Measurement Procedures for Design andEnforcement of Harm Claim Thresholds

Janne Riihijarvi and Petri MahonenInstitute for Networked Systems, RWTH Aachen University

Kackertstrasse 9, D-52072 Aachen, Germanyemail: {jar, pma}@inets.rwth-aachen.de

J. Pierre de VriesSilicon Flatirons Center

University of Colorado, Boulderemail: pierre.devries@colorado.edu

Abstract—Harm claim thresholds (HCTs) are a promisingapproach for regulators to specify interference limits in atechnology-neutral fashion, and a useful parameter spectrum ac-cess systems can use to manage the aggregate interference causedby transmitters they control. However, existing literature providesvery little guidance how HCTs should be set and enforced. In thispaper we propose a detailed regulatory framework for gatheringand processing of measurement data for enforcing and settingharm claim thresholds. We introduce the central concepts ofstratification and weighting of measurement data, and show theirimportance in ensuring representativeness of measurements andenabling robust estimation of statistical confidence on results.For deriving HCT thresholds from measurements, we proposeadditional representativeness criteria that a regulator shouldapply to avoid underestimation of field strength levels relatedto existing wireless services. We demonstrate application of ourproposed framework using an extensive drive test data set, andshow that the chosen HCT percentile is critical in determininghow much data needs to be gathered for enforcement. We alsodiscuss the various design choices and parameters needed by ourframework, and show through examples how they can be derivedin cooperation with the different stakeholders. The developedframework has several applications beyond HCT enforcement,some of which are briefly described in the paper.

I. INTRODUCTION

Harmful interference can be caused by unwanted transmis-sions and/or poor receiver performance. However, regulatorymandates of receiver performance are at best difficult to for-mulate and at worst inefficient. They are very rare, even thoughthey are much talked about since receivers that cannot rejectinterfering signals can preclude or constrain new spectrumallocations. Harm claim thresholds (HCTs) were introduced asa way for regulators to specify the interference environmentin which an affected radio systems should expect to operate,without specifying receiver performance [1].

A HCT defines the in-band and out-of-band interferingsignals that must be exceeded before a system can claim thatit is experiencing harmful interference. It is deemed to beexceeded if the measured or modeled signal strength exceedsa stated value for more than some percentage of locations andtimes, for a prescribed confidence level. In the example weuse throughout this paper, the HCT is 50 dB(µV/m) per MHzto be exceeded at no more than 5% of locations, at the 95%

confidence level.1 This is equivalent to imposing the thresholdon the 95th percentile of field strength.

HCTs are particularly useful in managing dynamic spectrumaccess since they allow a spectrum access system to ignore thelocations and (more importantly) the characteristics of indi-vidual receivers when calculating the allowed transmit powerof the radios it controls. As long as the aggregate resultingsignal strength statistics meet the HCT, then by definitionharmful interference has been avoided. This facilitates theimplementation of spectrum access systems and policies.

The first HCT papers provided little guidance for specifyingthe regions over which threshold measurements should bemade. Reference [2] suggests measuring every 250 m over a5 km ⇥ 5 km area, while [3] suggests an area of 1 km ⇥ 1 kmwith measurement points on a 50 m grid; neither justify theirprotocols beyond the need for a sufficiently large data set toprovide statistical reliability (n = 400 in both cases). In [4]we first studied the statistics of drive test measurements thatcould be used to make harm claims. We showed that assumingindependent measurements some hundreds of measurementswere needed for sufficient confidence for the 95th percentile offield strength, with much higher measurement counts neededfor the 99th percentile. However, these results do not yieldinformation on the needed measurement area, and the indepen-dence of measurements is a strong assumption that is usefulfor initial analysis but (as we shall illustrate in the followingsection) is untenable for actual claim determination.

The objective of this paper is to propose a concrete regula-tory framework for measurements to be conducted in relationto a claim for harm under HCT policy. We will also explainhow a regulator can formulate HCTs in a way that can be read-ily used by licensees making or defending claims of harmfulinterference, or wishing to ensure that their deployments arein compliance. It will also use a much larger data set than theprevious study [4] to show how a regulator could derive HCTsfor a cellular deployment.

1We emphasize that the value of 50 dB(µV/m) per MHz is chosen forillustrative purposes only. In particular, we have chosen a value that issufficiently low to enable us to demonstrate how a HCT violation wouldbe determined from measurements, using realistic data obtained from anactual operational network. We discuss in the latter half of the paper howthe regulator would actually select the threshold reliably so as not to placeexisting network deployments in violation.

This paper will use cumulative case study examples tomotivate and illustrate the regulatory specification which islaid out in Section VI. After giving the regulatory designgoals in Section II, we illustrate the limitations of naıvemeasurement specifications in Section III. In Section IV wework through the key elements of measurement procedure de-sign. Section V discusses confidence intervals, and Section VIexplains how a regulator would go about choosing a thresholdlevel, stratification distance and confidence interval in the firstplace. Section VI also summarizes the parameters a regulatorwould specify, and the key steps a claimant would have totake to show a HCT has been exceeded.

II. REGULATORY GOALS

The premise of the HCT approach is that a regulator woulddefine thresholds at a level of generality comparable to theway it specifies emission limits. Operators would then be ableto use the values in such rules to ensure that their operationswould not trigger a harm claim, or conversely, to prove a harmclaim against another party. Since HCTs are a regulatory tool,they need to be easy to understand and use by all concerned.We believe that goal can be achieved if the following designobjectives are met:

• Straightforward to specify at a high level in rules, e.g.a small number of technology- and service-neutral pa-rameters; implementation details can be promulgated inancillary publications, e.g. bulletins in the FCC OETKnowledge Database.

• Relatively easy to accommodate new technologies, e.g.by updating regulatory bulletins not changing rules.

• Easy to understand and apply, and in particular shouldnot require sophisticated knowledge of statistics.

• Contain as few parameters as possible.• Based on ex ante stratification distances (one of the key

parameters in our method, introduced in detail in thefollowing two sections) rather than estimates derived inthe course of a continuous drive test.

• Enable simple estimation and planning of measurements.Two key questions immediately arise:

1) What is the simplest way the regulator can specify aHCT and still meet its regulatory goals? This includeschoosing both the parameters to be used, and theirvalues.

2) Given the HCT parameters and values, how would anoperator go about proving that a HCT is (or is not) met?

When specifying a HCT, the regulator needs to determine thestatistic of interest — we select a point on a cumulative distri-bution function (CDF) of field strength — and the confidencelevel with which the statistic needs to be measured.

III. WHY SPECIFIC PROCEDURES FOR GATHERING ANDPROCESSING MEASUREMENT DATA ARE NEEDED

Let us begin by considering the data set shown in Figure 1,which corresponds to a 10 km ⇥ 10 km subset within a largedrive test campaign conducted in a major metropolitan area

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0

2500

5000

7500

10000

0 2500 5000 7500 10000

x−coordinate [ m ]

y−co

ordi

nate

[ m

]

10

20

30

40

50

dB(uV/m) per MHz

Fig. 1. Example drive test data set.

in the US. The full data set covered an area of approximately120 km ⇥ 170 km and consisted of 4 million measurementsin total. The gathered measurements are all for the 2 GHzdownlink band for a major cellular operator. We will firstuse this data set to illustrate the pitfalls of naıve statisticalanalysis when applied to drive test data, and will also use itlater on to motivate our suggested approach for data gatheringand processing.

The simplest approach for testing whether our data setindicates a violation of the HCT would be to ignore any depen-dencies in the data, and treat each of the 7266 measurementsas an equally valuable source of information. We can computethe 95th percentile from the data directly, or read it fromthe empirical complimentary cumulative distribution function(CCDF) as shown in the Figure 2 and compare it against theset HCT.2 As can be seen from the figure, the estimated valueof 46.7 dB(µV/m) per MHz for the 95th percentile is wellbelow the harm claim threshold, indicating that a violation isunlikely. Further, computing the confidence interval3 for thispercentile estimate using the measurement count n = 7266

yields “error bars” of well less than one dB, indicating highconfidence on the obtained estimate.

But how good is the obtained estimate really? In this case,since we have used a small fraction of a much larger dataset, the best comparison is against the 95th percentile valueobtained from the entire data set. If our 10 km⇥10 km samplewould be representative, and our data processing methodsound, these two estimates should agree relatively closely.Unfortunately the 95th percentile for the entire data set turnsout to be 53 dB(µV/m) per MHz which actually exceeds theHCT, showing that the tentative conclusions drawn from thedata set of Figure 1 are incorrect. The discrepancy becomeseven larger when we consider the field strength measured

2We emphasise again that even though we use throughout this paper thevalue of 50 dB(µV/m) per MHz as the putative HCT, not to be exceededmore than five percent of locations, it is not intended to suggest an actualHCT value. We discuss in later sections the procedures a regulator shouldactually use in order to derive suitable HCT values.

3We will discuss the exact procedure for this in Section V.

0.05

46.675

HCTviolation

0.00

0.25

0.50

0.75

1.00

20 40 60

Field strength [ dB(uV/m)/MHz ]

Prob

abilit

y of

exc

eeda

nce

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Fig. 2. The distribution of the raw field strength data from the drive shownin Figure 1, with the posited HCT violation region and estimated percentilemarked with green and red dashed lines, respectively.

by a typical user4 which turns out to be approximately55.8 dB(µV/m) per MHz. This strongly indicates that sucha naıve statistical treatment of the drive test data can resultin highly misleading results. In the following section we willdiscuss the origins of the observed discrepancy in more detail,and also formulate procedures for dealing with drive test datathat corrects the shortcomings of this naıve treatment.

IV. MEASUREMENT PROCEDURE DESIGN

We begin by arguing that the discrepancy observed in theprevious section arose for two distinct reasons. First, wetreated each measurement as being independent of every other.But by looking at Figure 1 we see only a few regions ofhigher field strength, suggesting that only a few transmittershave been deployed in the region. Measurements from anytwo nearby locations are therefore heavily correlated, andthis must be taken into account when estimating the effectivemeasurement data count. Second, much of the drive covershighways or other major road segments, making it unclearhow representative these measurements are for field strengthexperienced by a typical user. We can get insight into this bystudying the population density at the different measurementlocations which, as discussed in footnote 4, we use as a proxyfor user location.

In order to remedy these two shortcomings of the naıvemeasurement protocol, we argue that the following two keyconcepts need to be incorporated into the processing of drivetest data:

4By “as measured by typical user” we mean the distribution of field strengtha randomly selected member of the user population would be expected tomeasure, as opposed to simply considering the distribution of field strengthover space. These two distributions can differ substantially, since users are notuniformly spread around any larger region. In the following we always assumethat the user locations follow the overall population density, estimates of whichwe obtained from the ORNL LandScan global high-resolution populationdatabase [5].

1) We introduce a standard process called stratification toreduce the measurement data set to a much smallersubset in which measurements are approximately inde-pendent of each other. This can be done, for example, byimposing a minimal distance for any two measurementpoints that the reduced data set must satisfy. Stratifica-tion will be discussed in detail in Section IV.B.

2) Further, in order to ensure that the statistics are represen-tative, we further introduce weighting of measurementvalues, in which each measurement carries a weightthat is proportional to the density of the foreseen userpopulation at the measurement location. Weighting willbe further discussed in Section IV.C.

The purpose of these additions is to fairly estimate the numberof measurements for confidence interval computation, and tohelp ensure representativeness.

Figure 3 illustrates the outcome of applying these twosteps to our first example measurement data set. Stratificationhas drastically reduced the number of measurement pointsto consider (from n = 7266 down to n = 67), and thepopulation-weighting also shown in the figure further revealsthat only a small fraction of measurement points actuallycontribute to estimating interference on the expected user pop-ulation. Thus, it is not really surprising that the naıve statisticalapproach resulted in poor results. In fact, when computingthe confidence interval using the new effective measurementcount, it turns out to have a formally infinite length, stronglyindicating that no statistically reliable conclusions about the95th percentile of field strength can be drawn from the originaldata set.

A. Example Application to More Extensive Data Set

An obvious question to ask is whether the concepts ofstratification and weighting can be practically applied to drivetest data at all given the negative results obtained above?By way of example, let us consider another subset from thesame large-scale metropolitan measurement campaign as ouroriginal example. This alternative data set is illustrated inFigure 4 both in terms of samples remaining after stratificationas well as the corresponding population-weighting. Clearlydespite the same measurement region size, the new data setis much more dense even after stratification (with n = 260

samples remaining), and also much more representative asevidenced by the homogeneity of population weights.

When the stratified data set is combined with the populationweights, we obtain the weighted CCDF shown in Figure 5,now indicating a possible violation. Note also that the newpoint estimate of 56.5 dB(µV/m) per MHz is quite close tothe “ground truth” of 55.8 dB(µV/m) per MHz obtained byconsidering the entire data set. Note that these estimates arestill missing the needed confidence intervals, the additionof which we will discuss in Section V. However, beforeproceeding there we discuss the roles of stratification andpopulation-weighting in slightly more detail. In particular, ourobjective is to convince the reader that these are not ad hocmeasures, but are instead based on sound statistical reasoning.

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B. Purpose and Implementation of Stratification

Stratification serves two purposes in our proposed method.First, it is used to estimate fairly the number of independentmeasurements present in the data for the purposes of confi-dence interval estimation. Second, it also helps to reduce inho-mogeneity in the data, ensuring that the measurements coverthe intended region roughly uniformly. The latter functionis particularly important for processing data from urban testdrives, where traffic lights, congestion, varying speed limits,and complex routes that may cover individual roads more thanonce, all lead to highly uneven measurement densities overspace. Figure 6 illustrates this by showing the local density ofmeasurement locations for our second example data set, wherethe effects of both the traffic lights as well as overall speed of

the test vehicle are clearly visible.Stratification can be implemented in several ways, each with

different trade-offs between efficiency in terms of the numberof retained measurement locations, and computational burdenimposed. One possibility would be to consider the selection ofretained measurement locations as an optimization problem,where we would seek to maximize the number of retainedpoints under the constraint that no two locations would becloser apart than a set stratification distance5 dS . Unfortu-nately this is not computationally feasible as the number ofsubsets of locations to consider increases exponentially withoverall measurement data set size. A slightly less efficient but

5We will explain how a suitable stratification distance can be determinedthrough measurements or simulations in Section VI-B

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Fig. 5. The population weighted and stratified CCDF from the data set ofFigure 4.

Fig. 6. Illustration of the inhomogeneity of the density of measurementlocations arising from changes in velocity during a typical drive test, inparticular induced by traffic lights showing up as small dark spots in theplot.

also computationally lighter method would be analogous tohow carrier sense multiple access (CSMA) medium accesscontrol protocols operate. We would assign to each measure-ment location a random number (“arrival time”) uniformlyfrom the interval [0, 1], and retain a location if and only if it hasthe smallest arrival time of all the locations within distance dS .The most complex part here is the computation of distancesbetween the points, requiring O(n2

) operations.An even more light-weight approach is illustrated in Fig-

ure 7, where the measurement region is divided into squareswith side length dS , and only one measurement from eachsquare is retained. In our example we have chosen the locationthat is farthest away from the edge of the surrounding square,but other similar choices could be made as well. This is

Fig. 7. Example of a grid-based method for implementing stratification.

the approach we have used on the preceding data sets whenconstructing the stratified equivalents. Its downside comparedto the previous ones is that it does not guarantee that thedistances between nearby measurement locations are strictlylarger than dS , but this can be mitigated by a slightly moreconservative choice of the stratification distance. Since onlycomparisons of coordinates and distances to a fixed numberof squares need to be computed, only O(n) operations areneeded.

Notice that the three algorithms described above differ inother fundamental ways besides just their computational costs.For instance, the arrival time algorithm results in a randomstratified location set, whereas the grid-based algorithm isstrictly deterministic once the division of the measurement areainto squares is defined. Our examples in Figures 3 and 4 usegrid-based stratification.

C. Interpretation of Weighting when Estimating Percentiles

As discussed above, the purpose of weighting is to ensurethat the percentiles estimated are representative of what thepopulation of interfered users would measure, as opposedto raw spatial estimates. No weighting would be neededif the interfered-with population itself would conduct themeasurements,6 or if the measurement locations would becarefully selected to follow the corresponding spatial densityafter stratification. While theoretically possible, we believesuch an approach to be overly complex. Instead, we proposeto first obtain a spatially uniform sample of sufficient size (byconducting a conventional drive test followed by stratification),and then weight that sample with the estimated interfered-withpopulation density when computing the HCT percentile for thefield strength.

Weighted percentiles have an appealing geometric interpre-tation illustrated in Figure 8. In the figure we have appliedto each (stratified) measurement location the threshold of

6Crowdsourcing is of course a possibility here, but conducting extensivespatial field strength measurements through user terminals with highly varyingreceiver qualities and configurations in a reliable fashion is still very muchan open research problem.

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50 dB(µV/m) per MHz, with black circles corresponding tolocations that were measured below this value, and red circlesexceeding. For testing whether the unweighted percentile es-timated from the data would exceed the 95th, it is sufficientto check whether at least five percent of the dots are red. Ifyes, the measured 95th percentile has to exceed the threshold.When weights are applied (represented in the figure by thearea of the individual points), we compare the total areas ofthe points of the two colors instead of simply the counts.

V. ADDING CONFIDENCE INTERVALS

In the previous sections our focus has been on how to obtainreasonable estimates for the percentile of field strength given inthe HCT specification, together with the effective measurementcount n arising from our stratification procedure. In thissection we discuss how to further construct the confidenceintervals around these estimates; they can be used to quantifythe reliability of our decision on whether a given set of mea-surements indeed can be determined to indicate HCT violationor not. We begin by briefly discussing the precise meaning ofconfidence intervals as they are often misinterpreted in theliterature. We then outline how confidence intervals can beestimated first for unweighted measurement data, and thenfor weighted data as well. Finally, we give examples of thecomputations involved using our two example data sets.

A. Meaning of Confidence Intervals

Confidence intervals are an example of a so-called fre-quentist statistical tool, designed to have rigorously definedproperties as a statistical method applied a very large numberof times. In the case of a confidence interval for the pthpercentile, if we repeat taking a random sample from a givenlarge set of data, the true pth percentile of the underlying datawould fall within the 100(1 � ↵)% confidence interval withprobability (1 � ↵). This guarantees that even though for a

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single measurement run the true percentile can fall far outsidethe computed confidence interval in rare cases, the fraction ofsuch errors is guaranteed to converge to ↵ which we can makeas small as desired (at the cost of more measurements beingneeded in order to obtain tight enough confidence intervals).

Figure 9 illustrates this statistical meaning of confidenceintervals over 30 samples (with n = 260 for each sample)from the overall measurement data set, and the associated pointestimates and confidence intervals at the ↵ = 0.05 confidencelevel (all of these were computed using the procedures intro-duced in the following section). Approximately once every 20measurement runs we would expect the true value (indicatedby the dashed horizontal line) to fall outside the estimatedconfidence interval. This indeed corresponds well with theresults shown in the figure, with one run out of 30 (shown inred) resulting in a significant overestimation of the percentilealong with its confidence interval.

B. Confidence Intervals for Unweighted Data

How can we in practice find “good” confidence intervals?We give in the following one of the standard statisticalprocedures, but note that several alternatives exist [6]. Beforestating the computational procedures, we need to introducea small amount of mathematical notation and some auxiliaryconcepts. Let X1, . . . , Xn denote our n measurements, i.e.field strength values measured along a drive path. The orderstatistics of these are the measurement values sorted in as-cending order, denoted by X(1) X(2) · · · X(n). ThusX(1) = min{X1, . . . , Xn}, X(n) = max{X1, . . . , Xn}, withthe rest of the order statistics carrying information about thepercentiles F�1

X (p) of X , where FX denotes the distributionfunction of X . For large enough sample X(p⇥(n+1)) serves asan estimate for the pth percentile of field strength.

The confidence interval for the pth percentile can be con-structed from n measurements in the unweighted case asfollows. Letting Zp denote the pth percentile of the standard

normal distribution N(0, 1), the upper limit of the 100(1�↵)%confidence interval is given by X(u), where

u = p(n+ 1) + Z1�↵/2

pnp(1� p), (1)

and the lower limit by X(l), where

l = p(n+ 1)� Z1�↵/2

pnp(1� p). (2)

If u or l turns out to be non-integer, the corresponding endpointof the confidence interval can be determined by interpolatingbetween the nearest adjacent order statistics. The confidenceintervals shown in the example of Figure 9 were computedusing these procedures.

We will need the one-sided confidence intervals, giving onlythe upper or lower bound for the error, rather than these two-sided confidence intervals since the HCT is given as a valuenot-to-be-exceeded. These are obtained simply by replacingZ1�↵/2 by Z1�↵ in the corresponding formula above, withother end point being ±1.

C. Confidence Intervals for Population-Weighted Data

For weighted data the above procedure can be used withminor modification. Notice that the u and l values obtained asthe interval endpoints have a direct interpretation as percentilesof the measurement data. In order to compute the correspond-ing confidence intervals for weighted data, we simply needto find the corresponding weighted percentiles as discussed inSection IV-C, and use these as confidence interval endpointsinstead.

VI. MEASUREMENT-RELATED CONSIDERATIONS FORSETTING HCT POLICIES

In this section we focus on the measurement-related con-siderations and decisions the regulator should be mindful ofwhen setting HCT policies. We first discuss how the outlinedmeasurement procedures can be applied by the regulator inthe first place to arrive at a suitable field strength threshold,and also how the expected measurement burden influences thepercentiles that can be reasonably used in relation to HCTpolicy. We also discuss how the stratification distance dSshould be set, and what are the trade-offs involved.

A. Choosing the Threshold

Arguably the most critical part of a HCT policy is thechoice of the threshold field strength that is not to be exceedmore often than the chosen percentage. Values that are toolow could outlaw existing deployments, or greatly diminishthe value of spectrum by making the operation of a viablenumber of concurrent transmitters impossible. Too high avalue, on the other hand, offers insufficient protection, makingthe regulation ineffective.

When new services are introduced, simulation studies basedon realistic system deployment and propagation models mightbe needed. However, when dealing with existing servicesmeasurement-based methods as proposed above could also beused by the regulator to arrive at a reasonable field strengththreshold.

The only modification that seems unavoidable is the in-troduction by the regulator of additional controls on therepresentativeness of the measurements conducted or used.Even with population weighting, test drives in regions withsparse wireless infrastructure tend to result in underestimationof the field strengths compared to estimates from an entiremetropolitan regions. This is not a problem if the measure-ment region is selected by a plaintiff, since the introducedbias would in general be towards underestimating the fieldstrength level. However, if such sparsely built regions wouldbe measured by the regulator and used directly to set the HCT,the results could be disastrous.

A simple solution to this problem is to consider onlymeasurements from a region that has at least average userdensity. In our framework this translates to only utilising datathat comes from the areas of the drive where the stratifiedmeasurements carry a large enough total weight. Figure 10illustrates how this simple principle works by showing ascatterplot of total weights and the measured 95th percentileof field strength for all the distinct 10 km ⇥ 10 km regionspresent in our data. We see that for areas with low total weightsthe measurements are highly varying (with the downwardbias discussed above being clearly visible), but in the regionswith higher aggregate weights the measured values agree wellwith each other. Thus a practical approach would be to usemeasurement from such a high-weight region, and impose anadditional safety margin on top of the measured value. Thedashed lines in Figure 10 correspond to a 10 dB safety marginbeing imposed on top of the “ground truth” 95th percentilevalue. Using out data set, this would lead to the regulatorsetting a HCT of 65.8 dB(µV/m) per MHz (or suitably upwardsrounded number), rather than the 50 dB(µV/m) per MHz wehave been using for illustrative purposes.

B. Setting the Stratification Distance

The stratification distance dS entails a trade-off between thedegree of independence of the stratified measurements, and theeffort needed to construct the test drive. Large values of dSensure the most reliable percentile estimates and confidenceintervals for a given measurement count n, but will also requirevery large regions to be covered in order to harvest the nstratified measurements. As we saw in our initial case study(Figure 1), very small stratification distances risk on the otherhand spurious conclusions to be drawn from the data. In thissection we outline a statistical method enabling the derivationof dS based on “first principles”, including the formalizationof the trade-off discussed above.

For our proposed method we first need to choose a similaritymeasure, which given a distance r between two measurementsXi and Xj yields a quantitative measure of how similar Xi andXj are expected to be. The preferred choice for such a measurein the spatial statistics community—whose research focuses onapplications of statistical methods to spatially dependent dataas is definitely case in our domain—is the semivariogram [7]

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Fig. 10. Illustration on the use of total population weight as criteria when selecting which region to cover when conducting measurements for the initialthreshold specification.

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Fig. 11. Using the semivariogram to estimate correlation distance from data.Gray bars denote the histogram bins of distances (with � = 100 m) betweenmeasurement location pairs based on which the semivariogram is estimated.The theoretical model (solid black line) is then fitted to the estimates placedat the centers of the histogram bins (red dots).

but other choices are possible as well.7 For small r we wouldexpect little difference between the values of Xi and Xj ,resulting in small differences between them and correspond-ingly small values of �(r). For large r the values of the

7The most commonly suggested alternative is the autocorrelation functionC(r), defined as the correlation coefficient between measurements Xi andXj separated by distance r. For large enough data sets in terms of both mea-surement count and covered region the two are almost equivalent statistically.However, the semivariogram enables additional diagnostics to be applied forsmaller measurement data sets, as discussed in the text. [7]

semivariogram become larger and larger, until saturating atthe overall variance of the data.

We can estimate the value of �(r) simply by finding all pairs(Xi, Xj) of measurements where the locations are separatedby distance r ±�, where � essentially defines a width of ahistogram bin, followed by the computation of the variance ofXi�Xj over all such pairs. An example of such a computationis shown in Figure 11, illustrating both the histogram natureof this estimator (bars) together with the estimates of �(r)assigned in the centres of the histogram bins (red dots). Ascan be seen from the figure, the obtained estimates are quitenoisy, making them unsuitable for direct use in estimating asuitable stratification distance. Instead, we proceed by fitting aparametric model to the data. In the literature the exponentialform a+ b exp(�r/c) is commonly used [7], [8], and workswell also for our example data set as shown in the figure (blackline).

Once the parametric model for the semivariogram �(r) isobtained, we can choose a stratification distance dS basedon how close the semivariance �(dS) is to the asymptoticsaturation value (overall variance of the data set). A veryconservative choice would be to demand that at least 95%of the asymptotic level is reached, but as can be seen fromour example this results in very large stratification distances,and thereby impractically large drive test data sets beingneeded for any HCT related claim.8 In our opinion a judicioustradeoff is to choose a somewhat lower fraction, such ashaving �(dS) equal half of the saturation value, which resultsin slightly optimistic estimates of the stratified measurement

8It also might occur that the estimated semivariogram does not flatten outto an asymptotic value. This is a strong indication that the measurements aretaken from a region that is too small, resulting in a trend in field strength valuesacross the measurement region, which in turn presents itself as a constantlygrowing semivariogram values as r is increased.

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Fig. 12. Behavior of the one-sided confidence interval length as the size ofthe measurement data set is varied.

counts and thereby slightly tighter confidence intervals thancan be expected in ideal conditions, but requiring at least anorder of magnitude less data in order for the estimates to beobtained. For our example data set this prescription results ina stratification distance of dS = 305 m, as shown in Figure 11.

The obtained stratification distance will depend stronglyon the technology involved, deployment patterns, and thepropagation environment. The obtained value of 305 m istypical for small cell and microcellular deployments in urbanareas, while for rural macrocellular systems and broadcastingtechnologies much larger values would be expected.

Finally, we emphasise that while the above presentation isformulated in terms of measurement procedures, the defini-tions can directly be applied to simulation data and analyticalmodels as well. While exact field strength levels obtainedfrom such alternatives procedures tend to be unreliable, inour experience the correlation structure, whether expressedin terms of the semivariogram or autocorrelation function,is more reliable. Thus especially system level simulationswith appropriate propagation modeling tools might be valuablein helping to find initial stratification distance even prior tolarge-scale deployments of wireless communication systemsinvolved.

C. Specifying the Confidence Interval and Percentile

It is important to understand the relationships between thenumber of measurement points n, chosen HCT percentile, andthe arising confidence interval lengths, as they are directlyrelated to the expected size and complexity of the driveneeded to gather the data. Figure 12 illustrates the relationshipbetween n and obtained confidence interval for the overalldata set, again for 95th percentile with one-sided confidenceintervals computed at the ↵ = 0.05 level. For each n wegenerated 100 samples of n measurements each, and computedthe associated confidence interval lengths from the pointestimate of the percentile to the lowest edge of the one-sided confidence interval, the distributions of which are shownas the box and whiskers plot. We see strongly diminishing

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Fig. 13. Influence of the chosen HCT percentile on the one-sided confidenceinterval length for n = 260 measurement locations.

returns from collecting more data, with the first 200–300 mea-surements being sufficient to reduce the confidence intervallength to approximately 3 dB. We believe this to be sufficientaccuracy given the vagaries of RF field measurements. Thisindicates that for the 95th percentile, having some 200–300measurements after stratification forms a natural design targetwhen planning a test drive. However, if the estimated fieldstrength percentile is expected to be very close to the HCTone, arbitrarily large measurement counts might be needed toconfirm or rule out HCT violation.

Another major factor in the number of data needed toachieve a particular confidence interval length is the under-lying percentile for which the confidence interval is beingestimated. Figure 13 illustrates the distribution of the achievedconfidence interval lengths for different percentiles, in eachcase assuming n = 260 measurement locations as for oursecond example data set. We see that the confidence intervallengths increase rapidly as higher percentiles are estimated.For the 99th percentile n = 260 measurements no longer yielda finite confidence interval length, and for the 98th percentileindividual confidence intervals can already exceed 10 dB. Thisstrongly indicates that unless a significantly different measure-ment data processing method is adopted, imposing HCTs withhigher than 95th percentile specifications on field strengthswill require significantly more measurements (for both HCTdetermination and enforcement) than the few hundred we havefound to be sufficient for the 95th percentile case. This willlikely impose an unreasonable burden both on the regulatorand on parties disputing a HCT claim.

From (1) and (2) we see that for a fixed data set andpercentile p, the length of the confidence interval dependsfurther on the percentiles Z1�↵/2 of the standard normaldistribution. This essentially defines the relationship betweenthe length of the final confidence interval and the desiredconfidence level. However, this influence is decidedly smallerthan those of the stratified measurement count and the chosenHCT percentile. For example, going from 90% confidencelevel (↵ = 0.1) to 99% confidence level (↵ = 0.01) increases

the confidence interval length just by a factor of two (in termsof values in dB), despite the formally ten-fold reduction in therate of spurious findings.

D. What a Regulator Needs to Specify

We conclude this section by summarizing what a regulatorneeds to specify in order to apply the method described herefor determining and enforcing harm claim threshold policies.A high level summary of the different design parametersis given in Table I. We have divided these parameters intothree categories in order to facilitate their specification tobe split between rules yielding the high-level, unchangingrequirements, and bulletins for more detailed and dynamiclow-level specifications. This approach is similar to that used,for example, in the FCC’s regulation of wireless E911 locationsystems.9

In our proposed split, the HCT policy details would begiven in rules, consisting of the parameters comprising theoriginal HCT specification format [1], [2]. Bulletins wouldthen be used for specifying the measurement procedure relatedto the given HCT policy. Decisions involved here includethe stratification procedure to be used (algorithm and choiceof the stratification distance dS), weighting to be applied(presumably defaulting to population density), and the variousrequirements for actually submitting the drive data that wouldform a basis of claim. The latter should be carefully designedto avoid manipulating the measurement outcomes, for exampleby submitting only selected subsets of larger measurement datasets. Possible design choices include prior registration of alter-native drive paths from which the regulator randomly choosesone, combined with the requirement to submit complete rawlog files of the entire measurement drive.

Finally, for setting HCTs for emerging services the regulatormight need to specify the extent to which models and simula-tions can be used to derive these parameters. In particular, wesee these tools to be particularly useful in deriving the neededstratification distances dS , as such estimates are not sensitiveto small imperfections in propagation models for example.

VII. CONCLUSIONS

In this paper we proposed a regulatory framework forgathering and processing of measurement data for enforcingand setting harm claim thresholds. Our proposal is basedon the concepts of stratification and weighting, introducedto ensure representativeness of measurements and enablingrobust estimation of statistical confidence on results. We alsodemonstrated, using data from an extensive test drive for a realwireless network, how our proposed framework could be used

9General rules for accuracy and reliability requirements are given in Section20.18(h) and (j) of the Commission’s Rules: e.g. as of January 18, 2013,for handset-based technologies, “50 meters for 67 percent of calls, and 150meters for 80 percent of calls, on a per-county or per-PSAP basis” (47 C.F.R.§20.18(h)(2)(i)), and the provided data shall specify the “caller’s locationwith a uniform confidence level of 90 percent” (§20.18(j)(1)(i))). Detailedguidelines for testing and verifying the accuracy of wireless E911 locationsystems are given in OET Bulletin No. 71 [9] which gives general princi-ples, measurement conventions, and a statistical approach for demonstratingcompliance for empirical testing.

TABLE ISUMMARY OF REGULATORY PARAMETERS WITH

EXAMPLE VALUES USED IN THIS PAPER.

Category Parameters Examples

HCT policy Frequency band 2 GHzPercentile of field strength 95thField strength threshold 50 dB(uV/m) per MHzConfidence level 95% (↵ = 0.05)

Measurement Stratification procedure Grid-basedprocedure Weighting method Population weighting

Submission of drive data Complete without gapsResponsibility for processing ClaimantRequirements on equipment Standard drive test

Derivation Allowed methodologies Measurements orof dS data from planning tools

Threshold semivariance Half of saturation value/ autocorrelation (or correlation 0.5)

Flexibility in model choice Exponential only

to set HCT thresholds and enforce HCT rules. The techniquesdescribed here can be transposed to other settings as well,such as setting service level agreements (SLAs) for cellularcoverage. In the HCT case, the regulator specifies a highfield strength level that cannot be exceeded by a transmittinglicensee at more than a few locations without triggering harmclaim. In the corresponding SLA case, a cellular operatorwould specify a low field strength level that can be fallenbelow only rarely by a tower operator without triggeringan SLA default. Similar statistical considerations could beused by the FCC when providing guidelines for testing andverifying the accuracy of wireless E911 location systems.

REFERENCES

[1] FCC Technological Advisory Council, Spectrum / Receiver PerformanceWorking Group, “Interference Limits Policy and Harm Claim Thresholds:An Introduction,” 2014. [Online]. Available: http://transition.fcc.gov/oet/tac/tacdocs/reports/TACInterferenceLimitsIntrov1.0.pdf

[2] ——, “Interference Limits Policy: The use of harm claimthresholds to improve the interference tolerance of wirelesssystems,” 2013. [Online]. Available: http://transition.fcc.gov/bureaus/oet/tac/tacdocs/WhitePaperTACInterferenceLimitsv1.0.pdf

[3] J. P. de Vries, “Optimizing receiver performance using harm claimthresholds,” Telecommunications Policy, vol. 37, no. 9, pp. 757 – 771,2013, papers from the 40th Research Conference on Communication,Information and Internet Policy (TPRC 2012)Special issue on the firstpapers from the ’Mapping the Field’ initiative. [Online]. Available:http://www.sciencedirect.com/science/article/pii/S0308596113000670

[4] J. Riihijarvi, A. Achtzehn, P. Mahonen, and P. de Vries, “A study onthe design space for harm claim thresholds,” in 2014 9th InternationalConference on Cognitive Radio Oriented Wireless Networks and Com-munications (CROWNCOM). IEEE, 2014, pp. 377–382.

[5] E. Bright et al., “Landscan 2011.” [Online]. Available: http://www.ornl.gov/landscan/

[6] L. D. Brown, T. T. Cai, and A. DasGupta, “Confidence intervalsfor a binomial proportion and asymptotic expansions,” Ann. Statist.,vol. 30, no. 1, pp. 160–201, 02 2002. [Online]. Available: http://dx.doi.org/10.1214/aos/1015362189

[7] N. Cressie, Statistics for spatial data. John Wiley & Sons, 2015.[8] M. Wellens et al., “Spatial statistics and models of spectrum use,”

Computer Communications, vol. 32, no. 18, pp. 1998–2011, 2009.[9] Federal Communications Commission, “Guidelines for testing and

verifying the accuracy of wireless E911 location systems,” OET BulletinNo. 71, 2000. [Online]. Available: https://transition.fcc.gov/bureaus/oet/info/documents/bulletins/oet71/oet71.pdf