Nonlinear Energy Harvesting Models in Wireless Information and Power Transfer

Nonlinear Ener gy Harve s ting Models in W ireless Information and Po wer T ransfer Panos N. Alevizos, Georgios V ougiouka s , and Aggelos Bletsas School of ECE, T echnical Univ . of Crete, K ou n oupidiana Campus, Greece 73 1 00 e-mail: { pale vizos, g evou gioukas } @isc.tuc.gr, aggelos@telecom.tuc.gr Abstract —This work compares different linear and nonlinear RF energy har vesting models, inclu ding limited or unlimited sen- sitivity , f or simultaneous wireless infor mation and p ower transfer (SWIPT). The probability of successful S WIPT reception un der a family of RF harv esting models is rigorously quantified , using state-of-the-art rectifiers in the context of com mercial RFIDs. A significant portion of SWIP T literature uses ove rsimp lified models that d o not account f or limit ed sensitivity or nonlinearity of the un derlying harve sti ng ci rcuitry . This work d emonstrates that communications signals ar e not always appropriate f or simultaneous ener gy transfer and concludes that f or practical SWIPT stu dies, the inherent non-ideal characteristics of the har - vester sh ould be care f u lly taken i nto account; specific harv ester’s modeling method ology is also offered. I . I N T R O D U C T I O N Intense research has be e n d ev oted the last yea r s on simulta- neous wir eless informatio n and power transfer (SWIPT). The main concept in far field SWIPT systems is the exploitatio n of the comm u nication signals fo r radio freq uency (RF) energy harvesting, typically with r ectennas, i.e., an tenna and re c ti- fier(s). The latter p erform the required RF-to - DC conversion, including one (or more ) diod e(s). The main problem in far field RF energy harvesting is the limited sensitivity o f the circu it, currently in th e order of − 3 5 dBm to − 2 5 dBm, with slow improvement by a factor of 2 every ap proxim ately 5 years [1]. Such power levels below which en ergy tran sfer cannot be p erforme d , are orders o f ma gnitude h igher tha n cu r rent commun ications cir cuits sensitivity , which may reach values as low as − 130 d Bm to − 80 dBm, depend ing o n bandwidth . Thus, signals approp riate for communicatio n s m a y not b e simultaneou sly suitable for energy transfer [2], [3]. Another major issue in the SWIPT literature is the ado p tion of oversimplified RF harvesting m o dels, wh ich eith er exhibit a linear relationship b etween input RF and o utput harvested power or assum e unlimited sensiti v ity . Recten nas, d ue to the presence of diod e (s), exhibit a high ly non linear beh avior , with limited sensitivity , due to the n e ed for bias. Despite the vast amount of literatu r e in the wireless comm unications theory commun ity that ad heres to the above assump tions, excep tions have o nly recen tly started to em e rge; for example, work in [4], [ 5] u tilized c o n vex optimization tec hniques to op timize the parameters of mu lti-tone wav ef orms, which improve RF harvesting efficiency com pared to s in gle-tone, while takin g into accou nt the nonlinear ity of the rectifier . Other n onlinear RF har vesting models ha ve been recently propo sed, wh ic h howe ver miss the limited sen sitivity issue and will b e dis- cussed subsequen tly . Therefo re, there is a strong need to evaluate d ifferent RF har vesting mo dels, taking into acco unt both harvesting sensiti v ity and n onlinearity , as well as facts f rom the r elev ant microwa ve litera ture. Radio freq uency iden tificatio n (RFID) technolog y is the most prom inent example of SWIPT , with significant prior art, as well as co m mercial inter est. This work compare s different linear and no n linear energy ha r vesting models for SWIPT , taking also into accou nt limited or un- limited sensitivity; comp arisons are per formed based on real, state-of-the- art r ectifiers [6] in RFID, u sin g backscatter com- munication s. It is foun d that neglecting harvester’ s no nlinearity and limited sensitivity may offer misleading results. I I . S I G N A L M O D E L Backscatter rad io/RFID techno logy is th e most prom inent example o f SWIPT . A m o nostatic, single-an tenna reader topo l- ogy is examined with reader a nd tag, d epicted in Fig. 1. In that case, the illumina tin g car rier emitter and the receiver o f the tag-back scatter ed sign al is th e same, full-d uplex u n it, a.k.a. the reader; the latter is equip ped with a single antenna serving both reception and transmission , using an ap propr iate duplexer , the circulator . T hus, path-loss and small-scale fading are the same for both read er-to-tag (d ownlink) and tag -to-read e r (uplin k) links. Both links ar e subject to large-scale fading , wh ere the path-gain at tag-to-r e a der distance d is g i ven by: L ≡ L ( d ) =  λ 4 π d 0  2  d 0 d  ν , (1) where d 0 is a referen ce distance (assumed u n it there in after), λ is the wa velen gth and ν is the p ath loss exponent. Flat fading is assumed due to relatively small c o mmunica- tion ban dwidth. Thu s, small-scale fading coefficient, fo r b oth downlink and up link is given b y h = a e − j φ . Due to po tential strong line-o f-sight (LoS), Naka gami small-scale fading is assumed with E  a 2  = 1 an d Nakag a mi parame ter M ≥ 1 2 [7, p. 79]. The special cases o f Rayleigh fadin g and n o fading ( a = 1 ) are o btained for M = 1 and M = ∞ , respectively . Assuming the rea d er emits an unmodulated carrier with transmit power P R and fre q uency F c , the impinged signal at the tag signal can b e expre ssed as follows: c T ( t ) = p 2 L P R ℜ{ h e j 2 πF c t } . (2) Reader Matching Network Z 1 Backscattering Receiver RF Harvester Digital Control Logic T ag Z 0 Fig. 1. Monostatic backsca tter architec ture consisting of a reader and a passiv e (i.e., batteryless) RFID tag. Reader acts as carrier emitter , as well as recei ver of tag reflected/ba ckscattered informatio n. The received power at the tag is th en giv en by: P in = L P R | h | 2 = L P R a 2 . (3) According to the ab ove, P in follows Gamma distribution ( E  a 2  = 1 ): f P in ( x ) =  M L P R  M x M − 1 Γ ( M ) e − M L P R x , x ≥ 0 , whe re  M , L P R M  the shape an d scale param eter , re spectiv ely , and Γ ( x ) = R ∞ 0 t x − 1 e − t d t is the Gamm a fu nction. I I I . R F I D T AG O P E R AT I O N The RFID tag do es n ot include any power - d emandin g signal condition in g un its, e.g., a mplifiers, mixers o r o scillators (Fig. 1). I nstead, co mmunication is achieved by varying th e reflection co efficient be twe e n tag antenna and its termination loads, u sin g a RF switch. Binar y mod ulation is achieved with two different reflection coefficients (i.e., two different termination loads Z 0 , Z 1 ). This operatio n resu lts to mo dulation of tag info rmation on top of the r e ader illumin ating signal, reflected (fro m the tag) back to th e rea d er , in an ultra low- power fashion. A. RF Harvesting & T ag P owering In order fo r th e RFID tag to op erate, p ower mu st be harvested fro m the imping ed, reader-generated signal. Input power must be above the tag ha r vester sensitivity P sen , i.e., P in > P sen . P sen is a crucial paramete r in backscatter com mu- nication with p assi ve tags, du e to the fact that state-of -the-art, far field RF harvesters o ffer limited sensitivity . W ork in [3] estab lished that a high-o rder po lynomial in th e dBm scale ca n be safely co nsidered as g round tr uth mod e l fo r harvesting efficiency function ; th us, h arvested power can be modeled as a fun ction of inp ut power x as follows: p ( x ) =      0 , x ∈ [0 , P sen )  w 0 + P W i =1 w i (10 log 10 ( x )) i  · x, x ∈ [ P sen , P sat ] , p ( P sat ) , x ≥ P sat , (4) where x and p ( x ) take values in mW att, while the qu antity  w 0 + P W i =1 w i (10 log 10 ( x )) i  is the h a r vesting efficiency function , with W bein g the degree o f the polynomial an d { w i } W i =0 the correspo nding co efficients. For the analysis b e low we assum e that f unction p ( x ) is con tinuous and in creasing in [ P sen , P sat ] . As shown in [3], th e param e ters { w i } W i =0 in Eq. ( 4) can be obtain ed directly from harvesters’ data using stan dard conv ex optim ization fitting meth ods. Sev er a l models hav e been pro posed in order fo r th e har- vested power to be m athematically describ ed. These mo dels are summarized below: 1) Linear Mo del (L): Single p arameter mod el, where the harvested power can be expressed as p 1 ( x ) , η L x, x ≥ 0 . This is the m ost utilized model in SWIPT literature, it’ s linear and does not accou n t for har vesters’ sensitivity . 2) Constant Linear (CL): Linear model with the add ition of taking into acco unt the sensiti v ity of the h a rvester . Acco rding to that mod el, harvested power is expressed as p 2 ( x ) = η CL · ( x − P sen ) for x ∈ [ P sen , ∞ ) and zero in the rest o f its domain ; η CL is the constan t harvesting efficienc y . 3) Nonlinea r Norma lized Sigmo id: The m odel was pro- posed in [8] and assumes P sen = 0 , i.e., it does n ot acco unt for h arvesters’ sensiti v ity . Th e harvested power is expressed as: p 3 ( x ) , c 0 1+ exp ( − a 0 ( x − b 0 )) − c 0 1+ exp ( a 0 b 0 ) 1 − 1 1+ exp ( a 0 b 0 ) . (5) The shape of p 3 ( x ) is deter mined by three real numb ers a 0 , b 0 , and c 0 . A similar, sigmo id model accou nting howe ver for P sen , was p roposed in [ 9], where the harvested power is modeled as: p 4 ( x ) , ma x n c 1 exp ( − a 1 P sen + b 1 )  1+ exp ( − a 1 P sen + b 1 ) 1+ exp ( − a 1 x + b 1 ) − 1  , 0 o . 4) Secon d Order P olynomial: In [10] a mod el based on a second degre e polyno mial in m illiW att domain has b e en suggested. Following that mod el, h arvested power can be expressed as p 5 ( x ) , a 2 x 2 + b 2 x + c 2 . Th e above mod el does n ot acco unt f or P sen . In o rder to en c ompass the effect of sensiti v ity , p 5 ( · ) can be mod ified as p 6 ( x ) , a 3 ( x − P sen ) 2 + b 3 ( x − P sen ) . (6) The parameter s of the mo d el in Eq . (6) are a 3 , b 3 and P sen . 5) Piecewise Lin ear Model: Given a set o f J + 1 da ta pairs of input power and corre sponding harvested power , d enoted as { q j } J j =0 and { v j } J j =0 , re spectiv ely , slopes l j , v j − v j − 1 q j − q j − 1 , j ∈ [ J ] are d efined, where [ J ] , { 1 , 2 , . . . , J } . Modeling sensiti v ity a nd saturation character istics is don e thro u gh poin ts q 0 = P sen and q J = P sat . Having tho se slop es, the harvested power is given by: p 7 ( x ) ,      0 x ∈ [0 , q 0 ] , l j ( x − q j − 1 ) + v j − 1 , x ∈ ( q j − 1 , q j ] , ∀ j ∈ [ J ] , v J , x ∈ [ q J , ∞ ) . (7) Function p 7 ( x ) is defined u sing 2 ( J + 1) r eal numbers, easily av ailable from harvesters’ specification s; thus, determ ining p 7 ( x ) is straightfo r ward, without any tuning. It should be noted that th e last mod el can poten tially mod el energy harvesting from other sour c es, other than RF . For instance, if photodio d es a re u sed in o r der to har vest energy from e ither a m bient or solar light, the proposed mo del c a n Input Pow er (dBm ) -45 -40 -35 -30 -25 -20 Harvested Po wer (mW att) × 10 -3 -4 -2 0 2 4 6 8 10 Data Ground Truth Sigmoid Sigmoid + Sensitivity 2nd-Order Polynomial 2th-Order Polynomial + Sensitivity Fig. 2. Harvested po wer (in milliW att) versus input po wer (in dBm) for the harve ster proposed in [6] using nonlinea r harvested powe r functi on p n ( · ) , n = 3 , 4 , 5 , 6 , as well as for the ground truth model in Eq. (4). Input power range within [ − 45 , − 20] dBm. describe the harvested p ower , as a fu nction o f illumin ance (measured in lux ). This statement is based on the no nlinear behavior of th e pho to diodes (similarly to RF re c tification circuits), when used as harvesting elements (for examp le see work in [11], [12]). Fig. 2 illustrates the har vested power (in mW att) versus input power (in dBm) for the harvester p roposed in [6] using as groun d truth the specificatio n data; th e n o nlinear model in Eq. (4) adh e res to the data; the rest of the nonlinear ha r vested power fun ction p n ( · ) , n = 3 , 4 , . . . , 6 , discussed ab ove, are also depicted (using Matlab’ s fitting toolbox ). Due to strong nonlinear ity , th e line a r m o dels we re omitted from the plot. During norm a l o peration, tag s’ an te n na is terminated at load Z 0 (absorbin g state, see Fig. 1) for a time fraction of τ d while for the r est 1 − τ d , an te n na is conn e cted to Z 1 (reflection state). Given that the tag is at Z 0 , a portion χ of the received power is destined solely for e n ergy harvesting , i.e., ζ har = χ τ d ∈ (0 , 1) percentage of inpu t power is dedicated fo r RF energy har vesting. The rest (1 − χ ) τ d , is exploited for downlink commun ication purp oses. Thus, in order for the tag to operate, the total harvested power p ( ζ har P in ) must b e greater than the tag overall power consump tion P c . Th is is critical, g iv en the fact that b atteryless RFID tags typically incorpora te no energy storag e eleme nt, e.g., (super )capacitor, due to size and cost limitation s. B. Backscatter Commun ication As stated earlier, the tag alters the load terminatin g its an- tenna using a switch . Load Z 0 is, by con struction, design ed to match antenn as’ imped ance. Th us, w h en antenna is ter minated at Z 0 , the load abso r bs (ideally , if p erfectly matched ) all the power offered by the imp inged signal. When the antenn a is terminated at Z 1 , a fractio n ρ u ≤ 1 − τ d of the im pinged power is u sed for uplink scatter ra d io o peration. Parameter ρ u depend s on the tag scattering efficiency (which also in- corpor ates non-idealities from the above model). Modified reflection co efficient [13] Γ i , wh e n the antenn a is termin ated at Z i , i ∈ { 0 , 1 } , is given by Γ i = Z i − Z ∗ a Z i + Z a , whe r e Z a antenna’ s impedanc e. The b aseband equivalent of the tag - backscattered signal can be expressed as [13] A s − Γ i , which in tur n dep ends on the ( load-inde pendent) tag an tenna structura l mo de A s and the transmitted bit i ; th e backscattered baseban d signal, for a duration of N tag bits, is given by [14]: b ( t ) = p L ρ u P R h  A s − Γ 0 + ∆Γ N X n =1 s b n ( t − ( n − 1) T )  , (8) where, ∆Γ , (Γ 0 − Γ 1 ) , b n ∈ { 0 , 1 } is the n -th reflected bit, while fun ction s b n ( · ) is the backscatter ed sign a l b a sis fun ction, of duration T , when b it b n is transmitted . In or der to a ) balance th e time f o r which th e tag is absorbin g energy , indepen dently of the tag’ s d a ta bits, and b) av o id gho st tag recep tion, i.e., reader misinterpreting therm al noise as tag informa tio n, a line co de is used in co mmercial GE N2 RFIDs [15], selecting between FM0 and M iller . Under FM0 cod ing, observing 2 T signal duration for each b it (o f du ration T ) suffices for BER-optimal, cohere n t (differential) d etection and s b n ( · ) is a T / 2 -shifted waveform given by [16]: s 0 ( t ) , ( 1 , 0 ≤ t < T 2 , 0 , otherwise , s 1 ( t ) , ( 1 , T 2 ≤ t < T , 0 , other wise . (9) Assuming p erfect synchr onization, the o ptimal dem odulator projects th e rec ei ved sign al o n to the basis fu n ctions subspace using two correlato rs. Th e discrete b a seband signa l, at th e output of the corr elators, fo llows [17, T heorem 1]: y n = g s n + w n , n = 1 , 2 , . . . , N , (10) where g , L √ ρ u P R h 2 (Γ 0 − Γ 1 ) , and s n is the vector representatio n for the n -th transmitted signa l. For RFID systems, wh ich em ploy T / 2 -shifted FM 0 line-cod ing, s n ∈  [1 0] ⊤ , [0 1] ⊤  and w n ∼ C N ( 0 2 , σ 2 I 2 ) [16], [ 17], with σ 2 denoting the variance of each no ise compon ent. I V . R E A D E R A. Bit Err or Rate (BE R) Assuming coher ent ML d ifferential detection (with signa l of 2 T du ration, given known chann el g ), th e conditio nal bit error p robability for th e baseb and signal in Eq. (10) follows from [16], [18]: P (error | g ) = 2 Q  | g | σ   1 − Q  | g | σ  , (11) where Q ( x ) = 1 √ 2 π R ∞ x e − t 2 2 d t is the Q-fun ction. Interest- ingly , a similar expression applies to Miller lin e coding , whe n the receiver p e rforms coherent (ML) bit-by -bit detectio n. B. Outage S cenarios The rea d er receives successfully th e RFID tag’ s informatio n when: a) th e input RF power at the tag antenn a is above RF harvesting sensitivity , and b) the harvested power is ab ove tag’ s power consum p tion, given that the RFID tag d oes n ot include energy storage elem ents, and c) BER at th e reader is below a thresh o ld β . Proba b ility of th ese events is analyze d below . P sen (dBm) -45 -40 -35 -30 -25 -20 -15 -10 -5 Probability of Outage 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P R = 15 dBm, d = 3 m P R = 15 dBm, d = 9 m P R = 35 dBm, d = 3 m P R = 35 dBm, d = 9 m Fig. 3. Probability of sensitiv ity outage ev ent as a function of tag’ s harvest ing sensiti vity . The path-loss model of E q. (1) is employ ed with ν = 2 . 1 , λ = 0 . 3456 and M = 5 . 1) Outage due to limited ha rvesters ’ sensitivity: Con sider- ing th e definition of inp ut power in E q. (3), tag’ s h a rvesting sensiti v ity o utage metric is defined as fo llows: P ( A ) , P ( P in ≤ P sen ) = F P in ( P sen ) , (12) where F P in ( · ) is the cumu lati ve distribution func tio n (CDF) of P in . Eq. (12) mathematically d e scr ibes the prob ability that the input power P in at the RFID tag anten na (wh ic h depen ds on the wireless chan nel/fading), is below tag RF harvester’ s sensiti v ity P sen . Su ch outage event represen ts the fraction of time the tag’ s rectenna can not harvest RF energy du e to inadequ a te input RF p ower . Und er Nakagami fading such outage is given by: F P in ( P sen ) = 1 − Z ∞ P sen f P in ( y ) d y = 1 − Γ  M , M L P R P sen  Γ ( M ) , (13 ) where Γ ( α, z ) = R ∞ z t α − 1 e − t d t . At this po int, it must be emphasized th at RF recei ver sen siti vity for com munication purpo ses can ob tain values f rom − 8 0 dBm or less, while state- of-the- a r t rectennas offer harvesting sensiti vity in th e ord er of aro und − 40 to − 35 dBm [6]. Clearly , sign als useful for communica tion may not be usefu l for p ower transfer . Fig. 3 examin es Eq. (12) as a f unction of tag RF harvester’ s sensiti v ity . It can be clearly seen th at less-sensitiv e RF har- vesters, suffer from h ig her outage p robabilities. RF har vesting sensiti v ity is common ly n eglected in SWIPT r esearch, even though it tremendously impacts the power transfer par t and thus, overall perfo r mance [19]. 2) Outage due to limited power c onsumption : When in p ut power is above tag ’ s harvesting sensitivity , the next type of outage is whe n the h arvested power , p ( ζ har P in ) is n ot enoug h , i.e., below tag’ s power consumptio n P c : P ( p ( ζ har P in ) ≤ P c ) , (14) which d epends on (a) fading an d inpu t power at the tag , (b) the type of the RF harvester, and (c) tag’ s p ower co nsumption P c ; such prob ability d escribes the fraction of time the harvested power is no t a dequate for tag po wering and is critical for devices that cannot store harvested energy . If p ( · ) is strictly increasing an d continuo us aro und P c [20], the event in Eq. ( 1 4) can be simplified as fo llows: P ( B ) , P  P in ≤ p − 1 ( P c ) ζ har  = F P in  p − 1 ( P c ) ζ har  , (15) where p − 1 ( P c ) is the inverse function of p ( · ) at poin t P c . 3) Informa tion Outage: RFID tag inform ation outage at the reader is define d when BER in E q. (1 1) is below a predefin ed precision β . Setting R ( x ) , 2 Q ( x ) (1 − Q ( x )) , x ∈ (0 , ∞ ) , this event can be mathema tically expressed as [3]: P ( C ) , P  P in ≤ √ P R σ R − 1 ( β ) | Γ 0 − Γ 1 | √ ρ u  = F P in  √ P R σ R − 1 ( β ) | Γ 0 − Γ 1 | √ ρ u  , (16) where R − 1 ( x ) = Q − 1  1 − √ 1 − 2 x 2  , d efined fo r x ∈ (0 , 0 . 5) and Q − 1 ( · ) is the inverse o f Q-function . C. Pr obability Of Su ccessful Re ception T ag informatio n is unsuccessfully receiv e d wh en eithe r of previously d iscussed events A , B , C oc curs. Assuming that function p ( · ) is strictly in creasing an d con tinuous aro und P c and d enoting for an event D its comp lem ent as D C , the probab ility of unsucc e ssful SWIPT reception , den oted as event F , can be expressed as: P ( F ) = 1 − P ( F C ) = 1 − P ( A C ∩ B C ∩ C C ) = 1 − P ( P in > θ F ) = F P in ( θ F ) , (17) where θ F , max n P sen , p − 1 ( P c ) ζ har , √ P R σ R − 1 ( β ) | Γ 0 − Γ 1 | √ ρ u o . C o nse- quently , su ccessful SWIPT recep tion at the read er , under Nakagami fading, is g i ven in closed for m a s follows: P (SWIPT success) ≡ P ( F C ) = Γ  M , M L P R θ F  Γ ( M ) . (18) V . N U M E R I C A L R E S U LT S For the simulation r e sults the path-loss model of Eq. (1) is considered with ν = 2 . 3 an d λ = 0 . 345 6 ( UHF carrier frequen cy), and tag anten na r eflection coefficients Γ 0 and Γ 1 satisfying | Γ 0 − Γ 1 | = 1 . The ultra-sensitive h arvester in [6] is tested using para m eters τ d = 0 . 5 , χ = 0 . 5 , ρ u = 0 . 01 for RF harvesting and back scattering at the tag, while BER threshold is set β = 10 − 5 ; variance of no ise at th e re a der was set to 10 − 11 . Fig. 4 d epicts probability of succe ssfu l SWIPT rece p tion at the r eader, as a fu nction of tag ’ s power con sumption, in a strong LoS scenario (Nakaga m i param e te r M = 10 ), d = 4 m, and P R = 1 W att. Fig. 5 examines th e same relationship in a non-L o S scen ario ( M = 2 ) , d = 7 m, and P R = 2 . 5 W att. Both figur es clearly show that th e perfo rmance of the piecewise linear mod el p 7 ( · ) coincides with the exact (gro u nd- truth, p ( · ) ), data-driven mod el. The perfo r mance of p 1 ( · ) (L) , as we ll as p 2 ( · ) (CL) model deviate fro m reality , even tho u gh the best values fo r th e e ffi ciency par ameters wer e utilized P c (dBm) -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 Succes sful Recep tion at R eader 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Exact (Monte Carlo) Piecew ise Linear ( J + 1 = 118) L ( η L = 0 . 3) CL ( η CL = 0 . 3) Sigmoi d Sigmoi d + Sensitivit y 2nd-Or der Polyn omial 2nd-Or der Polyn omial + Sensi tivity Fig. 4. Probability of successful SW IPT receptio n at reader , as a function of tag power consumption-Strong L oS. P c (dBm) -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 Succes sful Recep tion at R eader 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Exact (Monte Carlo) Piecew ise Linear ( J + 1 = 118) L ( η L = 0 . 25) CL ( η CL = 0 . 25) Sigmoi d Sigmoi d + Sensitivit y 2nd-Or der Polyn omial 2nd-Or der Polyn omial + Sensi tivity Fig. 5. Probability of successful SW IPT receptio n at reader , as a function of tag power consumption-non LoS. (i.e., values that offered perform ance as close as possible to the ground -truth m odel). Bo th n onlinear sigmo id mod e ls tend to overestimate the event while th e one incorpo rating sensiti v ity , offers clo ser-to-reality results in the L oS scenario and deviates further in the non -LoS scenario. Finally , the second-o rder polyno mial p 5 ( · ) underestimates per formanc e , with p erforman ce gap that dep e n ds o n the scenario and tag’ s power con sumption, whereas energy har vesting mode l p 6 ( · ) overestimates the h a r vested power . In shor t, SWIPT resear ch requires accu rate energy harvesting models, otherwise mis- leading conc lu sions are unavoidable. V I . C O N C L U S I O N SWIPT research sho uld always take into acco unt all the non-id eal characte r istics o f the RF energy harvesting system; otherwise, oversimplificatio n due to overlooking fu ndamentals from electronics and micr ow ave engineer ing may lead to impractical re su lts. Th is work studied the sensitivity and the nonlinear ity o f th e h a rvester . I mpact of other mod ules, present in th e RF harvesting chain (e.g., b oost converter/maximum power point trackin g-MPPT), shou ld b e also examined. A C K N OW L E D G M E N T This r esearch is implemen ted throug h the Operational Pro- gram “ H u man Resources Development, E ducation an d Life- long Learnin g ” an d is co- fin anced b y the Eur opean Un ion (Europ ean Social Fund) and Gre e k nation al fu nds. R E F E R E N C E S [1] G. D. Durgin, “RF thermoelect ric generat ion for passi ve RFID, ” in Proc . IEEE R FID , Orlando, FL, May 2016, pp. 1–8. [2] P . 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