Mobility-Enhanced Simultaneous Lightwave Information and Power Transfer
11 Mobility-Enhanced Simultaneous LightwaveInformation and Power Transfer
Mingqing Liu, Mingliang Xiong, and Qingwen Liu*,
Senior Member, IEEE
Abstract —Simultaneous lightwave information and powertransfer (SLIPT) has been regarded as a promising technologyto deal with the ever-growing energy consumption and data-ratedemands in the Internet of Things (IoT). We propose a resonantbeam based SLIPT system (RB-SLIPT), which deals with theconflict of high deliverable power and mobile receiver positioningwith the existing SLIPT schemes. At first, we establish a mobiletransmission channel model and depict the energy distributionin the channel. Then, we present a practical design and evaluatethe energy/data transfer performance within the moving rangeof the RB-SLIPT. Numerical evaluation demonstrates that theRB-SLIPT can deliver W charging power and enable . Gbit/sachievable data rate with the moving range of -degree fieldof view (FOV) over m distance. Thus, RB-SLIPT can simulta-neously provide high-power energy and high-rate data transfer,and mobile receiver positioning capability. Index Terms —Simultaneous lightwave information andpower transfer; Resonant beam system; Wireless power transfer;Mobility and self-alignment; Retro-reflective resonator
I. I
NTRODUCTION
Simultaneous wireless information and power transferhas been regarded as one of the enabling technologies in 6Gnetworks [1]. Due to the spectrum crisis of Radio Frequency(RF), the SLIPT adopting visible light or lasers as carriershas become a promising altenative/complementary technol-ogy [2, 3]. However, as in Fig. 1, the visible-light-based SLIPTfaces challenges of low deliverable charging power [4, 5],and the laser-based SLIPT is difficult to position mobile re-ceivers [6, 7]. Thus, we propose an RB-SLIPT scheme, whichcan deal with the conflict between high deliverable power andmobile receiver positioning. The RB-SLIPT system is capableof simultaneously providing multi-Watt charging power andhigh-rate data transfer with self-alignment capability overmulti-meters distances.The RB-SLIPT system inherits the characteristics of theresonant beam system (RBS). RBS is essentially an open-cavity laser resonator, where a transmitter consists of high-reflective mirror and a gain medium, a receiver consists ofan output coupling mirror and a Photovoltaic (PV) cell arespatially separated to form a resonator [8–10]. The resonantbeam generated within the resonator acts as the carrier totransfer energy and information over the air. Thus, the narrowresonant beam can carry high power similar to the laser, andwill cease immediately once a foreign object invasions into
Mingqing Liu, Mingliang Xiong, and Qingwen Liu are with College ofElectronics and Information Engineering, Tongji University, Shanghai, Peo-ple’s Republic of China (e-mail: [email protected], [email protected],[email protected]).
Field of
View
Field of View
LEDUser Broadcast
Transmission Channel(a) Visible Light based SLIPT Laser User
Field of View
Mechanical Alignment (b) Laser based SLIPT
Narrow-Beam Transmission Channel
Field of View
Resonant Beam
Transmitter
User(c) Resonant Beam based SLIPT
Self-Alignment
Mobile Transmission Channel
Retro-Reflector
Incident Beam Reflective Beam
Retro-Reflector
Incident Beam Reflective Beam Retro-ReflectorRetro-Reflector
Fig. 1 Comparison of the resonant beam based SLIPT withthe existing SLIPT schemes.the resonator, which brings the features of high transmissionpower over long range with the premise of human safety [11].Moreover, two retro-reflectors are adopted at both endsof the RBS. As in Fig. 1, retro-reflector can reflect the incidentbeam back parallel to the original direction regardless of theincident direction. RB-SLIPT with retro-reflectors such ascorner-cube reflector (CCR) [12, 13] and cat’s eye [14] fea-tures with self-alignment. Therefore, receivers moving withinthe coverage of RB-SLIPT can be supplied with wirelessenergy and data through the mobile transmission channel. Themobility feature of RBS has been discussed in [8]. However,the model of the mobile transmission channel with self-alignment has not been established and the moving effectson energy/data transfer performance have not been analyzed.Thus, we analyze the energy distribution of the mobile trans-mission channel and propose a practical design of RB-SLIPT.In this paper, we at first present the RB-SLIPT archi-tecture. After revealing the self-alignment mechanism usingtransfer matrix method, we adopt the resonator mode analysisand laser output power calculation to depict the energy distri-bution in the mobile transmission channel. Then, we proposea practical RB-SLIPT design with a receiver adopting bothPV and avalanche photodiodes (APD) for energy and dataharvesting respectively, and evaluate the system performance.The RB-SLIPT system can simultaneously provide W wire- a r X i v : . [ ee ss . SP ] F e b Retro-reflector2:
70% Reflectivity
Transmitter Receiver
Resonant Cavity
Pump Source Power Splitter
Photovoltaic PanelAvalanche Photodiod
Extra-cavity BeamRetro-reflector1:
GainMedium
Retro-reflector2: 70% ReflectivityTransmitter ReceiverPump Source
Output
LaserRetro-reflector1: 100% Reflectivity
Power
Input P in Mobile Transmission
Channel
Power Output P out
Energy Harvesting and Data Receiving
Information
Source
ElectricalModulator Pump Laser
Diode
Resonant Beam Photovoltaic PanelRectifier Battery Demo-dulatorGainMedium I D i sig P pump P b P pv,o μ Field of View i pd I in P out μ Power SplitterADCAvalanche Photodiode
Mobile Transmission Channel
Retro-reflector2:
70% Reflectivity
Transmitter ReceiverPump
Source
Output LaserRetro-reflector1:
SourceElectrical
Modulator
Pump Laser Diode Resonant Beam
Photovoltaic
PanelRectifier Battery DemodulatorGain
Medium I D i sig P pump P b P pv,o μ i pd I in P out μ Power SplitterAvalanche PhotodiodeMobile Transmission Channel ADC
Fig. 2 Transceiver design of the resonant beam based simul-taneous lightwave information and power transfer system.less charging power and . Gbit/s achievable data rate withinthe moving range of m distance and -degree FOV.The contributions of this manuscript are:1) We establish a mobile transmission channel model in RB-SLIPT. It can reveal self-alignment mechanism and depictthe energy distribution in the channel with a single RB-SLIPT transmitter.2) We propose a practical design of simultaneous energyand information transfer using both PV and APD. Itcan quantitatively evaluate the performance of data/enrgytransfer with the impacts of moving factors.The remainder of this paper is as follows. In SectionII, we proposed the RB-SLIPT design and described itsarchitecture and principle. In Section III, we built a mobiletransmission channel model to prove the self-alignment anddepict the energy distribution in the channel. Afterwards,we established an analytical model of mobile energy andinformation transfer in RB-SLIPT in Section IV. In SectionV, we demonstrated the channel factor, charging power, andachievable data rate of the proposed system through numericalanalysis. Finally, we made a conclusion in Section VI.II. S YSTEM O VERVIEW
Figure 2 depicts the transceiver design of the RB-SLIPTsystem. The proposed system consists of the spatially sep-arated transmitter and receiver, between which the mobiletransmission channel is formed.The transmitter contains a pump source, an informationsource, an electrical modulator, a pump laser diode (LD), again medium, and a retro-relector1 with 100% reflectivity.In the transmitter, an alternating-current (AC) current i sig is generated from the information source and the electricalmodulator, which is biased by a direct-current (DC) current I D generated by the pump source. The current I D plus i sig as I in drives the pump LD together to generate the pump laserwith power of P pump . Then, the pump laser provides energyfor the gain medium to stimulate light radiation carrying dataand energy, similar to the RF amplifier. A retro-relector1with 100% reflectivity is adopted to reflect the light from thereceiver back towards the incident direction.The receiver contains a retro-reflector2 with 70% reflec-tivity, a PV panel, an APD, and corresponding energy/dataprocessing units. The output laser with power of P out is outputfrom the retro-reflector2 with 70% reflectivity. Then together with the background irradiance P b caused by the ambientlight, the output power enters a power splitter to be splitinto two streams with a specific ratio. One stream is sent toPV and converted to the charging current with P pv,o . Afterbeing rectified, the power is ready for charging the battery.One stream is sent to APD to be converted to the signalcurrent i sig,o . The signal current carries information entersthe demodulator for demodulation after passing the analog-to-digital converter (ADC).The mobile transmission channel is formed by two retro-reflectors and a gain medium. Similar to the traditional laser,the gain medium stimulates the light radiation, which can bereflected back and forth inside the resonant cavity and passthrough the gain medium multiple times to be amplified. Ifthe light power gain can compensate for the light power loss,the narrow laser can be stably output with high-power. Onthe other hand, the mobile transmission channel is actuallyan open-cavity, and the intra-cavity laser named as resonantbeam is used to transfer energy/data over the air. Thus, witha resonant cavity that allows light to be retro-reflected withinit and enough input power, the resonant beam can be self-established between the transceiver. The two retro-reflectors inthe mobile transmission channel form a mobile resonant cavity(MRC). Due to the retro-reflective characteristics of the tworetro-reflectors, the resonant beam can be established withinthe MRC even as the two reflectors are not strictly facing eachother, which guarantees the self-misalignment.III. M OBILE T RANSMISSION C HANNEL M ODEL
Mobile transmission channel of RB-SLIPT relies on theMRC to realize mobility. In this section, we investigate theMRC with two cat’s eye at both ends as a paradigm. We atfirst prove the self-alignment characteristic of the MRC, afterwhich we derive that the MRC with two deflected reflectorsis equivalent to a Fabry-Perot (FP) resonator. Then, we adoptlaser mode analysis method and laser output principle to obtainthe power output and depict the energy distribution in themobile transmission channel.
A. Self-Alignment Mechanism of the Channel
We adopt the transfer matrix (i.e., ABCD matrix) methodto define a round-trip transfer process of a ray inside theresonant cavity. Each component (including the free space)that a ray will pass through is described as a matrix with fourelements; for example, a lens with focal distance f is describedas M = (cid:20) − /f (cid:21) , and a ray represented by vector r after passing it is transferred to r as r = Mr , (1)where r = (cid:20) r r (cid:48) (cid:21) . r is the distance between the ray andoptic axis, and r (cid:48) is the slope of the ray about optic axis.Then, a round-trip transfer matrix of a ray inside aresonant cavity is the multiplication of the matrices that a raywill pass through in a round trip, i.e., M tot = M M ... M N ,where N is twice the number of components in the resonant z M1 M2L1 L2 l f lz= fd Δ r = -(Δ f )/( d - ) r '= Δ/( d - ) Fig. 3 Self-alignment of the mobile resonant cavity.cavity. Suppose a ray r can realize self-reproduction after around-trip transfer, i.e., M tot r = r , (2)then r can be regarded as a vector representing the axis ofthe cavity. Rays parallel to the axis can be reflected back andforth inside the resonant cavity.As in Fig. 3, the MRC of RB-SLIPT consists of two cat’seye, where a cat’s eye contains a mirror (M1/M2) and a lens(L1/L2) parallel to each other. The focal length of the lens is f , and the distance between lens and mirror is l . The cat’s eyeis ideal to retro-reflect incident beam as l = f . z -axis whichpasses through the centers of L1 and M1 is defined as theorigin optic axis of the MRC. Once the right-hand cat’s eyeconsisting of L2 and M2 is off the z -axis, the MRC is definedas an off-axis system.In an off-axis system, the misalignment vector of off-axiscomponent is defined as ∆ = (cid:20) ∆∆ (cid:48) (cid:21) , (3)where ∆ is the distance between element axis of off-axiscomponent and origin optic axis, and ∆ (cid:48) is the slope of theelement axis about the origin optic axis. Then, the relationshipof r and r before and after passing through an off-axiscomponent can be depicted as [15] r = Mr + E , (4)where E ≡ (cid:20) EF (cid:21) = [ M ∆ − M ] ∆ , (5)where M ∆ represents the optical length deference matrix ofthe off-axis component. Thus, the transfer process of (4) canbe depicted as an ABCDEF matrix [16]: r r (cid:48) = A B EC D F × r r (cid:48) . (6)As the case in Fig. 3, suppose a ray r starts from thefront face of L1, r can be self-reproduced after a round-triptransfer process inside the MRC as M tot r + E tot = r , (7)then r represents the new optic axis of MRC after the movingof the right-hand cat’s eye, where [16] r ≡ (1 − D ) E + BF − A − D , r (cid:48) ≡ CE + (1 − A ) F − A − D . (8) To figure out M tot and E tot , we expand (7) as follows: r = M fs r r = M cat r + E M r = M fs r r = M cat r , (9)where M fs = (cid:20) d (cid:21) , (10) M cat = (cid:20) − f (cid:21) (cid:20) l (cid:21)(cid:20) l (cid:21) (cid:20) − f (cid:21) = (cid:20) − f − (cid:21) , (11) E M = (cid:18)(cid:20) l (cid:21) − M cat (cid:19) (cid:20) ∆0 (cid:21) = (cid:34) − lf − f ) f (cid:35) . (12)Then, we have [15] M tot = M cat M fs M cat M fs E tot = M cat M fs ( E M ) . (13)According to (8), we can obtain r = − (∆ f ) d − f and r (cid:48) = ∆ d − f . (14)Evidently, r is coincident with the connection of the focusesof two cat’s eye, which represents the new optic axis of theMRC with one off-axis cat’s eye. Rays parallel to the newoptic axis can be retro-reflected inside the MRC rather thansplitting over it. Thus, MRC with two cat’s eye is capable ofrealizing self-alignment with new optic axis even if two cat’seye are not exactly facing each other due to the movement.As in Fig. 4, the line a2 passing though the focuses ofboth cat’s eyes and the gain medium represents a ray reflectedback and forth collinearly inside the MRC. Due to the off-axis of the right-hand cat’s eye, the angle between a2 and thenormal vector of the cat’s eye front face is θ . a1 is anotherray which is generated by the gain medium and parallel to a2.Then, a1 is retro-reflected by the right-hand cat’s eye throughpoints A, D, and C back towards the left-hand cat’s eye alonga3. Thus, there exists a resonant beam generated by and withinthe size of the gain medium between the two cat’s eye, andthe beam is symmetric about the new optic axis.Moreover, according to the Fermat principle, the opticallength of all rays inside the MRC are the same. Therefore, asthe free space transmission distance is significantly larger than f , the MRC can be regarded as an FP resonator where the twoend mirrors are located at the two focuses, and perpendicularto the new optic axis of the MRC. M1 L1 Gain l=f f
Incidence PlaneP1 a1 a2 a3 v1 E G l=f f B A C DP2 M2 L2 Active Reflecting Area of Cat EyeGain Medium
Size LimitActive Reflecting
Area of Cat Eye(0, 0) (0, 0)(0, a) (0, a) a~ θ a~ θ Fig. 4 Equivalent resonator for mobile resonant cavity.
B. Energy Distribution in the Channel
To find out the energy distribution of the mobile trans-mission channel, we should at first obtain the output laserpower P out in the receiver at any position within the system’sFOV. As in Fig. 4, P1P2 is the optic axis of the MRC. Weplace the diffraction limited gain medium at the focus ofthe left-hand cat’s eye, to generate the resonant beam insidethe MRC with the excitation of the pump power P in . M2 ispartially transmissive so that a portion of resonant beam willpass through M2 to form the laser beam with power of P out .Following the laser principle, the relationship between P in and P out can be depicted as [17] P out = A b I S (1 − R ) V − RV V + √ RV V [1 / ( V S V ) − V S ] × (cid:20) η excit P in A g I S − (cid:12)(cid:12)(cid:12)(cid:12) ln (cid:18)(cid:113) RV S V V (cid:19)(cid:12)(cid:12)(cid:12)(cid:12)(cid:21) , (15)where A g , I s , and V s are the cross sectional area, saturatedlight intensity, and loss factors of the gain medium, respec-tively; η excit is the excitation efficiency and R is the reflectivityof M2; A b is the overlapping area of resonant beam and gainmedium and V , V (=1-loss) depict the loss factors duringsingle intra-cavity transmission, respectively. To accuratelyobtain the P out , we should calculate V , and A b exactly.At first, we employ the resonator mode analysis method tocalculate the eigenmode of the MRC.The active reflecting area of the cat’s eye is affected bythe incident angle θ of the beam. We adopt the indicationfunction to depict the reflective area by 1 and non-reflectivearea by 0. Then as in Fig. 4, the active reflecting area of theleft-hand and right-hand cat’s eye can be depicted as T ( x, y ; r, θ ) = , x + y ≤ r , y ≥ a/ and x + ( y − a ) ≤ r , y ≤ a/ , else , (16)where a = 2 f tan θ , and r is the radius of L1, L2, M1, andM2. Moreover, the diffraction limited gain medium limits theactive reflecting area of the left-hand cat’s eye, which can bedepicted as T ( x, y ; r g , θ ) = (cid:26) , x + y ≤ ( r g cos θ ) , else , (17) 平面波源 一个面传播到另一个面 传输函数: 角锥棱镜 角锥棱镜 角锥棱镜 平面波源 一个面传播到另一个面 传输函数: 角锥棱镜 角锥棱镜 角锥棱镜 x zx y y U (x ,y ,0) U(x,y,0)Aperture Plane Observation PlaneComputation WindowLP P ( a ) ( b )( c ) One Roundtrip …… itr iterations Stable Self-Reproducing Mode x zx y y U (x ,y ,0) U(x,y,L)Aperture Plane Observation PlaneComputation Window LP P ( a )( b ) One Roundtrip …… itr iterations Stable Self-Reproducing Mode Fig. 5 Illustration of diffraction theory and self-reproducingmode calculation.where r g is the radius of the gain medium surface.For the equivalent FP resonator in Fig. 4, the activereflecting area of the right-hand mirror is T l = T · T , and T r = T for the right-hand mirror. Based on the above proofand inferences, we can calculate the modes of the FP resonatoras of the MRC using diffraction theories.As in Fig. 5 (a), if the light field distribution on one of thecavity mirror is known, one can obtain the amplitude and phasedistribution of light field at any position in the cavity [18]. TheFresnel-Kirchhoff diffraction integral formula reads: U ( x, y, L ) = exp( jkL ) jλL (cid:90) (cid:90) T U ( x , y , (cid:26) j k2 L (cid:104) ( x − x ) + ( y − y ) (cid:105)(cid:27) d x d y , (18)where j := √− , L is the resonator length, k = 2 π/λ is thewave number, and λ is wavelength of resonant beam. Suppose U ( x , y , represents the field on the left-hand mirror of theFP resonator, then U ( x, y, L ) is the field on the other mirrorand T is the active reflecting area of the left-hand mirror.For high-speed numerical calculation, Fast-Fourier-Transform (FFT) is adopted to find numerical solution ofdiffraction process [19]. (18) can be rewritten as the followingconvolution form: U ( x, y, L ) = (cid:90) (cid:90) T U ( x , y , h ( x − x , y − y ) d x d y , (19)where h ( x − x , y − y ) named as impulse response can beexpressed as h ( x, y ) = exp( jkL ) jλz exp (cid:20) jk L (cid:0) x + y (cid:1)(cid:21) , (20)then the formula can be rewritten as [19] F { U ( x, y, z ) } = F { U ( x , y , } · F { h ( x, y ) } , (21) where F denotes the Fourier transform. Moreover, the fieldsbefore and after passing through the cat’s eye’s front face U − ( x, y ) and U ( x, y ) have the following relationship [20]: U ( x, y ) = T ( x, y ) · U − ( x, y ) , (22)where T ( x, y ) represents the active reflecting area of the cat’seye. Thus, the self-consistent integral formula for one round-trip field transmission is U ( x, y, L ) = F − { F { F − { F { U ( x, y, L ) · T r ( x, y ) }· F { h ( x , y ) }} · T l ( x , y ) } · F { h ( x, y ) }}· T r ( x, y ) , (23)where F − denotes the inverse Fourier transform process.Based on Fox-Li method [21], we are supposed to iterate(23) t times to calculate the eigenmode of the resonator.As in Fig. 5 (b), suppose the original light field distribution U ( x, y, L ) = 1 , the light field on the output plane is graduallystable during iterations. Eventually, the forms of field distri-bution U t ( x, y, L ) after t iterations and U t − ( x, y, L ) after t − iterations are exactly identical, except for the constantfactor difference on amplitude and phase. Then U t ( x, y, L ) can be regarded as the self-reproducing mode, or namely theeigenmode of the stable resonator.Then, we can find the beam spot size A s using the methodfor determining Gaussian beam radius [22] with U t ( x, y, ,and the loss factor of the one-way transmission as V = | U t ( x, y, L ) | | U t ( x, y, | , V = | U t ( x, y, | | U t ( x, y, L ) | . (24)Finally, we can obtain the receiver’s output laser power P out with respect to the input power P in , the distance L between thetwo cat’s eyes, and the translation angle θ of the remote cat’seye. Figure 6 depicts the power distribution on the receivingplane when the input power is W and the receiving planeis m and m away from the transmitter.IV. E NERGY AND D ATA F LOW IN AN EXEMPLARY
RB-SLIPT
SYSTEM
In this section, we present a practical RB-SLIPT systemdesign embedding a PV panel for energy harvesting andan APD for data receiving respectively at the receiver. Wewill detail the energy and data transfer flow of RB-SLIPTfrom three aspects: signal generating and power input at thetransmitter, path loss in the mobile transmission channel, andenergy/data processing at the receiver.
A. Signal Generating and Power Input at the Transmitter1) Signal Generating:
We adopt the optical orthogonalfrequency division multiplexing (OFDM) method for signalmodulation [23]. At the transmitter, let s denote an inputbit stream, the peak amplitude and variance of which can bedepicted as − A c < i sig < A c and ε respectively for A c > and ε > . s is at first mapped to the discrete modulation symbols,i.e., s s · · · s N/ − , where N is the number of subcarriers.Then, the Hermitian symmetry is imposed on the data vectoras S = (cid:104) s s . . . s N/ − s ∗ N/ − · · · s ∗ s ∗ (cid:105) so that the (a)(b) Fig. 6 Optical energy distribution (output laser power P out inthe receiver) with the input power P in = 150 W . The heightof the transmitter is (a) 3 m; (b) 2 m.output of inverse discrete Fourier transform (IDFT) block canbe real [24]. As illustrated in Fig. 2, we denote i sig ( t ) as asource signal from the electrical modulator; then i sig ( t ) afterthe IDFT operation can be presented as i sig ( t ) = N − (cid:88) k =0 √ N S ( k ) e j πkN t (cid:124) (cid:123)(cid:122) (cid:125) i sig ,k ( t ) , t = 0 , , . . . , N − , (25)where i sig ,k ( t ) represents the signal on k th subcarrier, and S ( k ) is the corresponding element of S .Then, a DC component from the pump source acts as aDC offset to the source signal. Thus, the generated signal atthe transmitter can be given as I in ( t ) = I D + i sig ( t ) , (26)where I D is the DC offset and i sig is an AC component whichcarries the data that needs to be sent out.
2) Power Input:
For a thin-disk solid laser, an LD isadopted to pump the thin-disk gain medium. The electric current I in at first drives the LD to generate the pump laserwith power P pump with the relationship as P pump = hcqλ e η ν η e [ I in − I th ] (27)where h = 6 . × − J · s, c = 3 × m/s, q =1 . × − C, λ e = 808 nm are the Planck’s constant, the speedof light, the electron charge, and the emission light wavelength,respectively; η ν and η e are carrier injection efficiency and pho-ton extraction efficiency; and I th is a temperature-dependentconstant threshold current. I D contributes to the input currentexceeding the LD’s threshold current I th .Then, the pump power is absorbed by the gain mediumand converted to the power stored in the upper laser levelinside the gain medium P avail with efficiency η a as P avail = η a P pump = η excit P in , (28)where η excit = η a η P represents the excitation efficiency. P in denotes the input power to the laser diode, and η P is definedas the pump efficiency. Thus, P avail is available for generatingthe resonant beam, which can be regarded as the power of thetransmitted signal. B. Path Loss in the Mobile Transmission Channel
For traditional SLIPT systems, the path loss of transmis-sion channel is caused by the beam divergency and misalign-ment of the transceiver. For RB-SLIPT system, the resonantbeam power which carries information and energy will in-crease as passing through the gain medium, and decrease asexperiencing the diffraction losses, losses inside the medium,and output coupling. Due to the characteristics of long-range intra-cavity transfer and self-alignment, the intra-cavitydiffraction loss cannot be neglected in the mobile transmissionchannel. As in Sec III, we can obtain the diffraction lossof one-way transmission inside the MRC as (24). Thus, thediffraction loss factor η diff can be depicted as η diff = (cid:112) V V . (29)In the RB-SLIPT system, the diffraction loss is dominantto the path loss during long-range transmission. From Sec III,the diffraction loss in the mobile transmission channel relies onthe size of system components, and the distance and deflectionangle between the transceiver. C. Energy/Data Processing at the Receiver
Similar to the traditional laser system, the output laserpower P out will be extracted from P avail after experiencing thepath loss during the channel transmission, internal loss of thegain medium, and the loss due to the output coupling, wherethe extraction efficiency can be depicted as [17] η extr = η b (1 − R ) V − η diff R + η diff √ R [1 / ( V S V ) − V S ] , (30)with η b = A b /A g denoting the overlap efficiency of the gainmedium. I ph R s R sh Communication Branch v o +- R L r C R C L L s Energy Harvesting Branch I ph I d R s R sh I pv,o V pv,o +- R L Fig. 7 DC Equivalent Circuit of PV for Energy HarvestingThen, the output laser power can be presented from (15),(28), (29), and (30) as P out = η extr ( η excit P in − c ) , (31)where c = A g I s (cid:12)(cid:12)(cid:12) ln (cid:16)(cid:112) RV S V V (cid:17)(cid:12)(cid:12)(cid:12) represents the thresholdof laser output in the RB-SLIPT system. The parameter η extr contains the impacts of various losses in the system, and η excit depicts the stimulation process of the thin-disk gain medium.Then, given a split ratio ≤ µ ≤ , µP out is received by aPV panel for energy harvesting and (1 − µ ) P out is collectedby an APD for information decoding.
1) Energy Harvesting:
Figure 7 depicts the equivalentcircuit of PV for energy harvesting. PV under illumination canbe regarded as a constant current source in parallel with diode. I ph represents the photo-generated current, and I d denotesthe current that used to counteract the junction current ofp-n junction. The additional resistance due to PV’s materialproperties is represented by series resistance R s and the edgeleakage is modeled by a parallel shunt resistance R sh . Finally, R L represents the load, i.e., battery to be charged, with thePV’s output current I pv,o and output voltage V pv,o .Then according to Kirchhoff’s law, the current-voltage (I-V) characteristics of a PV panel at a maximum power pointcan be described as I pv , o = I ph − I d − V d R sh , (32)where V d is the voltage across the diode follows V d = V pv , o + I pv , o R s . (33)Moreover, the current I d through the diode is I d = I (cid:0) e c V d − (cid:1) , (34)where I is the reverse saturation current, c = 1 /n s nV T is thePV panel factor, with n s the number of cells connected insidea PV panel, n the diode ideality factor, and V T = ( kT ) /q is the thermal voltage of the diode, with k the Boltzmann’sconstant and T the temperature in Kelvin.Moreover, I ph depends on the light power received bythe PV panel P pv,i . Assume the output laser power for energyharvesting is 100% harvested by the PV, i.e., P pv,i = µP out ,the relationship between photocurrent I ph and PV’s input laserpower P pv,i can be depicted as I ph = ρ P pv,i = µρ η excit ( η extr P in − c ) , (35) where ρ is the conversion responsivity factor which depictsthe optical-to-electrical conversion efficiency and can be mea-sured in A/W. From (32), (33), and (35), we can obtain theoutput power P pv,o of the PV panel available for charging thebattery as P pv,o = I pv,o V pv,o . (36)
2) Data Receiving:
A portion of laser beam is receivedby the APD to be converted to the output signal current as P pd = (1 − µ ) P out , (37)At the receiver part, there are three following aspects need tobe detailed for the communication performance analysis. • Received Signal: To present the signal gain in the mobiletransmission channel of the RB-SLIPT, we can rewrite(37) as follows according to (27) and (31): i pd = (cid:112) − µ ( γ [ I in − I th ] + c ) , (38)where ρ is a constant representing the optical-to-electrical conversion responsivity of APD, and γ and c can be presented as follows: γ = ρ η extr η a η ν η e hcqλ e . (39) γ and c are constants at given transmission distanceand deflection angle between the transceiver, which il-lustrates the linear modulation ability of mobile trans-mission channel for communication. Then, γ is modelledas the channel gain for signal transfer in RB-SLIPT,which reflects the channel condition depending on thetransmission distances and deflection angles. Thus, thetime domain signal on k th subcarrier received by the usercan be described as [25] i pd ,k ( t ) = (cid:112) − µγi sig ,k ( t ) + n k ( t ) , (40)where n k ( t ) is the noise signal on the k th subcarrier. • Noise Analysis: We analyze the shot noise generatedthrough the optical-to-electrical conversion in the APDand the thermal noise caused by the resistors in the APDsystem. The variance of the noise signal with zero meanon k th subcarrier can be expressed as [24] σ k = N total W/N, (41)where W is the modulation bandwidth. The noise signalcan be modelled as additive white Gaussian noise withpower spectral density (PSD) profile denoted as N total ,which is the sum of shot noise and thermal noise: N total = N sh + N th . (42)The one-side PSD of the shot noise in A / Hz can bedepicted as [26] N sh = 2 qρ ( P pd + P b ) , (43)where P b is the background radiance caused by theambient light (sunlight or LED light), which can bedepicted as [27] P b = η Rx H b B IF A Rx Φ Rx Γ , (44) where η Rx is the optical efficiency of the signal receivingunit, H b represents the background irradiance, B IF isthe optical bandwidth of the filter installed behind theoutput coupler retro-reflector2; A Rx , Φ Rx , and Γ are thereceiving area, solid angle, and transmittance of retro-reflector2, respectively. In our settings, the backgroundirradiance is estimated as . × − W.The thermal noise is generated by the load resistor R L,pd ,of which the one-side PSD can be described as [28] N th = 4 kT /R L , pd . (45) • Signal-to-Noise Ratio (SNR): To evaluate the perfor-mance of the communication in the RB-SLIPT system,we analyze the SNR of the channel. Due to the OFDMmethod, we can choose appropriate modulation schemefor each sub-channel and design the optimized bit dis-tribution algorithm, so that the utilization of the channelcapacity can be maximized. For simplicity, we depict thechannel performance from the SNR of each sub-channel,and the SNR of the k th sub-channel can be [24] SNR k = (1 − µ ) γ E k σ k , (46)where E k represents the power of transmitted signal i sig ,k on k th subcarrier, which can be estimated as [24] E k = ( E [ i sig ,k ( t )]) η ( N −
2) = 2 εη ( N − . (47)It should be noted that only N − subcarriers carry dataand η denotes the DC bias factor.Then, according to the Shannon channel capacity, theachievable data rate of the RB-SLIPT system for com-munication can be depicted as [24] R a = N/ − (cid:88) k =1 ( W/N ) log (1 + SNR k ) . (48)V. N UMERICAL A NALYSIS
In this section, we numerically analyzed the channelfactor and the energy/data transfer capability of the RB-SLIPT system. As for the mobility-enhanced system, we willspecifically analyze the impacts of the moving range ( i.e.,transmission distance and deflection angle), and analyze theimpacts of the DC offset power and the split ratio on theperformance of the proposed system.
A. Parameters
The parameters of the gain medium are from an exampleof a diode-end-pumped Nd:YVO4 laser in [17, 29]. We choosethe infrared beam with the wavelength of nm. Then, weadopt a PV cell with . A/W and an APD with . A/Wconversion responsivity [24]. We specify the RBS parameters,energy and data transfer parameters, and FFT and FoxLialgorithm parameters in Table I, II, and III, respectively.For the FFT numerical calculation, the calculation planeand the impulse response function need to be sampled first, andthe sampling number S N is generally a power of . Moreover, TABLE I Parameter of Resonant Beam System
Parameter Symbol Value
Cat’s radius r mmGain medium radius r g mmResonant beam wavelength λ . × − mOutput coupler reflectivity R . Medium saturated intensity I s . × W/m Loss factor in medium V s . Excitation efficiency η excit . Gain stored efficiency η a . Carrier injection andphoton extraction efficiency η ν η e . TABLE II Parameter of Energy/Data Transfer
Parameter Symbol Value
PV conversion responsivity ρ . A/WReverse saturation current I . × − ADiode ideality factor n . Number of PV cell n s Series resistance R s m Ω Shunt resistance R sh PD load resistor R L m Ω Temperature in Kelvin T . KAPD conversion responsivity ρ . A/WModulation bandwidth W M/HzPD load resistor R L,pd K Ω DC bias factor η TABLE III Parameter of FoxLi and FFT algorithm
Parameter Symbol Value
FoxLi iteration number t Sampling number S N Computation window expand factor G zero-padding is needed to avoid aliasing effects as in Fig. 5.The computation window length Gr is defined as the lengthof zero-padded aperture, where G is the computation windowexpand factor, and r is the front face radius of cat’s eye. B. Channel Factor of the Mobile Transmission Channel
In this paper, we have proposed an analytical model forthe energy distribution analysis of the mobile transmissionchannel, so that we are capable of modelling the channelaccurately as a function of mobility factors such as trans-mission distance, i.e., cavity length L and the deflectionangle between transceiver θ . Figure 8 depicts the channelfactors γ of the proposed system with varying L and θ . γ doesn’t change obviously as the deflection angle between thetransceiver is below ◦ . However, as the angle is larger than ◦ , γ declines sharply and turns to with θ = 13 ◦ . Themaximum allowable angle depends on the parameters (i.e.,focus length and front face radius) of the cat’s eye. Moreover,as the transmission distance L changes from m to m, γ decreases correspondingly. C. Energy-Data Transfer Performance of RB-SLIPT
At the receiver, the output laser beam at first enters intoa power splitter and is split into two streams with ratio µ for L=1mL=2mL=3mL=4mL=5mL=6mL=7mL=8mL=9mL=10m
Fig. 8 Channel factors γ of the RB-SLIPT with differenttransmission distances L and deflection angles θ . Fig. 9 Charging power and achievable data rate as a functionof deflection angle θ with different split ratio µ under trans-mission distance L = 3 m.energy and data harvesting, respectively. Thus, as in Fig. 9,we analyze how the split ratio impacts the energy/data transferperformance. We can find as µ grows, the charging powerimproves significantly, while there is no obvious deteriorationin data transfer performance until µ = 1 . Thus, in thefollowing analysis, we choose the split ratio µ = 0 . formaximizing the energy/data transfer capability.Figure 10 shows the charging power and achievable datarate as a function of input power of the DC offset I D , withtransmission distance L = 2 m, m and deflection angle θ =0 ◦ , ◦ . As the input power increases, the charging power fromPV grows, while the communication performance gets poorerdue to the increase of noises.Figure 11 depicts the charging power and achievable datarate as a function of transmission distance L with the deflectionangle θ = 0 ◦ , ◦ , ◦ , and the input power to the system P in = 200 W. Evidently, both the energy and data transfer
150 160 170 180 190 20000.511.522.533.544.55 1.51.521.541.561.581.61.621.641.661.681.7
L = 2m, = 0 ° L = 2m, = 10 ° L = 3m, = 0 ° L = 3m, = 10 ° L = 2m, = 0 ° L = 2m, = 10 ° L = 3m, = 0 ° L = 3m, = 10 ° Fig. 10 Charging power and achievable data rate as a functionof input power of the DC offset I D with different transmissiondistances and deflection angles. = 0 ° = 10 ° = 11 ° = 0 ° = 10 ° = 11 ° Fig. 11 Charging power and achievable data rate as a functionof transmission distance L with different deflection anglesunder input power P in = 200 W.performances reduce with the increase of the transmissiondistance L . Moreover, L has more impact on the energytransfer than on the data transfer, and as the deflection anglegrows, the acceptable transmission distance decreases.In Fig. 12, we analyze the relationship between the charg-ing power/achievable data rate and the deflection angle θ . Theenergy-data transfer performance shows the similar tendencywith γ as a function of θ . The maximum operational deflectionangle between the transceiver with P in = 200 W, W is ◦ .Moreover, as the input power increases, the charging powerincreases and the achievable data rate decreases, and if theinput power is low, there will be no charging power outputfrom the PV. Furthermore, the proposed RB-SLIPT systemshows super performance of W wireless charging power and . Gbit/s data rate with the capability of large moving range. P in = 150WP in = 200WP in = 250W P in = 150WP in = 200WP in = 250W Fig. 12 Charging power and achievable data rate as a func-tion of deflection angle θ with different input power undertransmission distance L = 3 m.VI. C ONCLUSIONS
In this paper, we designed an RB-SLIPT system whichcan deliver multi-Watt power to the mobile receivers withself-alignment characteristic. We at first established a mobiletransmission channel model to reveal the mobility mechanismand quantitatively evaluate the energy distribution in the chan-nel. Then we proposed an exemplary SLIPT design to transferenergy and data using PV and APD respectively. Finally, weanalyze the impacts of moving factors on the energy/datatransfer performance (charging power and achievable datarate). Numerical analysis illustrates that SMIPT is a practicalsolution for realizing mobile energy supply and data transfer.Several interesting topics are worthy of further investi-gation in the future: 1) design and analysis for SWIPT withmultiple receivers; 2) methods of enhancing deliverable powerand data rate. R
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