies, namely waveform, beamforming, modulation, transmit antenna so as to additionally exploit a beamforming gain. diversity. The performance gain and feasibility of all those A fourth strategy is to use phase sweeping transmit di- four strategies, and combination thereof, in real-world environ- versity in a multi-antenna WPT setup to boost the RF-to- ments is assessed and verified experimentally for the first time1 DC conversion efficiency [21]. Transmit diversity aims at in the literature. In particular, we ask ourselves the following artificially inducing fast fluctuations of the wireless channel at questions: Can we establish an experimental environment of the input of the rectifier using dumb transmit antennas. Those open-loop and closed-loop WPT and verify the advantages fluctuations are shown to improve the RF-to-DC conversion of systematic signal design for WPT (including waveform, efficiency thanks to the rectifier nonlinearity. Interestingly, beamforming, modulation, transmit diversity) through experi- transmit diversity does not rely on CSIT and demonstrates mentation? Can we confirm theory from measurements? Can that multiple transmit antennas can be beneficial to WPT even we validate or invalidate the linear and nonlinear energy in the absence of CSIT. harvester models used in the WPT and Wireless Information The theoretical performance benefits of the aforementioned and Power Transfer (WIPT) literature? The contributions of four signal strategies have been studied in the literature, based the paper are summarized as follows. on simplified linear and nonlinear energy harvester models. First, we design, prototype and experiment a WPT system Since the theoretical analysis relies on numerous assumptions, that can operate in both open-loop and closed-loop modes. commonly made to simplify the signal and system design, it The setup consists of three important blocks, namely the remains to be seen whether those emerging signal designs for channel acquisition, the signal optimization and generation, WPT still deliver the expected benefits in a realistic setup. and the energy harvester(s). Software Defined Radio (SDR) is In particular, aside the crucial nonlinearity and nonidealities used to implement a wireless power transmitter and a channel of the energy harvester, real-world experimentation of WPT estimator, and various rectennas with single-diode and voltage is subject to numerous impairments such as amplifier nonlin- doubler rectifiers are designed to work as energy harvesters. earity and gain/phase offset, that are neglected, and can be Leveraging the flexibility and reconfigurability of the SDR, it overlooked, in any theoretical analysis. This calls for proto- is possible to implement various transmission signal design typing and experimenting those emerging signal strategies to and CSI acquisition strategies in one set of experimental assess their real-world performance and validate the feasibility equipment. In its open-loop WPT mode, the architecture does of the underlying signal theory for WPT. 1Recall that [24], [25], [26], [27], and [28] focus on beamforming-only There have been studies on WPT prototyping, in both the techniques where beamforming is optimized/designed for WPT. None of RF and the communication literature. In the RF literature, them focuses on energy modulation (designed to maximize the harvested DC multisine waveforms have been experimented in [6], [22], [23] power), waveform (designed to maximize harvested DC power), or transmit diversity. Any modulation or waveform used in those papers are conventional and the corresponding erf−dc has been measured. These exper- communication modulation/waveform, not signals designed/optimized for iments were performed using open-loop based prototypes with WPT. 3

not rely on any CSIT (and therefore the channel acquisition II. THE SYSTEMANDTHE SIGNAL MODELS module), though still increases the harvested DC power by We consider a Multiple Input-Single Output (MISO) WPT using energy modulation and transmit diversity. In its closed- system based on the four signal design strategies mentioned loop WPT mode, the architecture relies on a frame structure in the introduction. The general system model, along with switching between a channel estimation/acquisition phase and the mathematical model of each signal design technique, are wireless power transmission phase. Channel acquisition is presented in this section. performed every second and transmit signal is generated according to a joint waveform and beamforming design to maximize e − e − . A. MISO WPT System Model rf rf × rf dc Second, we implement the four signal design strategies The transmitter is equipped with M transmit antennas and mentioned above, namely waveform, beamforming, transmit uses N subbands, while the receiver is equipped with a single diversity and energy modulation, in the prototype. The real antenna. The transmit signal at time t on antenna m is written over-the-air performance are assessed experimentally for each as of the strategies and for a combination thereof. This contrasts N−1 with other WPT prototyping works that focus on the adap- xm(t)= sn,m(t)cos (2πfnt + φn,m(t)) tive beamforming approach only, e.g. [24]–[28], or on test- n=0 (1) ing conventional/non-adaptive (not WPT-optimized) waveform X N−1 j2πfnt [6], [8], [22], [23]. = ωn,m(t)e ℜ Third, the performance (in terms of harvested DC power) ( n=0 ) of the WPT architecture is investigated in a variety of de- X jφn,m(t) ployments, including frequency flat (FF) and frequency selec- with ωn,m(t) = sn,m(t)e where sn,m(t) and φn,m(t) tive (FS) channels, and under static and mobility conditions. refer to the amplitude and phase of the subband signal on Experiments highlight the suitability of each signal design frequeny fn and transmit antenna m at time t. Quantities S and Φ are N M dimensional matrices of the amplitudes under various propagation conditions and the role played by × various parameters such as the channel frequency selectivity, and phases of the sinewaves with their (n,m) entry denoted the velocity, the number of tones, the number of transmit as sn,m(t) and φn,m(t). The average transmit power constraint is given by M E 2 1 S 2 . Vector-wise, the antennas, the signal bandwidth and the rectenna design. m=1 xm = 2 F P transmit signal vector{|x(t|) }can bek writtenk ≤ as Fourth, and importantly, the experimental results of the P various signal strategies confirm and validate the observation N−1 j2πfnt made from the theory of the rectifier nonlinearity and the x(t)= wne (2) ℜ signal designs proposed and developed in [9], [10], [18]– ( n=0 ) X [21]. In particular, the following observations made from where w T . the theory are fully confirmed in the experiments: 1) The n = [ωn,1(t) ωn,M (t)] The transmit signal··· propagates through a multipath channel. diode nonlinearity is fundamental and beneficial to WPT We assume that the (frequency-domain) channel coefficient performance and is to be exploited in any systematic transmit changes at a rate slower than the transmission signal signal design for WPT and WIPT; 2) The linear model of hn,m(t) and that the channel is effectively stationary within a single the EH, obtained by ignoring the rectifier nonlinearity, is time frame (i.e., we drop the time dependency of the channel not validated by experiments and measurements and leads to coefficients). The received signal from transmit antenna is poor signal designs; 3) The wireless propagation channel and m written as fading has a significant impact on WPT signal design and system performance; 4) A systematic WPT signal and system N−1 design has a big influence on the energy transfer efficiency ym(t)= sn,m(t)An,m cos(2πfnt + ψn,m(t)) (3) n=0 with and without CSIT; 5) CSI acquisition and channel- X adaptive waveforms are essential to boost the performance in where the amplitude and phase An,m and ψn,m are such that frequency-selective channels; 6) Multiple antennas can be used jψn,m(t) j(φn,m(t)+ψ¯n,m) jφn,m(t) in conjunction with transmit diversity to improve the energy An,me = An,me = e hn,m transfer efficiency without CSIT; 7) Energy waveform and (4) and the frequency response of the multipath channel is given modulation can be used in conjunction with beamforming to ¯ by h = A ejψn,m . The channel vector h can be maximize erf−rf erf−dc and achieve a combined gain. n,m n,m n × written as hn = [hn, hn,M ]. Organization: Section II introduces the system model and 1 ··· Section III presents theoretical performance analysis. Section The total received signal is the sum of (3) over all transmit IV introduces the prototype design. Section V offers all ex- antennas, namely perimental results and observations and Section VI concludes M N−1 the work and discusses future works. y(t)= sn,m(t)An,m cos(2πfnt + ψn,m(t)) Notations: Bold letters stand for vectors or matrices whereas m=1 n=0 X X (5) a symbol not in bold font represents a scalar. . and . refer N−1 | | k k j2πfnt to the absolute value of a scalar and the 2-norm of a vector. = hnwne . ℜ E . refers to the averaging/expectation operator. ( n=0 ) { } X 4

At the receiver, the signal y(t) impinges on the receive t. The coefficient √2P is used to guarantee the average antenna and is absorbed by the rectifier. A simple and tractable transmit power constraint P . model of the rectenna, introduced in [9], is used in this paper We consider conventional modulation schemes (commonly for the analysis. The model expresses the output DC current used and designed for communication purposes) such as PSK, as a function of the input signal y(t) and relies on a Taylor QAM and Circularly Symmetric Complex Gaussian - CSCG expansion of the diode characteristic function. Following [9], (equally distributing power between the real and the imaginary the rectenna output DC power under perfect matching and dimensions, i.e., ω (0, P ) and ω (0, P )) and ideal low pass filter is related to the quantity compare with modulationsℜ{ }∼N specificallyℑ{ designed}∼N for wireless power delivery, such as Real Gaussian (allocating the transmit E 2 2 E 4 zDC = k2Rant y(t) + k4Rant y(t) (6) power to only one dimension e.g. ω (0, 2P )) [19], { } { } ℜ{ } ∼ N is and the recently proposed flash signaling [20] characterized with Rant the antenna impedance and ki = i for i = i!(nvt) by a uniformly distributed phase φ over [0, 2π) and the 2, 4, where is is the reverse bias saturation current, vt is the thermal voltage, n is the ideality factor. The fourth order term amplitude distributed according to the following probability E y(t)4 accounts for the rectifier nonlinearity. As a reference, mass function { } following [9], k2 = 0.0034 and k4 = 0.3829. Considering 1 Rant = 50Ω, the coefficient of the fourth order term is 5630 1 2 , s =0, p (s)= − l (8) times larger that the second order coefficient, and explains why s 1 √ ( l2 , s = l 2P, nonlinearity is non-negligible. with l 1. We can easily verify that E ω 2 = E s2 =2P , hence≥ satisfying the average power constraint.| | By increasing B. (Energy) Waveform and Beamforming     l, s = l√2P increases and ps(l√2P ) decreases, therefore Various channel non-adaptive (not relying on CSIT) and exhibiting a low probability of high amplitude signals. adaptive (relying on CSIT) multisine waveform strategies for WPT have been proposed in the past few years and can be D. Transmit Diversity used in single-antenna as well as multi-antenna setup [9], [10]. In contrast to (energy) waveform and modulation that in- Since those waveforms are deterministic, i.e. not modulated, duces amplitude fluctuations of the transmit signal, transmit we can drop the time dependency such that ωn(t)= ωn. diversity is designed to generate amplitude fluctuations of In Table I, we highlight various waveform design methods the wireless channel [21]. Those fluctuations of the wireless and the mathematical representations of the waveform coeffi- channel are beneficial to the energy harvester thanks to the cients ωn for single antenna and wn for multi antenna system, rectifier nonlinearity. To induce fluctuations of the wireless assuming the CSI (in the form of the frequency-domain channel, transmit diversity relies in its simplest form on response hn for all frequency component n) is available at the multiple dumb antennas fed with a low PAPR continuous wave transmitter. All those waveforms can be expressed in closed- and antenna-dependent time varying phases. In this case, the form and can therefore be implemented and tested in real- waveform design factor ωn,m(t) at the antenna m at time t on time over-the-air transmission. We do not consider the optimal carrier frequency f0 is expressed as follows waveform design of [9], [11], [12] because they result from a jφm(t) convex/non-convex optimization problem that cannot be easily ωn,m(t)= ωm(t)= se , (9) solved and implemented in real-time. 2P where s = M is the amplitude of the continuous wave on each transmitq antenna (with uniform power allocation), and C. (Energy) Modulation φm(t) is an antenna dependent time varying phase (whose Energy modulation is another strategy for WPT to induce rate of change can be predefined). The total transmit power fluctuations of the transmit signal amplitude of a single over all antennas is fixed to P . carrier and boost the harvested DC power. In contrast to the Transmit diversity can also be implemented in combination multisine waveform that is deterministic, energy modulation with the aforementioned energy modulation and waveform carries information due to the randomness inherent from the strategies. Transmit diversity with energy modulation can be modulation. However the modulation is designed in such a way designed by transmitting the same energy symbol on all that it maximizes the harvested DC power [20]. In its simplest antennas but applying an additional antenna-dependent random form, M =1,N =1, and the transmit signal ωn,m(t) at time phase φm,td(t), such that t on carrier frequency f0 can be written as jφm(t) ωn,m(t)= ωm(t)= s(t)e , (10) jφ(t) ωn,m(t)= ω(t)= s(t)e (7) 2P 2 2 where s(t) = M mI (t) + mQ(t) and φm(t) = 2 2 where s(t) = √2P mI (t) + mQ(t) and φ(t) = tan−1 mQ(t) + φq (t). The normalized complex modula- mI (t) m,tdp tan−1 mQ(t) . The message signal can be expressed in mI (t) p tion symbol m(t) = mI (t)+ jmQ(t) is the same for all an- complex form as m(t) = mI (t) + jmQ(t) and m(t) is a tennas. Similarly, transmit diversity with multisine waveform normalized (E m(t) 2 = 1) complex baseband equivalent transmits the same waveform on all antennas and applies an signal that represents{| | the} (energy) modulation symbol at time antenna dependent time varying phase before being launched 5

TABLE I. Various Waveform Design Methods and Descriptions

Waveform Antennas CSIT Design Expression Description Reference Method

√2P The uniform power allocation (UP) simply assigns the same power no CSIT UP ωn = [9] √N to all frequencies components, with a zero phase. The adaptive single sinewave (ASS) allocates power to the SISO ¯ jψn one frequency corresponding to the strongest channel n¯ = √2Pe− n =n ¯ CSIT ASS ωn = arg maxi hi . This is the optimal solution for the linear EH [9]  0 n =n. ¯ | | 6 model (2nd order term-only in (6)), and therefore aims at maxi- mizing erf rf . The uniform− power allocation and matched fiter (UPMF) allocates √2P jψ¯ CSIT UPMF ωn = e n the same amplitude for all frequencies components, but the [9] √N − channel phase is matched on each sinewave based on the CSIT. ¯ The matched filter (MF) allocates power to all sinewaves pro- 2P jψn CSIT MF ωn = An N−1 e− portionally to the frequency domain channel strengths. It is a [9] P A2 r n=0 n particular case of SMF with β = 1. ¯ The maximize PAPR (MAX PAPR) allocates power inversely 1 2P jψn MAX ωn = −1 e CSIT An N 1 − proportional to the channel strength to maximize the PAPR at [9] PAPR Pn=0 2 r An the rectifier input. The scaled matched filter (SMF) is a low-complexity multisine waveform design strategy motivated by observations of the op- ¯ β 2P jψn timized signal. β is a scaling factor, whose choice results from CSIT SMF ωn = An N−1 2β e− [10] r Pn=0 An a compromise between exploiting the EH nonlinearity and the channel frequency selectivity, and therefore aims at maximizing erf rf erf dc. The− uniform× − power allocation (UP) in MISO also simply assigns √2P no CSIT UP wn = the same power to all frequencies and spacial components, with [9] √NM MISO a zero phase. The uniform power allocation (UP) is applied in the frequency hH √2P n CSIT UPMF wn = domain, and the matched (or maximum ratio transmission) beam- [9] √N hn k k forming (MF) is applied in the spatial domain. ¯ jψn hH The single antenna channel gain An and optimal phase e− MISO n β 2P wn = hn −1 h CSIT SMF hn N h 2β are substituted by the multi-antenna effective channel gain n version k k k k r Pn=0 n H k k k k and the MRT beamforming vector h / hn , respectively. of [10] n k k over the air. Considering a channel non-adaptive in-phase mul- of transmission, we have added a channel instance factor k tisine waveform with uniform power allocation in frequency to the transmit and receive signal. The evolution of hk,n is and space (denoted as UP in Table I), ωn,m(t) on antenna m modeled by a first-order Gauss-Markov process at time t on frequency fn is expressed as follows 2 jφm(t) hk,n = ǫhk− ,n + 1 ǫ gk,n, (12) ωn,m(t)= ωn,m(t)= se , (11) 1 − 1×M p 2P where gk,n C has i.i.d. entries distributed according where s = and φm(t) is the antenna dependent time NM ∈ E ∗ varying phase of transmit diversity. to (0, 1) and hk− ,ngk,n = 0M , where 0M denotes q CN 1 M M zero matrix. We assume gk,n is i.i.d for all frequency × h i III. THEORETICAL PERFORMANCE ANALYSIS componets n in FS channel, and gk,n = gk n in FF channel. h is independent of g for all k 1∀. The coefficient The scaling laws of (6) have been introduced in [9] as a way 0,n k,n ǫ(0 ǫ< 1) quantifies the amount of the≥ correlation between to predict the theoretical performance benefits of WPT signal ≤ elements h − and h , and we assume all the elements designs and the key role played by the rectifier nonlinearity k 1,n,m k,n,m of h have the same ǫ. The time correlation coefficient ǫ and the signal parameters (e.g. N, M). The behavior predicted k,n follows Jakes’ model for fading channel [31] ǫ = J (2πf T ) from the scaling laws will be contrasted with the measurement 0 D where J (.) is the zeroth order Bessel function, T denotes the results. To that end, this section summarizes some of those 0 channel instantiation interval, and f = vfc is the maximum existing theoretical scaling laws for waveform designs [9] and D c Doppler frequency where v is the terminal velocity, f is for transmit diversity [21], and extends them to account for c carrier frequency, and c =3 108m/s. The time correlation mobility conditions and to (energy) modulation. coefficient ǫ is therefore a× measure of the channel time variation, and it is related to the velocity of the mobile terminal A. (Energy) Waveform and Beamforming (0 ǫ 1). ≤ ≤ The scaling laws for waveform designs under perfect CSIT Following the same approach as in [9], we calculated the are provided in [9]. We here extend them to account for scaling laws of UP and UPMF techniques with the above delayed CSIT due to mobility and time varying channels. delayed CSIT model in single and multi-antenna systems with To represent the delayed CSIT in a mobility condition and frequency flat and selective channels. To that end, we assumed account for the differences between the CSI acquired at the that the transmitter at time k does not know hk,n, but has only time of channel estimation and the actual channel at the time access to the channel at time k 1 to design the transmit signal − 6

TABLE II. Scaling Laws of Energy Waveforms

No CSIT CSIT zDC N,M zDC,UP zDC,UPMF

2 2 2 2 N 1, M = 1 k2RantP + 2k4RantP N k2RantP + 2k4RantP N FF Channel ≫ 2 2 2 2 ǫ k2RantPM + (1 ǫ )k2RantP + N 1, M 1 k2RantP + 2k4RantP N 4 2 2 2 − 2 2 2 2 ≫ ≫ ǫ k4RantP NM + 2(1 ǫ ) k4RantP N − 2 2 2 2 4 2 2 2 N 1, M = 1 k2RantP + 3k4RantP k2RantP + 3k4RantP + ǫ π /16k4RantP N FS Channel ≫ 2 2 2 2 ǫ k2RantPM + (1 ǫ )k2RantP + N 1, M 1 k2RantP + 3k4RantP 4 2 2 2 − 2 2 2 2 ≫ ≫ ǫ k4RantP NM + 3(1 ǫ ) k4RantP −

(i.e. a delayed version of the CSI). The scaling laws are shown A first observation is that the second order term of zDC in Table II. and (6), i.e. the linear model of the EH [5], [9], is the Since the UP strategy is non-adaptive to the CSI, the time same for all modulation schemes, cannot motivate the design correlation coefficient ǫ does not affect its performance. The of energy modulation and cannot predict the performance results of zDC,UP in Table II is indeed not a function of ǫ. A of energy modulation. A second observation is that there is waveform gain proportional to N is achieved in FF channels, a large performance gap between conventional modulations but not in FS channels. No beamforming gain is achieved and those designed for WPT. This is due to the rectifier either. However, with the channel-adaptive UPMF strategy, ǫ nonlinearity that favours modulations with large high- order has a significant effect on the z performance. When ǫ =1, moments E m(t) 4 . Among the conventional modulation DC {| | } the scaling laws zDC,UPMF boil down to those provided in [9], methods, the complex gaussian (CSCG) signal shows the and a gain proportional to N and M is observed in both FF and largest fourth order term compared to BPSK or 16QAM. A real FS channel conditions. On the other hand, as ǫ decreases and Gaussian, though suboptimal for communication purposes, is approaches 0, zDC,UPMF converges to zDC,UP. As ǫ decreases, more suitable for WPT since it leads to a higher fourth order the beamforming gain vanishes in FS and FF channels, while moment than its complex counterpart. Flash signaling further the waveform gain vanishes in FS channels but remains in FF boosts the fourth order term as l increases. For l> √3, flash channels. In other words, velocity and delayed CSIT incurs a signaling is expected to lead to a higher DC power than a real bigger hit in FS channels than in FF channels. Gaussian.

B. (Energy) Modulation C. Transmit Diversity This subsection derives the theoretical scaling laws of The performance of transmit diversity was analyzed in [21]. zDC for each modulated signal. The transmission is assumed It was shown that by randomly changing the phase of a narrowband and the channel assumed frequency flat. We can continuous wave on each transmit antenna, we achieve a gain write proportional to the number of antennas M in the fourth order term of zDC, despite the lack of CSIT. Additional benefits 2 3 2 4 2 zDC = k2RantE m(t) P + k4R E m(t) P are obtained by combining transmit diversity with (energy) {| | } 2 ant {| | } modulation and waveform. The scaling laws of zDC for trans- 3 2 E 4 2 = k2RantP + k4Rant m(t) P (13) mit diversity with continuous wave and modulation/multisine 2 {| | } waveform versus the single antenna continuous wave are where m(t) is the normalized complex modulation symbol mentioned in section II-C. Since all modulations are normal- displayed in Table IV. ized to have the same average transmit power, the difference TABLE IV. Scaling Laws of Transmit Diversity [21] between modulations can only be explained by the high-order 4 zDC Gain moments, namely E m(t) . Table III displayed zDC of sev- {| | } 3 2 2 eral modulation schemes such as PSK, QAM, Gaussians, and CW k2RantP + 2 k4RantP flash signaling and compare with the unmodulated Continuous 3 2 2 M 1 TD-CW k2RantP + k4RantP G G =1+ − Wave (CW). 2 td td M TD- 3 2 2 Gmod = k2RantP + k4RantP G G 4 TABLE III. Scaling Laws of Energy Modulation Modulation 2 td mod E m(t) {| | } TD- 3 2 2 N zDC k2RantP + k4R P G G ր 2N 2 ant td mt Gmt 3 Multisine ≈ 2 2 Continuous Wave (CW) k2RantP + 1.5k4RantP 2 2 BPSK k2RantP + 1.5k4RantP 2 2 16QAM k2RantP + 1.98k4RantP IV. PROTOTYPING AND TESTBED SETUP 2 2 Complex Gaussian k2RantP + 3k4RantP In order to verify that the proposed transmit signal design 2 2 Real Gaussian k2RantP + 4.5k4RantP methods are feasible and improve the performance in a real 3 2 2 2 world setting, a point-to-point WPT system prototype is re- Flash Signaling (with l) k2RantP + 2 l k4RantP quired. This section discusses the implementation of a WPT 7

Transmitter Tx 4 Rx Tx 3 Ant. Antenna 4 Block Tx 2 Antenna 3 Block Tx 1 Antenna 2 Block Power Antenna 1 Block Receiver Optimization Power Energy Harvester Amp Baseband Waveform Generation Coaxial Cable Power EH Block External Splitter CE Block Pilot IFFT Power Channel OFDM Modulator Amps FFT Estimation for Pilot Transmission LO OFDM Demodulator 2.45 GHz for Channel Estimation

PCI Express Bus

Fig. 1. System architecture with equipment and a peripherals connection. system consisting of a transmitter capable of generating and transmitting various types of signals, and a receiver capable of channel estimation and energy harvesting. This system enables performance evaluation and validation of various signal generation techniques under various wireless channel environments2.

A. Overall System Architecture and Hardware Setup (a) (b) The system operates in the 2.4 GHz ISM band. The target Fig. 2. WPT prototype (a) two antenna configuration (b) four antenna transmit antennas. operating range is to achieve an average received power of the order of -20 dBm at a distance of 5 meters. This is motivated by the fact that 10-100 µW is enough to power modern passes through the power splitter3 and delivers power to each wireless sensors and low-power devices [29]. In compliance block. For the single antenna system, the CE block is also with the Code of Federal Regulations, Title 47, Part15 (FCC implemented on the NI SDR platform by using independent Part15) regulation, the system is designed to operate with an RF transceiver and FPGA module. For the multi-antenna effective isotropic radiated power (EIRP) of less than 4 watt system, one of the FPGA and RF transceiver modules operate (36dBm) [32]. The system consists of up to four transmit as a transmitter and a receiver’s CE block at the same time. antennas and one receive antenna and can be operated in The transmit and receive signal paths in the same module are MISO or SISO mode depending on the transmit signal strategy operated completely independent and do not affect each other. considered. Fig.1 displays the system block diagram which We installed the hardware (a pair of FPGA module and RF includes the equipment and the peripheral connections. Fig.2 transceiver) responsible for the CE block in the same PCI illustrates the complete prototype. express chassis as the transmitter. This configuration enables We chose National Instrument (NI) software-defined radio CSI feedback from the receiver to the transmitter via the prototyping equipment to implement the transmitter that is PCI express bus, which allows the transmitter to recognize able to generate and transmit various types of WPT and pilot the changes of CSI in real time4. The cables connecting the signals. The transmitter hardware has been configured with a NI PXI platform and USRPs. Four pairs of RF transceivers 3We use a power splitter for measurement convenience, such as monitoring an RF input power to the energy harvester. An RF switch could have been were used to implement the four transmit antennas. The used instead of the power splitter and may be a better choice to maximize functions of signal design, optimization and generation on one the received power at the energy harvester. Unlike a power splitter that hand and pilot transmission/channel acquisition on the other distributes power by 50% to each block, it can send 100% of power to the energy harvester during the wireless power transmission phase. However, the hand are combined within the transmitter, and these functions objective of this paper is to compare the energy harvesting performance of are programmed and controlled using LabView. various signal design techniques. Therefore, using a power splitter does not The receiver is divided into two large functional blocks. affect the performance comparison, but makes the system easier to implement. 4A final WPT system would require an over-the-air CSI feedback. We here One is a channel estimation block (CE block) that receives use a wired (instead of wireless) feedback of the CSI as this experimental setup the pilot signal, estimates the channel, and feeds back to is sufficient to answer the main questions and objectives raised in the paper, the transmitter. The other is an energy harvesting block (EH namely to assess experimentally the advantages of closed-loop and open- loop systematic signal designs for WPT (including waveform, beamforming, block), made of a rectifier, that converts the received RF modulation, transmit diversity), confirm theory from measurement, and vali- signal to DC power. The RF signal received by the antenna date the crucial role played by the rectifier nonlinearity. Replacing the wired feedback of the CSI by a wireless counterpart, and accordingly implementing and validating the design of optimized WPT signals (joint waveform and 2It can also be used to perform simultaneous wireless information and beamforming) under limited feedback, is an important issue that is left for power transfer (SWIPT) in the future. future works. 8 equipment and the antenna are long enough so that various OFDM channel estimation block operates at 2.45 GHz center wireless channel environments can also be measured. frequency with 20MHz bandwidth and subcarriers spacing of 78.125KHz. The upper and lower 5MHz bands are used as guard bands, thus the effective region that can actually be B. Channel Estimation and WPT Signal Transmission used to estimate the channel is the 10MHz in the middle and The architecture of Fig. 1 requires the design of a suitable composed of 128 subcarriers. In other words, we can generate frame structure to enable channel acquisition and WPT signal a maximum 128-tone signal and acquire the CSI on those transmission, as per Fig. 3. The transmission signal includes 128 tones. The CSI is nevertheless commonly estimated on a two different types of signals, namely an OFDM signal for smaller number of subcarriers, since the WPT optimized signal multi-frequency channel estimation and an optimized WPT is transmitted on typically up to 16 tones because of the PAPR signal (unmodulated multisine waveform or energy modulated limits of the transmitter (that clips the signal when more than continuous wave) for power delivery. The frame structure has 16 in-phase sinewaves are transmitted). therefore been designed to accommodate two different signals WPT signals are generated based on the various signal in the time domain. The length of the time frame Tframe has design techniques introduced in Section II. The channel adap- been set by default to one second. One second was believed tive multisine waveforms are applied to single and multi- to be sufficient for deployments where the wireless channel antenna setups. The modulation signal is tested on a single does not change rapidly, such as in a static office environment antenna setup, and the transmit diversity signal is generated and where there is no moving object during the measurements. using two antennas. In order to illustrate the effect of the Nevertheless, Tframe can be adjusted and shortened to 200ms waveform designs of Table I, Fig. 4 displays the magnitude for deployments with moving objects. OFDM-based pilot of a measured channel frequency response (for single antenna signals are transmitted at the beginning of each frame for setup) and compares the allocated amplitudes for the different channel estimation and synchronization purposes. The duration types of multisine waveform strategies. It can be seen that Tpilot has been fixed to 512 µs for single antenna transmission SMF allocates power to all frequencies (so as to exploit the and includes therein a frame synchronization and pilot signals. rectifier nonlinearity), but emphasizes (more or less depending In the case of multi-antenna transmission, the duration Tpilot on the choice of β) the strong frequency components and is extended depending on the number of transmit antennas. attenuates the weakest ones (so as to benefit from the channel To estimate multi-antenna channels, each antenna transmits frequency diversity). This contrasts with MAX PAPR that a pilot in a different time slot. Therefore, Tpilot in the 2- inverts the channel (and allocates more power to the weakest antenna MISO experiment is 1 ms, and 4 ms for 4-antenna. At components) so as to maximize the PAPR of the signal at the the receiver, the CE block receives the pilot signal, estimates rectifier input. the channel, and feeds back the CSI to the transmitter. The transmitter then computes and generates an optimized WPT 0.25 signal based on the calculated CSI. The time required for the 0.2 computation and generation of the new signal (based on the 0.15 newly acquired CSI) is Tprev (approximately 30 to 40ms), CSI Magnitude and the signal optimized based on the CSI from the preceding non-adaptive UP 0.6 adaptive MAX PAPR frame is transmitted during this processing time. During the adaptive MF remainder of the frame, the wireless power signal optimized 0.5 for the current frame (based on the current CSI) is transmitted 0.4 and Tcurrent is usually within the range 960-970 ms. 0.3

͎!-( Continuous 0.2 Transmission WPT Waveform Amplitude 0.1

͎+$'*/ ͎+- 1 ͎0-- )/ -5 -4 -3 -2 -1 0 1 2 3 4 5 Transmit Signal Pilot WPT signal Wireless Power Transfer (WPT) Frequency [MHz] Frame Structure from previous frame based on CSI of current frame Fig. 4. Frequency response (magnitude) of the wireless channel and WPT waveform Receiver (CE) Receive Pilot / Channel Estimation Idle magnitudes (N = 16) for 10MHz bandwidth.

Receiver (EH) Convert RF signal to DC Remark 1: Note that the proposed closed-loop architecture Fig. 3. Frame structure and operations at the transmitter and receiver. contrasts with conventional open-loop approaches in the RF literature with waveform being static/non-adaptive [6]–[8], The system uses a pilot-based channel estimation method. [33], and beamforming relying on tags localization, not on the The pilot signal is generated based on OFDM signal for the channel state [16]. Indeed, the waveform adaptation, channel estimation of the channel on a various number of frequencies. estimation and frame structure are not present in those works, We use a block-type pilot that assigns a reference signal to all therefore preventing the signal at the input of the rectenna frequency components of interest. No interpolation is therefore to be truly optimized. The proposed closed-loop architecture needed. The Least-Square (LS) method is chosen as a chan- also differs from those of [24]–[28] in the communication nel estimation technique because of its low-complexity. The literature, where emphasis was on adaptive beamforming (to 9

maximize erf−rf ), rather than joint waveform and beamform- V. EXPERIMENTS AND VALIDATION ing design (to maximize e − e − ). rf rf × rf dc The WPT testbed introduced in Section IV has been experi- mented in various indoor propagation conditions. This section C. Rectifier Design reports the measured harvested DC power for the various To construct the receiver’s EH block, we first considered types of WPT signals. We compare the measured results with a single-diode rectifier circuit. It consists of an impedance the observations made from the theoretical results of Section matching circuit, a diode and a smoothing circuit (low pass III. We confirm experimentally the benefits of the systematic filter). The rectifier printed circuit board (PCB) is fabricated signal designs and the importance of modeling the rectifier with a λ/4 length of microstrip, L-matching network, and nonlinearity in order to explain the measured results. followed by a Schottky diode rectifier circuit. The diode and the low pass filter implemented in the prototype are the same A. Waveforms in SISO System as in the rectenna used for circuit simulations in [21]. The The harvested DC power has been measured in various values of the matching network components have however propagation environments with the objective to assess the been modified to fit the fabricated PCB and have been designed impact of the multisine waveform design, the number of under the assumption of a 4-tone in-phase multisine input sinewaves and the bandwidth. Measurements were carried out waveform as mentioned in [10] under -20 dBm input power in a normal office environment in static conditions. Test loca- condition. The assumption of 4-tone input is chosen because it tions involve LoS and NLoS conditions, and exhibit frequency- is a middle ground for all those test conditions (ranging from flat (FF) channels and frequency-selective (FS) channels, re- 1 tone to 16 tones). Also, though the input waveform can have spectively. 16 sinewaves, power allocation across all sinewaves is unlikely The transmit waveforms are designed according to each to be uniform due to the potential frequency selectivity. This waveform design schemes such as UP, MAX PAPR, ASS, implies that a subset of the sinewaves will be allocated power. MF, and SMF (β=3) with 1 to 16 tones of uniformly spaced Considering these cases, we have chosen the 4-tone as a robust sinewaves in 10MHz and 2.5MHz bandwidth. The inter- baseline to design the rectifier. The reflection coefficient S11 frequency spacing is given by B/N with B = 10, 2.5 MHz of the rectifier is less than -10dB between 2.38 GHz and 2.5 and N =2, .., 16. In all test cases, the transmit power was set GHz, and bandwidth is 120 MHz. We use Taoglas GW.15 to 33dBm and the RF power measured at the receiver based on antenna for the experiment. It is a universal 2.4 GHz band the CW signal was around -20dBm. The single-diode rectifier WiFi antenna, and the characteristics of the antenna are as of Fig. 5(a) was used. follows: frequency 2.4-2.5 GHz, peak gain in free space <= The harvested DC power was measured for 60 seconds for 2dbi, efficiency <= 80%, VSWR <=1.8. each test case and measurements were carried out five times5, In addition, a rectifier with a voltage doubler structure was with a 5min interval, at each location while maintaining static also built to verify the effectiveness of the nonlinear rectenna conditions, before taking the average. model and signal designs in other types of rectifier. The Fig.6 displays the received DC power measurement results structure is the same as a single diode rectifier, but the output as a function of N under various bandwidths (2.5 and 10 voltage is doubled using one rectifier for positive signals and MHz) and channel conditions (frequency flat and frequency one for negative signals, added via a series ouput. Circuit selective). Since the test locations are different for FF and FS diagrams and photograph of the both rectifiers are shown in channel, the absolute value of the received power is different, Fig. 5. but the relative performance gain according to different wave- form design schemes in different channel characteristics can L1 D1 0.3 nH SMS7630-079LF be observed. We make some important observations from the RFIN measurements. C1 D1 0.3 pF SMS7630-079LF C1 RF C2 C3 First, not all of the channel adaptive waveforms achieve In 1.5 pF 0.3 pF 2.7 nF better performance than the non-channel adaptive waveforms. L1 RL 2.4 nH C2 RL 12 kΩ The results of Adaptive SS (ASS) and MAX PAPR are indeed 1 nF 10 kΩ C4 1.6 mm FR4 substrate 2.7 nF worse than UP in frequency-flat (FF) and frequency-selective (FS) channel, respectively. ASS allocates the full power to only D2 1.6 mm FR4 substrate SMS7630-079LF one (though the strongest one) sinewave to maximize erf−rf , (a) (b) but at the cost of achieving a low erf−dc, and provides very little gain in FF channels because the waveform cannot benefit from any frequency diversity gain and does not exploit the rectifier nonlinearity. On the other hand, MAX PAPR scheme is inefficient in FS channel. MAX PAPR scheme inverts the channel to make the input waveform to the rectifier look like (c) (d) an in-phase multisine with uniform power allocation at the

Fig. 5. Fabricated rectifiers and circuit schematics, Single-diode rectifier (a) schematic, 5Splitting the total time duration into a number of short snapshots (60 sec- (c) photo, and Voltage-doubler rectifier (b) schematic, (d) photo. onds in this setup) is often used in channel characterization and measurement, e.g. [34]. 10

3.5 non-adaptive UP [9]. adaptive MAX PAPR Second 3 adaptive SS , increasing the number of sinewaves N boosts the adaptive MF performance in FF and FS channels. By increasing N, a 2.5 properly designed waveform can exploit the nonlinearity of the rectifier to boost erf−dc, but also exploits the frequency 2 diversity of the channel to boost erf−rf . This confirms re-

1.5 sults in [9] that the diode nonlinearity is beneficial to WPT performance and is to be exploited in systematic waveform. 1 If N increases continuously and the peak voltage increases above the breakdown voltage of the diode, the efficiency may 0.5 decrease sharply. However, since N is limited to 16 in the current prototype, the diode breakdown voltage is not reached. 0 1-Tone 2-Tone 4-Tone 8-Tone 16-Tone Third, significant performance gain with a channel-adaptive Number of Sinewaves N waveform strategy such as SMF can be obtained in FS (a) FF channel, 10 MHz 3.5 channel. Recall that an optimized waveform for WPT, in- non-adaptive UP cluding SMF, allocates power in a non-uniform manner to adaptive MAX PAPR 3 adaptive SS multiple sinewaves, with more power allocated to the strongest adaptive MF frequency components, so as to maximize erf−rf erf−dc [5], 2.5 [9], [10]. The gain of SMF with β =3 over non-adaptive× UP with 16-tone on FF channel is 9.27% but it reaches 90.85% 2 on the FS channel. Compared to conventional continuous wave

1.5 (single tone), the gain is as high as 150%. This confirms results in [9] that CSI acquisition and systematic channel-adaptive 1 waveforms that maximize erf−rf erf−dc are essential to boost the performance in frequency-selective× channels (as in NLoS 0.5 scenarios). In a SISO frequency-flat channel, the result also

0 confirms that CSI is not essential to the transmitter to design 1-Tone 2-Tone 4-Tone 8-Tone 16-Tone efficient waveforms since there is no frequency selectivity to Number of Sinewaves N be exploited to further boost e − . (b) FS channel, 10 MHz rf rf 3.5 Fourth, comparing 2.5MHz and 10MHz bandwidth signals, non-adaptive UP we note that spreading the frequencies across a larger band- adaptive MAX PAPR 3 adaptive SS width is beneficial as the waveform design, if adaptive to the adaptive MF CSI, can benefit from a channel frequency diversity gain. This 2.5 also confirms results in [9] that larger bandwidths can boost

2 the output DC power. Overall, those observations are inline with the observations 1.5 in the prior theoretical works [9], [10], and with the theoretical gain of the waveform design that scales with N (in the fourth- 1 order term of (6)) according to Table II. It is worth to recall that

0.5 all those four observations were already made in [9] and [10] based on analysis and circuit simulations. All experimental 0 results fully match with the theory and therefore validate 1-Tone 2-Tone 4-Tone 8-Tone 16-Tone Number of Sinewaves N the rectifier nonlinear model and the systematic waveform (c) FS channel, 2.5 MHz design methodology introduced in [9], [10] and subsequent works [11], [13]. Results also confirm experimentally the Fig. 6. Received DC power as a function of N under various bandwidths and channel conditions: (a) Frequency flat channel and 10 MHz, (b) Frequency selective channel and feasibility and the promising gains offered by a closed-loop 10 MHz, (c) Frequency selective channel and 2.5 MHz. WPT architecture. Remark 2: The above results and observations also confirm experimentally the inaccuracy of the linear model, obtained rectifier input. Therefore, MAX PAPR maximizes the PAPR by ignoring the fourth order term in (6), and its inefficiency of the input signal to maximize erf−dc at the cost of wasting in designing multisine waveforms [9]. Recall that the ASS an excessive amount of power in inverting the channel and waveform is motivated by the linear model, as it results from achieving a poor erf−rf . This confirms experimentally that allocating all power to the strongest frequency component [9]. focusing on maximizing PAPR in multisine waveform design Clearly, the fact that the ASS performance is poor and even (with the hope to maximize erf−dc), and allocating all power sometimes worse than non-adaptive waveforms demonstrate to the strongest sinewave (with the hope to maximize erf−rf ) that the linear model does not capture the essence of the are not suitable strategies in general settings, as highlighted in energy harvester, is inefficient for WPT signal designs, and 11 is inaccurate to predict the waveform performance6. DC power as a function of the waveform designs remains the same for both rectifiers. The tests were performed in the same B. Waveforms with Voltage Doubler Rectifier locations as the single diode rectifier experiment of Fig. 6, and In the previous subsection, we considered a rectifier com- the overall received power increased by 30% when using the posed of a single diode followed by a low-pass filter with a voltage doubler. The SMF signal has a maximum gain over CW of 170%, which is higher than that achieved in the single load RL, as illustrated in Fig. 5(a). This is the simplest rectifier configuration. In this subsection, the experiment is extended diode experiment. to other types of rectifiers with multiple diodes. Results confirm that the nonlinear rectenna model (6), used The nonlinear rectenna model was originally derived and for the design of systematic waveforms and for the prediction motivated by a single diode rectifier circuit in [9]. The model of the harvested DC power performance with various signal was then shown (analytically and through circuit simulations) design techniques, is valid not only for a single diode rectifier to hold for more general rectifiers with many diodes in circuit but also for a rectifier circuit using multiple diodes. [10]. In order to verify experimentally that the model and the corresponding signal designs are valid for other types C. Waveforms in Mobility Conditions of rectifier circuits with more diodes, the same test as in WPT technology is expected to be predominantly embedded previous subsection has been performed using the voltage in low-power tiny and portable devices such as IoT devices. doubler circuit using two diodes of Fig. 5(b). In the presence of mobility, CSI needs to be acquired on a regular basis. In the event where the channel changes rapidly 5 non-adaptive UP between two successive CSI acquisition at the transmitter, the 4.5 adaptive MAX PAPR adaptive SS CSIT is delayed and the harvested DC power zDC,UPMF drops 4 adaptive MF due to a loss in waveform and beamforming gains, as shown 3.5 in Section III-A. In this section, we investigate experimentally

3 the sensitivity of channel-adaptive waveform to mobility. We designed the experiment to check the relations between 2.5 the channel state information acquisition period and the ter- 2 minal velocity. In previous subsections, the time frame was 1.5 fixed to one second, i.e. the CSI was acquired every second. 1 In static channel conditions, such a time frame is sufficient

0.5 but in mobility conditions, it may not be enough to guarantee

0 a gain of channel-adaptive over non-adaptive waveforms. We 1-Tone 2-Tone 4-Tone 8-Tone 16-Tone here consider and compare two different frame structures, with Number of Sinewaves N 1 second and 200ms period, under various mobility profiles, (a) FF channel with the objective to shed some light on the sensitivity of WPT 5 non-adaptive UP signals to mobility. Different frame structures imply different 4.5 adaptive MAX PAPR adaptive SS channel acquisition periods. Since the period influences the 4 adaptive MF time correlation coefficient ǫ mentioned in Section III-A, both 3.5 frame structures experience different ǫ under the same velocity

3 condition. We set four different velocity of moving antenna, namely 0.01, 0.05, 0.5, and 1 m/s, and investigate the gains 2.5 over channel non-adaptive WPT. 1 m/s is approximately 4km/h 2 which corresponds to pedestrian speed. 1.5

1

0.5 Rx

0 1-Tone 2-Tone 4-Tone 8-Tone 16-Tone Number of Sinewaves N (b) FS channel

Fig. 7. Received DC power using voltage doubler rectifier as a function of N with 10 Linear Slider MHz bandwidth under two different channel conditions (a) Frequency flat channel (b) Tx Velocity : 0.01, 0.05, 0.5, and 1 m/s Frequency selective channel.

It appears that the observations made from Fig. 6 with the single diode rectifier also hold for the voltage doubler rectifier 0.5 m in Fig. 7. The increase and decrease trend of the harvested Fig. 8. Mobility Experiment Setup.

6ASS should achieve the highest performance according to the linear model, which is clearly not the case. Moreover the benefits of the other waveforms To generate controllable and reproducible mobility condi- cannot be explained from the linear model. tions, we used a linear slider of 50cm length, illustrated in 12

Fig. 8, to move the transmitter while the receiver remains fixed. other hand, at 1m/s pedestrian velocity, the gain of the SMF We compare the performance of a channel-adaptive SMF (with signal is almost zero when using the 1s frame, but a gain of β =3) and a non-adaptive UP waveform, both consisting of 16 12% is still observed when using the 200ms frame. sinewaves uniformly spaced in a 10 MHz bandwidth. For each These observations show the relation between the veloc- test case, measurements are carried out five times, each time ity of a mobile antenna, CSIT acquisition period, the time taken for a duration of 5-minutes. Results are then averaged correlation coefficient ǫ , and the harvested DC power. The over all measurements. influence of ǫ on DC power harvesting performance shown in Section III-A was confirmed in this experiment. The design 1.6 non-adaptive UP of an appropriate frame structure is important to cope with 1.4 various mobility conditions.

1.2 D. Joint Beamforming and Waveform in MISO System 1 The prototype system is equipped with two antennas, and 0.8 performance can therefore benefit from a beamforming gain 0.6 on top of the waveform gain already highlighted in previous subsections. According to the scaling laws in Table II, the 0.4 beamforming and waveform gains are cumulative as both 2 0.2 appear in the fourth order term of (6) through the term NM . As discussed in [9], this highlights that the number of transmit 0 0.01 0.05 0.5 1 antennas and number of sinewaves can be traded off to achieve Velocity (m/s) a given target performance. In this subsection, we assess the (a) 1s frame performance benefits of conducting a joint beamforming and 1.6 non-adaptive UP waveform design over the single-antenna waveform design

1.4 and over conventional multi-antenna energy beamforming with continuous wave [5]. 1.2 In other words, we assess the performance benefits of

1 exploiting jointly the spatial (beamforming) and frequency (waveform) domains of the transmit signal, and investigate 0.8 how one could leverage the frequency domain of the waveform

0.6 to decrease the complexity of the spatial domain beamformer (number of transmit antennas). 0.4 The experiments were performed in FF (LoS position)

0.2 and FS (NLoS position) channel conditions as in the single antenna system. UPMF and SMF signals on two antennas 0 0.01 0.05 0.5 1 and UP, UPMF, and SMF signal on one antenna are used for Velocity (m/s) performance comparison for various N. Recall that UPMF in (b) 200ms frame single-antenna setting relies on CSIT for channel phase com- pensation on each sub-carrier (in contrast to UP) and allocates Fig. 9. Received DC power as a function of terminal velocity with different signal frame structures. power uniformly over all sub-carriers (similarly to UP). The experiments were carried out at five different locations for each Fig. 9 shows the experimental results with the 1-second time FF and FS channel condition. Test locations were chosen to frame and 200 ms time frame. The graph first shows that the have FF channel on LoS position and FS channel on NLoS harvested DC power level with the non-adaptive UP waveform position with received RF power of about -20dBm based on is nearly constant regardless of the velocity of mobile antenna. CW signal. The harvested DC power was measured for 60 As shown in Section III-A the scaling law of the non-adaptive seconds, repeated five times, and results were averaged over all UP signal is not affected by the time correlation coefficient ǫ, measurement for each test case. Fig. 10 displays the harvested which is the same in the measurement results. The graph also DC power for each signal design and number of tones. We shows in both frame structure cases that the adaptive SMF make the following observations. signal exhibits some gain over non-adaptive UP signal in a First, we observe that spatial domain and frequency domain low-velocity condition but the gain decreases as the velocity processing can be traded off. Comparing 2-antenna SMF with of the mobile antenna increases (i.e. as ǫ decreases). Since CW (N = 1) and 1-antenna SMF with N 16, we note ǫ is related not only to the velocity but also to the channel that the 1-antenna waveform outperforms the 2-antenna≥ beam- estimation period, the gain reduction rate of the SMF signal forming in FS channel. This significant gain can be obtained due to the increase in velocity is different in the two frame in FS channel where the 1-antenna SMF with N 16 can structures. In a low-velocity test case such as 0.01m/s, adaptive jointly exploit the nonlinearity of the rectifier and the≥ channel SMF signals have a similar gain of about 40% over non- frequency diversity. This shows that the hardware complexity adaptive UP for both 1s and 200ms frame structure. On the increase in the spatial domain (having two antennas rather than 13

5 1 ant, non-adaptive UP of about 110% over the 2-antenna conventional beamforming 4.5 1 ant, adaptive UPMF with CW (N = 1) and close to 350% over the 1-antenna 4 2 ant, adaptive UPMF CW, in FS channel conditions. Interestingly, the sharp increase

3.5 in DC power with N achieved by the 1-antenna SMF is still observed in the 2-antenna setting. This highlights that 3 SMF jointly exploits the multi-antenna beamforming gain, the 2.5 channel frequency diversity gain and the rectenna nonlinearity. 2 Those results also show that various performance enhancement 1.5 factors can be superimposed and applied in WPT, which can

1 lead to significant performance improvements. Additional MISO joint beamforming and waveform exper- 0.5 iments were carried out using the four antenna prototype 0 1-Tone 2-Tone 4-Tone 8-Tone 16-Tone to verify the performance of multi-antenna with multi-tone Number of Sinewaves N WPT under many different wireless environments. Cumulative (a) FF channel distribution function (CDF) of measured DC output power 5 1 ant, non-adaptive UP with various numbers of antennas and tones is presented in 4.5 1 ant, adaptive UPMF Fig. 10(c). One tone MRT and eight tone SMF signals for each

4 2 ant, adaptive UPMF number of antennas were used and performance compared.

3.5 The measurement are taken at 100 different locations in the office and the distance between the transmitter and the receiver 3 varies between 3 and 5.5 meters. Each measurement was taken 2.5 1 second and repeated ten times with one minute of time in- 2 terval at each location. The graph clearly shows multi-antenna 1.5 with multi-tone SMF signals outperform multi-antenna with

1 single-tone MRT signals, and the gain is significant. Besides, the 4-antenna 1-tone waveform shows similar performance that 0.5 of the 2-antenna 8-tone waveform. In the same manner, 2- 0 1-Tone 2-Tone 4-Tone 8-Tone 16-Tone antenna single-tone and 1-antenna 8-tone show similar per- Number of Sinewaves N formance. Such behavior reaffirms the two observations we (b) FS channel identified earlier regarding the joint beamforming and wave- 100 form gain. Those observations are inline with the observations made from the theoretical gain of the joint waveform and 2 80 beamforming design that scales with NM (in the fourth order term of (6)) according to Table II. This indicates that the

60 theoretical analysis and simulation results provided in Section III-A are consistent with the experimental results in the actual

CDF (%) wireless environment. 40 CW 1ant 8tone SMF Remark 3: The key observation of this subsection is that 2ant 1tone MRT different types of gains can be accumulated by jointly using 20 2ant 8tone SMF 4ant 1tone MRT waveform and beamforming, such as a beamforming gain, a 4ant 8tone SMF frequency diversity gain and the gain from the rectifier non- 0 0 10 20 30 40 50 60 linearity. This contrasts with beamforming-only approaches, Output DC Power (uW) e.g., [24]–[26], that provide a beamforming gain-only. Recall (c) CDF that results of the beamforming-only approach (and therefore somewhat equivalent to [24]–[26]) is obtained by looking at Fig. 10. (a), (b)Received DC power as a function of N with 10 MHz bandwidth under 1-tone results in Fig. 10. Results here show that the gain of two different channel conditions (FF and FS) with one and two transmit antennas. (c) Measured CDF of DC output power in different locations the joint beamforming and waveform design scheme leads to significantly larger harvested DC power compared to the conventional beamforming-only schemes of [24]–[26]. . one) can be decreased by adopting a more efficient waveform. In other words, the use of SMF multisine waveform can decrease the need for multiple transmit antennas for a given E. Modulations performance target. According to the scaling laws of Table III, conventional Second, we observe that the gains from the spatial (beam- modulations used for communications such as BPSK, QAM forming) and frequency (waveform) domains are cumulative. and complex Gaussian (simply denoted as CG) should be out- For UPMF and SMF, the 2-antenna setting leads to about performed by energy modulations such as real Gaussian (RG) 100% gain over the SISO setting for all N in both channels. and flash signaling. We carried out a modulated waveform Remarkably, the 2-antenna SMF with N = 16 achieves a gain experiment in order to confirm the theoretical predictions of 14

Table III. The signal was generated with a modulation rate and only accounting for the rectifier nonlinearity through the of 2.5 MHz for all modulation types. To rigorously observe fourth order term E y(t)4 can explain the difference between the differences due to the modulation schemes (rather than the modulations. This{ further} demonstrates that the inaccuracy measuring the effect induced by the fluctuations of the chan- of the linear model highlighted in Remark 2 carries on to other nel), the experiment was conducted by feeding the transmitted types of signals such as modulation. signal directly into the rectifier through cable connections Remark 5: Energy modulation is not only important for im- (in contrast to the over-the-air radiation used in the other proving WPT efficiency but plays a major role in simultaneous subsections). The rectenna received input RF power was set at wireless information and power transmission (SWIPT) systems -20dBm, and the harvested DC power was measured for five [19], [20]. Conventional PSK/QAM modulations have been minutes and five times for each modulation type, before being used in SWIPT [35], [36], and measurement results here show averaged. Fig. 11 displays the measurement results. and confirm that we should depart from such modulation if one wants to make the best use of the radiowaves. Results show 2 here that energy modulations based on flash signaling, whose 1.8 randomness has been optimized to maximize the amount

1.6 of DC power with no consideration for information trans- fer, significantly outperform other modulations/distribution in 1.4 terms of harvested DC power. It is left as future work to 1.2 experimentally show how such modulations perform in terms 1 of information transfer and what is the tradeoff between rate 0.8 and power.

0.6

0.4 F. Transmit Diversity

0.2 The transmit diversity experiment was performed using two transmit antennas at six different LoS test locations located 0 CW BPSK 16QAM CG RG l=2 l=3 l=4 l=5 at a distance of 2.5 to 4m in a normal office environment. Modulation types At each test location, the transmitter generates different types Fig. 11. Received DC power vs. Modulation types. of signals such as single antenna continuous wave/complex Gaussian/multisine waveform (N = 8) and their two-antenna We observe that the general trend of Fig. 11 matches transmit diversity counterparts. The phase changing rate for well the theoretical results of Table III. Namely, the PSK transmit diversity signals and modulation rate for the complex modulations does not perform any better than CW because Gaussian signal is set to 2.5MHz. The DC power measure- PSK does not induce any amplitude fluctuation and does not ments were conducted for one minute and repeated five times affect the fourth order term E y(t)4 of z . 16QAM and DC with some time intervals, before being averaged to obtain the CG exhibit a respective 13% and{ 26%} gain compared to CW final measurements. Fig. 12 displays the measurement results because of the amplitude fluctuation that increases E y(t)4 . at the six different test locations. Similarly, RG achieves a 42% gain thanks to the larger{ fourth} moment of a RG distribution compared to a CG distribution. 3.5 Continuous Wave (CW) Flash signaling provides even higher DC power as it increases Transmit Diversity - CW 4 3 Complex Gaussian (CG) the fourth moment E y(t) as l increases by enabling a small Transmit Diversity - CG { } Multi-Tone (N=8) (MT) probability of very large amplitude signals. Nevertheless, the Transmit Diversity - MT 2.5 behavior does not match exactly what was predicted from Table III. The highest DC power is achieved at l = 3 with 2 an overall gain of 95% over CW, but decreases when l is further increased. This behavior is due to the peak voltage 1.5 of the received signal that exceeds the breakdown voltage of 1 the diode. Such breakdown voltage is not modeled in zDC.

A similar trend, though less severe, has been observed in 0.5 the circuit simulations provided in Appendix A, though the breakdown voltage of the diode was found to be lower in the 0 Loc.1 Loc.2 Loc.3 Loc.4 Loc.5 Loc.6 actual circuit than in the circuit simulations. Note that the Test Locations performance could be improved by designing a circuit that is Fig. 12. Transmit Diversity performance measurement in six different locations robust to diode breakdown and copes with high peak voltages (see discussions in [18], [29] and references therein). The experimental results show that the TD with CW signal Remark 4: It is important to recall that observations made has an average gain of about 28% compared to the CW signal from Fig. 11 cannot be explained from the linear model of the although there is some difference in each test position. TD with rectenna. All those modulations achieve the same second order CG and TD with multisine/multitone (N = 8) signal show a term E y(t)2 , and according to the linear model, they should 31% and a 66% gain respectively over the CW signal. Those all achieve{ the} same performance. Obviously this is incorrect results are inline with the observations from the theoretical 15 analysis of TD signals provided in Table IV. This indicates by a wireless counterpart. To that end, a low-power simple that the theoretical model that shows the energy harvesting method to feedback CSI from receiver to transmitter and performance improvement by using TD in subsection III-C accordingly design the joint waveform and beamforming, as is consistent with the actual experimental results over real- studied in [13], would be an interesting avenue that has not world wireless channels. Recall that those gains are achieved been experimented yet. Moreover, another interesting area without any CSIT. Transmit diversity is appealing for low- will be to consider a WPT architecture where the transmit complexity applications with a massive number of low-power signals and the rectennas adapt themselves dynamically as a devices because the transmitter is equipped with cheap/dumb function of the channel state [29], which requires the design of antennas, the receivers do not need power-consuming signal rectennas adaptive to their input waveforms (shape and power) processing block such as channel estimation and feedback, and [37]. These will be considered in future enhancements of our the energy harvesting performance can be improved simultane- testbed system. Moving beyond WPT, it is also interesting to ously for all receivers. Though the prototype was designed and study how the prototype could be expanded to a real SWIPT measurements were conducted with two transmit antennas, as system so as to assess the performance of SWIPT waveform mentioned in the theoretical model, the gain can be improved and the corresponding rate-energy tradeoff. Some preliminary by increasing the number of transmit antennas. results are available in [38].

VII. ACKNOWLEDGMENTS VI. CONCLUSIONS AND FUTURE WORKS We thank B. Lavasani and National Instruments for provid- A WPT testbed with and without CSIT acquisition and var- ing some of the equipments needed to conduct the experiment. ious signal transmission strategies (beamforming, waveform, modulation and transmit diversity) was designed, prototyped APPENDIX A and experimented. The harvested DC power achieved by those CIRCUIT SIMULATIONS strategies and combination thereof was analyzed as a function of various parameters such as the propagation conditions, Beamforming, waveform, modulation and transmit diversity CSIT quality, bandwidth, rectenna design and experimental performance have been analyzed using circuit simulations and results were contrasted with the theoretical analysis. results have been contrasted with the theory (using zDC scaling It has been shown that the design of an appropriate signal laws). Readers are referred to [9] and [10] for waveform generation method (such as SMF) that adapts as a function and beamforming, to [20] for modulation and to [21] for of the channel condition can significantly boost the harvested transmit diversity. In all cases, circuit simulations confirm DC power performance. Large gains are obtained when using the benefits of the four signal strategies. In the sequel, we a combination of waveform and beamforming. The larger the provide some more PSPICE circuit simulations for modulation number of tones in the waveform and the wider the bandwidth, to complement the ones obtained in [20]. The rectifier circuit the larger the gains. Significant performance improvements for the simulation is the same as the one used in [21] and we were possible through signal design based on CSIT under generate modulation signals with 2.5MHz symbol rate and - frequency-selective channel, so as to jointly benefit from a 20dBm of RF Power in Matlab. The simulations were repeated beamforming gain, a waveform gain, the rectenna nonlinearity 300 times using randomly generated modulation signals for and the frequency selectivity of the channel. In the case each modulation format, and the results were then averaged. where CSIT is not available, the power transmission efficiency Fig. 13 illustrates the received DC power simulation results of can be greatly improved by using proper energy modulations different modulations. or by generating artificial fading through a multi-antenna 4 transmit diversity strategy. Widely used modulations for data communication have also been shown to improve the power 3.5 transfer efficiency depending on the modulation type, but are 3 outperformed by modulation designed specifically for WPT. This work demonstrates experimentally the importance and 2.5 benefits of modelling and exploiting the harvester nonlineari- 2 ties originating from the convexity of the I-V characteristics of the diodes. On the other hand, it is also verified that the linear 1.5 model of the harvester obtained by ignoring the nonlinearity 1 leads to poor signal design. There are many interesting research avenues to pursue. 0.5

Beyond the MISO system, a large-scale multisine multiantenna 0 CW BPSK 16QAM CG RG l=2 l=3 l=4 l=5 WPT with jointly optimized beamforming and waveform, Modulation types applicable to both single-user and multi-user deployments, is Fig. 13. Simulated received DC power with several modulation schemes and flash a promising architecture [11]. It is also worth to implement signaling l = 2, 3, 4, 5. and investigate a larger number of transmit antennas in the transmit diversity experiment. When it comes to channel The results show that some of the conventional modulations acquisition, the wired feedback of CSI needs to be replaced are effective to boost the DC power. For instance, CG signals 16

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