Site-Specific Stochastic Propagation Model for

Automated RFID Network Planning

A. G. Dimitriou∗ S. Siachalou† A. Bletsas‡ J. Sahalos§

Abstract — In this paper, we propose a model tocalculate the probability of successful identificationof passive UHF RFID tags in a given environment.The validity of the proposed model is verified bycomparison with analytical ray-tracing results andmeasurements. The model can be included in auto-mated RFID network planning algorithms to evalu-ate the identification performance of different con-figurations.

1 INTRODUCTION

Radio Frequency IDentification (RFID) representthe key enabler of the ”Internet of Things” con-cept [1]. Among the key parameters for the market-penetration of the technology is to reliably designcomplex RFID networks that ensure excellent iden-tification performance.

In this context, we present a site-specific stochas-tic propagation model that is part of an automatedRFID site-selection planning problem. In auto-mated planning problems, one should select a sub-set, among a given a set of possible sites for in-stalling equipment (in our case RFID readers), sothat a given cost function is minimized (or maxi-mized) under specific quality of service constraints[2]. As the number of possible sites increases, theexact vector-solution cannot be calculated in rea-sonable time and search heuristics are invoked, e.g.genetic algorithm.

The typical reader-tag-reader link-model is pre-sented in [3]. Simple path-loss expressions aregiven. Stochastic propagation-prediction modelsare presented in [4]-[6]. The authors in [5] test dif-ferent stochastic models to better describe fadingin different indoor situations, e.g. Line Of Sight

∗Aristotle University of Thessaloniki, Dept. of Electricaland Computer Engineering, 54124, Thessaloniki, Greece, e-mail: antodimi@auth.gr, tel.: +30 6978896350.†Aristotle University of Thessaloniki, 54124, Thessa-

loniki, Greece, e-mail: ssiachal@auth.gr, tel.: +306977688284.‡Technical University of Crete, Dept. of Electronics

and Computer Engineering, Akrotiri Campus 73100 Chania,Crete, Greece, e-mail: aggelos@telecom.tuc.gr, tel.: +302821037377.§Aristotle University of Thessaloniki, 54124, Thes-

saloniki, Greece, e-mail: sahalos@auth.gr, tel.: +302310998161 and University of Nicosia, Dept. of Electricaland Computer Engineering,46 Makedonitissas Avenue 24005Nicosia, Cyprus, e-mail: sahalos.j@unic.ac.cy, tel.: +35722841740.

(LOS) or not (NLOS). In [6], the authors evaluatethe performance of different diversity schemes, as-suming Rayleigh distribution for fading. In [7], areading region is estimated as the ellipsoid, wherethe minimum power received from a two-ray model(considering only ground reflection), is greater thanthe wake-up threshold of the tag. The accuracy ofthe model depends on the position and direction ofthe reader’s antenna with respect to the environ-ment, as the basic assumption of the model is toconsider a reflection from a single surface.

Analytical ray-tracing calculations were pre-sented in [8]-[10], where maximization of thereader’s read-region was sought. Different methodsto minimize destructive interference effects, due tofading were proposed, including the introductionof a controllable phase shifter in multiple-antennasconfigurations.

In this paper, we model stochastically any site-specific environment, though we focus in a typicalroom. We consider a cubic calculations’ grid in-side the volume of interest and derive an appropri-ate Rice probability density function on each grid-point [11]. The Rice statistics for each calculations’point are derived by an analytic ray-tracing model.Then we calculate the probability of succesfull iden-tification of a tag anywhere in the volume underinvestigation, for a given ”wake-up’ tag-threshold.Furthermore, we derive the aggregate identifica-tion percentage in the entire volume of interest.We separately analyze identification performanceper tag’s polarization axis, as well as tag-diversityschemes. Performance of the proposed stochasticmodel is verified against analytic ray-tracing calcu-lations and measurements.

2 PROPOSED STOCHASTIC MODEL

2.1 Field at the Tag

Consider a transmitting antenna and a tag inside aroom, as shown in Figure 1. The total field at anypoint in the room can be evaluated as the phase-sum of several contributions that have traveled dif-ferent paths (multiple reflections, scattering). Duethe interactions with the environment, each pathhas suffered different losses and contributes to thetotal field with a different phase. By analyzing the

field at the receiver in orthogonal axes, the totalfield can be written as:

Etot =

√ηWt

2π(∑j

√Gt(φj , θj)Aje

i(2ωt+aj+krj)

rjx+

∑j

√Gt(φj , θj)Bje

i(2ωt+bj+krj)

rjy+

∑j

√Gt(φj , θj)Cje

i(2ωt+cj+krj)

rjz

), (1)

where Wt is the power of the transmitted car-rier, Gt(θj , φj) is the transmitting antenna’s gainat the direction defined by the horizontal and ver-tical angles φj , θj respectively, η is the free-spaceimpedance, k = 2π/λ, λ is the considered wave-length, rj the path traveled by the jth contributionand Aj , Bj , Cj size the field of each ray at thecorresponding polarization axis, defined by the or-thogonal vectors x, y, z, respectively.

2.2 Stochastic Model

Our target is to evaluate the read-range of a UHFRFID reader that identifies passive RFID tags.Considering the regulated maximum transmit-power constraints of the reader (∼35dBm EIRP),combined with the significant power needed by the(battery-less) tag to operate (∼-18dBm), the readercannot identify a passive tag blocked behind an ob-ject (succcesful identification of a blocked passiveRFID tag could occur only at very close proximitywith the reader’s antenna, ∼cm). Hence, a LOSstrong path should be present in the reader’s read-ing region. The propagation conditions of the prob-lem justify the selection of the Rice distribution tostochastically describe the expected fading. TheRice probability density function assumes the exis-tance of a strong path (in this case the LOS) andseveral smaller contributions (multiple reflections).The probability density function is given by:

f(x|ν, σ) =x

σ2e

(−(x2+ν2)

2σ2

)I0

(xν

σ2

). (2)

In (2), ν2 is the power of the LOS path and 2σ2 isthe average power of the other contributions. Thecumulative distribution function is given by:

FX

(x|ν, σ) = 1−Q1

(ν

σ,x

σ

), where

Q1 is the Marcum Q-function. (3)

Perspective

x

zy

Volume of Interest

Tx

z-slicetag

Figure 1: Representation of the modeled geometry.

In order to evaluate the probability of success-ful identification on a given point, we need to sep-arately calculate the LOS power and the averagepower of all other contributions at the location ofinterest. We expect the phases of the multiply re-flected rays to be uncorrelated, because of the largepath-length differences of the multipath compo-nents, with respect to λ; in (1), 2π(rm−rm−1)/λ�2π, ∀ m and rm − rm−1 6= rj − rj−1, ∀ m 6= j. Weconsider the phases of the multipath componentsas random variables identically and independentlydistributed, uniformly over [0,2π]. Under these as-sumptions, it can be shown that the average re-ceived power due to the terms in (1), except forthe LOS contribution, is given by the appropriatesum of the square of the magnitudes, [12], of eachcontribution. The average power on a receiving an-tenna with unity gain per polarization axis is thegiven by:

Px =ηWt

2π

∑j 6=LOS

Gt(φj , θj)A2j

rj,

Py =ηWt

2π

∑j 6=LOS

Gt(φj , θj)B2j

rj,

Pz =ηWt

2π

∑j 6=LOS

Gt(φj , θj)C2j

rj. (4)

We consider a calculations’ grid with M points inthe volume of interest. A passive tag is consideredsuccesfully identified if the power that reaches thetag is greater than its ”wake-up” threshold γ. Oneach position of the grid l, we calculate the proba-bility that a tag is succesfully identified as:

Pl(X ≥ γ) = 1− FX

(γ|νl, σl), (5)

-18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Iden

tific

atio

n Pe

rfor

man

ce

tag's threshold (dBm)

X-Pol Model Y-Pol Model Z-Pol Model XYZ-Pol Model X-Pol Anal. Y-Pol Anal. Z-Pol Anal. XYZ-Pol Anal.

Figure 2: Comparison between stochastic model andanalytical ray-tracing predictions.

x axis of the room (m)

y ax

is o

f the

room

(m)

Probability of reception x polarization

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

prob

abili

ty

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 3: Probability of successful identification of X-polarized tags for γ =-14dBm.

where FX

(γ|νl, σl) is given in (3); ν2l is the powerof the LOS path on the polarization axis of thetag and 2σ2

l is the power of the multiply reflectedcontributions, calculated by applying (4) for thetag’s polarization axis. As a consequence, fadingand the associated identification-probability is sep-arately evaluated at each location in the volumeof interest depending on the site-specifically cal-culated parameters of the distribution. Let U(γ)represent the percentage of the volume of interestV , where succesful identification of passive tags isaccomplished. U(γ) is evaluated as:

U(γ) =

∫V

PdV (X ≥ γ)dV =1

V

M∑l=1

Pl(X ≥ γ)dVl

(6)For a cubic calculations’ grid, with equal spac-ing among grid points, (6) reduces to U(γ) =∑M

l=1 Pl(X ≥ γ)/M .

x axis of the room (m)

y ax

is o

f the

room

(m)

Probability of reception y polarization

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

prob

abili

ty

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 4: Probability of successful identification of Y-polarized tags for γ =-14dBm.

3 RESULTS

We consider a 7dBic-gain circularly polarized(along the X and Z axes) reader-antenna, placed onthe center of a 4m-length wall, inside a 4m×5m×3mroom, as demonstrated in Figure 1. We calculatethe probability of successful identification for in-creasing tag’s threshold γ from -18dBm to -8dBm,by applying (4)-(5); then we calculate the percent-age of successful identification in the volume of in-terest from (6) for all polarizations and tags’ diver-sity. The results are compared with the correspond-ing results from an analytical ray-tracing model,where the percentage of succesfully identified tagsin the same volume of interest is calculated. The re-sults are summarized in Figure 2. Very good agree-ment is recorded for all polarizations and thresh-olds.

The probability of identification for X and Y po-larized tags, considered 1.1m above the ground, isdemonstrated in Figures 3-4. Notice the correctlycalculated reduced probability of identification forY polarized tags, as the reader’s antenna is polar-ized on the X and Z axes.

Comparison of the performance of the pro-posed model with measurements conducted in a3m×3.5m×3m room are given in Figures 5-6. Thetransmitted power from the reader was reducedfrom 30dBm to 15dBm. Details on the measure-ments can be found in [9]. Very good agreementwas again recorded.

4 CONCLUSIONS

In this work, we presented a stochastic model thatexploits site-specific data to evaluate the identifi-cation performance of RFID systems, employingpassive UHF tags. Performance of the model was

Thread

Tx Position: (x,y,z)=(1.75, 0, 1.45)Orientation (Hor, Downtilt)=(90°, 0°)

Measurements’ Configuration I

3m

3.5m

Tx

x

zy

Tags

7dBic Tx antenna

Figure 5: Measurements of orthogonally polarized tagsin a room.

30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 150.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Iden

tific

atio

n Pe

rfor

man

ce

Transmitted Power (dBm)

X-pol Meas. Z-pol Meas. XZ-pol Meas. X-pol Model Z-pol Model XZ-pol Model

Figure 6: Comparison between model estimations andmeasurements in a room.

validated from measurements and comparison withanalytical solutions. Further work should focus onacceleration techniques, e.g. reducing the numberof multipath components involved.

Acknowledgments

This research has been co-financed by the EuropeanUnion (European Social Fund-ESF) and Greek na-tional funds through the Operational Program ”Ed-ucation and Lifelong Learning” of the NationalStrategic Reference Framework (NSRF) - ResearchFunding Program: THALES. Investing in knowl-edge society through the European Social Fund.

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