5G Network Planning under Service and EMF Constraints: Formulation and Solutions
Luca Chiaraviglio, Cristian Di Paolo, Nicola Blefari-Melazzi
11
5G Network Planning under Service and EMFConstraints: Formulation and Solutions
Luca Chiaraviglio (1 , , Cristian Di Paolo, (2) , Nicola Blefari-Melazzi (1 ,
1) Department of Electronic Engineering, University of Rome Tor Vergata, Rome, Italy,email: [email protected], [email protected], [email protected]) Consorzio Nazionale Interuniversitario per le Telecomunicazioni (CNIT), Italy
Abstract —We target the planning of a 5G cellular network under 5G service and ElectroMagnetic Fields (EMFs) constraints. Weinitially model the problem with a Mixed Integer Linear Programming (MILP) formulation. The pursued objective is a weighed function ofgNB installation costs and 5G service coverage level. In addition, we precisely model restrictive EMF constraints and we integratescaling parameters to estimate the power radiated by 5G gNBs. Since the considered planning problem is NP-Hard, and therefore verychallenging to be solved even for small problem instances, we design an efficient heuristic, called PL
ANNING A LGORITHM T OWARDS
EMF E
MISSIONS A SSESSMENT (PLATEA), to practically solve it. Results, obtained over a realistic scenario that includes EMFexposure from pre-5G technologies (e.g., 2G, 3G, 4G), prove that PLATEA retrieves a planning that ensures 5G service and restrictiveEMF constraints. However, we demonstrate that the results are strongly affected by: i ) the relative weight between gNB installation costs and 5G service coverage level, ii ) the scaling parameters to estimate the exposure generated by 5G gNBs, and iii ) the amount of exposure from pre-5G technologies. Index Terms —5G Mobile Networks, 5G Network Planning, Base Station Deployment, Service and EMF constraints, EMF regulations (cid:70)
NTRODUCTION
The provisioning of the 5G service inevitably requiresthe installation of new 5G equipment, called next-generationNode-B Base Station (gNB), over the territory. The taskof selecting and configuring the set of sites hosting 5Gequipment is often referred as 5G cellular planning [1], acomplex problem that involves costs, service coverage andElectroMagnetic Field (EMF) constraints. In general, theplanning of a cellular network is a critical step that has ahuge impact on the CAPital EXpenditures (CAPEX) costsincurred by the operator [2], as well as on the Quality ofService (QoS) perceived by users [3], [4]. From an ope-rator perspective, the network planning should minimizethe costs for deploying new 5G sites and installing 5Gequipment. In addition, the operator aims at maximizing theperformance (e.g., throughput, delay) that is experienced by5G User Equipment (UE).Under realistic settings, the planning problem is stronglyaffected by the regulations governing the EMF levels radia-ted by 5G equipment [5]. In general, many countries in theworld ensure that the EMF levels radiated by 5G gNBs arelower than maximum values (often referred as EMF limits)[6], which depend on the frequency exploited by the 5GgNB. Traditionally, international/federal bodies like Inter-national Commission on Non-Ionizing Radiation Protection(ICNIRP) and Federal Communications Commission (FCC)define EMF limits for all the cellular frequencies, includingthe ones used by 5G equipment [7], [8]. Since no adversehealth effects have been scientifically proven so far whenEMF exposure is lower than the limits defined by interna-tional/federal bodies [9]–[11], a planning that ensures thiscondition is a mandatory step to preserve public health. Asa result, the constraints introduced by EMF regulations haveto be carefully taken into account during the installation and
SCHOOL
SaturatedAreaSensitive Area 4G Node-BSite 1 Site 2Site 3Site 45G gNB Installation Denied 5G gNB Installation Authorized5G UE
Fig. 1. The presence of sensitive areas and EMF saturation zonesheavily impacts the 5G cellular planning. then the operation of 5G equipment. Intuitively, the EMFconstraints tend to limit the number of 5G sites installedover the territory and/or the amount of radiated power byeach 5G gNB. Therefore, the EMF regulations have a largeimpact on the 5G gNB installation costs and the 5G servicereceived by UE [1], [5], [12].The picture is further complicated in different countries(such as Italy, Poland, and many others) [6], which introduceEMF regulations more restrictive that the ones defined byICNIRP and FCC, on the basis of the application of aprecautionary principle, in order to preserve the popula-tion from (still unknown) long-term health effects triggeredby EMF exposure. Additional rules include: i ) EMF limitsstrongly lower that the ones defined by ICNIRP/FCC [6],[13] and/or ii ) minimum distances between sensitive places(e.g., schools, hospitals public parks) and the installed 5Gsites [14]. For example, both i ) and ii ) are enforced in thecity of Rome, an area of 1287 square kilometers inhabited by a r X i v : . [ c s . N I] J u l almost 3 million people. As sketched in Fig. 1, the introduc-tion of strict EMF limits strongly affects the planning of the5G network. For example, the installation of new 5G sitesis prevented within a minimum distance from the center ofthe sensitive area (e.g., the school in the figure). In addition,the enforcement of very low EMF limits tends to generateEMF saturation areas (e.g., the one shown on top right ofthe figure), where the EMF levels from pre-5G technologiesare already close to the maximum limits. In such zones,therefore, the installation of new 5G sites is denied. As aresult, the 5G sites have to be installed locations, thus furtherimpacting the installation costs and the service level offeredby the 5G network.In this context, a natural question emerges: Is it possibleto deploy a heterogeneous 5G network, while ensuring 5Gservice and restrictive EMF constraints? The ambitions goalof the paper is to tackle such interesting - and challenging -problem. Our innovative contributions can be summarizedas follows. First, we take into account restrictive EMF reg-ulations affecting the 5G planning phase, i.e., EMF limitsstricter than ICNIRP/FCC ones, as well as enforcement ofminimum distances between 5G sites and sensitive places.Second, we optimally model the 5G planning problem un-der service and EMF constraints. The presented problem in-tegrates the widely used model of Marzetta [15] to computethe service level from a Massive Multiple-Input Multiple-Output (MIMO) system, as well as the EMF point sourcedescribed in International Telecommunication Union (ITU)K.70 recommendation [16], which is enriched by a set ofscaling parameters to take into account the temporal andstatistical variation of the radiated power from 5G MIMOsystems with beamforming capabilities. We also show thatthe complete formulation falls within the class of MixedInteger Linear Programming (MILP) problems and it is NP-Hard. Third, we design PL ANNING A LGORITHM T OWARDS
EMF E
MISSIONS A SSESSMENT (PLATEA), a novel heuristicthat is able to efficiently solve the 5G planning problemwhile ensuring adherence to strict EMF limits and 5G ser-vice for the set of pixels belonging to the area under consi-deration. Fourth, we evaluate PLATEA and two referencealgorithms in a realistic scenario, whose parameters havebeen measured on the field (e.g., the EMF levels radiated bypre-5G sites already deployed in the scenario). Results provethat PLATEA outperforms the reference algorithms, byefficiently balancing between 5G gNB installation costs andamount of 5G service coverage. In addition, we demonstratethat the scaling parameters used to compute the powerradiated by 5G gNBs play a critical role in determiningthe selected planning and theEMF levels over the territory.Eventually, we show that the exposure levels generated bypre-5G technologies have an impact on the 5G planning.To the best of our knowledge, previous works in theliterature are focused on orthogonal aspects w.r.t the onesinvestigated in this paper. For example, Oughton et al. [2]target the solution of the 5G planning problem by meansof techno-economic approaches, with little emphasis on theimpact of EMF constraints. On the other hand, Matalatala etal. [17], [18] design heuristics targeting the reduction of theradiated power, EMF and/or specific absorption rate (SAR),without considering: i) the linearization of the problem constraints, ii) the impact of the variation of the scalingparameters to compute the EMF levels from 5G gNBs, and iii) the introduction of constraints to ensure a minimumdistance between sensitive places and 5G gNBs. In thiswork, we show that both ii) and iii) are fundamental todetermine the actual planning. In addition, we propose aninnovative formulation with linear constraints, which arealso exploited by PLATEA to further reduce the algorithmcomplexity.The rest of the paper is organized as follows. Sec. 2reviews the related work. The main building blocks of theconsidered 5G framework are highlighted in Sec. 3. Sec. 4reports the problem formulation. The PLATEA algorithm isthoroughly described in Sec. 5. The scenario under conside-ration is detailed in Sec. 6. Results are analyzed in Sec. 7.Finally, Sec. 8 concludes our work. ELATED W ORKS
Tab 1 reports the positioning of this paper w.r.t. other rele-vant works that are focused on the planning of 5G networks[2], [17], [18]. More in depth, we consider the followingfeatures to classify the literature: i) pursued goal(s) (e.g.,cost reduction, power consumption reduction), ii) targeted5G equipment type (e.g., generic gNBs, micro and macrogNBs), iii) modeled 5G service (e.g., SINR, network spectralefficiency, throughput, maximum coverage distance), iv) EMF features (e.g., temporal and statistical models, presenceof exclusion zones in proximity to the gNB), v) conside-red EMF regulations (e.g., ICNIRP-based EMF limits, strictEMF limits, minimum site distance from sensitive places), vi) pursued methodology (e.g., model assessment, optimalformulation, heuristic) and vii) scenario complexity (e.g.,number of candidate sites, regular or irregular coveragelayout, size of the service area, pixel or user evaluation).Compared to the literature, our work moves one stepfurther by: i) explicitly targeting a weighed function of in-stallation costs and service coverage, ii) considering a hete-rogeneous 5G network composed of micro and macro gNBs, iii) precisely modeling multiple service metrics, includingthroughput, minimum SIR and maximum coverage dis-tance, iv) performing the variation of the scaling parametersto compute the EMF, as well as including exclusion zones inproximity to the gNB, v) integrating EMF regulations morerestrictive than ICNIRP/FCC, both in terms of maximumlimits and in terms of minimum distance between a 5Gsite and a sensitive place, vi) defining a linear formulation(MILP) and exploiting the linearized constraints to designthe heuristic, vii) analyzing a large scenario composed ofdozens of candidate sites with irregular coverage layouts,a service area in the order of different square kilometers,and service/EMF evaluations performed in each pixel of theterritory. UILDING B LOCKS
We briefly overview the main building blocks that are inte-grated in our 5G framework, namely: i) the model to assess
1. The authors of [18] introduce an optimal formulation, which ishowever not linear w.r.t. the signal-to-noise ratio (SNR) computation,the electric field computation and the SAR computation.
TABLE 1Work positioning w.r.t. the related literature.
5G Equipment 5G ServiceWork Goal Type Metrics EMF Features EMF Regulations Methodology Scenario Complexity O u g h t o n e t a l . [ ] Capacity andcosts assessment Micro & macro 5GgNBs signal-to-interferenceplus noise ratio(SINR), networkspectral efficiency - - Model assessment Hexagonalcoverage layoutswith 7 candidatesites, servicearea of fewsquare kilometers,evaluation doneon pixels. M a t a l a t a l a e t a l . [ ] Power consump-tion reduction,EMF exposurereduction Generic gNBsoperating at3.7 [GHz] Throughput,SINR Presence of exclu-sion zones Strict EMF limits Heuristic Dozens ofcandidate siteswith irregularcoverage layout,service area ofseveral squarekilometers,evaluation doneon users (not on apixel base). M a t a l a t a l a e t a l . [ ] Power consump-tion reduction,EMF exposure reduction,
SAR exposurereduction,dose exposurereduction
Generic gNBs operating at3.7 [GHz]
Throughput,
SINR Statistical models (with fixed para- meters), presenceof exclusion zones
ICNIRP-based
EMF limits Mixed IntegerNon-Linear
Programming (MINLP)optimizationmodel, heuristic Dozens ofcandidate siteswith irregularcoverage layout, service area of several squarekilometers,evaluation doneon users (not on apixel base). T h i s w o r k Installation costsreduction, maxi-mization of thenumber of servedpixels Micro & macro 5GgNBs Throughput,minimum signal-to-interferenceratio (SIR)threshold,maximumcoverage distance Temoporal andstatistical models(with variationof parameters),presence ofexclusion zones Strict EMF limits,minimum site dis-tance from sensi-tive places MILP optimiza-tion model,heuristic Dozens ofcandidate siteswith irregularcoverage layout,service areaof differentsquare kilometers,evaluation doneon pixels.
5G performance, ii ) the model to estimate EMF radiated bya set of gNBs and iii ) the EMF regulations for the installationof 5G sites. In the following, we provide more details abouteach building block. We adopt the widely known MIMO model of Marzetta [15]to evaluate the 5G performance for a set of installed gNBs.We refer to [15] for the details, while here we report thesalient features. In brief, the model assumes that each siteis equipped with arrays composed of a very large numberof antenna elements. In the work of Marzetta [15], thenumber of antennas is higher than the number of users.Since the number of antennas is very large, the downlinkSINR is dominated by the interference from neighboringgNBs rather than by the noise floor. More formally, the SIRof the k -th user served by l -th gNB operating on frequency f is defined as: S ( k,l,f ) = β l,k,l,f ) (cid:80) j (cid:54) = l β l,k,j,f ) (1)
2. In the original model of [15] a set of gNBs operating at the samecentral frequency is assumed. In this work, instead, we consider aheterogeneous network composed of multiple tiers of gNBs opera-ting at different frequencies. However, the extension of the model ofMarzetta [15] to the multiple frequencies case is straightforward, asonly gNBs operating on the same frequency have to be counted in theSIR computation of Eq. (1).
In the previous equation, the β terms are expressed as: β ( l,k,j,f ) = z ( l,k,j,f ) D γ f ( k,l,f ) (2)where D ( k,l,f ) is the distance between 5G UE k and gNBoperating on frequency f and installed at location l , γ f isthe path-loss exponent for frequency f and z ( l,k,j,f ) is a log-normal random variable, i.e., the quantity · log ( z ( l,k,j,f ) ) is a distributed zero-mean Gaussian with a standard devia-tion σ SHAD f [15].The β terms appearing in Eq. (1) are also sketched in thetoy-case scenario of Fig. 2, which is composed by two gNBsand three UE. Intuitively, each 5G UE is served by a singlegNB, while the other gNB contributes to the interferenceexperienced by the 5G UE. It is important to remark that,in the downlink direction, the contributions of interferenceare solely due to the neighboring gNB, and not to thesimultaneous transmissions to other UE in the same cell(e.g., terminals k and k in the figure), due to the fact thatan Orthogonal Frequency-Division Multiplexing (OFDM)technology is assumed.The downlink throughput received by user k from gNBinstalled at location l and operating on frequency f is thenexpressed as: T ( k,l,f ) = B f · Γ f (cid:15) SEC f · log (cid:0) S ( k,l,f ) (cid:1) (3)where: B f is the gNB bandwidth, (cid:15) SEC f ≤ is a parametergoverning the sectorization over frequency f (equal to 1 Signal Term 5G gNB j1 5G gNB j25G UE k35G UE k1 5G UE k2j1 Coverage Area j2 Coverage Area β (j1,k1,j1,f1) β (j1,k1,j2,f1) β (j1,k3,j1,f1) β (j1,k3,j2,f1) β (j2,k2,j2,f1) β (j2,k2,j1,f1) Interference Term
Fig. 2. Signal and interference terms in the 5G service model of [15] fora toy case scenario with two gNBs and three UEs.TABLE 2Expressions for the time-related parameters of [15].
Parameter Expression τ SLOT f (cid:104) N OFDM f · ( f ) (cid:105) + δ f τ PILOT f N OFDM-PILOT f · τ SYMBOL f τ SYMBOL f τ
COHERENCE fN OFDM f τ USEFUL f f when sectorization is not exploited), Γ f is a shaping factor,formally expressed as: Γ f = ( τ SLOT f − τ PILOT f ) · τ USEFUL f τ SLOT f · τ SYMBOL f (4)where τ SLOT f is the slot duration over f , τ PILOT f is the pilotduration over f , τ SYMBOL f is the symbol interval over f and τ USEFUL f is the useful symbol duration over f . The expres-sions for τ SLOT f , τ PILOT f , τ SYMBOL f and τ USEFUL f are reportedin Tab. 2, where N OFDM f is the number of OFDM symbolsover f , ∆ f is the subcarrier spacing over f , δ f is thecyclic prefix duration over f , N OFDM-PILOT f is the numberof OFDM symbols used for pilots over f and τ COHERENCE f isthe coherence time over f .Summarizing, the model of Marzetta [15] allows tocompute the SIR and the maximum throughput for eachUE, given the set of installed 5G gNBs and the UE-gNBassociation. The second building block that is instrumental to our frame-work is the computation of the EMF that is received bya 5G UE from a 5G gNB. In the literature, different EMFmodels have been proposed to this purpose. We refer theinterested reader to ITU-T K.70 recommendation [16] foran overview about the EMF models. In brief, the availableoptions include point source models, synthetic models andfull-wave models. In this work, we select the point sourcemodel, due to the following key properties: • the actual EMF levels that are measured over theterritory in the far-field region are typically lowerthan the ones estimated through the point sourcemodel of [16]. Therefore, when the EMF is computed Power Density Term 5G gNB j1 5G gNB j25G UE k35G UE k1 5G UE k2j1 Coverage Area j2 Coverage Area P (k1,j1,f1) P (k1,j2,f1) P (k3,j1,f1) P (k3,j2,f1) P (k2,j2,f1) P (k2,j1,f1) Fig. 3. Power density terms in the same toy case scenario of Fig. 2. through this model and the obtained level is belowthe maximum limit, the adherence to the limit isalways guaranteed; • a linear set of constraints to compute the total EMFlevels can be built when the model is integratedin our framework. Ensuring the linearity of theconstraints is a desirable property, which, in fact,allows to reduce the complexity of both the optimalformulation and the designed heuristic.In more detail, the point source model allows to computethe power density P ( k,l,f ) that is received by UE k from agNB located at site l and operating on frequency f . Clearly,the distance D ( k,l,f ) between gNB l and UE k is assumedto be in the far-field region [16]. More formally, P ( k,l,f ) isexpressed as: P ( k,l,f ) = EIRP ( l,f ) π · D k,l,f ) · F ( k,l,f ) (5)where EIRP ( l,f ) is the Equivalent Isotropically RadiatedPower (EIRP) from gNB operating on frequency f andlocated at site l and F ( k,l,f ) ≤ is the normalized numericgain over user k from an antenna installed at location l operating on frequency f . More in depth, EIRP ( l,f ) isformally expressed as:EIRP ( l,f ) = O MAX ( l,f ) · η GAIN f η LOSS f (6)where O MAX ( l,f ) is the maximum output power for a gNBoperating on frequency f and located at site l , η GAIN f isthe transmission gain on frequency f , and η LOSS f is thetransmission loss on frequency f .By assuming the maximum achievable numeric gain F ( k,l,f ) = 1 (as in [16]), Eq. (5) is simplified into: P ( k,l,f ) = EIRP ( l,f ) π · D k,l,f ) (7)Given P ( k,l,f ) , the electric field value E ( k,l,f ) is thenexpressed as: E ( k,l,f ) = (cid:113) P ( k,l,f ) · Z (8)where Z denotes the free space wave impedance.
3. The power density metric is commonly used to characterize thelevel of exposure. Other exposure metrics include electric field, mag-netic field and SAR. We refer the interested reader to [7] for an overviewand comparison of the different exposure metrics.
TABLE 3Comparison across ICNIRP guidelines [7], [19], Italian regulations [13], [20] and Rome regulations [13], [14], [20]. ( a ) , ( b ) Frequency Max. incident Max. incident Averaging Min. distance D MIN
ID Name range electric field power density L f time interval from sensitive places
400 - 2000 [MHz] 1.375 · f . [V/m] f /200 [W/m ] R1 ICNIRP 1998 Guidelines [19] 2 - 300 [GHz] 61 [V/m] 10 [W/m ] 6 [min] - up to 10 [GHz] -400 - 2000 [MHz] 1.375 · f . [V/m] f /200 [W/m ] R2 ICNIRP 2020 Guidelines [7] 2 - 300 [GHz] N/A 10 [W/m ] 30 [min] -Italian Regulation [13], [20] 3 - 3000 [MHz] 20 [V/m] 1 [W/m ] R3 (General Public Areas) 3 - 300 [GHz] 40 [V/m] 4 [W/m ] 6 [min] -Italian Regulation [13], [20] R4 (Residential Areas) 0.1 [MHz] - 300 [GHz] 6 [V/m] 0.1 [W/m ] 24 [h] -Rome regulation [13], [14], [20] 3 - 3000 [MHz] 20 [V/m] 1 [W/m ] R5 (General Public Areas) 3 - 300 [GHz] 40 [V/m] 4 [W/m ] 6 [min] 100 [m]Rome regulation [13], [14], [20] R6 (Residential Areas) 0.1 [MHz] - 300 [GHz] 6 [V/m] 0.1 [W/m ] 24 [h] 100 [m] (a) N/A stands for Not Applicable, meaning that the related quantity does not have to be taken into account when dealing with a compliance assessment. (b) f is the used frequency in MHz. Fig. 3 reports the power density terms P ( k,l,f ) in thesame toy-case scenario of Fig. 2, which is composed by twogNBs operating at the same frequency f and three UEs. Ac-tually, the total power density that is received by each UE isa linear combination of the single terms radiated by the twogNBs. For example, the total power density radiated over5G UE k is simply equal to P ( k ,j ,f + P ( k ,j ,f . Notethat, when considering the total electric field from multiplegNBs, a root mean square operator has to be applied. Byconsidering the previous example, the total electric field thatis radiated over UE k is equal to (cid:113) E k ,j ,f + E k ,j ,f .This operation introduces a non-linearity in the computationof the total exposure, which also generates non-linear con-straints when binary variables are employed to select the setof sites that have to be installed out of the candidate ones.To overcome this issue, in this work we consider the com-putation of the total exposure through the power densitymetric, which instead allows to preserve the linearity of theconstraints.When computing the exposure from a 5G gNB, a key roleis played by the EIRP value appearing in Eq. (7). Clearly, thehigher is the EIRP, the larger will be also the received powerdensity P ( k,l,f ) . This fact imposes to precisely estimate EIRPvalues that match real 5G gNB exposure patterns. In thiscontext, two important elements that affect the EIRP valuesof a 5G gNB are the temporal variation and the statisticalvariation of the radiated power. We refer the interestedreader to the International Electrotechnical Commission(IEC) standards [21], [22] for an overview about these as-pects. In brief, the temporal variation is due to the fact thatthe number of 5G UE (and their traffic over the cellularnetwork) exhibits a day-night pattern. Actually, the actualoutput power levels of the 5G gNB match this variation,with radiated power higher during the day and clearlylower during the night. On the other hand, the applicationof MIMO with beamforming features introduces strongvariations in the radiated power over the territory, resultingin an exposure that is concentrated only to the zones wherethe served users are located. This issue is typically takeninto account by solving statistical exposure models, whichallow to compute spatially averaged radiated power values,as a consequence of the actual user distribution over the territory.In this work, we take into account the temporal andthe statistical variability of the EIRP from 5G gNB by in-troducing two scaling parameters, denoted as R TIME ( l,f ) ∈ (0 , and R STAT ( l,f ) ∈ (0 , , respectively. Actually, the introduction ofparameters to scale the maximum EIRP is in line with otherworks that investigate the exposure modeling from 5G gNBs[22]–[25]. More formally, the scaled EIRP from gNB installedat site l and operating on frequency f is computed as:EIRP TS ( l,f ) = EIRP ( l,f ) · R TIME ( l,f ) · R STAT ( l,f ) (9)In addition, let us introduce the power density P TS ( k,l,f ) computed from EIRP TS ( l,f ) . By adopting Eq. (9) and the left-hand side of Eq. (7), P TS ( k,l,f ) is formally expressed as: P TS ( k,l,f ) = P ( k,l,f ) · R TIME ( l,f ) · R STAT ( l,f ) (10)In this work, we use Eq. (7),(10) to characterize the levelof exposure from a 5G gNB located at site l , operatingon frequency f and radiating over UE k . Moreover, wedemonstrate that the actual values of R TIME ( l,f ) and R STAT ( l,f ) havea crucial role in determining the level of exposure andconsequently the set of gNBs that are installed over theterritory. We then consider the third building block of our framework,i.e., the integration of the 5G EMF constraints defined in theregulations. To this aim, Tab. 3 reports the set of regulations R1 )- R6 ), which include ICNIRP guidelines ( R1 - R2 ), Italiannational regulations R3 )- R4 ), and the local EMF regulationsenforced in the city of Rome R5 )- R6 ). For each regula-tion/guideline, the table reports: i ) the frequency rangerelevant to 5G, ii ) the maximum electric field limit for eachfrequency f , iii ) the maximum power density limit L f foreach f , iv ) the time interval to compute the average EMFthat has to be compared against the limit value and v ) the(eventual) minimum distance constraints that have to be en-sured between the 5G installations and the sensitive places.As a side comment, we include in Tab. 3 the ICNIRP 1998guidelines [19] and ICNIRP 2020 ones [7], due to the factthat the formers are still adopted in many countries in the world, while the latters are the up-to-date regulations whichare going to be adopted in the forthcoming month/years,and hence in parallel with the deployment of 5G networks.Several considerations hold by analyzing Tab. 3. First ofall, R2 ) defines a power density limit and not a limit basedon electric field strength, for all the frequencies between2 [GHz] and 300 [GHz]. This fact further corroborates ourchoice for selecting the power density as the reference metricwhen performing the compliance assessment against themaximum limits. Second, the Italian regulations R3 )- R4 ) arein general stricter than R1 )- R2 ), both in terms of electric fieldand in terms of power density. Third, the Italian regulationsin R3 ) and R4 ) further differentiate between general publicareas (e.g., zones of the territory where the population is notcontinuously living) and residential areas (e.g., zones wherepeople tend to live and/or work), respectively. Interestingly, R4 ) regulations are more restrictive than R3 ). Fourth, the cityof Rome applies a minimum distance D MIN from sensitiveplaces in addition to the strict EMF limits defined in R3 )- R4 ).Therefore, the regulations R5 )- R6 ) further restrict R3 )- R4 ).Fifth, the averaging time interval strongly varies across thedifferent regulations, ranging from values of few minutesto 24 hours. This interval plays a crucial role in estimatingthe average EMF that has to be compared against the limitthresholds. Clearly, the lower is the time interval, the higherwill be the influence of (possible) spikes on the averageEMF. On the other hand, the higher is the time interval, thelower will be the impact of spikes on the average EMF. Asa side comment, the instantaneous EMF field can be higherthan the thresholds reported in Tab. 3. The actual metricthat is meaningful for comparison against the limit is infact the average EMF over the time interval defined in eachregulation.After analyzing the EMF regulations, a natural questionemerges: How to perform the compliance assessment w.r.t.the maximum limits when multiple Base Stations operatingat different frequencies radiate the same area of territory?To answer this question, let us denote with (cid:80) l ∈L P ( k,l,f ) the composite power density that is radiated over UE k byall the Base Stations operating on frequency f ∈ F , where F is the set of frequencies in use. The compliance w.r.t. thelimits is ensured over k if the following condition holds: (cid:88) f ∈F (cid:80) l ∈L P ( k,l,f ) L f ≤ (11)Clearly, the power density terms P ( k,l,f ) of Eq. (11) haveto be computed as average values over the time intervalsreported in Tab. 3. In addition, the actual EMF metric thatis measured under practical conditions is the electric fieldstrength E ( k,l,f ) , which is then translated into power density P ( k,l,f ) by applying Eq. (8). The model of Marzetta [15] is used to control the SIR andconsequently the maximum downlink throughput providedto the UE. The point source model of ITU-T K.70 [16],integrated with scaling parameters that characterize theexposure from 5G gNB, is instead used to compute an over-estimation of the power density. Finally, the limits definedby international/national bodies and local municipalities are used to ensure that the composite power density islower than the thresholds. In addition, a minimum distancerule from sensitive places is ensured in accordance to thelocal regulation. In the next section, we join together thesebuilding blocks, in order to build an innovative formulationable to balance between gNBs installation costs and 5Gservice coverage level, while ensuring QoS and strict EMFconstraints.
PTIMAL
5G P
LANNING F ORMULATION
We divide our formulation in the following steps: i ) prelim-inaries, ii ) set definition, iii ) constraint, variables and inputparameters, iv ) overall formulation. In the previous section we have provided the models tocompute the service coverage and the power density foreach UE in the scenario under consideration. In this section,we generalize these models by extending the evaluationsfrom a sparse set of UE to a tessellation of non-overlappingsquared pixels that fully cover the area under interest. Byapplying the pixel tessellation, three important goals can bemet, namely:1) the power density terms are computed over thewhole area under consideration. More in depth, weevaluate the power density that is received over thepixel center from all the installed gNBs. In this way,we are able to extend the EMF compliance assess-ment over the whole territory. In addition, we modelthe presence of exclusion zones in proximity to theinstalled gNBs, i.e., zones of the territory that arenot accessed by users and therefore in such zonesthe EMF compliance assessment is not required forthe general public;2) a dense scenario where users are located in eachpixel (and not in few locations) is introduced. Thisassumption appears to be meaningful in the contextof 5G, especially for the Enhanced Mobile Broad-band (eMBB) scenario [26]. In this way, it is possibleto control the amount of throughput provided toeach pixel, and consequently to the UE that arelocated in the pixel;
3) a minimum throughput requirement may be intro-duced for each pixel rather than for single users. Inthis way, it is possible to (indirectly) take into ac-count also the effects of UE densification and/or UEmobility. For example, by assigning different valuesof required throughput, it is possible to model highdensity zones, where the throughput requirementsare high, compared to other zones, which insteadare not visited by users. In a similar way, it is pos-sible to vary the throughput requirements based onthe UE mobility, e.g., by increasing the throughputfor the zones that are subject to high UE mobility,in order to take into account the effect of handoversand/or possible traffic spikes.
4. The evaluation of the UE throughput given the pixel throughputwill be done in a future work.
Focusing then on the modelling of the EMF regulations,we assume to enforce the most restrictive ones, namely R5 )- R6 ) of Tab. 3. Therefore, we distinguish between generalpublic areas, residential areas and zones within the mini-mum distance from sensitive places. However, we point outthat the other guidelines presented in Tab. 3 can be easilyimplemented in our framework by applying different limitthresholds and/or by setting the minimum distance D MIN to zero.
Let us denote with P the set of pixels under consideration. P RES ⊂ P and P GEN ⊂ P are the subsets of pixels inresidential areas and in general public areas, respectively.Moreover, P SENS ⊂ P is the subset of pixels in sensitiveareas. In addition, let L be the set of candidate locations(sites) that can host 5G gNB equipment. Eventually, let F bethe set of frequencies that can be exploited by 5G gNBs. We then detail constraints, variables and input parametersto our problem by adopting a step-by-step approach. Wealso refer the reader to Tab. 4 for the main notation that isadopted throughout the section.
5G Coverage and Service Constraints.
We initiallymodel the constraint that a pixel p ∈ P can be covered by a5G gNB located in l only if the distance D ( p,l,f ) between thepixel and the installed gNB is lower than a maximum one,denoted with D MAX f , where f is the operating frequency ofthe 5G gNB installed in l . More formally, we have: D ( p,l,f ) · x ( p,l,f ) ≤ D MAX f · y ( l,f ) , ∀ p ∈ P , l ∈ L , f ∈ F (12)where x ( p,l,f ) is a binary variable, set to 1 if p is served bygNB operating on frequency f and located at l (0 otherwise).Moreover, y ( l,f ) is another binary variable, set to 1 if 5GgNB operating on frequency f is installed at location l (0otherwise).We then impose the constraint that each pixel p can beserved by at most N SER ≥ gNBs at the same time: (cid:88) l ∈L (cid:88) f ∈F x ( p,l,f ) ≤ N SER , ∀ p ∈ P (13)In the following, we impose that the SIR value in eachpixel p that is served by a 5G gNB operating on frequency f has to be higher than a minimum value S MIN f . By adoptingthe SIR computation already introduced in Eq. (1), we have: β l,p,l,f ) · y ( l,f ) (cid:80) l (cid:54) = l ∈L β l,p,l ,f ) · y ( l ,f ) (cid:124) (cid:123)(cid:122) (cid:125) SIR S ( p,l,f ) ≥ S MIN f · x ( p,l,f ) (cid:124) (cid:123)(cid:122) (cid:125) Min. SIR Threshold , ∀ p ∈ P , l ∈ L , f ∈ F (14)
5. Although multiple coverage from different gNB is a desirablecondition, the increase in the number of gNBs covering the same pixelmay introduce side effects, like an increase in the handover rates forUE, which may dramatically decrease the perceived QoS [5]. Therefore,we introduce a constraint to control the number of gNBs serving thesame pixel.6. Since we have extended the evaluation from the single UE to thewhole set of pixels, the k index of Eq. (1) is replaced with p ∈ P . TABLE 4Main Notation.
Symbol Description P Set of pixels P RES ∈ P
Set of pixels in residential areas P GEN ∈ P
Set of pixels in general public areas P SENS ∈ P
Set of pixels in sensitive areas L set of candidate locations for installing 5G gNBs S e t N o t a ti o n F Set of operating frequencies for 5G gNB S MIN f Minimum SIR to achieve in order to guarantee therequired 5G service on frequency f ∈ F β ( l,p,l ,f ) Signal/interference contribution from 5G gNB l ∈ L on frequency f ∈ F over pixel p ∈ P served by gNB l ∈ L C SITE ( l,f ) Site installation cost of a 5G gNB site operating onfrequency f ∈ F at location l ∈ L C EQUIP f Equipment cost of a 5G gNB operating on frequency f ∈ F ; P BASE ( p,f ) Baseline power density on frequency f ∈ F receivedby pixel p ∈ P P ADD ( p,l,f ) Additional power density received by pixel p ∈ P from a 5G gNB installed at location l ∈ L operatingon frequency f ∈ F L RES f Power density limit over frequency f ∈ F for a pixelbelonging to a residential area L GEN f Power density limit over frequency f ∈ F for a pixelbelonging to a general public area D MIN
Minimum distance between an installed 5G gNB siteand a sensitive place D MAX f Max. 5G coverage distance between a 5G gNB operatingon frequency f and a covered pixel D ( p,l,f ) Distance between pixel p ∈ P and a gNB operating onfrequency f ∈ F and installed at location l ∈ L E ( p,l,f ) Exclusion zone indicator: 1 if pixel p ∈ P falls inside theexclusion zone of a 5G gNB installed at location l ∈ L and operating on frequency f ∈ F , 0 otherwise N SER
Maximum number of 5G gNBs that can serve a singlepixel N MAX
Maximum number of 5G gNBs that can be installed ina location I ( l,f ) Indicator parameter: 1 if gNB operating on frequency f ∈ F can be installed at location l ∈ L , 0 otherwise R TIME ( l,f ) Temporal scaling factor for a 5G gNB operating onfrequency f ∈ F and installed at location l ∈ L R STAT ( l,f ) Statistical scaling factor for a 5G gNB operating onfrequency f ∈ F and installed at location l ∈ L ; P a r a m e t e r s α ( l,f ) Objective weight factor for the service coverage varia-bles, depending on frequency f ∈ F and gNB location l ∈ L . y ( l,f )
5G gNB equipment binary variable: 1 if a 5G gNBequipment operating on frequency f ∈ F is installed atlocation l ∈ L , 0 otherwise x ( p,l,f ) Binary 5G service variable : 1 if pixel p ∈ P is servedby 5G gNB at location l ∈ L with frequency f ∈ F , 0otherwise P ADD-TS ( p,f ) Additional power density received by pixel p ∈ P from all the 5G gNBs operating on frequency f ∈ F ,computed over temporal and statistical scaling factors P ADD-NOTS ( p,f ) Additional power density received by pixel p ∈ P fromall the 5G gNB operating on frequency f ∈ F , com-puted without temporal and statistical scaling factors w p Pixel in exclusion zone binary variable : 1 if pixel p ∈ P falls inside an exclusion zone of an installed 5G gNB, 0otherwise V a r i a b l e s C TOT
Total installation costs for the 5G gNBs.
Clearly, the previous constraint is not linear, due to theoptimization variables y ( l,f ) that appear on both the numer-ator and the denominator of the left-hand side, coupled withthe presence of the x ( p,l,f ) variables on the right-hand sideof the constraint. In order to linearize Eq. (14), we initiallyexploit the following equivalence: (cid:88) l (cid:54) = l ∈L β l,p,l ,f ) · y ( l ,f ) = (cid:88) l ∈L β l,p,l ,f ) · y ( l ,f ) − β l,p,l,f ) · y ( l,f ) (15)By assuming that the right-hand side of Eq. (15) is greaterthan or equal to 0, we then replace the denominator of Eq. (14) with Eq. (15), thus obtaining: β l,p,l,f ) · y ( l,f ) ≥ S MIN f · x ( p,l,f ) ·· (cid:88) l ∈L β l,p,l ,f ) · y ( l ,f ) − β l,p,l,f ) · y ( l,f ) , ∀ p ∈ P , l ∈ L , f ∈ F (16)We then divide both sides of the constraint by the lefthand side term, thus obtaining: S MIN f · x ( p,l,f ) · (cid:34) (cid:80) l ∈L β l,p,l ,f ) · y ( l ,f ) β l,p,l,f ) · y ( l,f ) − (cid:35) ≤ , ∀ p ∈ P , l ∈ L , f ∈ F (17)The previous constraint is equivalent to the followingone: S MIN f (cid:34) (cid:80) l ∈L β l,p,l ,f ) · y ( l ,f ) · x ( p,l,f ) β l,p,l,f ) · y ( l,f ) − x ( p,l,f ) (cid:35) ≤ , ∀ p ∈ P , l ∈ L , f ∈ F (18)By recalling constraint (12), we know that x ( p,l,f ) = 1 only if y ( l,f ) = 1 (and both Eq. (12) and Eq. (13) areensured). In other words, x ( p,l,f ) can not be set to 1 if thegNB operating on f is not installed in l , i.e., y ( l,f ) = 0 . Asa result, the ratio x ( p,l,f ) /y ( l,f ) can be simply expressed as x ( p,l,f ) . Consequently, constraint (18) can be rewritten in thefollowing equivalent form: S MIN f · (cid:88) l ∈L β l,p,l ,f ) β l,p,l,f ) · y ( l ,f ) · x ( p,l,f ) − x ( p,l,f ) ≤ , ∀ p ∈ P , l ∈ L , f ∈ F (19)The previous constraint can be easily linearized by: i )introducing the binary auxiliary variable v ( l,p,l ,f ) ∈ { , } , ii ) replacing (19) with the following set of constraints: v ( l,p,l ,f ) ≤ x ( p,l,f ) , ∀ p ∈ P , l ∈ L , l ∈ L , f ∈ F (20) v ( l,p,l ,f ) ≤ y ( l ,f ) , ∀ p ∈ P , l ∈ L , l ∈ L , f ∈ F (21) v ( l,p,l ,f ) ≥ x ( p,l,f ) + y ( l ,f ) − , ∀ p ∈ P , l ∈ L , l ∈ L , f ∈ F (22) S MIN f · (cid:88) l ∈L β l,p,l ,f ) β l,p,l,f ) · v ( l,p,l ,f ) − x ( p,l,f ) ≤ ∀ p ∈ P , l ∈ L , f ∈ F (23) Power Density Limits.
We initially select the pixelsthat fall in the exclusion zones of the installed 5G gNBsand therefore are not subject to the EMF limits defined forthe general public. More formally, we introduce the binaryvariable w p , set to 1 if p is located inside an exclusion zone ofan installed gNB (0 otherwise). In addition, input parameter E ( p,l,f ) takes value 1 if pixel p is inside the exclusion zone ofgNB operating on frequency f and located at l (0 otherwise). The value of w p is then set through the following set ofconstraints: w p ≥ E ( p,l,f ) · y ( l,f ) , ∀ p ∈ P , l ∈ L , f ∈ F (24) w p ≤ (cid:88) l ∈L (cid:88) f ∈F E ( p,l,f ) · y ( l,f ) , ∀ p ∈ P (25)More in depth, constraint (24) activates w p if p is insideat least one exclusion zone of an installed gNB. On theother hand, constraint (25) forces w p to 0 if p is outside theexclusion zones for all the installed gNBs.In the following, we introduce the constraints to com-pute the power density received by pixel p over frequency f . Let us denote with input parameter P ADD ( p,l,f ) the additionalpower density that is received by pixel p when a gNBoperating on frequency f is installed in l . Let us denote with P ADD-TS ( p,f ) the variable storing the additional power densityfor pixel p over f , which is computed from P ADD ( p,l,f ) byapplying the scaling factors R TIME ( l,f ) and R STAT ( l,f ) . More formally,we include Eq. (10) to our problem, thus yielding: P ADD-TS ( p,f ) = (1 − w p ) (cid:88) l ∈L P ADD ( p,l,f ) · R TIME ( l,f ) · R STAT ( l,f ) · y ( l,f ) ∀ p ∈ P , f ∈ F (26)In the previous constraint, the term (1 − w p ) ensures thata pixel falling inside the exclusion zone of an installed 5GgNB is not considered when the power density is evaluatedagainst the limits.Since constraint (26) is not linear, we linearize it by: i )introducing the auxiliary variable z ( p,l,f ) ∈ { , } , and ii )replacing Eq. (26) with the following set of constraints: z ( p,l,f ) ≤ (1 − w p ) , ∀ p ∈ P , l ∈ L , f ∈ F (27) z ( p,l,f ) ≤ y ( l,f ) , ∀ p ∈ P , l ∈ L , f ∈ F (28) z ( p,l,f ) ≥ y ( l,f ) − w p , ∀ p ∈ P , l ∈ L , f ∈ F (29) P ADD-TS ( p,f ) = (cid:88) l ∈L P ADD ( p,l,f ) · R TIME ( l,f ) · R STAT ( l,f ) · z ( p,l,f ) ∀ p ∈ P , f ∈ F (30)In a similar way, we compute the additional totalpower density P ADD-NOTS ( p,f ) that is received by pixel p onfrequency f , without applying the scaling factors R TIME ( l,f ) , R STAT ( l,f ) . P ADD-NOTS ( p,f ) is meaningful when p belongs to a generalpublic area (e.g., R5 of Tab. 3). In this case, in fact, the scalingparameters are not applied. Therefore, we have: P ADD-NOTS ( p,f ) = (cid:88) l ∈L P ADD ( p,l,f ) · z ( p,l,f ) , ∀ p ∈ P , f ∈ F (31)We then impose the power density limit on residentialareas, which has to be ensured for each pixel p ∈ P RES . Moretechnically, we include the compliance assessment model ofEq. (11) in our problem, thus obtaining: (cid:88) f ∈F P BASE ( p,f ) · (1 − w p ) + P ADD-TS ( p,f ) L RES f ≤ , ∀ p ∈ P RES (32)
7. A revision in the regulations may be introduced in the future inorder to introduce scaling parameters also for general public areas. P BASE(p1,f1) (1-w p1 )
4G Node-B 5G gNB5G gNB p1w p1 =0y (l2,f2) =1 y (l1,f2) =1P ADD(p1,l2,f2) z (p1,l2,f2) P ADD(p2,l2,f2) z (p2,l2,f2) Term ≥ (a) Pixel outside the exclusion zone P BASE(p2,f1) (1-w p2 )4G Node-B 5G gNB5G gNB P ADD(p2,l1,f2) z (p2,l1,f2) y (l2,f2) =1P ADD(p2,l2,f2) z (p2,l2,f2) w p2 =1p2 y (l1,f2) =1Term ≥ (b) Pixel inside the exclusion zone Fig. 4. Computation of the power density terms in a toy-case scenariothat includes exclusion zones from the newly installed gNBs. where P BASE ( p,f ) is the baseline power density over p from allthe radio-frequency sources operating of frequency f andalready installed in the scenario under consideration.In a similar way, we impose the power density limit ongeneral public areas, which has to be ensured for each pixel p ∈ P GEN , by introducing the following constraint: (cid:88) f ∈F P BASE ( p,f ) · (1 − w p ) + P ADD-NOTS ( p,f ) L GEN f ≤ , ∀ p ∈ P GEN (33)In order to clarify how the computation of the powerdensity is governed by the optimization variables modellingthe exclusion zones, Fig. 4 shows a graphical representationof P ADD ( p,l,f ) · z ( p,l,f ) terms that appear in Eq. (30)-(31) as wellas P BASE ( p,f ) · (1 − w p ) that are included in Eq. (32)-(33). More indepth, the considered toy-case scenario includes one legacy4G Node-B already installed over the territory and twonewly installed gNBs. Fig. 4(a) focuses on a pixel p outsidethe exclusion zones of the gNBs. By applying Eq. (24)-(25), itholds that w p = 0 . Then, by applying constraints (27)-(29),it holds that: z ( p ,l ,f = 1 , z ( p ,l ,f = 1 . Consequently,the computation of the total power density in (32)-(33) willinclude the contributions from the newly installed gNBsas well as the already installed 4G Node-B. Therefore, theinstallation of the newly installed gNB is possible only ifthe EMF compliance assessment constraints (32)-(32) areensured. On the other hand, Fig. 4(b) reports the powerdensity terms when the considered pixel p falls inside theexclusion zone of a gNB. By applying Eq. (24)-(25),(27)-(29)it holds that: w p = 1 , z ( p ,l ,f = 0 , z ( p ,l ,f = 0 . Asa result, the power density terms P ADD ( p ,l,f ) · z ( p ,l,f ) and P BASE ( p ,f · (1 − w p ) are now set to zero. Therefore, the EMF compliance assessment constraints (32)-(33) are alwaysensured for p . Minimum Distance from Sensitive Places.
We thenintroduce the distance constraints that are included in reg-ulations R5 )- R6 ) of Tab. 3. We remind that these constraintsdefine a minimum distance between each installed 5G gNBand a sensitive place. More formally, we have: D ( p,l,f ) · y ( l,f ) ≥ D MIN , ∀ p ∈ P SENS , l ∈ L , f ∈ F (34)
Site Constraints.
In the following, we impose that eachsite location can host up to N MAX gNB types operating atdifferent frequencies. More formally, we have: (cid:88) f ∈F y ( l,f ) ≤ N MAX , ∀ l ∈ L (35)In addition, we introduce the indicator parameter I ( l,f ) ,taking value 1 if gNB of type f can be hosted at location l , 0 otherwise. Clearly, a gNB operating on frequency f canbe installed at l only if the indicator parameter is 1. Moreformally, we have: y ( l,f ) ≤ I ( l,f ) , ∀ l ∈ L , f ∈ F (36) Total Cost Computation.
Finally, we compute the totalcosts for installing the 5G gNBs. To this aim, let us denotewith parameter C EQUIP f the monetary costs of a 5G gNBequipment operating on frequency f . In addition, let usdenote with parameter C SITE ( l,f ) the site installation cost fora 5G gNB operating on frequency f and installed at location l . The total costs C TOT for installing the new 5G gNBs areformally expressed as: C TOT = (cid:88) l ∈L (cid:88) f ∈F (cid:16) C EQUIP f + C SITE ( l,f ) (cid:17) · y ( l,f ) (37) The considered objective function targets the minimiza-tion of the total costs for installing the 5G gNBs and themaximization of the number of pixels that are served bythe installed 5G gNBs. The two terms are properly takeninto account by the weight factor α ( l,f ) , which depends onfrequency f and on gNB location l . By tuning α ( l,f ) , theoperator can easily control the CAPEX costs and the level ofservice coverage over the territory. The complete O
PTIMAL P LANNING FOR
5G N ET - WORKS UNDER S ERVICE AND S TRICT
EMF C
ONSTRAINTS (OPTPLAN-5G) is formally expressed as:min C TOT − (cid:88) p ∈P (cid:88) l ∈L (cid:88) f ∈F α ( l,f ) · x ( p,l,f ) (38)
8. Other alternative formulations commonly adopted during thecellular planning phase include the minimization of the CAPEX costsunder a given percentage of service coverage. However, this goal doesnot always guarantee problem feasibility. To overcome this issue, in thiswork we keep the service coverage in the objective function. As a result,our choice allows to preserve the problem feasibility on one side and toexplore the impact of α ( l,f ) on the obtained planning on the other one. Algorithm 1
Pseudo-Code of PLATEA algorithm
Input:
Parameters and sets defined in Tab. 4, assumed to be available through global variables
Output:
Variables y , x , P ADD-TS , P ADD-NOTS , w , C TOT for the best solution found // Step 1: Initialization num f1 max= (cid:80) l ∈L I ( f ,l ) ; // Max. number of installable f gNBs num f2 max= (cid:80) l ∈L I ( f ,l ) ; // Max. number of installable f gNBs best obj=inf; // Best objective initialization [ y , x , P ADD-TS , P ADD-NOTS , w , C TOT ]= INITIAL SOL (); // Solution variables initialization // Step 2: iteration over candidate deployments with frequency f for num f1=1:num f1 max do [flag end x curr, y curr, pd curr]= SELECT BEST SET F // Selection of the best deployment withnum_f1 gNBs // Step 3: iteration over candidate deployments with frequency f for num f2=1:num f2 max do if flag end==false then sites f2 perm= EXTRACT SITES (num f2, f2); // Extraction of the candidate deployments withfrequency f for sites f2 in sites f2 perm do [flag check, y curr, pd curr]= INSTALL CHECK (sites f2, y curr, pd curr); // Based on Eq. (24), (25),(27)-(36) if flag check==true then [x curr]= ASSOCIATE PIXELS (y curr, x curr); // Based on Eq. (12),(13),(20)-(23) curr obj=
COMPUTE OBJ (x curr, y curr); // Based on Eq. (37), (38) if curr obj < best obj then best obj=curr obj; [ y , x , P ADD-TS , P ADD-NOTS , w , C TOT ]= SAVE SOL (y curr, x curr, pd curr); // Best Solution Saving end if if ( ALL SERVED (x curr)==true) then flag end=true; // All pixels served end if [x curr, y curr, pd curr]=
UNINSTALL ( f , x curr, y curr, pd curr); // Revert changes for f end if end for end if end for [x curr, y curr, pd curr]= UNINSTALL ( f , x curr, y curr, pd curr); // Revert changes for f end for subject to:5G Coverage and Service: Eq. (12 , , (20) − (23) Power Density Limits: Eq. (24 , , (27) − (33) Min. Distance Constraint: Eq. (34)
Site Constraints: Eq. (35) , (36) Total Cost Computation: Eq. (37) (39)under variables: C TOT ≥ , x ( p,l,f ) ∈ { , } , y ( l,f ) ∈{ , } , w p ∈ { , } , v ( p,l,l ,f ) ∈ { , } , z ( p,l,f ) ∈ { , } . Proposition 1.
The
OPTPLAN-5G problem is NP-Hard.Proof.
Let us consider a special case of the problem, wherea single pixel is evaluated. Moreover, let us assume that thissingle pixel is covered if the gNB operating on frequency f is installed in l , i.e., x ( p,l,f ) = y ( l,f ) , ∀ l ∈ L , f ∈ F . Letus also consider the possibility to install up to one gNB ineach site, i.e., N MAX = 1 . Consequently, constraint (35) canbe rewritten as: (cid:88) f ∈F y ( l,f ) ≤ , ∀ l ∈ L (40)Moreover, let us assume that the considered pixel is outsidethe exclusion zone of each installed gNB, i.e., w p = 0 .
9. In this way, we assume that the pixel is within D MAX distance fromall the gNBs and that the minimum value of service throughput is equalto 0.
Consequently, z ( p,l,f ) = y ( l,f ) , ∀ l ∈ L , f ∈ F . Moreover,we consider: i ) the application of general public limits, i.e.,the scaling parameters are not applied and ii ) a relaxation ofthe power density constraints in (33) with no backgroundpower density (i.e., P BASE ( p,f ) = 0 , ∀ f ∈ F ) and the limitverification for each frequency in isolation w.r.t. the otherfrequencies. More formally, constraint (33) is replaced withthe following one: (cid:88) l ∈L P ADD ( p,l,f ) · y ( l,f ) ≤ L GEN f , ∀ f ∈ F (41)We then assume the maximization of the service coverage,which in our problem is equivalent to the maximizationof the number of installed gNBs, weighted by α ( l,f ) . Moreformally, we have:max (cid:88) l ∈L (cid:88) f ∈F α ( l,f ) · y ( l,f ) (42)subject to: Eq. (40), Eq. (41); under variables: y ( l,f ) ∈ { , } .It is therefore trivial to note that the aforementioned for-mulation is the well-known G ENERALIZED A SSIGNMENT P ROBLEM (GAP), which is NP-Hard [27]. Since GAP isa special case of our problem, we can conclude that alsoOPTPLAN-5G is NP-Hard. ALGORITHM
Since the OPTPLAN-5G is NP-Hard, and therefore verychallenging to be solved even for small problem instances,we design an efficient algorithm, called PL
ANNING A LGO - RITHM T OWARDS
EMF E
MISSION A SSESSMENT (PLATEA)to practically solve it. We base our solution on the followingintuitions:1) we apply a divide et impera approach, in whichthe complex planning problem is split into setsof subproblems. More in depth, since the differentfrequencies used in 5G have in general differentgoals (e.g., throughput maximization and/or cove-rage maximization), we exploit the gNB operatingfrequency as the main metric to split the originalproblem into smaller subproblems;2) we restrict the exploration of the solution spaceby evaluating controlled sets of candidate deploy-ments. However, we introduce a parameter to con-trol the exploration level of the candidate deploy-ments;3) we exploit the linear constraints introduced in theprevious section to limit the computational comple-xity of PLATEA.Alg. 1 reports the high-level pseudo-code of PLATEA.The presented algorithm is tailored to the case in whichtwo frequencies f and f are exploited, with f targetingthroughput maximization and f targeting coverage ma-ximization. In order to ease the presented pseudo-codes,we adopt the following guidelines: i ) the input parametersand sets defined in Tab. 4 are assumed to be availablethrough global variables, and ii ) the subscripts appearingin the parameters/variables are hindered. The algorithmthen produces as output the selected deployment y , thepixel to gNB association x , the power density variables P ADD-TS , P ADD-NOTS , the exclusion zone variable w and thetotal installation costs C TOT for the selected deployment.We then describe the operations performed by PLATEA.Initially, the maximum number of installable gNB is com-puted (lines 2-3). In the following, all the variables areinitialized to zero values by the
INITIAL SOL function (line5). PLATEA then iterates over the possible candidate de-ployments with frequency f (lines 7-31). In particular, the SELECT BEST SET F f gNB,starting from one up to the maximum number (line 7).In the following, we provide more details about the SELECT BEST SET F num_f1 . Then, the function pro-duces as output a flag (indicating if a feasible deploymenthas been found), as well as temporary variables storing thecurrent set of installed f gNBs, the current pixel to gNBassociation, and the current power density over the set of
10. In our case, f is a mid-band frequency, while f is a sub-GHzfrequency. These two sets of frequencies are the ones currently in useby 5G, while the exploitation of frequencies in the mm-Wave bandis still at the early stage in many countries in the world. However,PLATEA can be easily generalized also to the case in which three typesof frequencies (i.e., sub-GHz, mid-band, mm-Waves) are employed. Weleave this aspect as future work. Algorithm 2
Pseudo-Code of the
SELECT BEST SET F
Input: num f1 deployed gNBs with frequency f Output: flag end flag with installation status (false = instal-lation successful, true = installation unsuccessful), temporaryvariables x best, y best, pd best best obj=inf; flag end=true; sites f1 perm= EXTRACT SITES (num f1,f1); //Extraction of the candidate deploymentswith frequency f for sites f1 in sites f1 perm do [x temp y temp pd temp]= INITIALIZE (); [flag check, pd temp]= INSTALL CHECK (sites f1,y temp, pd temp); // Based on Eq. (24), (25),(27)-(36) with frequency f if flag check==true then flag end=false; [x temp]= ASSOCIATE PIXELS (y temp, x temp); // Based on Eq. (12),(13),(20)-(23) withfrequency f temp obj= COMPUTE OBJ (x temp, y temp); //Based on Eq. (37), (38) with frequency f if temp obj < best obj then best obj=temp obj; x best=x temp; y best=y temp; pd best=pd temp; end if end if end for pixels. After an initialization step to setup the routine varia-bles (line 1-2), the function retrieves the possible permuta-tions of f gNBs, by running the EXTRACT SITES routine(line 3). Since enumerating all the possible permutationsis a challenging step in terms of computational require-ments, we control the amount of generated permutationsby assuming that up to num_f1 candidate deployments arerandomly generated. Intuitively, when num_f1 is low, it isnot meaningful to explore the whole space of permutations,since the number of served pixels will be in any case ratherlimited. On the other hand, we consider more permutationsas num_f1 increases, since the impact on service coveragemay be not negligible in this case.In the following (lines 4-18), the
SELECT BEST SET F f . If the previous constraints areall met, the pixels are associated to the installed gNBs (line9) and the objective function is evaluated (line 10). Morein depth, the association of pixels in line 9 is performedby sequentially analyzing the set of installed gNBs and byassociating each pixel while ensuring the 5G coverage andservice constraints of Eq. (12),(13),(20)-(23) with frequency f . Clearly, if the previous constraints are not met, the cur-rent pixel is not associated to the gNB under consideration.In addition, the computation of the objective function inline 10 exploits constraints Eq. (37),(38) with frequency f .Eventually, the best solution is updated in lines 11-16.When SELECT BEST SET F TABLE 5Computational complexity of the routines and PLATEA algorithm
Procedure Complexity
INITIAL SOL O ( |P| × |L| × |F| ) EXTRACT SITES O ( N PERM ) INSTALL CHECK O ( |P| × |L| × |F| ) ASSOCIATE PIXELS O ( |P| × |L| × |F| ) COMPUTE OBJ O ( |P| × |L| × |F| ) SAVE SOL O ( |P| × |L| × |F| ) INITIALIZE O ( |P| × |L| × |F| ) ALL SERVED O ( |P| × |L| × |F| ) SELECT BEST SET F O ( N PERM × |P| × |L| × |F| ) PLATEA O ( N PERM × |P| × |L| × |F| ) forms lines 9-31 of Alg. 1. In particular, the algorithmiterates over the candidate deployments on frequency f (line 10). Clearly, this step is performed only if a feasiblecandidate deployment over frequency f has been found(line 11). In the following, the algorithm generates num_f2 permutations of f gNBs (line 12), and then iterates overeach candidate deployment (lines 13-27) in order to verifythe constraints (line 14) and eventually to perform the gNB-pixel association (lines 15-16). The functions used in thesesteps are exactly the same adopted in Alg. 2, except fromthe adopted frequencies, which now also include f gNBs.In the following, the objective function is evaluated (line 17),and the best solution is eventually updated (lines 18-21).The algorithm then stops evaluating further deploymentsif all the pixels have been served (line 22-24). Clearly,when passing between the evaluation of one deployment tothe following one, the changes operated on the temporaryvariables are reverted to the previous state (lines 25,30). Computational Complexity.
Tab. 5 reports the com-putational complexity of the routines, functions and thewhole PLATEA algorithm. Several considerations holdby analyzing the table. First, we denote with N PERM thenumber of permutations that are generated by the EX - TRACT SITES routine. Second, the computational complexityof
INSTALL CHECK , ASSOCIATE PIXELS and
COMPUTE OBJ are derived from the implementation of constraints Eq. (24),(25), (27)-(36), (12),(13), (20)-(23), (37), (38). Third, the wholecomputational complexity of PLATEA grows linearly withthe number of pixels and with the number of frequen-cies. Fourth, although the complexity of PLATEA mayappear substantially large at a first glance, due to the term N PERM × |L| , we remind that the number of candidate sites |L| is rather limited in practice, due to the intrinsic difficultyin finding suitable locations that can host gNB equipment. Inaddition, in our work we constrain N PERM to be in the sameorder of magnitude of |L| . Therefore, overall complexity ofPLATEA is in the order of O ( |P| × |L| × |F| ) . CENARIO D ESCRIPTION
We consider as reference scenario the Torrino MezzoCam-mino (TMC) neighborhood in Rome, Italy. The area un-der consideration, spanning over . [km ], is actually Fig. 5. TMC map with candidate locations for f gNBs (orange pins) andfor f gNBs (blue pins). populated by more than 10000 inhabitants. We select theTMC neighborhood due to the following reasons: i ) TMCincludes residential areas and sensitive places (i.e., publicparks, schools, churches, recreation centers); therefore, itsterritory is subject to very stringent EMF regulations (i.e., R6 regulation of Tab. 3), ii ) the terrain is almost plain, i.e., thereare not steep hills and/or large obstacles (apart from thebuildings), which would otherwise affect the propagationconditions, iii ) 5G coverage is not actually provided in theneighborhood, iv ) pre-5G base stations are installed onlyoutside the neighborhood, v ) background information aboutpre-5G coverage and QoS levels experienced in TMC isalready available in [5].We then focus on the set of frequencies F that areemployed by 5G gNBs. More in detail, we consider theexploitation of two distinct frequencies, namely f [MHz] and f [MHz]. Both f and f have beenrecently auctioned to 5G operators in Italy [28]. Therefore,we expect that both f and f will be used by 5G equipmentin the forthcoming years. In this work, we assume that f is exploited by micro gNBs, while the f is employed bymacro gNBs. We believe that this choice is meaningful, as f will be mainly used to provide capacity, while f willensure coverage.In the following, we provide more details about the areaunder consideration, the set of pixels, the set of candidategNBs and the set of sensitive places. To this aim, Fig. 5reports: i ) the TMC neighborhood (transparent blue area), ii )the set of locations L that can host 5G gNBs (i.e., the unionof blue and orange pins), iii ) the subset of locations that canhost f gNBs (orange pins), and iv ) the subset of locationsthat can host f gNBs (blue pins). The selection of locationsin iii ) and iv ) is driven by the following principles: a )installation of f gNBs mainly on top of buildings, in order
11. Apart from f and f , the auction of 5G frequencies in Italyincluded also a band at 26 [GHz] (i.e., close to mm-Waves) [28].However, the 26 [GHz] frequency is intentionally left apart from thispaper, due to the following reasons: i ) at present time, it is unclear atwhich extent 5G devices operating at 26 [GHz] will be installed over theterritory, and ii ) there are not commercial gNBs operating at 26 [GHz]currently installed in Italy. Fig. 6. TMC map with sensitive places highlighted in yellow. to maximize the coverage over the territory, b ) installation of f gNBs close to the zones where capacity is needed (alongthe roads and in proximity to the residential buildings). Asa result, a total of |L| = 69 candidate locations are takeninto account in this work. In the following, we move ourattention to the set of pixels P . More in detail, we assume apixel tessellation over the TMC area, with a pixel granularityequal to × [m ]. The total number of pixels |P| is thenequal to 24318. Focusing then on the sensitive places, Fig. 6highlights in yellow the areas hosting public parks, schoolsand/or churches. By adopting R6 ) regulation from Tab. 3,the installation of gNBs is prohibited within a minimumdistance of D MIN = 100 [m] from the external perimeter ofthese sensitive places.We then analyze the setting of the remaining frequency-dependent parameters that are required as input. To thisaim, Tab. 6 reports: i ) I ( l,f ) parameter (obtained from Fig. 5by assuming N MAX = 1 ), ii ) distance-based parameters, iii ) 5G EMF parameters, iv ) 5G performance parameters,and v ) 5G costs parameters. We now focus on the settingof the key parameters, while we refer the reader to thereferences reported in Tab. 6 for more information aboutthe setting of each single parameter. More in depth, weassume that the maximum power O MAX ( l,f ) that is radiatedby a gNB operating over f is actually higher than theone radiated by a gNB operating over f . Although thissetting may appear quite counter-intuitive at a first glance,since a micro gNB is expected to radiate less power than amacro gNB, we remind that O MAX ( l,f ) refers to the maximumpower, which can clearly differ w.r.t. the actual one that isreceived over the territory. When considering micro gNBs, O MAX ( l,f ) is split across the radiating elements, and thus theactual power that is received over the territory is clearlylower compared to the maximum one. This effect is takeninto account when setting the statistical scaling factor R STAT ( l,f ) .More in detail, we assume a strong statistical scaling factorthat is applied to micro gNBs operating on f , while nostatistical scaling factor is applied to macro gNBs operatingon f . This choice is also motivated by the different goalsof two gNB types, i.e., maximizing throughput for f (andhence large spatial power variability) vs. ensuring coverage TABLE 6Setting of the frequency-related parameters.
Parameter f . [GHz] f [MHz] I ( l,f ) Based on TMC scenario with N MAX = 1 .gNB height 10 [m] (Pole mounted) 25 [m] (Roof-top mounted)Pixel height 1.5 [m] (std. evaluation height) D i s t a n c e D ( p,l,f ) Based on TMC scenario and gNB/pixel heights. O MAX ( l,f )
200 [W] ∀ l ∈ L [29] 65 [W] ∀ l ∈ L (as-sumed to be in linewith pre-5G technolo-gies [16]) η GAIN f
15 [dB] [16] η LOSS f R STAT ( l,f ) ∀ l ∈ L [23] 1 ∀ l ∈ L (max. value) R TIME ( l,f ) ∀ l ∈ L [24]Excl. Distance 11 [m] [30] 5 [m] (Roof excl. zone) E ( p,l,f ) Based on the TMC scenario and the exclusiondistances. P BASE ( p,f ) Based on real EMF measurements in TMC sce- nario. G E M F P ADD ( p,l,f ) Based on point source model [16] over TMC sce-nario and EMF parameters. L f R6 of Tab. 3) D MAX f
200 [m] [31] 900 [m] γ f σ SHAD f z ( l,p,j,f ) Log normal random variable [15]. β ( l,p,j,f ) Marzetta model [15] based on TMC scenario, γ f and z ( l,p,j,f ) . N OFDM f
14 [33] N OFDM-PILOT f τ COHERENCE f
500 [ µ s] [15] δ f µ s] [33], [34] 4.7 [ µ s] [33], [34] ∆ f
30 [kHz] [33] 15 [kHz] [33] B f
80 [MHz] [28] 20 [MHz] [28] G P e rf o r m a n c e (cid:15) SEC f S MIN f Set to ensure30 [Mbps] of min.throughput. - C SITE ( l,f ) e ] ∀ l ∈ L [31] 20101 [ e ] [31] ∀ l ∈ L C EQUIP f e ] [31] 45673 [ e ] [31] C o s t s α ( l,f ) [10 − ] [ e ] ∀ l ∈ L [10 − ] [ e ] ∀ l ∈ L for f (and hence less spatial power variability). Focusingthen on the exclusion zones, we assume again two distinctvalues for f and f , which are set in accordance to theminimum distance guaranteeing a EMF level below thelimit of 6 [V/m] for a single gNB. Eventually, P BASE ( p,f ) isretrieved from real measurements over the real scenario,with the methodology described in Appendix A. Moreover,we assume that the minimum SIR is set in order to ensure aminimum pixel throughput of 30 [Mbps] for f . In addition,we do not constrain the SIR over f , since the goal of gNBsoperating over this frequency is mainly to provide coverage.Therefore, even low throughput values may be admitted
12. The EMF is also computed in this case by applying the pointsource model of [16]. TABLE 7Breakdown of the evaluation metrics.
Metric Notation/Expression Reference Equations
Total Installation Costs C TOT
Eq. (37) (total costs computation).Number of Installations N f = (cid:80) l ∈L y ( l,f , N f = (cid:80) l ∈L y ( l,f -Served Pixels X SERVED f = (cid:80) p ∈P (cid:80) l ∈L x ( p,l,f , X SERVED f = (cid:80) p ∈P (cid:80) l ∈L x ( p,l,f -Unserved pixels [%] X NOT-SERVED = 100 · (cid:80) p ∈P : { (cid:80) l ∈L (cid:80) f ∈F x ( p,l,f )==0 } (cid:16) − (cid:80) l ∈L (cid:80) f ∈F x ( p,l,f ) (cid:17) |P| -Pixel Throughput T p = (cid:80) l ∈L (cid:80) f ∈F Bf Γ f(cid:15) SEC f log (cid:0) S ( p,l,f ) (cid:1) · x ( p,l,f ) Eq. (14) (SIR computation on left handside), Eq. (4) ( Γ f computation), Eq. (3)(throughput computation).Average Pixel Throughput T AVG = (cid:80) p ∈P Tp |P|· (1 − X NOT-SERVED / See computation of T p and X NOT-SERVED .Pixel EMF E p = (cid:114)(cid:80) f ∈F (cid:104) P BASE ( p,f ) · (1 − w p ) + P ADD-TS ( p,f ) (cid:105) · Z Eq. (32) (total power density computa-tion in the numerator on left-hand side),Eq. (8) (electric field computation).Average Pixel EMF E AVG = (cid:115) (cid:80) p ∈P RES (cid:80) f ∈F (cid:20) P BASE ( p,f ) · (1 − wp )+ P ADD-TS ( p,f ) (cid:21) |P RES | · Z See computation of E p . for f . Although these throughput settings may appearrelatively loose at a first glance, we will show that the actualthroughput levels experienced over the served pixels arenot negligible and in line with the 5G service requirements[26]. Finally, the α ( l,f ) parameter, which acts as a weightfor the number of served pixels in the objective function, isvaried over a huge range, in order to test its sensitivity onthe obtained planning.Eventually, we provide the setting for the remainingparameters, namely Z and N SER . In particular, we set Z = 377 [Ohm] (in accordance to [16]). In addition, weimpose N SER = 2 . In this way, we consider a conservativecase in which each pixel is served by at most two gNBs. ESULTS
We code PLATEA algorithm in MATLAB R2019b and werun it on a Dell PowerEdge R230 equipped with Intel XeonE3-1230 v6 3.5 [GHz] processors and 64 [GB] of RAM. Wethen describe the following steps: i ) introduction of tworeference algorithms as terms of comparison, ii ) definitionof evaluation metrics, iii ) tuning of PLATEA parameters, iv ) comparison of PLATEA vs. the reference algorithms, v )impact of planning parameters, and vi ) impact of pre-5Gexposure levels. Reference Algorithms.
In order to introduce a termof comparison, we code two reference algorithms, namedE
VALUATION A LGORITHM (EA) and M
AXIMUM C OVERAGE M ACRO A LGORITHM (MCMA). We refer the reader to Ap-pendix B for a detailed description of EA and MCMA, whilehere we briefly summarize their salient features. In brief, EAand MCMA evaluate the feasibility constraints of a randomset of installed gNBs, without exploring the possible sitepermutations (which are instead analyzed by PLATEA).More in depth, EA explores a single possible deployment(which is generated from a fixed number of gNBs, passedas input to the algorithm). On the other hand, MCMA
13. We remind that, in any case, pixels beyond the maximum distancecoverage D MAX f from a given gNB can not be served by the gNB.14. The evaluation of N SER values greater than 2 is left for futurework. goes one step further, by selecting the set of macro gNBsoperating on f maximizing the service coverage, given aninteger number of f gNBs that have to be installed over theterritory. We refer the reader to Appendix B for the pseudo-code of the two solutions, including also the evaluation oftheir computational complexity. Evaluation Metrics.
We then formally introduce themetrics to evaluate the performance of PLATEA, EA andMCMA. To this aim, Tab. 7 reports: i ) total installation costs C TOT , ii ) number N f ( N f ) of f ( f ) gNBs installations, iii ) number of pixels X SERVED f ( X SERVED f ) served by f ( f )gNBs, iv ) percentage of unserved pixels X NOT-SERVED , v )pixel throughput T p , vi ) average pixel throughput T AVG ,computed over the pixels that are served by gNBs, vii ) pixelEMF E p , viii ) average pixel EMF E AVG , computed over thewhole set of pixels in the scenario. For each metric, the tablereports the metric name, the mathematical notation, and thereference equation(s) used to compute the metric.
Tuning of PLATEA Parameters.
We initially concentrateon the impact of the α ( l,f ) terms that are included in theobjective function of PLATEA. As reported in Tab. 6, we ex-plore a wide range of values for both α ( l,f and α ( l,f . Forthe sake of simplicity, we impose the same weights appliedfor all the candidate gNB s working at the same frequency. In addition, we initially assume the dismission of legacy pre-5G Base Stations that radiate over TMC, in order to evaluatethe performance of PLATEA in a clean-slate condition.Therefore, we set P BASE ( p,f ) = 0 ∀ f ∈ F , p ∈ P . We thenrun PLATEA over the selected ranges of α ( l,f and α ( l,f ,by picking values on logarithmic scales. Fig. 7 highlights theobtained results in terms of: i ) total installation costs C TOT (Fig. 7(a)), ii ) number N f of f gNBs (Fig. 7(b)), iii ) number N f of f gNBs (Fig. 7(c)), iv ) percentage of not servedpixels X NOT-SERVED (Fig. 7(d)), v ) average pixel throughput T AVG (Fig 7(e)) and vi ) average electric field E AVG (Fig. 7(f)).Several considerations hold by analyzing in detail Fig. 7.First, C TOT is proportional to α ( l,f and α ( l,f (Fig. 7(a)),
15. In more complex scenarios, the values of α ( l,f ) may be tunedfor each location l , in order to prioritize locations that require hugeamount of traffic (e.g., shopping malls, train stations, or airports) w.r.t.other ones. The evaluation of this aspect is left for future work. (l,f1) ( l ,f ) (a) C TOT [M e ] (l,f1) ( l ,f ) (b) N f (l,f1) ( l ,f ) (c) N f (l,f1) ( l ,f ) (d) X NOT-SERVED [%] (l,f1) ( l ,f ) (e) T AVG [Mbps] (l,f1) ( l ,f ) (f) E AVG [V/m]
Fig. 7. Impact of α ( l,f ) variation on: i ) total installation costs C TOT , ii )number N f of f gNBs, iii ) number N f of f gNBs, iv ) percentageof not served pixels X NOT-SERVED , v ) average pixel throughout T AVG , vi )average electric field E AVG . due to the fact that the weights play a major role in de-termining the objective function, e.g., cost minimization,service maximization or a mixture between them. Clearly, α ( l,f ( α ( l,f ) only affects N f ( N f ), as shown in Fig. 7(b)(Fig. 7(c)). In addition, X NOT-SERVED is inversely proportionalto α ( l,f (Fig. 7(d)). For example, when α ( l,f ≈ , morethan 10% of pixels are not served by any gNB. This is dueto the fact that the number of f gNBs that are installedpasses from 3 to 1 (see Fig. 7(c)), thus creating coverageholes. On the other hand, the variation of α ( l,f has a clearimpact on X NOT-SERVED only when α ( l,f ≈ , i.e., when f gNBs are not able to cover the whole territory. Moreover,Fig 7(e) reveals that T AVG has a complex trend, which resultsfrom the combination of: i ) the coverage provided by f and f gNBs installed over the territory, ii ) the amount ofinterference, which tends to be impacted by the number ofneighboring gNBs operating at the same frequency, and iii )the percentage of served pixels, since T AVG is computedover the pixels that receive service coverage from at leastone gNB. As a consequence, T AVG is not always propor-tional or inversely proportional with α ( l,f ) . For example,the maximum value of T AVG is achieved when α ( l,f = 10 ,which however leads to a huge number of unserved pixels(i.e., more than 10%). Finally, E AVG is proportional to α ( l,f ) ,due to the variation in the number of radiating sources thatcontribute to the EMF exposure. However, we point out thatthe average EMF level is almost one order of magnitude (a) Map of installed gNBs (orange pins: f gNBs,blue pins: f gNBs) [m] [ m ] [ V / m ] (b) Electric field levels E p [V/m] Fig. 8. Visualization of the best scenario retrieved by PLATEA with α ( l,f = 50 [ e ] and α ( l,f = 500 [ e ]. lower than the 6 [V/m] restrictive limit.Based on the above considerations, we select α ( l,f =50 [ e ] and α ( l,f = 500 [ e ] henceforth. In this way, webalance between: i) increasing T AVG , ii) reducing C TOT , iii)minimizing X NOT-SERVED , iv) reducing E AVG . To give moreinsights, Fig. 8 shows a run of the planning selected byPLATEA with the aforementioned setting. Interestingly,only a subset of the candidate gNBs, i.e., 11 f gNBs and 3 f gNBs, is deployed over the TMC scenario (Fig. 8(a)). Onthe other hand, the resulting EMF levels are always prettylow (see Fig. 8(b)), with an electric field close to the 6 [V/m]limit only in proximity to the f gNBs. Algorithms Comparison.
In the following, we comparethe performance of PLATEA against EA and MCMA. Un-less otherwise specified, we compute each metric by avera-ging the results over 10 independent runs. Focusing on thenumber of f and f gNBs selected by PLATEA, we havefound that our solution requires on average N f = 10 . and N f = 3 , respectively. Consequently, we have passedto EA and MCMA a number of f gNBs equal to 11. Inaddition, EA requires the number of f gNB, which is setto 3. Tab. 8 reports the performance of the algorithms overthe different metrics. More in detail, the total installation TABLE 8Comparison of PLATEA vs. reference algorithms EA and MCMA.
Metric EA MCMA PLATEA C TOT [k e ] 391.4 588.7 386.1 N f
11 11 10.7 N f X SERVED f X SERVED f X NOT-SERVED [%] 10.11 0 0.06 T AVG [Mbps] 241.1 257.1 353.9 E AVG [V/m] 0.57 0.64 0.57 costs C TOT of PLATEA and EA are clearly lower than theones of MCMA. Clearly, since EA requires as input thesame (integer) number of f and f gNBs of PLATEA, it isnatural that the two solutions achieve almost the same C TOT .On the other hand, MCMA requires a larger number of f gNBs, in order to ensure full coverage. Focusing then onthe number of pixels served by f and f gNBs, PLATEAoperates a wiser choice compared to EA and MCMA, withseveral pixels that are served by f gNBs. Clearly, MCMAguarantees full coverage of the territory, X NOT-SERVED = 0 %.On the other hand, more than 10% of pixels are not servedwith EA. Eventually, PLATEA ensures service coveragefor 99.4% of pixels. Moreover, PLATEA achieves a clearlyhigher throughput T AVG compared to EA and MCMA. Inparticular, the throughput difference of PLATEA w.r.t. EAand MCMA is huge, i.e., more than 95 [Mbps] on average.Finally, the EMF levels introduced by PLATEA and EAare clearly lower than MCMA. In conclusion, PLATEAoutperforms both MCMA and EA when the different met-rics are jointly considered. We refer the interested reader toAppendix C for further comparisons between PLATEA andthe reference algorithms. In the following, we will analyzein more detail the impact of the planning parameters on thePLATEA performance.
Impact of planning parameters.
We then focus on theimpact of the planning parameters, namely: i ) the scalingparameters R TIME ( l,f ) and R STAT ( l,f ) , which affect the EIRP andconsequently the EMF exposure generated by gNBs and ii )the minimum distance from sensitive places D MIN , whichinfluences the subset of sites that can host gNBs. Focusingon i ) we perform a sensitivity analysis by running PLATEAover a wide range of R TIME ( l,f ) and R STAT ( l,f ) values. For the sakeof simplicity, we impose R TIME ( l,f ) ∈ [0 . − . ∀ f ∈ F , l ∈ L .On the other hand, we set R TIME ( l,f ∈ [0 . − . ∀ l ∈ L and R STAT ( l,f = 1 ∀ l ∈ L . In this way, f gNBs are subject totemporal and statistical scaling factors, while f gNB areaffected only by temporal scaling factors.Fig. 9 reports the obtained results in terms of: i ) averageEMF E AVG , ii ) number N f of f gNBs, iii ) number N f of f gNBs, iv ) average throughput T AVG , v ) percentage ofnot served pixels X NOT-SERVED , vi ) number of pixels servedby f gNBs X SERVED f . Interestingly, the choice of R TIME ( l,f ) and R STAT ( l,f ) has a huge impact on the obtained planning. In par-ticular, when R TIME ( l,f ) and R STAT ( l,f ) are close to 0.1, the averageEMF exposure is very low (i.e., lower than 0.4 [V/m]), asshown at the bottom left corner of Fig. 9(a). In this region,PLATEA installs more than 10 f gNB (Fig. 9(b)) and 3 f R STAT(l,f) R T I M E ( l ,f ) (a) E AVG [V/m] R STAT(l,f) R T I M E ( l ,f ) (b) N f R STAT(l,f) R T I M E ( l ,f ) (c) N f R STAT(l,f) R T I M E ( l ,f ) (d) T AVG [V/m] R STAT(l,f) R T I M E ( l ,f ) (e) X NOT-SERVED [%] R STAT(l,f) R T I M E ( l ,f ) (f) X SERVED f Fig. 9. Impact of the variation of the scaling parameters on: i ) averageelectric field E AVG , ii ) number N f of f gNBs, iii ) number N f of f gNBs, iv ) average throughput T AVG , v) percentage of not served pixels X NOT-SERVED , vi ) number of pixels served by f gNBs X SERVED f . gNBs (Fig. 9(c)). In addition, a large throughput is achieved(Fig. 9(d)) and (almost) all the pixels are served Fig. 9(e).On the other hand, when R TIME ( l,f ) and R STAT ( l,f ) are increased, theaverage EMF tends to increase and therefore it is challengingto ensure the strict EMF constraints in the proximity of theinstalled gNBs. Therefore, the number of installed gNBs isreduced, the throughput is decreased and the percentage ofnot served pixels abruptly increases. Eventually, for largevalues of R TIME ( l,f ) and R STAT ( l,f ) (top right corner of subfigures), itis not possible to install any gNB and therefore all the pixelsare unserved. In addition, we can note that a frontier regionemerges for intermediate values of the scaling parameters.Interestingly, for most of R TIME ( l,f ) and R STAT ( l,f ) combinationslaying on the frontier, a huge amount of pixels is servedby f gNBs (Fig. 9(f)).Summarizing, our results demonstrate that the setting ofthe scaling parameters will play a major role in the planningof 5G networks, especially for countries adopting strict EMFlimits. As a side comment, we believe that the methodologyto estimate the values of R TIME ( l,f ) and R STAT ( l,f ) should be inte-grated in the national EMF regulations. Clearly, the exactsettings of the scaling parameters depend on the consideredscenario.We then evaluate the impact of varying D MIN , which weremind is an additional restriction imposed by the munic- ipality of Rome. We report here the main outcomes fromthis test, while we refer the interested reader to Appendix Cfor more details. In brief, values of D MIN < [m] donot significantly alter the results presented so far. On thecontrary, a value of D MIN = 150 [m] introduces hugelimitations on the gNBs installations, and consequently onthe 5G service in terms of throughput and number of servedpixels.
Impact of pre-5G exposure levels.
In the last part of ourwork, we study the impact of adding the pre-5G exposureterm on the 5G planning. As detailed in Appendix A,the actual electric field strength in TMC hardly exceeds1 [V/m], even for the pixels that are at the shortest distanceand Line-of-Sight (LOS) conditions w.r.t. the serving gNB.On the other hand, the electric field rapidly decreases tonegligible values (below 1 [V/m]) as the distance betweenthe pixel and the radiating gNBs increases. However, inorder to introduce a set of conservative (and worst case)scenarios, we assume: i ) three different settings of pre-5G exposure, namely 1 [V/m], 1.5 [V/m] and 2 [V/m],and ii ) a uniform term of pre-5G exposure for all thepixels in the TMC scenario. As a consequence, the cu-mulative pre-5G power density is set as (cid:80) f ∈F P BASE ( p,f ) = { . , . , . } [ W/m ] , ∀ p ∈ P , respectively.In addition, since the same restrictive limit is applied for allthe pixels of TMC, Eq. (32) is rewritten as: (1 − w p ) · (cid:88) f ∈F P BASE ( p,f ) (cid:124) (cid:123)(cid:122) (cid:125) pre-5G Exposure Term + (cid:88) f ∈F P ADD-TS ( p,f ) (cid:124) (cid:123)(cid:122) (cid:125)
5G Exposure Term ≤ L RES , ∀ p ∈ P RES (43)where L RES = 0 . [W/m ] (in accordance to R6 of Tab. 3).Intuitively, the introduction of the pre-5G exposure termmay limit the amount of 5G gNBs that are installed overthe territory, since it is more challenging to ensure Eq. (43)compared to the case in which the pre-5G technologies aredismissed.Tab. 9 reports the performance metrics of PLATEA(averaged over 10 runs) vs. the different values of pre-5Gexposure. When the pre-5G exposure is increased, we cannote: i ) a reduction in the number of f gNBs, and conse-quently of total costs, ii ) an increase in the number of pixelsserved by f gNBs, iii ) a slight throughput decrease, and iv )an EMF increase, mainly due to the pre-5G exposure term.Overall, these results prove that the performance metrics areimpacted by the level of background exposure. However,PLATEA is always able to retrieve a feasible planning, witha percentage of unserved pixels at most equal to 0.16%. ONCLUSIONS AND F UTURE W ORKS
We have focused on the problem of planning a 5G net-work under service and EMF constraints. To this aim, wehave targeted an objective function that balances betweengNB installation costs and 5G service coverage level. Afterproviding the OPTPLAN-5G MILP formulation, we have
16. The application of a background exposure of 2 [V/m] is equiv-alent to the case in which the limit L RES equal to 4 [V/m], a valuecurrently in use in many Swiss cantons and in Monaco. Alternatively,the background exposure can be also seen as a margin that is left forthe deployment of post-5G networks.
TABLE 9PLATEA performance vs. different pre-5G exposure terms.
Pre-5G ExposureMetric 1.0 [V/m] 1.5 [V/m] 2.0 [V/m] C TOT [k e ] 371.9 343.3 267.9 N f N f X SERVED f X SERVED f X NOT-SERVED [%] 0.01 0.16 0.11 T AVG [Mbps] 354.5 332.3 324.9 E AVG [V/m] 1.18 1.62 2.06 demonstrated that the considered problem is NP-Hard,and therefore very challenging to be solved even for smallproblem instances. To face this issue, we have designed thePLATEA algorithm, which is able to select a 5G planningby iterating over the set of candidate gNBs. In addition,PLATEA exploits the linear constraints that have been de-fined for OPTPLAN-5G. We have then considered the TMCscenario, which is subject to very strict EMF regulations thatinclude minimum distances from sensitive places and verystringent EMF limits.Results, obtained by running PLATEA over the conside-red scenario, prove that our solution outperforms EA andMCMA. In addition, we have demonstrated that the 5Gplanning is overall feasible, i.e., it is possible to serve a hugeamount of pixels while limiting the installation costs andwhile ensuring the EMF constraints outside the exclusionzones of the installed gNBs. However, our work pointsout an important aspect: the scaling parameters that areused to estimate the exposure level from 5G gNBs play afundamental role in determining the problem feasibility andconsequently the set of installed gNBs. Eventually, whenpre-5G exposure is considered, PLATEA is still able toretrieve an admissible planning, with a moderate impact onthe pixel throughput.We believe that this work could be the first step towardsa more comprehensive approach. First of all, the integrationof gNBs operating on mm-Waves may be an interestingfuture work. In addition, the optimization of the scalingparameters may be another research avenue. This step couldinclude e.g., the optimal setting of the scaling parametersbased on the chosen location and the selected frequency, aswell as the evaluation of the chosen set of values duringthe management phase (e.g., when the 5G network is underoperation). Eventually, we plan to integrate detailed propa-gation models (e.g., including indoor evaluation) and morecomplex EMF models in the planning phase. R EFERENCES [1] L. Chiaraviglio, A. S. Cacciapuoti, G. Di Martino, M. Fiore,M. Montesano, D. Trucchi, and N. Blefari-Melazzi, “Planning 5gnetworks under emf constraints: State of the art and vision,”
IEEEAccess , vol. 6, pp. 51021–51037, 2018.[2] E. J. Oughton, K. Katsaros, F. Entezami, D. Kaleshi, andJ. Crowcroft, “An open-source techno-economic assessment frame-work for 5G deployment,”
IEEE Access , vol. 7, pp. 155930–155940,2019. [3] E. Amaldi, A. Capone, and F. Malucelli, “Planning umts basestation location: Optimization models with power control andalgorithms,” IEEE Transactions on Wireless Communications , vol. 2,no. 5, pp. 939–952, 2003.[4] A. R. Mishra,
Fundamentals of cellular network planning and optimi-sation: 2G/2.5 G/3G... evolution to 4G . John Wiley & Sons, 2004.[5] L. Chiaraviglio, J. Gal´an-Jim´enez, M. Fiore, and N. Blefari-Melazzi,“Not in my neighborhood: A user equipment perspective ofcellular planning under restrictive emf limits,”
IEEE Access , vol. 7,pp. 6161–6185, 2018.[6] H. M. Madjar, “Human radio frequency exposure limits: Anupdate of reference levels in europe, usa, canada, china, japanand korea,” in
5G mobile networks and health
ITU-T K Supplement 14: The impact of RF-EMF exposure limitsstricter than the ICNIRP or IEEE guidelines on 4G and 5G mobile net-work deployment
Legge quadro 22/02/2001, n. 36 (G.U. 08/03/2001, n. 55) “Leggequadro sulla protezione dalle esposizioni a campi elettrici, mag-netici ed elettromagnetici”
Regolamento per la Localizzazione, L’installazione e la ModificaDegli Impianti di Telefonia Mobile, ai Sensi Dell’art. 8, Comma6, Della Legge n. 36 Del 22 Febbraio 2001 e per la Redazionedel Piano, ex Art. 105, Comma 4 Delle NTA del PRG Vi-gente, Nonche per L’adozione di un Sistema di MonitoraggioDelle Sorgenti di Campo Elettrico, Magnetico ed Elettromagnetico documents/DACDelib N 26 14.05.2015.pdf, Last Accessed on
IEEE Transactions on WirelessCommunications , vol. 9, no. 11, pp. 3590–3600, 2010.[16]
ITU-T K.70: Mitigation techniques to limit human exposure to EMFsin the vicinity of radiocommunication stations
Proc. 29th Annual International Symposium on Personal, Indoorand Mobile Radio Communications (IEEE PIMRC), Bologna, Italy ,pp. 1208–1214, Sep. 2018.[18] M. Matalatala, M. Deruyck, S. Shikhantsov, E. Tanghe, D. Plets,S. Goudos, K. E. Psannis, L. Martens, and W. Joseph, “Multi-objective optimization of massive MIMO 5G wireless networkstowards power consumption, uplink and downlink exposure,”
Applied Sciences , vol. 9, no. 22, 2019.[19] International Commission on Non-Ionizing Radiation Protection(ICNIRP), “Guidelines for limiting exposure to time-varying elec-tric, magnetic, and electromagnetic fields (up to 300 GHz),”
HealthPhysics , vol. 74, no. 4, pp. 494–522, 1998. [20]
TESTO COORDINATO DEL DECRETO-LEGGE 18 Ottobre 2012,n. 179 Ulteriori Misure Urgenti per la Crescita del Paese.
IEC 62232:2017 Determination of RF field strength, power density andSAR in the vicinity of radiocommunication base stations for the purposeof evaluating human exposure . Available at https://webstore.iec.ch/publication/28673, Last Accessed on 27th Feb. 2020.[22]
IEC TR 62669:2019 Case studies supporting IEC 62232 - Determina-tion of RF field strength, power density and SAR in the vicinity ofradiocommunication base stations for the purpose of evaluating humanexposure . Geneva, Apr. 2019. Available at https://webstore.iec.ch/publication/62014, Last Accessed on 27th Feb. 2020.[23] B. Thors, A. Furuskr, D. Colombi, and C. Trnevik, “Time-averagedrealistic maximum power levels for the assessment of radio fre-quency exposure for 5G radio base stations using massive MIMO,”
IEEE Access , vol. 5, pp. 19711–19719, 2017.[24]
5G Is Landing: Are We Ready?
Evaluation criteria for authorization requests of radiobase stations with mMimo (in Italian)
Service requirements for the 5G system (3GPP TS 22.261 version . Available at https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=3107, Last Accessed on 28th July 2020.[27] S. Martello, “Knapsack problems: algorithms and computer im-plementations,”
Wiley-Interscience series in discrete mathematics andoptimiza tion , 1990.[28]
5G Frequency Auction in Italy (In Italian)
Antenna Integrated Radio Unit Description - Ericsson
Impact of EMF limits on 5G network roll-out
Telematics and Informatics ,vol. 37, pp. 50–69, 2019.[32] S. Sun, T. S. Rappaport, T. A. Thomas, A. Ghosh, H. C. Nguyen,I. Z. Kov´acs, I. Rodriguez, O. Koymen, and A. Partyka, “Investiga-tion of prediction accuracy, sensitivity, and parameter stability oflarge-scale propagation path loss models for 5g wireless commu-nications,”
IEEE Transactions on Vehicular Technology , vol. 65, no. 5, pp. 2843–2860, 2016. [33]
5G NR Physical channels and modulation (3GPP TS 38.211 version15.3.0 Release 15) (a) Pole mounted (b) Roof mounted (free)(c) Roof mounted (hidden) Fig. 10. Three examples of pre-5G Base Stations serving the TMCneighborhood. misurazioni wave control
TMC
Fig. 11. Measurement locations in the TMC scenario. A PPENDIX
AEMF
MEASUREMENTS IN THE
TMC
SCENARIO
We describe here the methodology adopted to perform theEMF measurements in the TMC scenario, as well as themain outcomes from the measurements. Actually, the TMCneighborhood does not host any installation of legacy pre-5G Base Stations, mainly due to the following reasons: i )TMC is a relatively new neighborhood, which was buildduring the last decade and ii ) all the requests done byoperators to install Base Stations in the neighborhood havebeen denied by the municipality, since the selected locations (a) Roadside (b) Countryside (c) Main Square Fig. 12. Three examples of EMF measurement location in the TMCneighborhood. did not ensure the minimum distance from the sensitiveplaces. As a result, the cellular service over TMC is providedby a set of Base Stations installed in other neighborhoods.We refer the interested reader to Fig. 8 of [1] for the mapsreporting the localization of pre-5G Base Stations servingTMC. In brief, these Base Stations include pole mounted androof mounted installations (with some examples reportedin Fig. 10), mainly close to the north-east and east bordersof the neighborhood. Therefore, rather than measuring theEMF levels in each pixel of TMC neighborhood (whichwould require a huge amount of time), we concentrateon the TMC zones in close proximity to the Base Stationsinstalled in the other neighborhoods, since these zones areexpected to receive the highest EMF exposure levels. To thisaim, Fig. 11 reports the considered measurement locations,each of them labelled with a unique ID. In addition, weplace the EMF meter in outdoor locations and in general inzones not covered by obstacles. To this aim, Fig. 12 reportsthree examples of measurement locations, by differentiat-ing between: roadside positioning (Fig 12(a)), countrysidepositioning (Fig. 12(b)), and positioning in the main square(Fig. 12(c)).In the following, we measure the electric field in eachmeasurement point, by adopting a professional EMF meter,whose settings are detailed in Tab. 10. More in depth, themeter provides the total electric field over the set of fre-quencies used by cellular operators. In addition, all the mea-surements have been performed during morning/afternoonhours of business days. In this way, the measured elec-tric field is retrieved under moderate/high utilization ofthe cellular network. In addition, we consider the valueof 6 [min] as the reference time interval to compute theaverage electric field (in accordance to regulation R1 ofTab. 3). Although Italian regulations integrate longer time-intervals to compute the average electric field (see e.g., R3 - R4 of Tab. 3), we believe that the considered scenario israther conservative, since the measurements are performedduring moderate/high utilization of the cellular network,and hence during time intervals during which the electricfield is higher compared to low traffic conditions (e.g., atnight, during holidays, during week-ends).Fig. 13 reports the average EMF levels over the measure-ment locations. Several consideration hold by analyzing thefigure. First, the average electric field is always pretty low, TABLE 10Main settings/features of the EMF meter
Setting/Feature Value
Measured Frequencies 700-900 [MHz], 1800-1900 [MHz],2100 [MHz], 2600 [MHz]Measurable EMF Range 0.04-65 [V/m]Average Interval 6 [min]Height from ground 1.5 [m]
Fig. 13. Average EMF of each measurement in the TMC scenario. i.e., always lower than 0.9 [V/m]. Second, the electric fieldgenerally varies across the locations. Third, very low levelsof electric field are measured over locations not in proximityto the TMC border (e.g., locations with ID 24, 25, 26, 10 ofFig. 11). This fact further corroborates our intuition that theelectric field from pre-5G Base Stations is almost negligiblefor most of the pixels in the TMC neighborhood.In the following part of this step, we analyze in moredetail the EMF measurements. To this aim, Fig. 14 reportsthe electric field vs. the measurement ID. Bar report av-erage electric field values, while error ranges denote theconfidence intervals (which are computed by assuming a95% of confidence levels). Interestingly, we can note that theconfidence interval tends to be reduced when the measuredelectric field level decreases.Finally, we remind that all the EMF measurements basedon electric field are then converted to power density byapplying Eq. 8 with Z =377 [ Ω ], in accordance to [16]. A PPENDIX BR EFERENCE A LGORITHMS
We describe here in more detail the EA and MCMA algo-rithms.
B.1 EA Description
Alg. 3 reports the EA pseudo-code. This algorithm takes asinput the number of deployed gNBs over the two frequen-cies, which are stored in the num_f1 and num_f2 parame-ters. EA then returns as output a warning flag, which isset to false if the installation have been unsuccessful (dueto the fact the constraints are not ensured), true otherwise.
Measurement ID AV G E M F [ V / m ] Fig. 14. Measured electric field vs. measurement ID.
In addition, the information about the obtained planning isreturned in the y , x , P ADD-TS , P ADD-NOTS , w , C TOT variables.Initially (line 1), EA generates a random deployment with num_f1 f gNBs and num_f2 f gNBs. In the following,EA initializes a set of internal variables (line 2). Then, EAperforms in line 3 the feasibility checks of: i ) power densitylimits outside exclusion zones, ii ) minimum distance fromsensitive places, iii ) maximum number of gNBs installedin each site and iv ) site installation constraints. If all theseconstraints are ensured (line 4), EA performs the pixel-gNBassociation (by first iterating over the f gNBs and thenover the f gNBs) and then the solution is saved (lines 5-6). Computational Complexity.
The
GENERATE SITES func-tion has a complexity of O ( |L| ) . The complexity of INITIA - LIZE , INSTALL CHECK , ASSOCIATE PIXELS and
SAVE SOL is reported in Tab. 5. Therefore, the total computationalcomplexity of EA is in the order of O ( |P| × |L| × |F| ) . B.2 MCMA Description
Alg. 4 reports the pseudo-code of MCMA algorithm. Thealgorithm requires as input the number of f gNBs tobe installed. MCMA then produces as output a flag, in-dicating if a feasible solution has been found, and theproblem variables y , x , P ADD-TS , P ADD-NOTS , w , C TOT . Themain intuition behind MCMA is to sequentially iterate overthe number of f gNBs to be installed, i.e. from 1 up to num_f2_max (lines 5-21). In particular, MCMA generatesthe set of candidate gNBs from num_f1 and num_f2 (line6), initializes the variables (line 7), runs the INSTALL CHECK function (line 8) and eventually associates the pixels to theinstalled gNBs (line 10). The iteration stops if all the pixelshave been served or the maximum number of f gNBs havebeen evaluated (line 13). Under this condition, the currentsolution is eventually saved and the algorithm is ended(lines 14-17). Otherwise, the current number of f gNB isincreased (line 18) and lines 5-21 are evaluated again. Computational complexity.
The functions employed byMCMA are the ones also used by EA (detailed in Sec. B.1)and PLATEA (detailed in Tab. 5). In addition, the whilecycle in line 5 has a complexity of O ( |L| ) . Therefore, the totalcomplexity of MCMA is in the order of O ( |P| × |L| × |F| ) . Algorithm 3
Pseudo-Code of the E
VALUATION A LGORITHM (EA)
Input: num f1 of deployed gNBs with frequency f , num f2 of deployed gNBs with frequency f Output: flag check flag with installation status (true = installation successful, false = installation unsuccessful),variables y , x , P ADD-TS , P ADD-NOTS , w , C TOT cand sites= GENERATE SITES (num f1,num f2); // Random generation of a candidate deployment [x temp y temp pd temp]= INITIALIZE (cand sites); [flag check, pd temp]= INSTALL CHECK (cand sites, y temp, pd temp); // Based on Eq. (24), (25), (27)-(36) if flag check==true then [x temp]= ASSOCIATE PIXELS (y temp, x temp); // Based on Eq. (12),(13),(20)-(23) [ y , x , P ADD-TS , P ADD-NOTS , w , C TOT ]= SAVE SOL (y temp, x temp, pd temp); // Solution saving end if Algorithm 4
Pseudo-Code of the M
AXIMUM C OVERAGE M ACRO A LGORITHM (MCMA)
Input: num f1 of deployed gNBs with frequency f Output: flag sol flag with installation status (true = feasible solution found, false = no feasible solution found),variables y , x , P ADD-TS , P ADD-NOTS , w , C TOT num f2 max= (cid:80) l ∈L I ( f ,l ) ; flag end=false; flag sol=false; num f2=1; while flag end==false do cand sites= GENERATE SITES (num f1,num f2); // Random generation of a candidate deployment [x curr y curr pd curr]= INITIALIZE (cand sites); [flag check, pd temp]= INSTALL CHECK (cand sites, y curr, pd curr); // Based on Eq. (24), (25), (27)-(36) if flag check==true then [x curr]= ASSOCIATE PIXELS (y curr, x curr); // Based on Eq. (12),(13),(20)-(23) flag sol=true; end if if ( ALL SERVED (x curr)==true) or (num f2==num f2 max)) then if flag check==true then [ y , x , P ADD-TS , P ADD-NOTS , w , C TOT ]= SAVE SOL (y curr, x curr, pd curr); // best Solution Saving end if flag end=true; // Stop condition else num f2++; end if end while A PPENDIX CA DDITIONAL R ESULTS
In this section, we provide a set of additional results, inorder to better position the PLATEA algorithm and theresults presented in Sec. 7.
C.1 Throughput Comparison
Tab. 8 in Sec. 7 highlights that PLATEA achieves a betteraverage throughput T AVG compared to EA and MCMA.However, no indication about the throughput of the singlepixels (which we remind is denoted with T p ) is provided.Therefore, a natural question is: which is the performanceof PLATEA when considering T p and not T AVG ? To ans-wer this question, Fig. 15 reports the Cumulative Distri-bution Function (CDF) of the throughput T p obtained withPLATEA. In addition, the figure shows the CDF obtainedby running EA. Three considerations hold by analyzingFig. 15. First, PLATEA is able to guarantee more than500 [Mbps] of throughput for more than 20% of pixels.Second, the percentage of pixels receiving very low through-put is overall pretty limited (less than 10%). Third, EAperforms consistently worse, being its CDF clearly movedon the left w.r.t. PLATEA. Throughput [Mbps] CD F PLATEAEA
Fig. 15. CDF of the pixel throughput T p obtained by PLATEA and EA. C.2 Number of f gNBs selected by MCMA According to Tab. 8 in Sec. 7, MCMA requires a consi-stently higher amount of f gNBs compared to PLATEA.However, a natural question is: Does MCMA always installmore f gNBs w.r.t. PLATEA? To answer this question, werun MCMA by varying num_f1 between 1 and 24 (whichcorresponds to the maximum number of gNB installed by N f1 N f PLATEAMCMA
Fig. 16. Number of f gNBs installed by PLATEA and MCMA fordifferent numbers of f gNBs. PLATEA for very large values of α ( l,f ). For each valueof num_f1 , we then perform 10 executions of MCMA, andthen we collect the average number of installed f gNBsover the 10 runs. Fig. 16 reports the variation of the averagenumber of installed f gNBs vs. num_f1 . For completeness,the figure reports also the number of f gNBs that areinstalled by PLATEA. Interestingly, we can note that theaverage number of installed f gNBs is always higherthan the one selected by PLATEA. This difference maybe explained in the different planning policies adopted bythe two solutions. MCMA, in fact, sequentially evaluatesan increasing number of f gNB, given the number of f gNBs that is passed as input parameter. On the other hand,PLATEA operates a wiser choice, by: i) evaluating a numberof permutations that increases with the number of gNBs thatneed to be installed, and ii) jointly varying the number of f gNB and f gNB when evaluating the problem constraintsand the objective function. C.3 Impact of minimum distance constraint
The set of regulations taken under consideration in thiswork (namely R6 of Tab. 3) includes a minimum dis-tance D MIN between each installed gNBs and each sen-sitive place. A natural question is then: What is the im-pact of D MIN variation on the planning? To answer thisquestion, we have assumed that D MIN can take differentvalues w.r.t. the ones reported in the regulations. In par-ticular, we have considered the following range of valuesfor D MIN = { , , , , , } . We have then runPLATEA algorithm for each D MIN value, and we have col-lected the performance metrics. Fig. 17 reports the obtainedresults in terms of: i ) average electric field E AVG , ii ) averagethroughput T AVG , iii ) number N f of f gNBs and iv )percentage of not served pixels X NOT-SERVED . We remind that D MIN = 100 [m] is the value currently enforced in the Romeregulations. Interestingly, when D MIN < [m], E AVG , T AVG and N f tend to be increased, due to the fact that it ispossible to install more gNBs over the territory while ensu-ring the minimum distance constraint. On the other hand,the opposite holds D MIN > [m]. In particular, when D MIN = 150 [m], an abrupt decrease of E AVG , T AVG and N f is observed. These results are a direct consequence ofthe D MIN , which prevents the installation of gNBs in many
25 50 75 100 125 150 D MIN [m] . . . E AV G [ V / m ] (a) E AVG [V/m]
25 50 75 100 125 150 D MIN [m] T AV G [ M bp s ] (b) T AVG [Mbps]
25 50 75 100 125 150 D MIN [m] N f (c) N f1
25 50 75 100 125 150 D MIN [m] X N O T - SE R VE D [ % ] (d) X NOT-SERVED [%]