Cross-City Validation and Refinement of a Path-Loss Model for NB-IoT in Urban Scenarios

1 Cross-City Validation and Refinement of a Path Loss Model for NB-IoT in Urban Scenarios Federico Ferretti*, Giuseppe Caso*, Luca De Nardis, Marco Savelli, Anna Brunstrom, Özgü Alay, Marco Neri, Maria-Gabriella Di Benedetto Abstract—The Narrowband Internet of Things (NB-IoT) technology has an important role in the mobile cellular ecosystem, enabling massive Machine Type Communication (mMTC) services. NB-IoT propagation was preliminarily analyzed via a measurement campaign carried out in 2020 in the city of Oslo, Norway. This investigation resulted in Oslo-2020, the first NBIoT-specific Alpha-Beta-Gamma (ABG) path loss (PL) model, which showed higher prediction accuracy compared to models developed for different technologies but often used for NB-IoT. In this paper, to further investigate NB-IoT PL in urban scenarios, we analyze new measurement campaigns performed in 20202021 and 2023 in the city of Rome, Italy. First, we use the 2020-2021 measurements to derive Rome-2021, a new NB-IoTspecific ABG PL model. We show that Rome-2021 preserves the statistical properties of Oslo-2020 (e.g., the Gaussianity of the PL exponent distribution across base stations), although the moments of the distributions are different due to city-specific environmental characteristics. We also use new data on signal losses due to outdoor-to-indoor propagation to refine the analysis of this scenario. Finally, we propose a methodology to combine Oslo-2020 and Rome-2021 into a more general model. Our methodology uses so-called Mixture Distributions (MDs), thus leveraging the shared statistical properties between Oslo-2020 and Rome-2021. By using the 2023 measurements, we show that our MD-based approach estimates PL model parameters with higher accuracy compared to Oslo-2020 and Rome-2021 models used separately, thus providing an effective solution for predicting NB-IoT urban PL in lack of site-specific measurements and information. Index Terms—Cellular Internet of Things, massive Machine Type Communication, Narrowband Internet of Things, Path Loss Empirical Models I. INTRODUCTION Narrowband Internet of Things (NB-IoT) is a widely adopted Low-Power Wide-Area Network (LPWAN) technology that enables low-cost and power-efficient massive Machine-Type Communication (mMTC) on mobile cellular systems. It was first standardized by the 3rd Generation Partnership Project (3GPP) in Release 13 (Rel-13) and then enhanced in later releases, to ensure inter-working in licensed spectrum portions with 4th Generation (4G) Long Term Evolution (LTE) and 5th Generation (5G) New Radio F. Ferretti and Marco Savelli are with TIM S.p.A., Rome, Italy. G. Caso and A. Brunstrom are with Karlstad University, Karlstad, Sweden. L. De Nardis and M.-G. Di Benedetto are with Sapienza University of Rome, Rome, Italy. Ö. Alay is with University of Oslo, Oslo, Norway, and Karlstad University, Karlstad, Sweden. M. Neri is with Rohde&Schwarz, Rome, Italy. * These authors contributed equally to this paper. Corresponding author: G. Caso ([email protected]). 41°50'N 41°52'N 41°54'N Latitude 12°26'E 12°28'E 12°30'E 12°32'E Longitude Esri, HERE, Garmin, USGS 1 mi 2 km Measurement Locations Positions of BSs from Op1 Positions of BSs from Op2 Positions of BSs from Op3 Fig. 1: Routes covered during the measurement campaign in 20202021, along with the estimated positions for the NB-IoT BSs of three Italian MNOs (Op1, Op2, and Op3). For each route, measurements were collected multiple times, for a total of 49 sub-campaigns (see §III for more details on measurement setup and methodology). (NR) systems, that are mostly focused on enhanced Mobile BroadBand (eMBB) and Ultra-Reliable Low Latency Communication (URLLC) use cases [1]–[3]. As for all wireless technologies in general, a proper understanding and accurate modeling of NB-IoT radio propagation and coverage is key toward supporting, on the one hand, mobile network operators (MNOs) in efficiently deploying and configuring their networks and, on the other hand, researchers in performing analyses and proposing improvements, e.g., via simulations. Several research and standardization activities are indeed devoted to path loss (PL) modeling, with a focus on the so-called empirical models. These estimate PL values through well-established, physically-grounded equations embedding specific parameters, e.g., the PL exponent (see §II). The values of the parameters are obtained by fitting the equations on real-world measurements, aiming at minimizing the difference between measurements and model estimates. The derivation of PL empirical models is often challenged by the scarcity of measurements, and NB-IoT makes no exception. In the context of LPWAN technologies, empirical PL models were more often derived for proprietary technologies alternative to NB-IoT, i.e., Long Range (LoRa) and SigFox (see Table I in [4] for a summary of such works). These two technologies operate in unlicensed spectrum portions, This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply. 2 over dedicated infrastructures and using specific configurations (e.g., signal bandwidth, transmission power, and receiver sensitivity, to mention a few), which limit the applicability of the obtained PL models to NB-IoT, as observed in [5] and also verified in §IV on our measurements. Therefore, so far, simulation-based investigations on NB-IoT mostly utilized models derived for other cellular technologies, such as Universal Mobile Telecommunications System (UMTS) and LTE (e.g., [6]–[17]). In [18], we provided two empirical models for the NB-IoT PL in an urban scenario, by leveraging a largescale measurement campaign executed in the city of Oslo, Norway, in 2020 [19]. By following the approach adopted in [20] for other technologies, and using measurements for a large number of Base Stations (BSs) forming the NBIoT networks of two Norwegian MNOs, the work in [18] provided statistically-extended versions of well-known PL empirical models, i.e., Close-In (CI) [21] and Alpha-BetaGamma (ABG) [22] (the latter referred to as Oslo-2020 in this paper), with model parameters not fixed to a single value but randomly generated from well-known distributions. This enables a more accurate PL estimation for NB-IoT urban deployments with multiple BSs, overcoming the limitation of models derived via measurements collected for a single BS, which thus have fixed-value parameters [23]–[27]. Results in [18] also highlighted that the specific characteristics of NBIoT compared to other cellular technologies, e.g., in terms of occupied bandwidth and configurations, introduce remarkably different propagation characteristics, confirming the need for dedicated PL assessments and model validation/refinement via additional measurements in multiple scenarios. In this paper, we follow up on the investigation in [18], with the main goal of validating and refining the empirical characterization of NB-IoT PL in urban scenarios. We thus make the following contributions: •We introduce a large-scale measurement campaign executed in the city of Rome, Italy, in 2020-2021, covering 396 NB-IoT BSs from three Italian MNOs (Fig. 1). By leveraging the collected measurements, we derive a new statistically-extended ABG PL model for NB-IoT, referred to as Rome-2021, which includes the distributions for the ABG parameters and for the PL shadowing term. Similarly to Oslo-2020,Rome-2021 improves PL estimation accuracy compared to models developed for other technologies but often used in NB-IoT investigations, thus enabling realistic simulations of NB-IoT PL in urban areas with multiple BSs; •We compare Oslo-2020 and Rome-2021 and discover that the statistical properties of the former are preserved by the latter (e.g., Gaussian distributions are a good fit for both Oslo-2020 and Rome-2021 ABG model parameters), but present different moments (e.g., mean and standard deviation). This validates the analyses in [18] but also highlights the impact of city-specific environmental and deployment characteristics on signal propagation; •We refine the analysis in [18] on the additional losses due to outdoor-to-indoor propagation. On the one hand, we confirm that deep indoor (DI) scenarios (i.e., enclosed areas below the ground floor) result in significantly higher losses compared to typical indoor scenarios (i.e., rooms with windows at high floors). On the other hand, we highlight that such losses significantly vary across locations, also as a function of BS positions/heights, thus making the common approach of using a constant loss value questionable, and opening up for model improvements; •We propose a PL model generalization where we combine Oslo-2020 and Rome-2021 models via Mixture Distributions (MDs) [28], thus leveraging the knowledge of the parameters’ distribution across cities. We validate the MD-based modeling approach by exploiting a new measurement campaign carried out in Rome in 2023. In particular, we show that the MD-based model can estimate the PL values observed in Rome in 2023 with a higher accuracy compared to using Oslo-2020 and Rome2021 separately, thus providing an effective solution for predicting NB-IoT urban PL in lack of site-specific measurements and environmental/deployment information and requirements, e.g., for simulation-based studies. The paper is organized as follows. The background is provided in §II, while §III presents the measurement setup and campaigns executed in Rome in 2020-2021 and 2023, along with the data processing carried out prior to the following analyses. The Rome-2021 model is introduced in §IV, where an in-depth comparison with the previous Oslo-2020 model is also presented. The MD-based modeling approach is detailed and evaluated in §V. Finally, §VI concludes the paper. II. BACKGROUND AND RELATED WORK This section provides the background for our work, by discussing on a high level PL modeling solutions for cellular systems and their application to NB-IoT. A. PL Modeling for Cellular Systems In outdoor-to-outdoor propagation modeling, it is assumed that a transmitter (TX) and a receiver (RX) communicate over an outdoor wireless link, and the PL [dB] is commonly represented as follows: PL =PL +X,(1) where PL is the PL average term and Xis a random variable representing PL variations around the average term, that are caused by slow fading phenomena, such as shadowing due to the presence of surrounding objects. CI and ABG are most widely used empirical models in estimating PL in cellular systems up to 5G [22], [26], [27]. The CI model estimates PL as follows: PLCI = 10γlog10 d d0+A,(2) where dis the TX-RX distance, d0is a reference distance, γis a distance-related parameter usually referred to as PL exponent, and Ais either set to the loss at d0estimated via the Free Space (FS) model (see later) or optimized, along with γ, via model fitting on real measurements. A single value for γand Acan be then obtained if measurements for a single This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply. 3 TX-RX pair are available at different distances (e.g., one BS and several measurement points). Similarly, the ABG model estimates PL as follows: PLABG = 10γlog10(d) + 10βlog10(fc) + l0,(3) where fcis the carrier frequency, βis a frequency-related exponent, and l0is a constant loss term.1Also in this case, the values for γ,β, and l0can be obtained via model fitting, and a single value for each parameter can be obtained with one BS and several measurement points at different distances. Note that ABG generalizes the FS model, where it is assumed γ= 2,β= 2, and l0= 20 log10(4π c), with cindicating the speed of light (l0≈32.44 dB if dis in km and fcis in MHz). As shown in (1), the estimated PL is complemented by a sample extracted from a random variable X, which quantifies how much PL deviates from the real measurements due to shadowing. Xis commonly assumed to be distributed according to a Gaussian distribution with mean µ= 0 and standard deviation σdetermined after fitting the PL model, i.e., X ∼ N (µ= 0, σ). For outdoor-to-indoor propagation, a common solution is to add a term to (1), i.e., li, to account for the additional losses experienced by the signal when penetrating walls, floors, and/or windows before reaching the RX. lican be obtained, empirically, by quantifying the difference between PL outdoor estimates vs indoor measurements at similar distances. In Technical Specification (TS) 38.901 [29], 3GPP proposes li= 0.5di, where diis the indoor component of the TX-RX path, from the outer wall to the RX (in meters). B. PL Modeling for NB-IoT As mentioned in §I, NB-IoT is a radio interface for mMTC services. It uses either a 200 kHz Global System for Mobile Communications (GSM)-like channel or an LTE Physical Resource Block (PRB) of 180 kHz, and adopts one out of three possible operation modes: (a) stand-alone, over a 200 kHz channel in the GSM spectrum, (b) in-band, over a single PRB within a set of LTE PRBs, (c) guard-band, within a guard band among different sets of LTE PRBs. A detailed description of NB-IoT is out of scope for this paper. We refer the interested reader to [1]–[3] and references therein for more details on this technology, which is being enhanced across 3GPP releases. Propagation conditions significantly affect NB-IoT operations and performance, and this highlights the need for accurate PL modeling. In particular, NB-IoT BSs transmit the Narrowband Reference Signal (NRS), used by NB-IoT devices to measure the (Narrowband) Reference Signal Received Power (RSRP [dBm]). Based on the measured RSRP, devices estimate their propagation conditions in terms of Coverage Level (CL), ultimately using CL-dependent configurations, e.g., transmission power and number of repetitions, for different operations, including data transmission. Modeling options currently available for NB-IoT are summarized below. They typically extend CI and ABG models, 1A different notation uses variables α,β, and γfor the PL exponent, constant losses, and fc-related parameters, thus explaining the name ABG (e.g., see [26] [27]). and were fitted on measurements collected for UMTS and LTE (except for the models derived in [18]). 3GPP UMTS 30.03 model as per TR 45.820 [30] [31]. Originally proposed for vehicular scenarios in urban and suburban areas with buildings of uniform height, this model has γand l0values depending on the BS antenna height (expressed in meters). Moreover, dis in km and fcis in MHz. In 3GPP Technical Report (TR) 45.820, the model is specified by assuming a BS antenna height of 15 meters and fc= 900 MHz [32], i.e., in LTE Band 8, which is available for NB-IoT deployment [1] [33]. For the shadowing term, 3GPP suggests σ= 10 dB in UMTS 30.03 and σ= 8 dB in TR 45.820. The model is largely used in the NB-IoT literature (e.g., [6]–[12]), and a simple recalculation allows to use it at fc= 800 MHz, i.e., in LTE Band 20, which is adopted for NB-IoT deployment by the Italian MNOs considered in this paper (see §III). Okumura-Hata (OH) model [34]. OH is a traditional model for cellular propagation at frequencies ranging from 150 to 1500 MHz. For urban environments, it is based on measurements collected in the city of Tokyo, Japan. γand l0values depend on the BS antenna height (in meters), d(in kilometers), and fc(in MHz). A specific term in the OH model depends on fcand the height of the mobile device (in meters), and changes as a function of the considered scenario (e.g., small-to-medium vs. large cities). For NB-IoT, OH is used in [13]–[15], with the latter adopting σ= 9.4dB. 3GPP Urban Macro (UMa) models [35]. These models estimate the PL for Line of Sight (LoS) and Non LoS (NLoS) separately, by using din meters and fcin GHz. The UMa LoS model also defines (a) a break point distance, where the propagation is assumed to start having a slightly different behavior, and (b) effective BS and device heights, obtained by adjusting the original values [18]. For UMa NLoS, two further parameters are needed, i.e., street width and building height, both in meters, with ranges reported in [35] along with the values for σ(4dB for UMa LoS and 6dB for UMa NLoS). For NB-IoT, UMa models are used for example in [16] [17]. Oslo CI and ABG models [18]. These are statisticallyextended CI and ABG models obtained by fitting (2)(3) on NB-IoT PL measurements collected in 2020 in Oslo for multiple BSs from two MNOs, with NB-IoT networks operating in the guard bands of LTE Band 20. For both models, dis in km and fcis in MHz. For CI, γvalues across BSs are modeled via a Gaussian distribution, while Avalues are represented by a single constant term. Shadowing is modeled by N(0, σ), with σvalues across BSs following a Weibull distribution. For the ABG case (i.e., Oslo-2020 in this paper), γand βvalues across BSs are modeled via Gaussian distributions, l0is a constant term, and σvalues also follow a Weibull distribution (see Table I). The results in [18] are used in [36], [37] to benchmark measurements in Hong Kong and Chile. Moreover, recent results in [37] show a good fit between the Oslo models and the measurements, with possible accuracy improvement, in line with our insights reported in the next sections. For outdoor-to-indoor propagation, most simulation-based works use livalues of 10,20, or 30 dB [31] to represent different indoor scenarios. In [38]–[40], it is empirically verified that the 3GPP distance-based model for liis fairly This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply. 4 TABLE I: CI and ABG models proposed in [18] for NB-IoT PL. Parameter Oslo CI Oslo ABG (Oslo-2020) γN(2.36,1.15) N(2.78,3.17) β–N(2.81,0.60) Aor l0[dB] 81.31 32.44 X N (0, σ)N(0, σ) σ[dB] Wbl(6.670,2.289) (a) Wbl(4.709,2.218) (a) Wbl(x,y)stands for Weibull distribution with scale xand shape y. accurate above the ground level, but it performs poorly below the ground level. In [18], measurements in a few indoor and DI locations are used to estimate the additional losses with respect to the average models in Table I. For ABG, it is suggested that li∈[8,13] dB for indoor scenarios, and liis up to 50 dB for DI. Slightly higher values are obtained for the CI model. III. METHODOLOGY AND DATA PROCESSING In this section, we first describe our measurement setup and campaigns in 2020-2021 and 2023 (§III-A), and then discuss how PL measurements were extracted from the collected data and prepared for the subsequent analyses (§III-B). A. Measurement Setup and Campaigns NB-IoT measurements were collected in Rome in 20202021 and 2023 by using the Rohde & Schwarz (R&S) TSMA6 system, embedded with Radio Frequency (RF) and Global Positioning System (GPS) antennas. In our setup, the R&S TSMA6system included a spectrum scanner and an embedded PC where the R&S software for data collection, visualization, and exporting was running. Prior to the measurement campaigns, the setup was calibrated toward enabling accurate coverage measurements for all 3GPP technologies operating in the measurement areas. For this paper, we used it for (a) detectingand-decoding the control signals (e.g., NRSs) broadcast by NB-IoT BSs, (b) collecting coverage measurements on them (e.g., RSRP values), and (c) obtaining an estimated position of the detected BSs. Knowing the position of the BSs and of the measurement points (via GPS) allowed to evaluate the distance dbetween each detected BS and measurement point, needed in (2)(3). Since the position was in geographical coordinates, we used the Haversine formula [41] to obtain distance values. The 2020-2021 campaign covered 7weeks between December 2020 and January 2021. We enabled the R&S TSMA6 to perform passive measurements on several LTE bands. By doing so, we detected three Italian MNOs, denoted Op1, Op2, and Op3, providing NB-IoT services in the LTE Band 20 guard bands. The campaign was divided into multiple sub-campaigns, carried out in different areas. We conducted outdoor sub-campaigns while walking or driving along the routes depicted in Fig. 1, for a total of 49 sub-campaigns. We also collected static measurements in indoor and DI locations, for a total of 13 locations: 9offices at the 2nd floor of the Department of Information Engineering, Electronics and Telecommunications (DIET Dept.) of Sapienza University, 1 flat at the 6th floor of a 7-floor residential building, and 3DI locations (1at DIET Dept., 1at the parking lot of the building, and 1at the parking lot of a commercial store). The 2023 campaign covered 4weeks between March and July 2023. We configured our setup to operate in the same conditions of the 2020-2021 campaign and, also in this case, we collected NB-IoT measurements from Op1, Op2, and Op3 in the LTE Band 20 guard bands. The campaign was divided into 6sub-campaigns carried out in different areas of the city, partially overlapping with the areas covered in 2020-2021. Due to our focus on benchmarking outdoor PL models, we did not collect indoor and DI measurements in 2023.2 We further observe that both 2020-2021 and 2023 campaigns were carried out to address the main goal of validating and refining a city-wide NB-IoT PL model, as a follow up of our previous work in [18] and in line with previous works on other technologies (e.g., 5G [26], [27] and LoRa/SigFox [5], [42]). Hence, as also reported in Fig. 1, our campaigns were executed by driving along paths of several kilometers, where urban environmental conditions were extremely variable and, thus, not precisely categorizable (e.g., in terms of building density and terrain characteristics). This measurement methodology and, thus, the focus on city-wide PL modeling, is also justified by the nature of the NB-IoT technology, which is expected to cover large urban areas from the same BS – as verified by our measurements as well as in other experimental works on NB-IoT [5] – with the same signal facing heterogeneous environmental conditions. B. PL Derivation from Measurements and BS Filtering Given a NB-IoT BS xand a measurement point at distance d, we evaluated the PL as follows: PL(d) = PNRS TX,x −RSRP(d),(4) where PNRS TX,x [dBm] is the power used by BS xto transmit the NRS. The decoding of control messages by the TSMA6 allowed to retrieve PNRS TX for several BSs. This parameter is named nrs_Power_r13 and is broadcast by BSs in System Information Block 2(SIB2) messages. For all MNOs, we observed that BSs used slightly different PNRS TX values, confined in the range of a few dBs. To reduce variability, we used the median value across the BSs of each MNO in (4), i.e., 21,22, and 24 dBm for Op1, Op2, and Op3, respectively. Considering that our measurements were collected under mobility, we performed a further filtering to remove fast fading effects. Similarly to [18], we adopted the rule in [43], thus applying a ±20λmoving average window to the set of PL measurements for each BS. Finally, to limit the impact of positioning errors due to GPS inaccuracy, we defined a distance threshold of 0.05 km and discarded, for each BS, all PL measurements collected at distances below this threshold. We also applied manual BS filtering to remove BSs detected by our system, but represented by too few measurements, thus not allowing accurate PL characterizations. In summary, we performed the analyses reported in the next sections on 396 BSs detected in 2020-2021 (107 of Op1,143 of Op2, and 146 of Op3), and on 204 BSs detected in 2023 (71 of Op1,63 of Op2, and 70 of Op3). 2Both datasets are available for further exploration upon request. This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply. 5 IV. MODEL VALIDATION AND REFINEMENT: FROM Oslo-2020 TO Rome-2021 In this section, we present the steps leading to the NBIoT-specific ABG PL model derived in this paper, i.e., Rome2021. After assessing the accuracy of existing models (§IV-A), we characterize the main terms of Rome-2021, as in (1). Therefore, by using the 2020-2021 measurements in Rome, we first fit the ABG model for PL estimation (§IV-B) and then analyze the shadowing term (§IV-C). Finally, we characterize outdoor-to-indoor additional losses (§IV-D). Throughout the section, we extensively compare Rome-2021 and Oslo-2020, in order to highlight both similarities and differences.3 A. Comparison of Existing Models As a first step, we verify how well the models presented in §II-B estimate the PL measurements collected in Rome in 2020-2021. For each BS, we evaluate the root mean square error (RMSE) between the PL estimated by the models and the measurements collected at different distance. For the models that need specific settings, we use values commonly adopted in the literature, i.e., 15 meters for the BS antenna height, 1.5 meters for the device height, and 25 and 12 meters for building height and street width, respectively. For Oslo-2020, we use the mean values of the distributions for γand β, i.e., 2.78 and 2.81, respectively (see Table I). We consider the FS model for further comparison, as well as two popular models derived for LoRa and SigFox in [42] and [5], respectively. These are CI models fitted on LoRa and SigFox measurements in the cities of Oulu, Finland, and Brno, Czech Republic, resulting in γ= 2.32 and A= 128.95 dB for LoRa and γ= 3.76 and A= 118.04 dB for SigFox. Figure 2 shows the boxplot of the RMSE values obtained across BSs. We observe that most of the models result in rather high RMSE values (e.g., a median above 25 dB for FS and between 12-20 dB for OH, UMa LoS/NLoS, and LoRa models). Due to similar γand Avalues, TR 45.820 and SigFox models show similar performance, with a median RMSE around 10.5-11 dB. Finally, Oslo-2020 shows the lowest median RMSE (9dB). This highlights that, on the one hand, a model specifically derived on NB-IoT measurements, although collected in a different city, is more accurate than models derived for different technologies. On the other hand, it hints that further accuracy improvements can be obtained by exploiting site-specific measurements and executing a dedicated fitting procedure, as analyzed in the next sections. B. Characterization of PL We now start deriving the Rome-2021 model. We thus evaluate the PL term in (3) by using the 2020-2021 measurements. To determine if, similarly to what obtained in [18], a single value can be associated to the l0term in (3), we first use an Unconstrained Fitting (UF) approach, i.e., we fit the ABG model on the measurements with no constraints on the 3Note that we performed similar analyses for the CI model and obtained results in line with [18], i.e., a higher accuracy for the ABG model compared to the CI model, which justify the focus on the ABG model in this paper. FS TR 45.820 @ 800 MHz TR 45.820 @ 900 MHz OH UMa LoS UMa NLoS LoRa Model SigFox Model Oslo-2020 (Mean) PL Model 0 10 20 30 40 50 60 RMSE [dB] Fig. 2: Comparison of existing PL models adopted for NB-IoT. FS and two models derived for LoRa [42] and SigFox [5] are presented for further comparison. For each model, the boxplot for the RMSE values across BSs is reported. Fig. 3: Empirical PDF of the values of l0obtained across BSs for the Rome-2021 model via UF. possible values for γ,β, and l0. Figure 3 shows the empirical probability density function (PDF) of the values obtained for l0 across BSs by applying UF on (3). We observe that l0presents a distribution that concentrates around its average value of 36.37 dB. Differently from Oslo-2020, the distribution of l0 values only covers positive values, thus hinting at a lower variability of the 2020-2021 measurements in Rome compared to the 2020 measurements in Oslo, despite the higher amount of MNOs, BSs, and data points in the former case. The average value differs by around 4dBs from the value adopted in the FS and Oslo-2020 models, a fact that does not allow to use the same approximation proposed in [18]. Results thus confirm that the l0term can be approximated to a single value, but this value is different from the one obtained for Oslo-2020. For Rome-2021, we fix l0= 36.37 dB and move on in the PL modeling by applying a Constrained Fitting (CF), i.e., we only derive the γand βterms in (3). Figure 4 shows the empirical PDFs of γ(a) and β(b) values obtained across BSs via CF. As shown in the figure and confirmed via the Akaike Information Criterion (AIC), both parameters are well-modeled by Gaussian distributions, i.e., N(1.86,1.89) for γand N(2.70,0.39) for β. Similarly to the results related to the l0term, the Gaussianity of the This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply. 6 -2 0 2 4 6 8 0 0.05 0.1 0.15 0.2 0.25 Empirical PDF (a) 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Empirical PDF (b) Fig. 4: Empirical PDFs of the values of γ(a) and β(b) obtained across BSs for the Rome-2021 model via CF. The nearest Gaussian approximation is also reported. distributions for γand βvalidate the findings in [18] and, thus, the Oslo-2020 modeling approach, where both γand β were already found to nearly follow Gaussian distributions, although with different means and standard deviations. More specifically, compared to Oslo-2020, the increased l0value of Rome-2021 results in lower mean values of the distributions for γand β. The standard deviations for Rome-2021 are also lower compared to Oslo-2020, hinting again at less variability of the 2020-2021 measurements in Rome. Finally, we observe that, similarly to Oslo-2020, the distribution of γfor Rome2021 also includes negative values, due to the presence of buildings that may obstruct the signal from some BSs at short distances but not at longer distance [24] [25]. We now verify the accuracy of Oslo-2020 and Rome-2021 compared to other models used in literature but not fitted on NB-IoT measurements. To do so, we define GRMSE = RMSEm /RMSEABG M, where m∈[TR 45.820, OH, UMa LoS, UMa NLoS, LoRa Model [42], SigFox Model [5]]and M∈[Rome-2021,Oslo-2020], representing the gain/loss in terms of average RMSE across BSs of Rome-2021 or Oslo2020 compared to the other models. GRMSE >1means an accuracy gain in adopting the model at the denominator, as it indicates a lower average RMSE compared to the model at the numerator. Figure 5 shows that both Rome-2021 and Oslo-2020 provide accuracy gains, thus further confirming that NB-IoT measurements and model fitting are needed to increase accuracy. Moreover, Rome-2021 shows higher gains compared to Oslo-2020, thus also confirming the importance of site-specific measurements. C. Characterization of X After the analysis of PL, we now study the shadowing component X. As described in §II-A, given a BS, Xfollows a zero-mean Gaussian distribution, i.e., N(µ= 0, σ), if the PL model accurately estimates the average term. In order to verify how well Rome-2021 performs on this aspect, we report in Fig. 6 the boxplot of the mean µof the Gaussian distributions that best approximate Xacross BSs. For comparison, we report the results for the models that perform relatively well in characterizing PL, i.e., Oslo-2020 FS TR 45.820 @ 800 MHz TR 45.820 @ 900 MHz OH UMa LoS UMa NLoS LoRa Model SigFox Model 0 1 2 3 4 5 6 7 8 GRMSE Rome-2021 Oslo-2020 Fig. 5: GRMSE for Rome-2021 and Oslo-2020 compared to FS, TR 45.820, OH, UMA LoS/NLoS, LoRa [42] and SigFox [5] models. Rome-2021 Oslo-2020 TR 45.820 @ 800 MHz FS PL Model -20 0 20 40 [dB] -2 0 2 10-5 Fig. 6: Boxplot of the values of µobtained across BSs for the Rome2021 model via CF. Boxplots for Oslo-2020, TR 45.820, and FS models are reported for comparison. and TR 45.820, along with the results for the FS model for a worst case comparison. We observe that, for Rome-2021, µvalues are very close to zero for all BSs, thus confirming the accuracy in modeling PL. For the other models, µvalues spread more significantly, which is in line with the results in §IV-A. In particular, the positive median values of 4and 2.6dB for Oslo-2020 and TR 45.820 models, respectively, suggest that these models have a tendency in underestimating PL; moreover, the range around such medians also spans over negative values (±20 dB for Oslo-2020 and slightly This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply. 7 larger for TR 45.820), thus highlighting that the same models alternatively underestimate and overestimate PL. It can also be observed that, as expected, FS always underestimates PL, resulting in a high median µvalue, around 24.7dB (it was 19 dB for the 2020 measurements in Oslo), and a large positive range around such value. 02468 0 0.05 0.1 0.15 0.2 0.25 Empirical PDF Fig. 7: Empirical PDFs of the values of σobtained across BSs for the Rome-2021 model via CF. The nearest Weibull approximation is also reported. We now analyze the distribution of the standard deviation σ of the Gaussian distributions that best approximate Xacross BSs. Figure 7 shows that, for Rome-2021,σfollows a leftskewed distribution. The AIC confirms that the Weibull distribution Wbl(4.539,2.155) approximates well the measured values, as depicted in Fig. 7. In line with the analyses presented above, these results once again validate the main findings in [18], where a Weibull distribution was also found to be a good approximation for the σvalues across BSs. As for the distributions of γand β, the different parameters of the distributions of σin Rome-2021 vs. Oslo-2020 highlight once again the impact of specific environmental characteristics in the two cities on signal propagation and, thus, PL. D. Characterization of Indoor and DI Additional Losses We now provide further insights on the additional losses due to outdoor-to-indoor propagation (i.e., end devices within buildings). For this analysis, we leverage the 2020-2021 static measurements in 13 locations, 10 identifiable as typical indoor scenarios and 3as DI (see §III-A). In particular, for all BSs detected at each location, we average all the measurements and provide a unique PL value. Then, we evaluate Din-out [dB] as the difference between the average measured PL and the PL estimated via Rome-2021 at same distance, adopting the mean values of the distributions for γand β. Figure 8 shows Din-out for all BSs detected at each location. Several interesting insights can be derived. For the indoor case, i.e., Locations 1-9(2nd floor of the DIET Dept.) and Location 10 (6th floor of a residential building), many BSs (often the majority) have Din-out >0, thus implying the presence of outdoor-to-indoor additional losses. The median Din-out is between 10 and 20 dB for Locations 6–9and reduces 1 2 3 4 5 6 7 8 9 10 11 12 13 Location -40 -30 -20 -10 0 10 20 30 40 50 60 Din-out [dB] Fig. 8: Din-out for each BS (represented by dots) detected at indoor (Locations 1–10) and DI (Locations 11–13) locations. 0 0.2 0.4 0.6 0.8 1 Distance [km] 60 80 100 120 140 PL [dB] Detected BSs (one per point) BSs at greater height FS Rome-2021 (Mean) Fig. 9: PL measured for each BS (black markers) in indoor and DI locations, as a function of the average distance between BSs and locations. For a BS detected at multiple locations, the average PL and average distance across locations are reported. The PL estimated by Rome-2021 and FS are reported for comparison. For Rome-2021, we considered the mean values of the distributions for γand β. to less than 2dB for Location 10. The latter result reflects a rather favourable propagation condition for Location 10, with our tools placed at the 6th floor facing a set of BSs on a visible tower. As analyzed later in the section, Locations 1-5 and, at least partially, Locations 6-9, also present favourable propagation conditions for some BSs, as highlighted by the occurrence of negative Din-out values. For the DI case, i.e., Location 11 (basement at DIET Dept.), Location 12 (parking lot of a commercial store), and Location 13 (parking lot of a residential building), we consistently observe positive Din-out values, with a median between 30 and 40 dB for the deeply enclosed spaces at Locations 11 and 12. The median reduces to around 15 dB for Location 13, as a result of a more favourable propagation condition, with our tools placed in a parking lot below the ground floor but with openings in the ceiling still favouring signal propagation. At the indoor locations of DIET Dept., we also observe a negative Din-out for some BSs, with Din-out <−10 dB This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply. 8 for 2BSs across Locations 1–5(another BS also shows mostly negative Din-out values at these locations but with larger variability, i.e., Din-out <−10 dB at Locations 1and 2and Din-out >−10 dB at Locations 3–5). The PL measured for these BSs is thus lower than the one estimated by the Rome2021 model. We further investigate this aspect in Fig. 9, where we report the average PL for each BS (black markers) as a function of the average distance between BSs and locations (i.e., for a BS detected at several locations, Fig. 9 shows the average PL and average distance across locations). In agreement with Fig. 8, Figure 9 shows that, due to outdoor-to-indoor additional losses, the PL measured for the majority of BSs is higher than the one estimated by Rome2021. However, for 2BSs at around 300 and 700 meters from the DIET Dept., the measured PL is significantly lower. These are the same BSs that, in Fig. 8, have Din-out <−10 dB at Locations 1–5. Further inspection of the position of these BSs, also via the online maps at www.lteitaly.it (accessed in May 2024), showed that these are placed in rather peculiar spots, i.e., on the rooftop of a quite high building and on the bell tower of a church (the bell tower is 78-meter tall, the highest in Rome), both visible from the DIET Dept. and in clear LoS with Locations 1–5, as visually represented in Fig. 10. This evidently favours the propagation towards the DIET Dept., resulting in a lower PL compared to the one estimated by Rome-2021, which is fitted on a large set of BSs without accounting for BS height. Although not invalidating our model, this result highlights that knowing the BS height and embedding such information in PL models may further improve PL estimation accuracy, particularly for BS placements significantly deviating from expected nominal cases. We thus plan to get access to information on the BS heights and further study this aspect in future work, towards providing an additional assessment on the trade off between model simplicity and accuracy. In summary, compared to the values in the literature and found in [18] (see §II-B), the outdoor-to-indoor additional losses measured in Rome are reasonably in alignment for the indoor locations, apart for specific BS/location pairs, with median values in between 10 and 20 dB. For the DI case, excluding the specific situation of Location 11, we observe median values higher than 30 dB (used in literature). Using a range of 30–40 dB seems to be a reasonable choice for accounting such additional losses. V. MODEL GENERALIZATION VIA MIXTURE DISTRIBUTIONS In this section, we leverage previous results and move a step forward, aiming at proposing and validating a methodology for combining PL models obtained in different urban scenarios (e.g., different cities), thus making it possible to use a more general model for the generation of PL values in lack of site-specific measurements and/or environmental/deployment information, e.g., for simulation-based studies. A. Motivation and Proposed Approach Our analyses and results in §IV demonstrate that the statistical properties of Oslo-2020 remain valid for RomeFig. 10: Relative positions between Locations 1–9and the two BSs detected with the lowest PL (Fig. 9). The figure shows that both BSs are in LoS with Locations 1–5(straight lines), while a building partially obstructs the LoS with Locations 6–9(dashed lines), which explains the lower PL measured at Locations 1–5(Fig. 8). 2021. In particular, across multiple BSs, γand βcan still be modeled as Gaussian distributions, and σstill follows a Weibull distribution. The moments of such distributions, however, change across the two cities due to site-specific environmental/deployment factors. The need for generating PL values under more general settings, e.g., for simulation-based studies with no site-specific information and requirements, would thus pose the challenge of deciding which model to use, i.e., Oslo-2020 or Rome-2021. Motivated by the above observation, we propose a methodology that enables the definition of a more general PL model starting from city-specific models. In particular, we investigate a scenario where third-party users need to generate PL values for their studies (e.g., based on simulations), but do not have access to city-specific measurements and datasets, i.e., in our case, such users have access to neither PL measured values nor general statistics (e.g., the number of BSs) of the 2020 measurements in Oslo and the 2020-2021 measurements in Rome. Therefore, they can only access to the derived Oslo2020 and Rome-2021 PL models, i.e., the values of l0and the distributions for γ,β, and σ. Within the above scenario, one solution would be to simply select one of the available PL models, i.e., either Oslo2020 or Rome-2021. This would however lead to synthetic PL values that closely reflect the propagation characteristics encountered in the city associated to the selected model during the specific measurement campaign. Aiming at a more general characterization of PL, we instead propose to exploit Oslo2020 and Rome-2021 as initial components from which a more general model can be defined. In particular, we leverage the concept of MDs, i.e., probability distributions expressed as collections (often finite) of component distributions. Given n probability density functions p1(x), ..., pn(x)and corresponding cumulative distribution functions P1(x), ..., Pn(x), a MD can be represented as f(x) = Pn i=1 wipi(x), and similarly for cumulative function F, where the weights w1, ..., wnare This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply. 9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mixing Proportion for Rome-2021 0 0.1 0.2 0.3 0.4 KL Distance from Rome-2023 GMD Oslo-2020 Rome-2021 (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mixing Proportion for Rome-2021 0 0.1 0.2 0.3 0.4 KL Distance from Rome-2023 GMD Oslo-2020 Rome-2021 (b) Fig. 11: KL divergence between the distributions in the Rome-2023 model and the ones in Oslo-2020,Rome-2021, and in the GMD between these two, for γ(a) and β(b) parameters. For the GMD, results are presented as a function of the mixing proportion used for Rome-2021. defined such that wi≥0∀iand Piwi= 1. The individual distributions are often referred to as mixture components, while the weights associated to each component are often referred to as mixing proportions. The mixture components are often not arbitrary probability distributions, but are instead members of a parametric family (e.g., Gaussian distributions), with different values for their statistical parameters (e.g., means and standard deviations) [28]. The above description highlights the potential of MDs to display non-trivial higher-order moments such as skewness, kurtosis, and multi-modality, even in the absence of such features within the components themselves. In our specific context, we thus propose to use Gaussian Mixture Distributions (GMDs) for γand β, and a Weibull Mixture Distribution (WMD) for σ, thus leveraging the fact that, when Oslo-2020 or Rome-2021 models are taken separately, γand βfollow Gaussian distributions and σfollows a Weibull distribution across BSs, respectively. As regards l0, we instead propose to use the average of the Oslo-2020 and Rome-2021 values. B. Evaluation We evaluate our MD-based PL modeling approach by leveraging the new set of measurements collected in Rome in 2023, described in §III. As a first step, we build a new PL model, referred in the following to as Rome-2023, by adopting the same procedure used for deriving Rome-2021 in the previous sections. We fix l0to the average of the values obtained for Oslo-2020 (32.44 dB) and Rome-2021 (36.37 dB) and perform a CF to derive the distributions of γ,β, and σ across the BSs detected in 2023. By doing so, we once again obtain Gaussian distributions for γ, i.e., N(1.983,3.370), and β, i.e., N(1.392,0.343), and a Weibull distribution for σ, i.e., Wbl(5.766,3.011). We use this newly derived model as a benchmark, in order to understand how good Oslo-2020,Rome-2021, and the MDbased approach perform in estimating the values measured in 2023 and included in Rome-2023. Figure 11 shows the Kullback-Leibler (KL) divergence between the distributions in the Rome-2023 model and the ones in Oslo-2020,Rome2021, and in the GMD between these two, for γ(a) and β(b) parameters. For the GMD, results are presented as a function of the mixing proportion used for Rome-2021 (by definition, the proportion for Oslo-2020 is the complement to 1). As regards γ(Fig. 11a), we observe that Rome-2021 is closer to Rome-2023 than Oslo-2020, which can be somehow expected considering that Rome-2021 and Rome-2023 are obtained through measurements in the same city. In between these two models, our GMD solution performs closer to Oslo2020 when the mixing proportion is higher for this model, and approaches Rome-2021 when the two initial models are mixed equally (i.e., by using mixing proportions equal to 0.5). As the mixing proportion of the Rome-2021 model increases beyond 0.5, GMD performs better than both Oslo-2020 and Rome-2021 separately, minimizing the KL divergence when the mixing proportion for Rome-2021 is between 0.6and 0.9; as expected, the performance converges eventually to the one observed for Rome-2021 when the corresponding mixing proportion reaches 1. Similar results are obtained for β(Fig. 11b), although with a lower variability of the KL divergence between the two initial models and, in turn, a lower gain achievable by the GMD approach, which still slightly decreases the KL divergence towards Rome-2023. Finally, for σ, we again observe a low variation between the initial two models and the WMD obtained by mixing them, with the KL divergence towards Rome-2023 confined to a narrow range between 0.22 and 0.24. As a further example, Figure 12 shows a comparison between the distributions of the γvalues for all models involved in our analysis (for the GMD approach, we show the distribution obtained with mixing proportions of 0.7and 0.3 for Rome-2021 and Oslo-2020, respectively). In the figure, we observe that the GMD model is closer than the other models to Rome-2023, thus being able to better represent the values measured in 2023 and included in the latter. We can further highlight that the GMD distribution is, in this case, unimodal, as a result of the closeness of the two initial models in terms of mean values [44]. This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2025.3557172 © 2025 IEEE. All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 07,2025 at 08:04:12 UTC from IEEE Xplore. Restrictions apply.