Placement of multiple RFID reader antennas to maximise portal read accuracy

Int. J. Radio Frequency Identification Technology and Applications, Vol. x, No. x,x 1

Placement of Multiple RFID Reader Antennasto Maximize Portal Read-Accuracy

Lin Wang, Bryan A. Norman* andJayant Rajgopal

Department of Industrial Engineering,School of Engineering, University of Pittsburgh,Pittsburgh, PA, 15212Fax: 412-624-9830E-mail: [email protected]: [email protected]: [email protected]∗Corresponding author

Abstract: A critical factor in the adoption of Radio Frequency Identi-fication (RFID) technology is the level of read-accuracy that is achieved.With passive tags, the read-accuracy depends on the volume of the re-gion that receives sufficient power from the reader. Most current re-search considers the powering region of a reader to be determined onlyby its read range (i.e., distance). However, read-accuracy also dependson the relative orientations of reader and tag antennas and their polar-izations. In particular, when tag positions are not fixed, the locations ofreader antennas relative to the tags can have a significant effect on thesuccess of the interrogation processes. This paper uses Friis’ Equationto explicitly consider orientations and polarizations while addressing theproblem of determining the best locations for a set of reader antennas ata scanning portal. The objective is to maximize the size of the poweringregion in order to maximize read-accuracy. A methodology for deter-mining the powering region with multiple antennas is developed alongwith an enumeration approach to determine optimal antenna locations.

Keywords: RFID; Antennas; Automatic Identification; Optimization.

Reference to this paper should be made as follows: Lin Wang, BryanA. Norman and Jayant Rajgopal (2007) ‘Placement of Multiple RFIDReader Antennas to Maximize Portal Read-Accuracy’, Int. J. RadioFrequency Identification Technology and Applications, Vol. x, No. x,pp.xxx–xxx.

Biographical notes: Lin Wang received his Bachelor’s degree in Me-chanical Engineering from Shanghai JiaoTong University in China. Heis a Ph.D. candidate in the Department of Industrial Engineering at theUniversity of Pittsburgh. His research are centered around issues relatedto RFID in supply chains.

Bryan A. Norman received his Ph.D. in Industrial and Operations En-gineering at the University of Michigan. His primary research interests

Copyright c© 200x Inderscience Enterprises Ltd.

2 Lin Wang, Bryan A. Norman and Jayant Rajgopal

include logistics and the application of operations research models toproduction and logistics systems. In particular, his research foci in-clude scheduling resources and personnel in both manufacturing andservice organizations and methods for achieving efficient facility designand material handling in manufacturing and service environments. He isa member of the University of Pittsburgh’s RFID Center for Excellenceand conducts research related to the application of RFID technologiesto enhance supply chain management and for asset management andcontrol. Dr. Norman also conducts research concerning manufacturingprocess analysis and energy modeling. His research has been funded bythe National Science Foundation, the state of Pennsylvania, and com-panies both in Western Pennsylvania and across the country.

Jayant Rajgopal holds a Ph.D. in Industrial and Management Engi-neering from the University of Iowa, and has been on the faculty of theDepartment of Industrial Engineering at the University of Pittsburghsince 1986. His main areas of interest are optimization, supply chains,system reliability, and RFID applications; he has taught, conductedsponsored research, published papers and consulted in all these areas.He is a senior member of the Institute of Industrial Engineers, and theInstitute for Operations Research and the Management Sciences, and isa licensed professional engineer in the state of Pennsylvania.

1 Introduction

In recent years, Radio Frequency Identification (RFID) has attracted a lot ofattention and experienced strong growth in industrial applications (Woods, 2005).Much of this has been fueled by mandates from Wal-Mart and the Departmentof Defense, but many other companies are independently recognizing the potentialbenefits from using RFID technology, which is becoming increasingly common inapplications where tracking of physical objects in real time is needed. Examples in-clude production, logistics, supply chain management and asset tracking (Gaukler,2005; Michael and McCathie, 2005; Lee et al., 2004; Asif and Mandviwalla, 2005).Although RFID is often referred to as the next-generation bar code, one of theissues that troubles end-users is that RFID tags usually cannot be read with 100%accuracy (Rothfeder, 2004) in the real world due to factors such as limitations inthe read range, tag orientation or interference (from water, metal or other tags)(Ramakrishnan, 2005; Penttil et al., 2006). In item-level applications, this can bea major issue since a missed read might mean a lost sale. Another complicatingfactor is that in RFID scanning processes the locations of tags are often not fixedexactly because items are of different sizes and might be moving on a truck, mate-rial handling equipment such as a pallet, forklift or conveyor belt, or even within acontainer. However, it is usually possible to specify some three dimensional spacewithin which the tags are known to lie. To mitigate the problem of imperfect read-rates, multiple readers or a reader with multiple antennas are commonly used forentry way, portal or overhead scanning. (Note: Sometimes the term read-rate isused to refer to the rate of transfer of data to a reader; in this paper we use theterm to indicate the the likelihood that a tag is correctly read by a reader.) Giventhat tag locations cannot be isolated and fixed, an important first step in maxi-

Placement of Multiple RFID Reader Antennas to Maximize Portal Read-Accuracy 3

mizing tag read-rates is to optimize and fix the locations of multiple RFID readerantennas so that the powering region within some given three dimensional space ismaximized.

The RFID reader antenna location problem could be viewed as falling into thegeneral domain of 3D coverage in wireless communications. Examining some of theprior work in this area, Huang et al. (2004) proposed a polynomial algorithm for theα-coverage wireless sensor networks problem. In their problem the sensing range ofeach of α different sensors was assumed to be a sphere. Path loss and interference forindoor applications are considered in Panjwani et al. (1996), while Rajkumar et al.(1996) use a ray tracing approach to predict radio frequency coverage. In Adickeset al. (2002), a heuristic algorithm using a ray tracing method is used to optimizethe layout of indoor wireless networks. However, these researchers use read range(Nikitin et al., 2005) as a basis for the coverage calculation and consider the powerreceived by an RFID tag to only be related to the path that the signal traverses,therefore neglecting the factors of orientation or polarization of the antennas inboth the RFID readers and the tags. The maximum read range used in all of theabove research can only be obtained when the antennas are perfectly aligned, i.e.,at the most favorable orientation. The read range obtainable at some other antennaorientation is dependent upon the radiation pattern, which might differ based onthe specific design used for the antenna (Ramakrishnan, 2005; Keskilammi et al.,2003). In particular, a non-omni-directional antenna is orientation-sensitive so thatwhether a tag with such an antenna can be activated depends not only on its relativedistance to the reader but also the relative orientations of the tag and the reader.

In many RFID applications, such as mixed totes and item-level tracking, usersmight not have full control over the tag orientations. Therefore there is a needfor a more comprehensive model in which orientations are included in the coveragecalculation. Such a model based on Friis’ Equation was first proposed by Greene(2006); Greene and Mickle (2006) for a single reader with a single antenna, and tocompensate for the increased computational complexity resulting from the addeddimensions of orientations and polarizations, a scaling factor was used. While thiswork constitutes a significant contribution it is valid only for the case of a singlereader with a single antenna. Extending this work to the situation when multiplereader antennas are involved is a complicated task, and the powering regions for aspecified read-rate cannot be determined by simply merging the regions obtainedfrom several single reader antennas considered individually. This paper provides amethodology for accomplishing this task and for then determining the number andthe locations of multiple reader antennas to maximize the overall powering region.

The use of multiple reader antennas to increase the chances of successful RFIDinterrogation is not new. However, typically the locations of these antennas are de-termined by trial and error and ad hoc techniques that are in the design engineer’s“back pocket”. To our knowledge, this work represents the first effort to system-atically analyze from a theoretical viewpoint issues such as (1) how to determine asuitable powering region with multiple antennas, (2) how to place multiple antennasat a portal or other large space, (3) why certain locations are better than others,and (4) how many antennas are required and what marginal benefit can be gainedfrom additional antennas. It should be emphasized that our approach provides atheoretical upper bound with respect to readability that can be used as a sounddesign starting point; clearly, factors that cannot be controlled or systematically


modeled (e.g., reflection, scattering, interference) need to be considered along withphysical experimentation in order to arrive at the final design.

The remainder of the paper is organized as follows: Section 2 provides theproblem statement and the assumptions made. Section 3 discusses Friis’ Equationin detail and presents some preliminary background and results. The antennaplacement methodology is presented in section 4 , followed by numerical examplesin Section 5. We present our conclusions and discuss directions for future work inSection 6.

2 Problem Statement and Assumptions

2.1 Problem statement

Before the problem is stated, we first define some of the terminology used inthis paper.

tag space — A three-dimensional region within which RFID tags can be locatedduring the interrogation processes.

read accuracy — The percentage of all possible orientations of a tag that canbe adequately powered by one or more of the reader antennas (given the locationof the tag within the tag space and the locations of a set of reader antennas).

100α% read accuracy region — The set of all locations within the tag space thatcan achieve at least 100α% read accuracy (given the locations of a set of readerantennas).

100α% coverage fraction — The ratio between the volume of the 100α% readaccuracy region and the volume of the tag space.

Given the locations and orientations of the reader antennas along with a specifictag location, if we assume that any orientation for the tag is equally likely, thenthe read accuracy could also be interpreted as the probability that the tag at thespecified location can be read.

In our problem we are given N potential locations where we can place one ormore of a set of n reader antennas along with a fraction α, and we assume that thetag space is discretized into L points. The objective is to determine the numberof reader antennas n, along with their locations, so as to maximize the number ofpoints in L that can be powered with at least 100α% read accuracy, i.e., to maxi-mize the coverage fraction. In the context of this problem, the solutions space forthe antenna locations is restricted to the N potential locations given in advance,and the term “optimal solution” is with respect to this solution space. It should benoted that the solution obtained approaches the ideal one as we increase the num-ber of potential reader antenna locations and the granularity of the discretization.However, it is not necessary to pinpoint the exact locations because most readerantennas are several orders of magnitude larger than tags.

Fig. 1 shows an example where items moving on a conveyor have to be scannedas they go through a portal-like structure. Assume that up to n separate readerantennas can be placed along the beams of the structure. Then our problem is tofind the number of reader antennas and their locations so that the coverage fractionfor the portal is maximized.


Figure 1 A conveyor scanning example

2.2 Assumptions

RFID relies on frequency waves that transmit a signal to activate a transpon-der (tag) which in turn transmits data back to an antenna. The success of anyRFID application, therefore, depends on the wireless links between antennas andtransponders. There are two components to the wireless link: the power link andthe data link. The first component refers to the amount of power received by thetransponder - the tag will not work unless the power and voltage level are above acertain value. The second component refers to the ability of the reader to receivethe signal from the transponder and is a function of the reader’s sensitivity. Forease of exposition, in this paper we focus only on the power link and assume thata reader with a sufficiently high sensitivity is chosen, so that a tag can always suc-cessfully backscatter its data back once it is powered sufficiently. Although the datalink is not considered, it is determined by a function of the radar cross section ofthe tag antenna and can be examined with an approach similar to the one describedhere in order to determine the minimum reader sensitivity required.

To improve read accuracy it is possible to either use multiple readers or multipleantennas for a single reader (or perhaps a combination of both). In this work weassume that there is a single reader with multiple antennas and that the antennasare synchronized with the reader such that only one antenna at a time is active;.Thus there is minimal interference between the antennas (caused by residual signals)and we therefore do not consider these possible interference effects.

There are many different types of RFID tags and antennas. We select themost commonly used ones for analysis in this paper: a patch antenna with circularpolarization for the reader and a half-wave dipole antenna for the tag. Most RFIDreaders use the first type of antenna since they are less sensitive to tag orientations.Similarly, passive backscatter tags (Rao, 1999) with half-wave dipole antennas arecommon in far-field applications and usually have longer read ranges than inductivetype tags (Finkenzeller, 2003).

Finally, we assume that the interrogation process is under ideal conditions infree space. There are two reasons that tag visibility issues such as shadowing andinterference are not considered in this paper. First, while it is true that in realityreflection, scattering, diffraction and shadowing may occur in signal propagation,the read range (Nikitin et al., 2005) for a typical passive backscatter RFID tagwhen reader antennas and tags are perfectly aligned, is usually between 0.3 meterand 6 meters depending on the operational power of the readers and other factors;


thus the multi-path effects are not significant for most such applications. Secondly,effects such as interference, shadowing, scattering and mutual coupling, etc. arehard to control or model explicitly. In general, such effects decrease the actualcoverage fraction. Therefore results obtained from the free space assumption canbe viewed as an upper bound on the real coverage fraction.

3 Background

In this section, we first review how to calculate the power received by an RFIDtag using Friis’ Equation. Following this we discuss how Friis’ Equation can beused to compute read-rates with a single reader antenna.

3.1 Friis’ Equation

The power received by an RFID tag is determined by Friis’ Equation, which islisted below (Balanis, 1997).

PR = PTGT (θT , φT )GR(θR, φR)λ2

(4πr)2· (1− |ΓT |2)(1− |ΓR|2)|p̂T · p̂R|2 (1)

where:PR — received powerPT — transmitted powerr — distance between the transmitter (reader)

and the receiver (tag)(r, θT , φT ) — location of the receiver relative to the transmitter(θR, φR) — relative orientation of the receiverGT (θT , φT ) — transmitter gainGR(θR, φR) — receiver gainΓT — transmitter reflection coefficientΓR — receiver reflection coefficientp̂T — transmitter polarization vectorp̂R — receiver polarization vectorλ — wavelength

The reflection coefficients ΓR and ΓT account for the impedance mismatch be-tween the antenna and circuitry, which are introduced in the simple modulation ofthe backscatter (Greene, 2006). In an ideal situation its value is 0, which means nopower will be reflected back due to mismatch. In reality its magnitude is between 0and 1 depending on the circuit design. In this research, we assume |ΓR| = |ΓT | = 0.The squared dot product of the polarization vectors |p̂T · p̂R|2 is called the polar-ization loss factor (PLF) and reflects the loss due to the mismatch between thepolarization of a transmitter antenna and a receiver antenna. When readers have acircular-polarized antenna, the PLF is 0.5 no matter what polarization the dipoletag antenna has (Finkenzeller, 2003). Finally, the transmitter and receiver antennagains are determined by θT , φT , θR and φR. The convention used in this paperis described in the next subsection along with a discussion on the computation ofantenna gains.


3.2 Antenna Gains

In (1), the antenna gain is not a constant. Rather, it is a function of theantenna’s own orientation. Let θ (zenith) and φ (azimuth) be spherical coordinatesthat are used to define an orientation. The convention followed in this paper is thatφ is the angle with the x-axis in the x-y plane, while θ is the angle with the z-axis;Fig. 2 illustrates this convention.

Figure 2 The spherical coordinate system

P

x

y

z

r

o

f

θ

We start by defining the reader axis as the straight line connecting the centerpositions of the reader and the tag. As mentioned in the previous section, there aretwo types of antennas used in this study (a half-wave dipole antenna for the tagand a patch antenna for the reader), neither of which radiates power isotropically.

For a half-wave dipole antenna (tag), we first define the z-axis as the antennadirection. Then θR is defined as the angle between the reader axis and the antennadirection, while φR is the angle between the projection of the reader axis on to thex-y plane and the x-axis; this is illustrated in Fig. 3.

Figure 3 Dipole Antenna Angle Definition

r

y

x

z

Dipole

antenna

θr

fr

With the preceding coordinate definition, the following formula in Greene (2006)for a dipole antenna’s gain shows that it is omni-directional (Balanis, 1997) and


only depends on θR.

GR(θR, φR) = 1.641[cos(π

2 cos θR)sin θR

]2

(2)

Based on (2), a half-wave dipole antenna’s gain is a function of θR with a periodof π and is symmetric about θR = π/2. From Fig. 4, it can be seen that at thedirection which is perpendicular to the antenna, the gain reaches its peak of 1.641.However, if a reader is aligned parallel to that of the antenna direction, theoreticallyno power can be received by the tag.Figure 4 A half-wave dipole antenna’s gain versus θR

0π

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

GR

θR

π/2

For a patch antenna (reader), the gain function is given by Greene (2006)

GR(θT , φT ) = 3.136[sin θT

sin(π2 cos θT )cos θT

cos(π

2sin θT sin φT )

]2

(3)

In (3), θT and φT are defined as in Balanis (1997) and shown in Fig. 5.Figure 5 A patch antenna and its coordinate system

Fig. 6 shows a particular patch antenna gain in three dimensional space. Thegain has a football shape with its maximum gain obtained in the direction which isperpendicular to the patch surface; we define this to be the direction of the x-axis.Any cutting plane parallel to the patch surface will result in a cross section that isa perfect circle. This means that the radiation pattern will not change if the patchsurface rotates in its own plane (the y-z plane). In other words, once the x-axis isdefined, how we define the exact direction of the y and the z axes does not affectthe patch antenna gain, so that the radiation pattern of a patch antenna is fullydefined by its position and its direction of maximum gain. In particular, we cansimplify (3) further by choosing the z-axis such that the reader axis is contained in


Figure 6 Patch antenna gain in three dimensional space

the x-z plane. Then φT = 0 and θT = π/2 -(angle between the reader axis and thex-axis).

3.3 Read accuracy analysis for the single reader case

Friis’ Equation gives the power received by an RFID tag given the positions andorientations of the tag and the reader antenna. Suppose that at a fixed location wediscretize the set of all possible orientations of an RFID tag into M unit vectors;then Friis’ Equation needs to be evaluated M times to compute all possible valuesof the power that could be received at that location. The tag’s position is defined aspossessing 100α% read accuracy as long as αM of the values computed are greaterthan Pmin, the minimum operational power required to activate the tag.

The characteristics of a dipole antenna’s gain analyzed in the previous subsectioncan simplify the procedure used to evaluate each individual position in our searchspace. In Friis’ Equation, given the information on the location and orientation ofthe reader antenna and the location of the tag, all variables are fixed except θR andφR. From Fig. 4 and (2), a dipole antenna’s gain is a sine-shaped function of θR.Therefore if we replace PR by Pmin, we can find a value θmin from (1) such that anyorientation which forms an angle with the reader antenna axis that is smaller thanθmin will not be readable. This makes the evaluation much more efficient becauseat each location one only needs to evaluate orientations with θ ≥ θmin.

4 Methodology

4.1 Read accuracy analysis with multiple reader antennas

For a single reader antenna, the 100α% read accuracy region is fixed with respectto the reader antenna’s location. However, with more than one reader antenna, theset of locations with 100α% read accuracy is not simply the union of the individuallocations with 100α% read accuracy. Consider Fig. 7, where a unit ball is usedto represent all possible orientations for an RFID tag located at the center of the


sphere. Suppose α is specified as 0.95, and suppose further that each of the twoRFID reader antennas shown can cover only 90% of all orientations. By definition,the current tag position does not meet the read accuracy specifications for eitherreader antenna individually. However, because the unreadable orientations mightbe mutually exclusive with respect to each other, it is possible that all orientationscould be covered by at least one of the reader antennas; hence the position canactually be read with 100% accuracy using two reader antennas. Thus, the unionof the 100α% read accuracy regions for each reader antenna in a set of readerantennas potentially underestimates the real coverage volume of the set of readerantennas because there might be points that could be considered unreadable byevery reader antenna individually, yet would be readable when all of the readerantennas are considered jointly.Figure 7 Unreadable orientations for the two-reader antenna case

RFID reader antenna 1

RFID reader antenna 2

Another complicating factor with multiple reader antennas is that the shapeof the 100α% read accuracy region can be irregular and hard to define. There isno straightforward way of adapting the scaling factor used in Greene (2006) forcalculating the boundary of the 100α% read accuracy region because the scalingfactor was based on the fact that with one antenna, all points in the tag spacecould be characterized in a binary manner as 100α% readable or not. However,with multiple reader antennas one cannot use a binary classification obtained witheach individual antenna. Rather one must evaluate the extent to which a point isreadable by the set of reader antennas. The proposed method accomplishes this bydiscretizing the set of possible orientations and then determining if 100α% of theseare readable by one or more of the reader antennas. Moreover, the 100α% readableregions might not be contiguous when one considers multiple reader antennas atdifferent locations.

4.2 Uniform discretization of orientations

Typically, in item-level applications tags can randomly take on many differentorientations. To determine the 100α% read-accuracy region it is necessary to beable to represent and evaluate the readability of all these different possible tagorientations. In this research, the tag orientations are modeled as M discretizedunit vectors on a unit sphere. If there is no bias towards a specific orientation


then each of the M discretized unit vectors describing these orientations should beuniformly distributed on a unit ball.

The conventional approach is to discretize uniformly around the latitude andthe longitude (e.g., say every 3◦ from 0◦ to 360◦); however this approach leads to abiased sample which is highly anisotropic and has a stronger concentration of direc-tions pointing towards the poles. Determining the optimal uniform configurationof the orientation vectors is a hard problem (Croft et al., 1991; Saff and Kuijlaars,1997). Before any method is discussed, we need to first examine what it means tosay ”uniformly distributed on a unit ball.” While a continuous spherical uniformdistribution is explicitly defined by Fisher et al. (1987), there is unfortunately nosingle definition of a corresponding discretized uniform distribution. Researchersin different fields such as geometry, climate modelling, molecular structure or elec-trostatics have studied the problem with their own definitions, each of which maylead to some slightly different distribution (Croft et al., 1991; Katanforoush andShahshahani, 2003). In Saff and Kuijlaars (1997), a set of generalized spiral pointsare constructed with an explicit closed form. In this paper, an approximation algo-rithm provided by Rusin (1998) is used, which is essentially a simplified version ofa generalized spiral set method. In this approximation method, a sphere is first cutby a series of evenly spaced horizontal planes, each of which forms a latitude circleon the sphere. On each latitude circle, points are placed so that the arc distancebetween each pair of adjacent points is the same. This distance is kept the samefor all of the latitude circles. Thus, circles closer to the pole have smaller radii andsubsequently a smaller number of points on them. The detailed algorithm is listedbelow.

input : Moutput: M unit vectors

K ← b√4π·Mc;Divide a meridian into K equal segments with K − 1 points(p1, p2, . . . , pK−1);for i ← 1 to K do

Draw a latitude circle Ci at each pi;Divide Ci into b2K·cos(−π

2 + i·πK )c equal segments;

endAdd two points from each pole;

Algorithm 1: Approximation algorithm for M uniform-distributed unitvectors on a unit ball

Therefore, the total number of points is given by∑b√4π·Mci=1

⌊2b√4π·Mc· cos

(− π2 + i·π

b√4π·Mc)⌋

+ 2.This number will be slightly different from M due to rounding. The value of M hasa great impact on the complexity of the problem and the precision of the solution;therefore it is beneficial to use as small a value as possible without compromisingprecision. How to select an appropriate value of M will be discussed in the nextsection.


5 Numerical Examples

In order to evaluate our approach to the reader antenna placement problem, adetailed numerical analysis was conducted using the portal structure shown in Fig.8.Figure 8 A portal design with 18 candidate reader antenna positions

In Ex. 1, which is shown in Fig. 8, a portal with dimensions 3×3×3 m3 has18 candidate reader antenna positions on three walls spaced at 0.5 meter intervals.The smaller cube (2×2×2 m3) inside the portal represents the tag space, i.e., theset of all possible tag locations during the interrogation processes. Ex. 2 furtherallows each of the 18 reader positions to have three antenna orientations: 45◦, 0◦

and −45◦ respectively. In our tests, we set n to either 2 or 3 in both examples, andused a value of 90% for the required read accuracy. The transmit power from anRFID reader was assumed to be 0.5W with 50µW needed to activate an RFID tagthat operates at 915MHz. The remainder of this section discusses the results andthe impact of different parameter settings on the results. All of the computationaltests were conducted on a PC with a 2 GHz Pentium-4 CPU and 512 MB of RAMrunning Windows XP Professional.

5.1 Enumeration

To solve this problem, we propose an enumeration method. The actual enumer-ation scheme is straightforward for a given number of reader antennas n: assumethe tag space has been uniformly discretized into L points and the orientationsinto M directions using the procedure described in Section 4.2. Now suppose wehave reader antennas mounted at n specific locations (out of the N possible loca-tions). We start with the first reader antenna and evaluate each of the L locationsfor readability using the procedure described in Section 3.3: a point is consideredreadable if at least 100α% of the M possible orientations at the point receive suffi-cient power for a tag to operate. We then consider the second reader antenna andevaluate those points that are not covered by the first reader antenna, and thenthe third reader antenna while evaluating points not covered by the first two readerantennas, etc. At the end of this pass we have a determination of the total number


of points that are readable with the current locations for the n reader antennas.The process is repeated for each of the CN

n choices of reader antenna locations tofind the one that yields the maximum coverage fraction across the tag space.

Although theoretically the optimal solutions can always be found by using theabove scheme, the computational effort increases tremendously with an increasein search resolution. For example, when the number of orientations M is equalto 450, it took a little over 1 hour to solve the three-reader antenna placementproblem for Ex. 2 using 0.2 meters as the resolution for the tag space. When asearch resolution of 0.1m was used, it took about 86 hours to solve the two-readerantenna placement problem for the same example. In general there are a maximumof CN

n ×L×M evaluations possible and L rises rapidly with an increase in the tagspace resolution: for our example, going from 0.2 to 0.1 meters increases this fromabout 1,000 to about 8,000. Of course, not all of these evaluations need to be donebecause at each specific choice of locations for the n reader antennas (1) we onlyneed to evaluate (for a given reader antenna) points that are not covered by readerantennas previously evaluated, and (2) the number of orientations evaluated at eachpoint is usually less than M because of the discussion in Section 3.3. It is also truethat some combinations of reader antenna locations can be easily eliminated basedon past experience and knowledge, although this sort of preliminary eliminationbecomes much more difficult if at a specific location each reader antenna also has theflexibility of being placed with different orientations as in Ex. 2. Furthermore, whendifferent reader antenna orientations are permitted, the value of N also increases,which makes enumeration more difficult. Nevertheless, by limiting the size of N , theenumeration method can provide good solutions as initial input for other approachessuch as integer programming or heuristic methods.

In summary, exhaustive enumeration is feasible but can be very time-consuming.The time complexity is determined by the number of search points (L), the numberof orientations (M), the number of candidate reader antenna locations (N) and thenumber of reader antennas to be placed (n). An increase in the value of any of theparameters will result in increased computational time, albeit to a different degree.In the next subsection we analyze the appropriate setting for these parameters sothat optimal or near-optimal solutions can be found within a reasonable amount oftime.

Before doing this we mention that with a resolution of 0.1 meter for the tagspace and 450 possible orientations for the tag antenna at each location the optimalsolution for Ex. 1, which chooses positions 3 and 16, will cover 71.8% of the 8,400 taglocations with 90% read accuracy. When three reader antennas are to be placed,the extra reader antenna, which is placed at position 9 in the optimal solution,increases coverage by another 14.8%. In other words, the extra reader antennaresults in coverage of approximately 1.18m3 more of the tag space with 90% readaccuracy. Even though reader antennas may be placed with different orientationsin Ex. 2, the optimal solution yields the same set of reader antenna locations withreader antennas mounted perpendicular to the walls.

It is interesting to note that the solution to the two-reader antenna problem(using locations 3 and 16) may seem counterintuitive. However, Fig. 9 indicateswhy the optimal solution selects two reader positions that are directly across fromone another (Fig. 9 is not drawn precisely to scale but shows the general antennacoverage relationships). The regions covered by the reader antennas at locations


Figure 9 Coverage illustration by optimal two reader antennas placement

3 and 16 do intersect with one another which results in a small area of doublecoverage. This double coverage is inefficient with regard to maximizing the overallcoverage region. However, in addition to the 90% read accuracy region generatedby each reader antenna, each of the reader antennas also provides less than 90%coverage to areas surrounding their 90% read accuracy region. For example, theremay by a point just outside of the 90% read accuracy region for the reader antennaat location 3 that has 89% read accuracy based only on the reader antenna atlocation 3 but exceeds the 90% threshold when the orientations covered by thereader antenna at location 16 are also considered. In fact, what Fig. 9 shows isthat the portion of the 90% read accuracy region that is gained by being able toinclude points that have tag orientations that are covered by one or the other readerantennas is much larger than the portion of the 90% read accuracy region that isdouble covered; thus the benefits of choosing two reader antenna locations directlyacross from each other, where it is possible to have points benefit from the union ofthe two reader antenna coverage regions, outweigh the costs of having a relativelysmall region of intersection.


5.2 Analysis of problem parameters

The tag space resolution, which determines the value of L is a critical parameterbecause this determines the number of evaluations for each set of reader antennas.Moreover, a decrease in search resolution by a factor of ten leads to an increase in Lby a factor of 1000. To determine an acceptable resolution, it should be noted thatsimply looking at the percentage of the tag space that is covered can be misleading.To illustrate this point consider Fig. 10 which shows five consecutive grid points.Figure 10 Coverage fraction calculation with different search resolution

1 2 3 4 5

Suppose the vertical line represents the actual 90% read accuracy boundary fora single reader antenna, i.e., with a coverage of 60% (points 1 through 3) in thiscase. If we now assume that under a coarse search resolution only every other pointwill be examined, then the coverage actually increases to 66.67% since points 1 and3 are within the boundary. By the same token if the boundary had been betweenpoints 2 and 3 then the coverage would have dropped from 40% to 33.33%. In fact,since the coverage fraction should ideally be calculated in continuous 3-dimensionalspace, a higher search resolution is always preferred because the results in such acase are always closer to the actual coverage for the ideal case.

However, from a computational viewpoint, if a coarse search resolution can leadto the same optimal placement of reader antennas, then it would be desirable touse such a resolution for determining the actual placement of the reader antennas;a finer resolution can then be used at the end to obtain the precise coverage frac-tion obtained with this placement. Fig. 11 displays results from different searchresolutions that were used to find the best reader antenna placements in Ex. 1, butwith coverage re-evaluated at the end with the finest resolution feasible (0.1 meter).In all cases, 450 discretized orientations were used for read accuracy calculations.The coverage fraction is represented by the proportion of discretized points in the2×2×2 m3 cube that can be read with 90% read accuracy. It can be seen thatcoarser search resolutions may or may not find the same solution as a finer searchresolution. Therefore, we use a resolution of 0.1 meter for the numerical examplesin the remainder of this paper; this leads to about 8,000 points being examined inthe 2×2×2 m3 cube.

Similar to the tag space search resolution, for every point, the coverage forvarious orientations should also ideally be calculated in continuous 3-dimensionalspace; therefore a larger value of M is always preferred. In our tests, we evaluatedvalues of M ranging from 25 to 2000 (the actual values of M are slightly smallerbecause of rounding as described in Section 4.2) and compared the results for smallervalues of M with the largest value of M =1916.

A less than ideal value of M could give rise to two types of errors. A Type1 error occurs when a point for which more than 100α% of the orientations canactually be covered is (mistakenly) classified as not being covered when using asmaller value for M . Conversely, a Type 2 error occurs when a point that does not


Figure 11 Optimal coverage fraction for Ex. 1 with different search resolutions

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Table 1 Percentage of errors caused by different values of M

M 20 44 80 246 450 984 1454

Type 1 error 38.2 3.8 11.0 2.7 0.2 0.2 0.4

Type 2 error 0.6 3.9 0.3 0.2 0.3 0.2 0.1

achieve the minimum coverage of 100α% is classified as being covered when usingthe coarser resolution. Table 1 shows the percentage of both types of errors fordifferent values of M , relative to the largest value of M=1916.

It may be seen that the percentage of points covered is less sensitive to thenumber of orientations than to the tag space search resolution used in the for-mulation. The two types of errors stabilize and quickly converge to a very smallvalue as M increases. In particular, the total classification error is well below 1%once M reaches a value of 450. This point is further illustrated by Fig. 12 whichshows the optimal coverage fraction that results from using the optimal solutiondetermined by using different numbers of orientations. For example, the readerantenna placement found using a value of M=20 results in an actual coverage ofabout 63% which is much smaller than the 72% found by using a larger value of M .In the three-reader antenna placement case, the optimal reader antenna placementis found even when M is as small as 20. But for the two-reader antenna placementproblem, a smaller value of M can result in a sub-optimal solution which covers asmuch as 10% less of the tag space than the best solution. In our example problems,the optimal two-reader antenna placement solution can only be found when thevalue of M is greater than 100.

Besides search resolution and number of orientations, the number of candidatereader antenna locations also has an impact on the enumeration scheme in thatthe running time has a non-polynomial order of growth in N . Although the com-putational time is also affected by the number of reader antennas to be placed n,usually n is not very large in practice. The marginal benefit from increasing n isdiminishing as shown in Fig. 13. With three reader antennas, about 86.5% of thetag space can be covered. The 4th reader antenna brings another 4% of the tagspace into the 90% read accuracy region; the covered space soon becomes saturatedas n increases.


Figure 12 Optimal coverage fraction for Ex. 1 with different numbers of discretizedorientations

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Figure 13 Optimal coverage fraction for Ex. 1 with different numbers of readerantennas

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6 Conclusions and Future Research

In this paper, we have introduced a new methodology to evaluate and optimizethe placement of multiple RFID reader antennas in order to maximize the 100α%read-accuracy region. Unlike most prior work which only considers distance, weexplicitly account for factors such as polarization mismatch and the relative orien-tations of the RFID reader antennas and tags since these factors, along with thetransmitted power, determine the size and shape of the 100α% read-accuracy region.The initial work done in this regard by Greene (2006) only considers placement ofa single reader antenna and extending this to multiple antennas is nontrivial. Bydeveloping analytical expressions to model the use of multiple reader antennas it ispossible to enhance RFID portal design and operation. The choice of where to placea set of reader antennas has a great impact on the size and shape of the 100α%read-accuracy region. However, the optimization becomes time-consuming whenorientations are considered in the evaluation of a set of reader antennas. We eval-uate and determine reasonable settings for the parameters considering trade-offsbetween computational time and the precision of the results.

The authors are continuing to work on a number of important extensions to theresearch described herein. First, in this paper we assumed that an RFID tag isequally likely to be placed at any position inside the tag space, but other distrib-utions are plausible for different applications. For example, in pallet-level logisticsapplications, cases are usually stacked onto pallet jacks so that RFID tags aremore likely to be present in the lower levels of the 3D tag space. In other cases,


when items are moved on a conveyor belt, they are usually placed in the middle ofthe belt. In these cases, a lower read-accuracy at some remote or less frequentlyused position is less important, so that read-accuracy is defined differently withdifferent parts of the tag space having different weights. Similarly, all orientationsmight not be equally important; for instance, it might be critical to read all ori-entations along the axial planes if the shapes of the containers on which the tagsare applied are all rectangular, while other oblique orientations might be less crit-ical. This notion could again lead to an alternative definition of read-accuracy. Athird extension examines portals and tag spaces that are not symmetric or regu-larly shaped. Although the reader antenna placement methodology is essentiallythe same in these situations, it would be interesting to gain insight into how theoptimal reader antenna-placements differ in these different scenarios. Fourth, whileour approach is based on discretizing the search space to a level that is compu-tationally feasible, in the ideal case, the tag space as well as the points where areader antenna can be located are continuous. Thus it is important to investigateheuristic procedures that would yield good solutions to problems with much higherlevels of discretization than those considered in this work. Fifth, we are evaluatingdifferent power levels for the transmitter; a complicating factor here is that in or-der to remain in compliance with FCC regulations the power levels must be withinspecified limits and cannot be raised arbitrarily. Finally, we are also studying thesensitivity of the solution to various values of α (that determines read-accuracy),as well as alternative definitions of read-accuracy.

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Placement of multiple RFID reader antennas to maximise portal read accuracy

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