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1 Original citation: Gao, Yan, Chen, Yunei and Bekkali, Abdelmoula. (06) Perormance o passie UHF RFID in cascaded correlated generalized Rician ading. IEEE Communications Letters. doi : 0.09/LCOMM Permanent WRAP url: Copyright and reuse: The Warwick Research Archie Portal (WRAP) makes this work by researchers o the Uniersity o Warwick aailable open access under the ollowing conditions. Copyright and all moral rights to the ersion o the paper presented here belong to the indiidual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made aailable in WRAP has been checked or eligibility beore being made aailable. Copies o ull items can be used or personal research or study, educational, or not-or proit purposes without prior permission or charge. Proided that the authors, title and ull bibliographic details are credited, a hyperlink and/or URL is gien or the original metadata page and the content is not changed in any way. Publisher s statement: 06 IEEE. Personal use o this material is permitted. Permission rom IEEE must be obtained or all other uses, in any current or uture media, including reprinting /republishing this material or adertising or promotional purposes, creating new collectie works, or resale or redistribution to serers or lists, or reuse o any copyrighted component o this work in other works. A note on ersions: The ersion presented here may dier rom the published ersion or, ersion o record, i you wish to cite this item you are adised to consult the publisher s ersion. Please see the permanent WRAP url aboe or details on accessing the published ersion and note that access may require a subscription. For more inormation, please contact the WRAP Team at: publications@warwick.ac.uk

2 IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXXX XXXX Perormance o Passie UHF RFID in Cascaded Correlated Generalized Rician Fading Yan Gao, Yunei Chen, Senior Member, IEEE, Abdelmoula Bekkali, Member, IEEE Abstract Ultra high requency radio requency identiication (UHF RFID) systems can use passie tags to relect the signal rom the reader s transmitting antenna back to the reader s receiing antenna or inormation deliery. This gies a cascaded channel that is a product o two ading components. In this work, the probability o detection, deined as the probability that the receied power is aboe the receier sensitiity, is deried when the two ading components suer rom correlated generalized Rician ading. This includes the Rayleigh, Rician and Nakagamim channels in the literature as special cases. Numerical results are presented to show the eects o link distances, receier sensitiities and channel parameters on the detection probability. Index Terms Correlation, detection probability, generalized Rician, radio requency identiication. I. INTRODUCTION Ultra high requency radio requency identiication (UHF RFID) systems hae been widely used in arious applications. In these applications, passie tags proide a iable solution by receiing power rom the reader or battery-less operation. To enable such operation, two links are usually inoled: the orward link rom the reader to the tag that powers up the passie tag and the reerse link rom the tag to the reader that deliers inormation. In this case, the passie tag does not generate its own signal or inormation deliery. Instead, it simply relects the signal rom the reader with added modulation. This leads to a cascaded channel. Preious works on perormance analysis o UHF RFID systems include the ollowing. In [], the eects o arious channel impairments, including Rayleigh or Rician ading, on the link budget o the RFID system were discussed. Reerence [] examined the coerage probability or ast and slow ading channels using the Rician and log-normal models. The eect o material was also discussed. Reerence [3] considered the use o multiple RF tag antennas to achiee pinhole diersity. Numerical examples were obtained using Monte Carlo simulation. In [4], the reerse link interrogation range o the reader was analyzed as the distance at which a predetermined threshold or the receied signal-to-noise ratio at the reader can be achieed. Cascaded Nakagami-m ading channels or monostatic and bistatic structures were considered. In [5], the outage perormance o the RFID system with correlated orward and reerse links was obtained, assuming Rayleigh Yan Gao is with the School o Electronic Inormation, Nanjing College o Inormation Technology, Nanjing, China 003 ( gaoyan@njcit.cn). Yunei Chen is with the School o Engineering, Uniersity o Warwick, Coentry, U.K. CV4 7AL ( Yunei.Chen@warwick.ac.uk). Abdelmoula Bekkali was with Qatar Mobility Innoations Center, Doha, Qatar, during this work. Now he is with KDDI R&D Laboratories, Inc. Saitama , Japan ( bekkali@ieee.org) channels and multiple antennas at the reader. In the seminal paper [6], the authors proided a detailed analysis o the detection probability or a cascaded Rician ading channel. Based on the deried detection probability, the maximum distance, similar to that in [5], was calculated. The aorementioned works hae considered either Rician, Nakagami-m or Rayleigh channels. Howeer, it is well known that the generalized Rician model includes all these channels as special cases and thereore, can describe more small-scale ading conditions in the RFID system. Also, these works hae assumed either totally correlated orward and reerse links or the monostatic structure or independent orward and reerse links or bistatic structure. Howeer, in some cases, such as collocated backscatter, the transmitting antenna and receiing antennas o the reader may be close such that the orward and reerse links may only be partially correlated. Motiated by these obserations, in this letter, the perormance o passie UHF RFID system is analyzed in a cascaded channel with correlated generalized Rician ading. Closedorm expressions or the detection probability are deried. Numerical results are presented to show the eects o link distances, receier sensitiities and channel parameters on the detection probability. II. SYSTEM MODEL Consider the same system as that in [6]. The receied power at the tag in the orward link can be gien as [6, eq. ()] O r,t = ρ L O tx G T G R L(d ) h () where ρ L is the polarization loss incurred by the mismatch between the polarization o the reader s transmitting antenna and the tag s antenna, O tx is the reader transmission power, G T and G R are the antenna gains o the tag and the reader in the orward link, respectiely, L(d ) is the path loss, d is the distance in the orward link, and h is the ading coeicient in the orward link. Details about the deriation o () and its releant parameters can be ound in [6] and are not discussed here to sae space. Upon the reception o (), a backscatter signal is sent rom the tag to the reader. The receied power at the reader in the reerse link can thereore be written as [6, eq. ()] O r,r = τµ T ρ L O tx G T G R G RL(d )L(d ) Γ h h () where τ is related to the speciic coding and modulation schemes used at the tag, µ T is the power transer eiciency determined by the impedance between the tag s antenna and the rest o the tag, G R is the antenna gain o the reader in the reerse link, L(d ) is the path loss in the reerse link, d is

3 IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXXX XXXX the distance in the reerse link, Γ is the dierential relection coeicient o the tag, and h is the ading coeicient in the reerse link. One sees rom () that the receied power at the reader is determined by the cascaded channel gain h h. To detect the tag successully, the receied power o the tag in () must be larger than the tag sensitiity and the receied power o the reader in () must be larger than the reader sensitiity. Thus, the probability o detection can be deined as = Pr{O r,t >,O r,r > }. (3) In this work, the ading coeicients h and h are assumed to be correlated generalized Rician random ariables with joint probability density unction (PDF) gien by [7] h, h (x,y) = t m e (+λ σ 0 e W W m (λ σ λ σ ) m + λ σ )t Im (W t)x m e x I m ( xσ λ t Ω )y m e y I m ( yσ λ t Ω )dt, x > 0,y > 0 (4) where W = m l= (m 0l + m l ) represents the power o the line-o-sight (LOS) component in the channel, m 0l and m l are the in-phase and quadrature parts o the l-th LOS, respectiely, σ and σ represent the aerage ading powers in the orward and reerse links, respectiely, m is the shape parameter o generalized Rician, I m ( ) is the (m )- th order modiied Bessel unction o the irst kind [8, eq. (8.406.)], Ω = σ ( λ )/, Ω = σ( λ )/, λ and λ determine the correlation coeicient between h and h as ρ = λ λ with 0 < λ < and 0 < λ <. One can eriy that, whenm =, (4) becomes the joint PDF o two Rician random ariables, and when m = and W = 0, it becomes the joint PDF o two Rayleigh random ariables. Further, when W = 0, using [9, eq. (9.6.7)], it becomes the joint PDF o two Nakagami-m random ariables. Thus, the generalized Rician model can describe more RFID channel conditions. Also, i one integrates (4) oer x or y, the marginal PDF o a generalized Rician random ariable can be obtained or h and h, where their Rician K actors can be deried as W λ and W λ, respectiely, using [0, eq. (3)]. It is important to note that λ 0 and λ 0 in (4), as discussed in [7] and [0]. This means that the cases o independent links is not a special case o (4), that is, one cannot set λ = λ = 0 in (4) to obtain the joint PDF o two independent generalized Rician links. Thus, (4) can only describe the general correlation case. Next, the probability o detection is deried. III. DERIVATION Using () and () in (3), one has = Pr{ h > γ, h h > γ } (5) where γ = ρ LO txg TG R L(d ) τµ Tρ LO tx G T G R G R L(d )L(d ) Γ and γ =. Then, using (4) in (5), the detection probability can be calculated as = γ γ /x h, h (x,y)dydx. (6) To calculate (6), we simpliy (4) irst. Using [8, eq. (8.445)] to expand the Bessel unctions in (4) and using [8, eq. (6.643.)] to sole the resulting integral, one has h, h (x,y) = ( σ λ e W W m (λ σ λ σ ) m ) m +i ( σλ ) m +j x m +i y m +j i!j!γ(m+i)γ(m+j)e x + y Γ(m+i+j)e W U M (m/+i+j),(m )/ ( W U ) WΓU m/+i+j. (7) where Γ( ) is the Gamma unction [8, eq. (8.30.)], U = + λ σ + λ σ and M, ( ) is the Whittaker unction [8, eq. (9.0.)]. Using (7) in (6), the calculation o the detection probability boils down to the calculation o the double integral V = γ γ /x x m +i y m +j e x y dydx. (8) Using [8, eq. (3.38.3)] and [8, eq. (8.35.)], this gies V = m+j Γ(m+j)( ) m+j 4k!( /γ )k γ t m+i k e t γ t dt. (9) Finally, using the aboe results, the probability o detection is deried as = ( σ λ e W + W U W m (λ σ λ σ ) m m+j (0) ) m +i ( σλ ) m +j ( ) m+j Γ(m+i+j) i!j!γ(m+i)4k!( /γ )k ΓU m/+i+j M ( m +i+j),m ( W U ) γ t m+i k e t γ t dt. One sees that (0) has a computational complexity similar to that in [6] with two ininite series. Two special cases can be discussed to urther simpliy (0). First, i γ 0 or reerse link limited (RLL) systems, using [8, eq. (3.47.9)], one has ( σ λ e W + W U W m (λ σ λ σ ) m m+j ) m +i ( σλ ) m +j ( ) m+j Γ(m+i+j) i!j!γ(m+i)k!( /γ )k ΓU m/+i+j M ( m +i+j),m ( W U )(Ω γ γ () ) m+i k K m+i k ( ) Ω Ω Ω where K n ( ) is the n-th order modiied Bessel unction o the second kind [8, eq. (8.407.)]. Second, i γ 0 or orward

4 IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXXX XXXX 3 link limited (FLL) systems, using [8, eq. (3.46.3)] and [8, eq. (3.38.3)], one has e W + W U Γ(m+i+j) W m (λ σ λ σ) m ( σ λ Γ(m+i, ) m +i ( σλ ) m +j ( )m+i ( ) m+j i!j!γ(m+i)4γu m/+i+j γ )M (m/+i+j),(m )/ ( W ). () U The results in () and () are approximations but are closed-orm expressions. It can be eriied that the results or Rician channels can be obtained by setting m = in (0) - (). Also, the results or Nakagami-m channels can be obtained by setting W = 0 in (0) - (). For example, by setting W = 0 in (0), the result or Nakagami-m channels in the general case is = ( σ λ γ (λ σ λ σ ) m m+j (3) ) m +i ( σλ ) m +j ( ) m+j Γ(m+i+j) i!j!γ(m+i)4k!( /γ )k ΓU m+i+j t m+i k e t γ t dt where [8, eq. (9.0.)] and [8, eq. (9.0.)] can be used to expand the Whittaker unction. Equation (3) is deried rom (0) by using W = 0 only and does not use any other assumptions, including γ 0 or γ 0. For Rayleigh channels, the results can be obtained by setting W = 0 and m = in (0) - (). IV. NUMERICAL RESULTS AND DISCUSSION In this section, ollowing [6], we set G T = 0 dbi, O tx = +33 dbm,g R = G R = +9 dbi,τ =,ρ L =,µ T =, Γ = 0., the operating requency MHz, σ = σ =. The ininite series is truncated to 0 terms. Fig. shows the detection probability under dierent sensitiities or the correlated generalized Rician links. Firstly, rom Fig., the detection probability always decreases when the distance d increases, as expected, as larger distances lead to larger path loss such that the receied power is smaller or detection. Secondly, rom Fig., the detection probability decreases when the tag or reader sensitiities decrease. Howeer, is more sensitie to the tag sensitiity than the reader sensitiity in the case considered, as the tag needs to relect the signal back to the reader. It can also be shown that in this case the detection probability changes little when the distance d changes. This implies that the system is FLL, gien the settings used in this case, as the detection probability is much more sensitie to d than to d. To sae space, the relationship between and d is not presented here. Fig. shows the detection probability s. d or dierent W in correlated Rician links when m =. In this case, the Rician K actor is W λ and is determined by W or ixed λ. One sees that the alue o W has a signiicant 5 5 d = 3 m, W =, m = = -5 dbm = -70 dbm, = -5 dbm = -0 dbm d Fig.. s. d or dierent sensitiities when the orward and reerse links are correlated generalized Rician channels with λ =. 5 5 d = 3 m, = -75 dbm, = -5 dbm, λ = W =, m = W =, m = W = 3, m = W = 4, m = d Fig.. s. d or dierent W when the orward and reerse links are correlated Rician channels with λ =. impact on the detection probability. For example, when W changes rom to 4 at d = m, increases rom to, almost 50% increase. Fig. 3 shows the detection probability s. d or dierent Nakagami m parameters in correlated Nakagami-m links when W = 0. From this igure, one sees that the Nakagami m parameter has a signiicant impact on the detection perormance too. At d = m, the detection probability increases rom 0.45 to nearly, when the m parameter increases rom to 4, giing an increase o more than 00%. Thus, the detection perormance is more sensitie to the parameter m than to the parameter W. Fig. 4 compares the detection probability or dierent channel models included in the generalized Rician model when the orward and reerse links are correlated. As can be seen, the Rayleigh ading channel has the smallest detection probability, while the generalized Rician ading channel has the largest detection probability, as expected, as the Rayleigh ading is the worst channel condition while the generalized Rician ading is the best channel condition, among the cases considered. Fig. 5 shows s. d or dierent λ. In this case, λ = λ = λ = 0.,0.4,, such that ρ = λ =

5 IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. X, XXXX XXXX d = 3 m, = -75 dbm, = -5 dbm, λ = W = 0, m = W = 0, m = W = 0, m = 3 W = 0, m = d Fig. 3. s. d or dierent Nakagami m parameters when the orward and reerse links are correlated Nakagami-m channels with λ =. 0.04,,0.36,4, respectiely. One sees that increases when λ increases. Reerence [] reported that the perormance improes when the link correlation decreases or Rayleigh links. This can be explained as ollows. The alue o λ determines the correlation coeicient as ρ = λ, but also determines the Rician K actor in generalized Rician channels as W λ rom [0, eq. (3)]. From [], should decrease when λ increases, as ρ increases. Howeer, or generalized Rician ading, the perormance also improes when λ increases, as a largerλgies a larger Rician K actorw λ and thereore better channel conditions in the indiidual links. The oerall eect o λ depends on whether is more sensitie to ρ or the Rician K actor. It can be shown that in the setting o Fig. 5 the detection probability is more sensitie to the Rician K actor. Consequently, the Rician K actor dominates such that increases when λ increases. On the other hand, or Rayleigh links, λ only aects the correlation coeicient and hence the perormance degrades when λ increases, as in []. 5 5 d = 3 m, = -5 dbm W = W = 0, m =, Rayleigh W = W = 0, m =, Nakagami W = W =, m =, Rician W = W =, m =, generalized Rician d Fig. 4. The detection probability s. d or dierent channel models when the orward and reerse links are correlated with λ =. 5 5 d = 3 m, W =, m =, = -5 dbm λ = λ = λ = 0.4 λ = d Fig. 5. The detection probability s. d or dierent λ when the orward and reerse links are correlated generalized Rician channels. V. CONCLUSION Analytical results on the detection probability o the UHF RFID system hae been deried or cascaded correlated generalized Rician channels. Numerical examples hae shown that the detection probability is quite sensitie to the orward link distance, the channel conditions and the tag sensitiity. REFERENCES [] D. Griin and G. D. Durgin, Complete link budgets or backscatterradio and RFID systems, IEEE Antennas and Propagation Magazine, ol. 5, pp. - 5, Apr [] A. Lazaro, D. Girbau, and D. Salinas, Radio link budgets or UHF RFID on multipath enironments, IEEE Transactions on Antennas and Propagation, ol. 57, pp. 4-5, Apr [3] J. D. Griin and G. D. Durgin, Gains or RF tags using multiple antennas, IEEE Transactions on Antennas and Propagation, ol. 56, pp , Feb [4] D.-Y. Kim, H.-S. Jo, H. Yoon, C. Mun, B.-J. Jang, J.-G. Yook, Reerselink interrogation range o a UHF MIMO-RFID system in Nakagami-m ading channels, IEEE Transactions on Industrial Electronics, ol. 57, pp , Apr. 00. [5] Y. Chau, Outage perormance o RFID systems with multiple reader antennas oer correlated orward and backscatter ading channels, in Proc. st Annu. WOCC, Apr. 0, pp [6] A. Bekkali, S. Zou, A. Kadri, M. Crisp, R.V. Penty, Perormance analysis o passie UHF RFID systems under cascaded ading channels and intererence eects, IEEE Transactions on Wireless Communications, ol. 4, pp , Mar. 05. [7] N.C. Beaulieu and K.T. Hemachandra, Noel simple representations or Gaussian class multiariate distributions with generalized correlation, IEEE Transactions on Inormation Theory, ol. 57, pp , Dec. 0. [8] I. S. Gradshteyn and I. M. Ryzhik, Table o Integrals, Series, and Products, 7th edition. Academic, 007. [9] M. Abramowitz and I. A. Stegun, Handbook o Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 4th edition. Doer, 970. [0] Q. Shi, Y. Karasawa, On correlated generalized Rician ading based on Gaussian class multiariate distributions with generalized correlation, IEEE Communications Letters, ol. 6, pp , Dec. 0. [] J. Schlenker, J. Cheng, R.Schober, Improing and bounding asymptotic approximations or diersity combiners in correlated generalized Rician ading, IEEE Transactions on Wireless Communications, ol. 3, pp , Feb. 04. [] J.D. Griin and G.D. Durgin, Link enelope correlation in the backscatter channel, IEEE Communications Letters, ol., pp , Sept. 007.