Модель для анализа блочных ошибок в низкоорбитальных системах связи NB-IoT

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1. Introduction While modern networks are pervasive, terrestrial infrastructure fails to cover more than 80% of the Earth’s surface [1]. This connectivity gap presents a significant barrier to industrial massive machine- type communication (mMTC) applications, such as maritime logistics, global asset tracking, and remote environmental monitoring, which often operate in isolated territories [2]. To bridge this divide without the prohibitive costs of ground-based expansion, the 3GPP has integrated non-terrestrial networks (NTN) into the 5G framework [3]. By leveraging a multi-layered architecture of high-altitude platforms (HAP) and low/middle/geostationary Earth orbiting satellites, NTNs extend the reach of mMTC services to the most remote corners of the globe [4, 5]. © 2026 D. V. Shilonosov, A. A. Likhtenshtein, V. A. Beschastnyi, Y. V. Gaidamaka This work is licensed under a Creative Commons “Attribution-NonCommercial 4.0 International” license. The adaptation of NB-IoT for low-earth orbiting (LEO) constellations is emerging as a definitive solution for ubiquitous IoT connectivity [6]. Although the low-throughput, delay-tolerant traffic design of NB-IoT makes it a prime candidate for NTN integration, the transition from terrestrial to satellite- based architectures introduces formidable physical layer hurdles. The extreme altitudes of spaceborne platforms exacerbate path loss, demanding enhanced link budgets through increased transmit power or higher antenna gains. Furthermore, the rapid orbital velocities of LEO constellations induce significant Doppler shifts and create a highly dynamic environment in which, unlike static terrestrial cells, the base station’s continuous movement results in transient visibility and rapidly fluctuating channel states [7]. The mobility of BS, coupled with large communication distances, creates unique problems for NB-IoT operations. Specifically, the elevation angle between the satellite and the User Equipment (UE) is a decisive factor in link reliability. Lower inclinations exacerbate signal attenuation, shadowing, and multipath fading, leading to a significant increase in the block error rate (BLER) and degradation of service quality [8, 9]. This dependency is accurately captured in the 3GPP TR 36.763 specification. Depending on the UE positioning, additional shadowing can be induced when satellites move over the deployment location [10]. Specifically, when the UE is located in complex propagation conditions, that is, in city centers surrounded by large buildings or in deep forests under the hills, not only do the propagation losses affect the LEO-based narrowband IoT (NB-IoT) communications performance, but also additional losses caused by the so-called shadowing phenomena, which is the partial blockage of the propagation path by large objects in the channel [11]. In 3GPP, these blockage losses are modeled using simple Markov chains with two or three states inherited from ITU-R standards [12]. While these models are appropriate for assessing the average performance of the system, they are not suitable for many practical optimizations, such as choosing the best time instant when the UE needs to send a message to the BS in NTN NB-IoT deployment. The aim of this study is to evaluate the BLER for the NTN NB-IoT channel with major impairments. To this end, we carefully introduce the 3GPP propagation model with scintillation, shadowing, and elevation-dependent impairments. Our model accounts for user-specific deployments and can be fine-tuned for different deployment conditions, including city centers and deep forests. We then utilized the combined model to assess the BLER experienced by the UE at different elevation angles. The remainder of this paper is organized as follows. In Section 2 we review the recent progress in the 3GPP standardization of LEO-based NB-IoT systems. The considered system model is introduced in Section 3. The proposed propagation model, which includes the impact of path loss, elevation angle, scintillations, and deployment conditions, is described in Section 4. The BLER estimation algorithm is presented in Section 5. In Section 6 we report our numerical results. Finally, conclusions are drawn in the last section. 2. Background and related work The evolution of NB-IoT within the NTN framework has been characterized by the systematic adaptation of terrestrial protocols to the distinctive propagation environments of space-borne communications. The foundational efforts, codified in Releases 13 and 14, focused on establishing the baseline feasibility of satellite-based NB-IoT. These early investigations prioritized the characterization of the non-terrestrial channel, specifically regarding path-loss modeling for the L and S frequency bands. Furthermore, preliminary analyses of timing offsets and Doppler shifts were conducted to determine the constraints for maintaining signal decodability over vast distances associated with various orbital altitudes [13, 14]. Subsequently, Release 15 introduced critical physical layer enhancements to ensure practical deployment stability in the presence of extreme-signal attenuation. This release implements robust synchronization and channel estimation procedures designed to mitigate the high Doppler characteristics typical of non-terrestrial environments. To ensure uplink reliability despite the stringent power constraints of mMTC terminals, the single-carrier frequency division multiple access (SC-FDMA) waveform was optimized, ensuring that these spaceborne adaptations remained backward- compatible with the existing terrestrial NB-IoT infrastructure [15]. Release 16 expanded the scope of comprehensive system-level integration and mobility management within the broader 5G service architecture. Key advancements include alignment with the 5G core (5GC) and the introduction of refined random-access procedures specifically tailored to track the high-velocity trajectories of LEO satellites. To counteract the volatile and time-varying propagation conditions inherent in low-Earth orbits, enhanced hybrid automatic repeat request (HARQ) schemes and semi-persistent scheduling mechanisms have been integrated to improve link-level resilience [3, 16]. The challenges of intermittent connectivity and sparse constellation coverage were explicitly addressed in Release 17. This release codified the link budget requirements for LEO, medium-earth orbiting (MEO), and geostationary (GEO) constellations, while introducing standardized procedures for coverage recovery. These mechanisms allow the UE to autonomously detect and reconnect after unavoidable “off-coverage” periods. Moreover, advanced beam management and resource allocation strategies have been standardized to mitigate access contention during the short visibility windows characteristic of initial NTN deployments [17]. Under the 5G-Advanced initiative, Release 18 addresses the complexities of highly dynamic network topologies. It introduced refined tracking area and cell identity mechanisms to address the “moving cell” phenomenon, in which a satellite beam footprint shifts rapidly across the terrestrial surface. To accommodate the significant propagation delays associated with higher orbits, the protocol stack was modified with extended Non-Access Stratum (NAS) supervision timers, ensuring stable mobility management across diverse satellite configurations [18]. The ongoing Release 19 represents a shift toward a fully autonomous and intelligent network architecture. This release proposes state-aware reacquisition strategies that enable terminals to maintain operational continuity during prolonged outages without constant reliance on GNSS timing. Furthermore, it integrates AI/ML-assisted beam tracking and adaptive scheduling to minimize control plane overhead. The inclusion of the RedCap device support ensures that low-complexity, cost-efficient terminals can operate effectively within the NTN ecosystem, even under the most stringent link budget and power conditions [19]. Note that the propagation model defined for LEO systems accounts for many physical phenomena, including scintillations and elevation angle, as discussed further in Section 3. However, one critical factor directly related to communication performance, that is, shadowing, is still modeled using simple two- or three-state Markov chain models [12]. These models directly account for additional attenuation in the shadowed state but fail to scale that for a given environment. To this end, in this study, we extend the 3GPP propagation model to the case of deployment-dependent shadowing. 3. System model In this study, we investigated a communication scenario involving a UE, specifically an NB-IoT device, that establishes a direct link with an LEO satellite for network attachment and the transmission of small data payloads. Similar to [20], the operational context is characterized by intermittent satellite coverage, a prevalent condition during the initial phases of constellation deployment, as illustrated in Figure 1. Consequently, data transmission by the UE is constrained to discrete intervals referred to as contact windows. It is further assumed that the UE has data pending for transmission at the commencement of each contact opportunity. The scope of this analysis is limited to the preamble transmission procedure, which constitutes the initial stage of both the 2-step and 4-step Random Access Channel (RACH) procedures. During a contact window, the satellite traverses its orbit at an altitude denoted as hsat, with its position relative to the UE parametrized by the elevation angle . In the context of NTN for NB-IoT, a minimum elevation angle of = 10∘ is typically established as a baseline to ensure adequate link budget management, maintain acceptable handover frequencies, and guarantee the signal reliability. While adopting a lower minimum elevation threshold (e.g., = 5∘) would extend the duration of Low Earth Orbit Preamble transmission Altitude, hsat HPBW, α IoT device Elevation, θ Horizon Blocker Coverage area No satellite coverage Coverage area Figure 1. The LEO-based communications system model considered in this paper [20] the contact window, it would also result in a greater slant range between the UE and satellite. This increased distance leads to heightened path loss and, consequently, a reduced signal power at the receiver. Owing to the min = 10∘ minimum elevation requirement combined with the high orbital velocity characteristic of LEO satellites, the effective duration of active contact windows is constrained to approximately 10-15 min per satellite pass for a given UE [21]. The channel gain is a fundamental metric that characterizes the end-to-end signal power attenuation (or occasional amplification) as it propagates from the NB-IoT user equipment (UE) to the LEO satellite. Formally defined as the ratio of the received power to the transmitted power, the channel gain encapsulates all physical phenomena that alter the signal along the path, such as the inverse-square law decay of free-space path loss, large-scale shadowing by buildings or vegetation, and rapid multipath fading caused by reflections and interference. BLER is the primary reliability metric for preamble transmission in the considered LEO NB-IoT system. The BLER quantifies the probability that a transport block (e.g., preamble message) is incorrectly decoded at the satellite receiver. This study evaluates the BLER as a function of the fine-grained propagation model defined in the following section, the satellite elevation angle, and the number of repetitions Nrep used for the transmission. We also report this metric for different UE deployment conditions. 4. Fine-grained propagation model In this section, we introduce a fine-grained propagation model that captures the fundamental characteristics of the NTN NB-IoT channel. We begin with path loss models, proceed with channel gain characterization, and then account for elevation and shadowing dependent losses. 1. Path loss and scintillation models Satellites and UE are assumed to be equipped with antenna arrays characterized by the receive and transmit gains GTx and GRx, respectively, which can be calculated as shown in [22]. Antenna arrays can form a beam with a half-power beamwidth (HPBW) of degrees. We model the NTN path loss as 4 d PL = 20 log10( ) - GTx - GRx + PLPo + PLSc + PLAt, where the free-space term follows the Friis equation [23], d is the satellite-to-device distance (km), is the carrier wavelength (m), and the additional loss terms follow ITU-R P.676 [24]: § PLPo, polarization mismatch loss: 3 dB, typical for cross-polarized IoT terminals; § PLSc, ionospheric scintillation loss: 1-3 dB, elevation-dependent, higher at low elevation angles; § PLAt, atmospheric absorption: 0.5-2 dB, frequency- and weather-dependent [24]. The elevation-dependent scintillation is modeled as PLSc( ) = 3 - 2 sin( ), for elevation angle ∈ [10∘, 90∘], following the recommendations of 3GPP TR 38.811 [25]. A statistical characterization of the channel gain is essential to accurately model the air-to-ground propagation channel for LEO satellite systems. This section presents the generative model for the instantaneous channel gain based on ITU-R P.681 [26], followed by an elevation-dependent parameterization for three representative environments: urban, village, and rural wooded. The analysis focuses on the combined effects of the direct signal and multipath scattering, providing a foundation for Monte Carlo simulations [27] of channel state distributions without temporal correlations. 2. Channel gain characterization The channel gain characterizes the signal power attenuation (or occasionally amplification) as it propagates from the transmitter to the receiver and is expressed as the ratio of the received power to the transmitted power. It encapsulates all physical effects that alter the signal along the path, including the inverse-square law decay of the path loss over distance, large-scale obstruction shadowing from buildings or terrain, and rapid multipath fading caused by signal reflections and interference. Because the wireless environment is dynamic owing to movement, changing obstacles, or atmospheric conditions, the channel gain is inherently time-varying. In our study, the instantaneous channel gain Gch (in dB) represents the combined effects of the direct signal and multipath scattering. Following the generative procedure proposed by [26], we generated independent Monte Carlo samples of the channel state without temporal correlation as follows: 1. Sample direct signal amplitude: A = 10(MA+ A⋅ZA)/20, where ZA ∼ (0, 1) models the amplitude fluctuations, and the transformation from dB to linear units follows the lower processing path. 2. Compute multipath I/Q standard deviation: mp = √10MP/10/2, corresponding to the upper processing path, where the in-phase (I) and quadrature (Q) components represent the two orthogonal dimensions of the complex multipath signal. 3. Sample independent multipath components nI, nQ ∼ (0, 1). 4. Compute received power (Rice+Rayleigh envelope): Gch = 10 log10 [(A + mp ⋅ nI)2 + ( mp ⋅ nQ)2] (dB). Note that for the Monte Carlo simulation, we skip the temporal filtering stages (Doppler spread filter and low-pass correlation filter HA(Z)) as we focus on the evaluation of statistical distributions rather than time-correlated sequences. Figure 2 illustrates the channel gain in urban, village, and rural scenarios as a function of the satellite elevation angle. The horizontal reference line at -3 dB represents a commonly assumed constant shadow fading value in LEO link budget analyses. 3. Elevation-dependent parameterization The ITU-R report [26] provides distribution parameters for five reference elevation angles: {20°, 30°, 45°, 60°, 70°} and deployment scenarios at 2.2 GHz. For an arbitrary elevation ∈ [20°, 70°], we employ a Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) to ensure monotonic interpolation. We focused on three scenarios for which complete parameter sets were available across all reference angles: urban, village, and rural wooded. We specifically outline our key observations as follows: § Urban scenario exhibits severe attenuation at low angles ( [Gch] ≈ -13 dB at = 20°) due to high buildings creating deep shadowing, improving rapidly with elevation; § Village shows best performance across all angles due to lower building heights. Rural wooded areas exhibit moderate attenuation with slow improvement, as tree-induced scattering persists even at high angles. Algorithm 1: Loo Channel Gain Generation (ITU-R P.681-11 Section 6.2) 1 Input: § - elevation angle (degrees), ∈ [20∘, 70∘] § Scenario ∈ {Urban, Village, Rural wooded} § ITU-R parameters from Annex 2 (interpolated at ) Output: Gch - channel gain (dB) // Compute state durations using ITU-R formula (17a) 2 Compute ⟨dur⟩G, ⟨dur⟩B; // Compute transition time using ITU-R formulas (17b), (18a), (18b) 3 Compute MA,min,B, MA,max,B using Equations (18a) and (18b); 4 Compute ⟨dur⟩T using formula (17b) // Compute BAD state probability using ITU-R formula (19b) 5 Compute pB; // Sample channel state 6 Sample S ∼ Bernoulli(pB) ; // S = 0: ``GOOD'', S = 1: BAD // Generate Loo parameters triplet (ITU-R Table 6) 7 if S = 0 then // ``GOOD'' state 8 Sample MA ∼ ( MA,G , MA,G , MA,G - 1.645 MA,G , MA,G + 1.645 MA,G ); 9 A = g1G ⋅ MA + g2G; 10 MP = h1G ⋅ MA + h2G dB; 11 else // ``BAD'' state 12 Sample MA ∼ ( MA,B , MA,B , MA,min,B, MA,max,B); 13 A = g1B ⋅ MA + g2B; 14 MP = h1B ⋅ MA + h2B dB; // Generate complex envelope (ITU-R Figure 18, Monte Carlo mode) 15 Sample ZA ∼ (0, 1); 16 A = 10(MA+ A⋅ZA)/20 ; // direct signal amplitude 17 mp = √10MP/10/2 ; // multipath I/Q std deviation 18 Sample independent nI, nQ ∼ (0, 1) Compute Gch = 10 log10 [(A + mp ⋅ nI)2 + ( mp ⋅ nQ)2] dB 19 return Gch; 4. Shadowing model In this study, we incorporate the stochastic channel model for satellite systems provided in [12]. The model captures both large-scale shadow fading and small-scale multipath effects using a two-state Markov process. The model distinguishes between the “GOOD” and “BAD” channel states, which are 0 Channel gain, Gch, db -2 -4 -6 -8 -10 -12 -14 Village Rural Urban 20 30 40 50 60 70 Elevation angle, θ , degree Figure 2. Mean channel gain as function of elevation angle characterized by distinct statistical distributions of signal attenuation and multipath scattering. The behavior of the model is governed by a set of environment- and geometry-dependent parameters. The primary inputs are the environment type (urban, rural wooded, or village), satellite elevation angle (typically ranging from 10∘ to 80∘), and carrier frequency (between 1.5 and 20GHz). For each combination, ITU-R P.681-11 provides tabulated values of the state transition probabilities pGB and pBG, the mean sojourn times (or the parameters of the log-normal dwell-time distributions) for the good and bad states, and the Loo distribution parameters (diffuse power), (mean of the log-normal shadowing), and √d0 (standard deviation of the log-normal shadowing) for each state. Additional parameters include the mobile terminal speed (which scales the dwell times by the Doppler effect) and the azimuth angle relative to the satellite, which are neglected in this study. The steady-state probability of being in the “BAD” state, denoted pB, is derived from the mean durations of each state and the transition times between them. Following [26], these parameters are characterized as functions of the elevation angle and deployment scenario. The mean durations of “GOOD” and “BAD” states are computed from truncated lognormal distributions using (1), log durmin,B,G-( G,B+ 2 ) 2 1 - erf ( G,B ) ⟨dur⟩G = exp ( + G,B ) √2 , (1) ,B G,B 2 1 - erf ( log durmin,B,G- G,B ) √2 where G, G, durmin G for the “GOOD” state and B, B, durmin B for the “BAD” state are scenario- dependent parameters tabulated in [26]. The mean transition time between states is computed using formula (2), which includes a correction term accounting for the statistical bias introduced by truncating the signal attenuation distribution in the “BAD” state. M ⟨dur⟩T = f1 × ( M,A,G - M,A,B - 2 ,A,B× (2) pN (MA,min; M,A,B, M,A,B) - pN (MA,max; M,A,B, M,A,B) × FN (MA,min; M,A,B) - FN (MA,max; M,A,B) ) + f2. The truncation bounds are defined by (3) and (4), with pB,min and pB,max representing the confidence interval range: and also MA,min,B = M,A,B + √2 M,A,B erf-1(2pB,min - 1), (3) MA,max,B = M,A,B + √2 M,A,B erf-1(2pB,max - 1). (4) Finally, the steady-state probabilities pG and pB are computed using pG = ⟨dur⟩G + ⟨dur⟩T , pB = ⟨dur⟩B + ⟨dur⟩T . (5) ⟨dur⟩G + ⟨dur⟩B + 2⟨dur⟩T ⟨dur⟩G + ⟨dur⟩B + 2⟨dur⟩T Initialize parameters for all elevation angles Compute FSPL Parameterize Loo channel model (Alg. 2) Evaluate mean Compute SNR Output BLER Figure 3. Flowchart of the proposed BLER evaluation framework For each channel state (“GOOD” or “BAD”), the Loo model characterizes three signal components that together define the instantaneous channel realization as follows: 0. Direct signal attenuation (MA): the direct path experiences attenuation MA (dB) modeled as a truncated normal distribution. For the “GOOD” state, the truncation range is [ MA,G - 1.645 MA,G , MA,G + 1.645 MA,G ] as specified in [26]. For the “BAD” state, the truncation bounds are determined by (3) and (4) with the confidence interval [pB,min, pB,max] (typically [0.1, 0.9] for Urban at 2.2 GHz). 1. Amplitude fluctuations ( A): the RMS fluctuation of the direct signal amplitude depends linearly on MA: A = g1 ⋅ MA + g2, where regression coefficients g1, g2 differ between “GOOD” and “BAD” states. This models the variability in shadowing severity within each state. 2. Multipath power (MP): the multipath scattering power also depends linearly on MA ∶ MP = h1 ⋅ MA + h2, with state-dependent coefficients h1, h2. This captures the correlation between direct-path obstruction and multipath richness. 5. BLER estimation The proposed methodology evaluates the elevation-dependent BLER through a link budget analysis incorporating the Loo channel model and other impairments introduced earlier. Our framework operates through six computational steps executed for each elevation angle j ∈ [20°, 70°], as shown in Figure 3. We began with the parameterization of the considered environment. The physical constants and system parameters were defined in accordance with the NB-IoT specifications for LEO satellite communications. The coding gain for each repetition level is modeled as Gcode(Nrep) = 2 ⋅ log2(Nrep) dB, which is calibrated empirically from link-level simulations [16]. Once the initial parameters are obtained, for each elevation angle j we compute the distance for the communication link employing spherical geometry dj = (RE + hsat)2 - R2 cos2 j - RE sin j (km), √ E and the free-space path loss that follows the Friis equation LFSPL( j ) = 20 log10(dj) + 20 log10(fc) + 20 log10(4 /c) (dB). We then proceeded to evaluate the channel condition using the Loo channel model. To do this, all ITU-R parameters for the selected scenario are interpolated at every angle value j using PCHIP and the “BAD” state probability pB( j ) as shown in Algorithm 2. In this phase, the statistical model is prepared for the subsequent Monte Carlo sampling. After defining the parameter values for the channel model, we began the simulation. We generate NMC independent channel realizations at j using Algorithm 1 and compute the mean channel gain 1 NMC Ḡch( j ) = N ∑ Gch,i. MC i=1 Now we are at evaluation of SNR at j for each repetition number Nrep which is given by SNR( j , Nrep) = PTX - LFSPL( j ) - Ltotal + GRX - N0 + Ḡch( j ) + Gcode(Nrep). 1.0 0.8 BLER 0.6 o ○ □ ◇ § □ ◇ § □ ◇ o o □ ◇ § □ ◇ § □ ◇ § ◇ § □ ◇ § □ ◇ § □ ◇ § Village, Nrep=1 □ Rural, Nrep=1 § Urban, Nrep=1 § Village, Nrep=16 0.4 0.2 § □ ◇ § □ ◇ § □ ◇ § □ ◇ o □ ◇ § □ ◇ § □ ◇ § □ ◇ § □ ◇ § □ ◇ § □ ◇ § □ ◇ § Rural, Nrep=16 § Urban, Nrep=16 § Village, Nrep=128 o Rural, Nrep=128 o Urban, Nrep=128 0.0 § □ ◇ § □ ◇ § □ ◇ 25 30 35 40 45 50 55 60 EIRP, dBm Figure 4. BLER as function of EIRP for 90∘ elevation angle The final step involves obtaining the BLER by interpolating link-level simulation data provided in [8] BLER( j , Nrep) = ℒ(SNR( j , Nrep)), where ℒ ∶ ℝ → [0, 1] is a PCHIP interpolator constructed from digitized BLER-SNR pairs at ref = 50° with a transport block size of 408 bits. Algorithm 2: Loo Channel Model Parameterization 1 Input: o - elevation angle (degrees), ∈ [20∘, 70∘] o Scenario ∈ {Urban, Village, Rural wooded} Output: pB - BAD state probability // Interpolate all ITU-R parameters from Annex 2 at 2 Interpolate G, G, durmin G, B, B, durmin B via PCHIP; 3 Interpolate MA,G , MA,G , MA,B , MA,B via PCHIP; 4 Interpolate g1G, g2G, g1B, g2B, h1G, h2G, h1B, h2B using PCHIP Interpolate f1, f2 via PCHIP; // Compute state durations using ITU-R formula (17a) 5 Compute ⟨dur⟩G, ⟨dur⟩B; // Compute transition time using ITU-R formulas (17b), (18a), (18b) 6 Compute MA,min,B, MA,max,B using Equations (18a) and (18b); 7 Compute ⟨dur⟩T using formula (17b); // Compute BAD state probability using ITU-R formula (19b) B 8 p = ⟨dur⟩B+⟨dur⟩T ; ⟨dur⟩G+⟨dur⟩B+2⟨dur⟩T 9 return pB; 6. Results In this section, we present our numerical results. Specifically, we considered the elevation angle, deployment type, and number of repetitions as the main parameters and reported the associated BLER values. The default 3GPP LEO NB-IoT system parameters are listed in Table 1. We begin in Figure 4 demonstrating the BLER as a function of EIRP for different deployments conditions including rural wooded, urban, and village and different number of repetitions. In this illustration, the elevation angle is set to 90∘, that is, the satellite is in the zenith location. Default system parameters Table 1 Notation Description Value RE Earth radius 6371 km hsat Satellite altitude 600 km fc Carrier frequency (NB-IoT uplink, S-band) 2.0 GHz GRX Satellite antenna gain 30 dB Ltotal System losses 5.3 dB N0 Thermal noise floor (15 kHz bandwidth) -118.4 dBm PTX Transmit effective Isotropic Radiated Power 42 dBm Nrep Number of repetitions 2{0,…,7} NMC Number of samples 105 1.0 0.8 BLER 0.6 Village Rural Urban 0.4 0.2 0.0 20 30 40 50 60 70 Elevation angle, θ , degree Figure 5. BLER as function of elevation angle for fixed number of repetitions, Nrep = 1 By analyzing the results presented in Figure 4 one may observe that the most impact is produced by the number of repetitions utilized at the wireless channel. Specifically, the subsequent increase in the number of repetitions from 1 to 16 and finally to 128 shifts the associated BLER curves by approximately 8-10 dB along the x-axis. However, this improvement is associated with the increased access delay associated with preamble reception and thus successful resolution of the access procedure at the BS side. The impact of deployment conditions was less pronounced but still noticeable. Specifically, as shown in Figure 4, changing from village to rural wooded and then to urban deployments shifts the BLER curves by around 1-2 dB. In terms of BLER, this may still be noticeable by increasing it by approximately 0.2 with respect to each other. In general, the BLER is very sensitive to both repetitions and deployment conditions and must be considered during the deployment phase. Yet, another critical parameter for system design is the elevation angle. Its impact on the BLER under different deployment conditions is shown in Figure 5 for the number of repetitions set to 1 and EIRP of 42 dBm. By analyzing the presented results, it can be observed that the elevation angle has a critical 1.0 0.8 BLER 0.6 Village Rural Urban 0.4 0.2 0.0 20 30 40 50 60 70 Elevation angle, θ , degree Figure 6. BLER as function of elevation angle for a fixed number of repetitions, Nrep = 4 effect on the preamble reception probability. Specifically, for a given number of repetitions, the system may go from a totally unusable regime with a BLER of 1 to perfect conditions with a negligible BLER. This makes the problem of optimal transmission time instant with systems with interrupted LEO coverage important. The impact of deployment conditions is also visible and can amount to 0.4 difference in BLER for a given elevation angle. Finally, we examine when the number of repetitions may improve the system’s performance for the considered elevation angles. To this end, Figure 6 shows the BLER for the number of repetitions set to 4 and EIRP of 42 dBm. By cross-comparing the results presented in this illustration and Figure 5 we see that increasing the number of repetitions from 1 to 4 already have a drastic impact of BLER. Specifically, all the curves move to the left, allowing efficient communication at angles that are totally prohibited with Nrep = 1. This is the case, for example, for an elevation angle of 50∘ the BLER is close to zero for Nrep = 4 for all the considered deployment conditions, while it is higher than 0.2 for the best possible village deployment for Nrep = 1. 7. Discussion The primary goal of this study was to evaluate the block error rate (BLER) for LEO-based NB-IoT systems under elevation-dependent channel impairments and deployment-specific shadowing and to determine whether a simple elevation-agnostic propagation model suffices for performance analysis. Our results directly address the questions raised in the Introduction, namely, (i) how severely does the elevation angle affect the BLER across different environments, and (ii) can deployment-dependent shadowing be captured with sufficient accuracy to guide transmission-timing decisions. The results show that the elevation angle is the dominant factor affecting the BLER. At a fixed number of repetitions (Nrep = 1) and an EIRP of 42 dBm, the BLER decreases from approximately 1 at low elevations (≈ 20∘) to below 0.1 at high elevations (≈ 70∘) in all three environments (Figure 5). This finding answers the first question: elevation should not be neglected in link budget analysis. Regarding the second question, deployment conditions produced a secondary but measurable effect-urban scenarios exhibited up to 0.4 higher BLER than village environments at the same elevation (Figure 5). Thus, a model that ignores deployment-specific shadowing would systematically overestimate the performance for urban UEs and underestimate it for village deployments. Our fine- grained, parameterized Loo model (Algorithm 1) captures this variability, confirming the hypothesis that environment-dependent parameterization is necessary for an accurate BLER prediction. The observed strong elevation dependence aligns with 3GPP TR 36.763 and earlier studies [8, 9], which reported that lower elevation angles exacerbate path loss and multipath. However, prior studies using two- or three-state Markov chains [26] treated shadowing as a static or memoryless process without fine-grained elevation-dependent parameter recovery. Our extension, which interpolates ITU-R P.681-11 parameters via PCHIP and derives state probabilities from (5), provides a more accurate mapping of elevation to channel statistics. The results in Figure 4 also confirms the well-known trade-off between repetitions and reliability: increasing Nrep from 1 to 128 shifts the BLER curve by 8-10 dBm, consistent with the coding gain model Gcode(Nrep) = 2 log2(Nrep) dB adopted from [8]. No inconsistencies with prior experimental or simulation results were observed. The elevation dependency can be explained by three coupled mechanisms. First, the slant range d( ) increases sharply below 30∘, directly increasing the free-space path loss (Friis equation). Second, the scintillation loss PLSc( ) = 3 - 2 sin amplifies the attenuation at low angles. Third, the “BAD” state probability pB( ) derived from (5) increases as the elevation decreases because the signal path intersects more obstacles. The Loo model’s separation of direct signal attenuation MA (truncated normal) and multipath power MP (linear regression on MA) captures the physical reality that heavy shadowing correlates with reduced multipath richness, a feature missing from simpler Markov models. This study provides a quantitatively validated and deployable model for predicting the BLER in LEO NB-IoT systems across three representative environments. The key practical implication is that fixed-time or random transmission schemes are suboptimal; a UE can reduce its BLER from near 1 to < 0.1 simply by delaying transmission until the satellite reaches a higher elevation angle (e.g., > 50∘ with Nrep = 4). Our model enables such elevation-aware scheduling without requiring real-time channel sounding because the elevation angle is known from ephemeris data. First, the temporal correlation of the Loo process should be reintroduced to model the burst errors and optimize the HARQ parameters. Second, the model should be extended to lower elevation angles (10∘-20∘) where the minimum specified in 3GPP TR 38.811 is critical. Third, the interaction between repetitions and elevation can be formulated as an optimization problem: minimize access delay subject to a BLER constraint by jointly selecting Nrep and the transmission wait time. Finally, experimental validation using real LEO satellite data will confirm the simulation-based findings presented in this study. This study aimed to develop a fine-grained model that accounts for satellite NB-IoT channel conditions and estimates the BLER. Our results directly fulfill this aim by providing a complete parameterized algorithm (Algorithms 1-2) and numerical BLER tables for urban, village, and rural wooded scenarios. 8. Conclusion LEO-based NTN NB-IoT systems provide a convenient way to enable mMTC services in locations that cannot otherwise be covered by terrestrial wireless communication systems. However, the specifics of propagation conditions, including large communication distances modulated by the LEO elevation angle, scintillation, and shadowing caused by different deployment conditions, require careful planning of the link budget to enable efficient random access and data transmission. To this end, in this study, we exhaustively characterized the BLER performance of LEO-based NB-IoT systems. Our numerical results demonstrated that the elevation angle has the greatest impact on the elevation angle. The effect of the deployment conditions is of second-order importance. Specifically, urban scenarios suffer severe attenuation at low elevation angles (≈ -13 dB at 20∘), whereas rural wooded areas exhibit moderate but persistent scattering, and village environments provide the best overall channel conditions. We also showed that the number of repetitions trading off latency for reliability is an efficient way to conceal the deteriorating impact of path loss. However, when latency is critical, one needs to carefully plan the transmission time instants for UEs avoiding low elevation angles.

Об авторах

Д. В. Шилоносов

Российский университет дружбы народов

Email: shilonosov-dv@rudn.ru
ORCID iD: 0009-0002-0327-4739

Student of the Department of Probability Theory and Cybersecurity, RUDN University

ул. Миклухо-Маклая, д. 6, Москва, 117198, Российская Федерация

А. А. Лихтенштейн

Российский университет дружбы народов

Email: 1132229533@rudn.ru
ORCID iD: 0009-0003-4821-2192

Student of the Department of Probability Theory and Cybersecurity, RUDN University

ул. Миклухо-Маклая, д. 6, Москва, 117198, Российская Федерация

В. А. Бесчастный

Российский университет дружбы народов

Email: beschastnyy-va@rudn.ru
ORCID iD: 0000-0003-1373-4014
Scopus Author ID: 57192573001

Candidate of Physical and Mathematical Sciences, assistant professor of the Department of Probability Theory and Cybersecurity, RUDN University

ул. Миклухо-Маклая, д. 6, Москва, 117198, Российская Федерация

Ю. В. Гайдамака

Российский университет дружбы народов; Федеральный исследовательский центр ``Информатика и управление'' РАН

Автор, ответственный за переписку.
Email: gaydamaka-yuv@rudn.ru
ORCID iD: 0000-0003-2655-4805
Scopus Author ID: 35106984800
ResearcherId: E-5620-2014

Doctor of Physical and Mathematical Sciences, Full Professor of Department of Probability Theory and Cybersecurity, RUDN University; Senior Researcher of Institute of Informatics Problems of Federal Research Center ``Computer Science and Control'' Russian Academy of Sciences

ул. Миклухо-Маклая, д. 6, Москва, 117198, Российская Федерация; ул. Вавилова, д. 44, корп. 2, Москва, 119333, Российская Федерация

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