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The Impact of Mobile Blockers on Millimeter Wave Cellular Systems

Ish Kumar Jain, Rajeev Kumar, Shivendra Panwar

arXiv:1807.04388v2eess.SP

TL;DR

Frequent and lengthy mmWave blockages challenge URLLC service, and prior work did not provide the multi-BS dynamic-blockage analysis needed to evaluate these events. The paper models blockage across LOS and NLOS links and finds that blockage and latency constraints, rather than coverage or capacity, drive URLLC BS-density requirements.

  • Problem

    The paper addresses the need to quantify blockage probability and duration in mmWave networks where blockage frequency and duration matter for URLLC, beyond prior coverage and capacity analyses.

    Source: §I · pp. 1–2, §II · p. 3

  • Method

    The paper develops a stochastic-geometry model combining dynamic, static, and self-blockage, analyzes LOS and NLOS paths, and checks the model with MATLAB simulations.

    Source: §I · p. 2, B. LOS Blockage Probability · p. 5, §VIII · p. 12

  • Results

    In the urban scenario, around 200 BS/km2 may be needed for latency requirements, and URLLC density may be uneconomically high relative to coverage and capacity needs.

    Source: A. Open Park Scenario · p. 10, B. Urban Scenario · p. 12

  • Takeaways & Limitations

    The analysis suggests URLLC BS density is driven mainly by blockage and latency constraints, and tight coupling among 5G NR, LTE, and WiFi may help meet QoS requirements.

    Source: §I · p. 1, B. Urban Scenario · p. 12

    The conclusions are tentative because mmWave 5G networks were only beginning deployment, and deployment experience or technological improvements may require revision.

    Source: B. Urban Scenario · p. 12

Abstract

from arXiv · show

Millimeter Wave (mmWave) communication systems can provide high data rates, but the system performance may degrade significantly due to interruptions by mobile blockers such as humans or vehicles. A high frequency of interruptions and lengthy blockage durations will degrade the quality of the user's experience. A promising solution is to employ the macrodiversity of Base Stations (BSs), where the User Equipment (UE) can handover to other available BSs if the current serving BS gets blocked. However, an analytical model to evaluate the system performance of dynamic blockage events in this setting is unknown. In this paper, we develop a Line of Sight (LOS) dynamic blockage model and evaluate the probability, duration, and frequency of blockage events considering all the links to the UE which are not blocked by buildings or the user's own body. For a dense urban area, we also analyze the impact of non-LOS (NLOS) links on blockage events. Our results indicate that the minimum density of BS required to satisfy the Quality of Service (QoS) requirements of Ultra Reliable Low Latency Communication (URLLC) applications will be driven mainly by blockage and latency constraints, rather than coverage or capacity requirements.

I. INTRODUCTION

The paper studies how blockage probability, frequency, and duration affect mmWave reliability and latency, then develops a macrodiversity model and network-planning analysis for URLLC. It extends earlier blockage work to include mobile blockers alongside static and self-blockage, and considers NLOS paths in urban settings.

I. INTRODUCTION

  • The analysis targets URLLC planning because frequent, lengthy mmWave outages can undermine service, making blockage probability, frequency, and duration important alongside coverage and capacity.The paper combines blockage mechanisms in a stochastic-geometry model and examines BS density needed to meet QoS requirements.Source: §I · p. 2, §II · p. 3

II. RELATED WORK

  • Earlier models addressed single-link dynamic blockage or macrodiversity with static blockage, while this paper extends the analysis to mobile blockers and LOS/NLOS paths.The paper also builds on prior open-park work by considering a hexagonal layout and an urban setting.Source: §II · pp. 2–3

III. SYSTEM MODEL

  • The system model places a typical UE at the center of a disc containing BSs and blockers, with service quality subject to static, self-, and dynamic blockage.BS locations are modeled as a homogeneous Poisson point process.Source: Figure 1 · p. 3, A. Assumptions • · p. 3

A. Assumptions

  • Static blockage is modeled using building dimensions and density, while self-blockage excludes BSs within a body-oriented sector.The orientation of the user’s body is uniform in [0, 2π].Source: A. Assumptions • · pp. 3–4
  • Dynamic blockers form a homogeneous Poisson point process, and each link’s blockage arrivals are modeled as Poisson with exponentially distributed blockage duration.The resulting on-off process uses arrival rate α_i and unblocking rate µ.Source: A. Assumptions • · p. 4
  • NLOS candidates are limited to BSs within radius R̃ and modeled as virtual BSs uniformly distributed on a circle at the corresponding actual BS distance; the UE is blocked when all potential LOS and NLOS links are blocked.The equal-radius placement is a best-case assumption used to obtain a lower bound on blockage probability.Source: A. Assumptions • · p. 4

B. Dynamic Blockage Model for a Single BS-UE Link

The single-link model derives blocker arrivals from blocker motion across the effective link region, then approximates blockage as an exponential on-off process. The model supports the later multi-BS analysis, which assumes zero service interruption time during handover.

B. Dynamic Blockage Model for a Single BS-UE Link

  • The blockage arrival rate is α_i = C r_i, with C proportional to blocker density and the crossing geometry determined by blocker motion across the effective link region.The derivation averages the perpendicular velocity component over uniformly distributed blocker directions.Source: B. Dynamic Blockage Model for a Single… · p. 5
  • The model approximates each link’s blocked and unblocked intervals as exponential, treating simultaneous blockage by multiple blockers as negligible.The authors report that the approximation works over a wide range of blocker densities, as verified by simulations.Source: B. Dynamic Blockage Model for a Single… · p. 5
  • For the subsequent multi-BS analysis, the UE is assumed to track available BSs through beam-steering and handover with a service interruption time of 0 ms.Source: B. Dynamic Blockage Model for a Single… · p. 5

IV. GENERALIZED LOS BLOCKAGE MODEL

The generalized LOS model treats the UE as blocked only when all candidate BS links are blocked. It separately defines LOS coverage by the presence of at least one BS not blocked by static obstruction or the user’s body.

IV. GENERALIZED LOS BLOCKAGE MODEL

  • The generalized model considers a BS link blocked if static, dynamic, or self-blockage affects it, and defines overall LOS blockage as all available links being blocked simultaneously.Source: §IV · p. 5

A. LOS Coverage Probability

  • The number of BSs unblocked by static or self-blockage is modeled as Poisson with parameter p q λ_T πR^2.The passage identifies p and q as defined in equation (15), without providing their meanings here.Source: A. LOS Coverage Probability · p. 5
  • LOS coverage requires at least one BS within the modeled region that is not blocked by static obstruction or self-blockage.Source: A. LOS Coverage Probability · p. 5

B. LOS Blockage Probability

The section models simultaneous LOS blockage across all in-range BSs, combining static, dynamic, and self-blockage. It derives marginal and coverage-conditioned blockage probabilities, including a closed-form open-park case.

B. LOS Blockage Probability

  • Correlated link blockages are treated as independent, leaving their correlation analysis for future work.A nearby blocker may block multiple BS links simultaneously.Source: B. LOS Blockage Probability · p. 6
  • The model derives marginal and coverage-conditioned probabilities of simultaneous LOS blockage across available BS links.It averages conditional blockage over BS distances and then over the number of BSs; the model assumes independent blockage across links.Source: B. LOS Blockage Probability · pp. 5–6
  • For the open-park case, the paper gives closed-form coverage and dynamic blockage probabilities without static blockages.The blockage result is conditioned on coverage.Source: B. LOS Blockage Probability · p. 6
  • Required BS density approximately scales linearly with blocker density λB when targeting a blockage-probability threshold.This scaling follows from the stated required-density result.Source: B. LOS Blockage Probability · p. 6

C. Expected Blockage Duration

The section characterizes simultaneous LOS blockage duration using independent per-link blockage durations, then gives a high-BS-density approximation and an open-park special case.

C. Expected Blockage Duration

  • For n covered BSs, independent exponential link-blockage durations with mean 1/µ yield simultaneous LOS blockage duration with mean 1/nµ.The expected duration conditioned on LOS coverage is given in Theorem 2.Source: C. Expected Blockage Duration · p. 6

where, Ei

  • The series used in the derivation can be written as an exponential integral function, and its convergence is shown using the Cauchy ratio test.Source: where, Ei · p. 7
  • A high-BS-density approximation to the blockage-duration expression is provided and justified in Appendix D.The approximation applies to expression (29).Source: where, Ei · p. 7
  • The open-park expected blockage duration follows from (29) by setting q=1, corresponding to β=0 and β0=0.Source: where, Ei · p. 7

D. Expected Blockage Frequency

The section defines expected blockage frequency for the open-park LOS case and extends blockage analysis to include NLOS links. Its NLOS analysis specifies coverage assumptions and derives a blockage-probability expression using a lower-bound model.

D. Expected Blockage Frequency

  • The open-park expected blockage frequency is the rate of simultaneous blockage of all BSs within the UE range, with a closed-form expression conditioned on coverage.The frequency definition conditions on the BS count and UE-BS distances.Source: D. Expected Blockage Frequency · p. 7

A. Coverage Probability incorporating NLOS links

  • With LOS and NLOS links, coverage means at least one link is unblocked by static or self-blockage; NLOS links are assumed available only within distance R̃.The model assumes LOS and NLOS link availability are independent.Source: A. Coverage Probability incorporating… · p. 7

B. Incorporating NLOS links in Blockage Probability

  • The NLOS blockage model gives a lower bound by placing virtual BSs at distance ri and spreading them uniformly over the full angular range, minimizing blockage incidence.Source: B. Incorporating NLOS links in… · p. 7
  • The resulting blockage probability expression accounts for both LOS and NLOS links under independent blocking assumptions.The derivation averages over the BS count and locations.Source: B. Incorporating NLOS links in… · p. 8

C. Expected Blockage Duration considering NLOS links

The NLOS duration analysis counts LOS and NLOS paths together and estimates expected blockage duration over the distributions of BS counts and virtual links. A first-order approximation is identified as accurate for high BS densities.

C. Expected Blockage Duration considering NLOS links

  • The duration model counts n LOS paths and ˜n k NLOS paths, then takes an expectation over n, ˜n, and k.˜n is the number of BSs in B(o, ˜R), modeled as Poisson with mean λT π ˜R².Source: C. Expected Blockage Duration… · p. 8
  • Expected blockage duration is expressed using the combined LOS/NLOS path count and the expected reciprocal blockage rate.The supplied expression conditions on coverage; its expectation is over the path-count variables.Source: C. Expected Blockage Duration… · p. 8
  • The first-order duration approximation is reported to be good for high BS densities.The text refers to approximation (47) and its discussion in Appendix D.Source: C. Expected Blockage Duration… · p. 8

VI. HEXAGONAL CELL LAYOUT

The paper analyzes a planned hexagonal deployment and evaluates open-park and urban scenarios. In the open park, denser BS deployments, greater communication range, or greater BS height can reduce blockage-related service constraints; planned hexagonal placement can require fewer BSs than random placement in the stated comparison.

VI. HEXAGONAL CELL LAYOUT

  • The hexagonal model places the BS at the origin and the UE uniformly in the central cell; blockage probability is integrated over the UE location.For self-blockage, the analysis chooses a user location and orientation that block the maximum number of BSs, yielding an upper bound.Source: §VI · pp. 8–9

VII. NUMERICAL EVALUATION

  • The open-park scenario omits static blockages and assumes no strong NLOS paths, while the urban scenario includes buildings, NLOS paths, dynamic blockers, and self-blockage.Numerical analysis considers both outdoor settings.Source: §VII · p. 9

A. Open Park Scenario

  • For 0.01 bl/m2, analytical and simulation results are approximately equal; at 0.1 bl/m2, they deviate modestly, especially at high BS densities.The model assumes no more than one blocker blocks a link at a time, unlike the simulations.Source: Figure 6 · p. 10, A. Open Park Scenario · p. 11
  • At R = 200 m, V2X requires about 200 BS/km2 for latency; reliability requires fewer than 100 BS/km2 at 0.1 bl/m2 and fewer than 50 BS/km2 at 0.01 bl/m2.The reliability target is 99%; caching is not viable for meeting V2X latency in this analysis.Source: Figure 7 · p. 10, A. Open Park Scenario · p. 10
  • At R = 200 m, AR/VR car entertainment requires fewer than 100 BS/km2 at 0.01 bl/m2 and fewer than 150 BS/km2 at 0.1 bl/m2.At 150 BS/km2, 40–60 ms of cached data is required for uninterrupted service.Source: Figure 7 · p. 10, A. Open Park Scenario · pp. 10–11
  • Doubling BS height from 4 m to 8 m reduces the required BS density by approximately 20% at the stated blockage-probability target.The height–density trade-off is presented for fixed P(Bd|Cd) = 10^-5.Source: Figure 8 · p. 10, A. Open Park Scenario · p. 11
  • With 0° self-blockage, the hexagonal layout reaches 10^-4 blockage probability with fewer than 100 BS/km2 at 0.01 bl/m2 and fewer than 200 BS/km2 at 0.1 bl/m2.At 60°, the upper bound is 200 BS/km2 for 0.01 bl/m2, versus 300 BS/km2 for the random topology.Source: Figure 9 · p. 11, A. Open Park Scenario · p. 11
  • At R = 100 m, average handover rates are 0.05 handovers/s/UE for 0.01 bl/m2 and 0.5 handovers/s/UE for 0.1 bl/m2.The paper notes these rates are much higher than those typically seen in 4G systems.Source: A. Open Park Scenario · p. 11

B. Urban Scenario

In the urban scenario, NLOS reflections improve coverage, but provide only modest relief from blockage. The analysis concludes that blockage and latency constraints, rather than coverage or capacity, drive the BS density needed for URLLC QoS.

B. Urban Scenario

  • 90% urban coverage requires around 200 BS/km2 without NLOS paths, but fewer than 100 BS/km2 with them.The analysis attributes the difference to reflections providing additional NLOS paths.Source: B. Urban Scenario · p. 11
  • The NLOS-range analysis assumes PLE=2.69 at 73 GHz and average reflection attenuation γ_NLOS=5 dB, giving 65 m for a 100 m LOS range and 130 m for a 200 m LOS range.The paper contrasts the URLLC densities with prior capacity estimates of 30–100 BS/km2.Source: B. Urban Scenario · p. 12
  • NLOS paths provide only a modest reduction in blockage probability and expected duration, in part because few BSs may lie within the shorter NLOS range.Nearly isolated UEs connected to only a few distant BSs may have no NLOS paths to mitigate blockages.Source: B. Urban Scenario · p. 12, Figure 11 · p. 12
  • At a 200 m communication range, fewer than 200 BS/km2 may achieve 99.999% reliability, while about 200 BS/km2 may be needed to meet latency requirements for applications that cannot use caching.The cited applications include V2X, tactile Internet, and smart grid.Source: B. Urban Scenario · p. 12
  • The authors describe their URLLC density conclusions as tentative because mmWave 5G networks were only beginning deployment and later experience may require revision.They state that the methodology may still inform future network design with appropriate amendments.Source: B. Urban Scenario · p. 12

VIII. CONCLUSIONS

  • For the scenarios considered, required BS density for URLLC QoS is much higher than density for capacity or coverage, making blockage a potential driver of mmWave network engineering.The conclusion notes that the model does not capture correlation between blockage events, which may result in an even higher blockage probability.Source: §VIII · p. 12, B. Urban Scenario · p. 12
  • The conclusion suggests sub-6 GHz connectivity during dynamic blockages, but says it requires tight control-plane integration and traffic engineering to avoid overwhelming sub-6 GHz capacity.The authors identify addressing traffic overflow and blockage correlation as future work.Source: §VIII · pp. 12–13

APPENDIX

The appendix derives the distribution of BS links available after static and self-blockage, then uses it in the LOS blockage analysis. It also derives the conditional LOS blockage probability and simplifies the dynamic-blockage case.

A. Proof of Lemma 2

  • The probability that a BS-UE link escapes static and self-blockage is obtained by combining the two blockage probabilities and averaging over the BS distance distribution.The derivation then models the number of unblocked BSs with a binomial distribution, conditional on the number of BSs in range, and averages over that number's distribution.Source: A. Proof of Lemma 2 · p. 13

B. Proof of Theorem 1

  • Theorem 1 derives LOS blockage probability by integrating over BS locations and averaging over the Poisson-distributed BS count, then conditions the result on LOS coverage.The proof notes that the multi-dimensional integral separates into identical integrals.Source: B. Proof of Theorem 1 · p. 13
  • For the dynamic-blockage-only case, the proof sets β=β0=0 (equivalently q=1) and simplifies the expression used in the general blockage derivation.The proof states that the remaining analysis follows the earlier derivation steps.Source: B. Proof of Theorem 1 · pp. 13–14

C. Proof of Theorem 2

The appendix obtains expected blockage duration conditional on coverage from earlier results. It then approximates the expectation of 1/n using Poisson moments and gives a high-BS-density approximation.

C. Proof of Theorem 2

  • Theorem 2's proof uses the preceding results to obtain expected blockage duration conditioned on the LOS coverage event.The proof concludes after stating this conditional expectation.Source: C. Proof of Theorem 2 · p. 14

D. Approximation of the expected duration

  • The expected duration approximation uses a Taylor expansion for E[1/n] and substitutes the Poisson random variable's mean and variance.The cited passages identify μ_n and σ²_n as the mean and variance of N and give both as p_qλ_TπR².Source: D. Approximation of the expected… · p. 14
  • At high BS densities, the proof further simplifies the duration approximation and obtains expression (30) by substituting the coverage probability.The intermediate high-density approximation is given in (62), and the final substitution uses P(C_LOS) from (16).Source: D. Approximation of the expected… · p. 14

E. Proof of Theorem 3

The appendix derives the expected frequency of dynamic blockage conditioned on coverage and derives coverage probability when LOS and NLOS links are treated as independent. It simplifies the dynamic-blockage expression in the absence of static blockages.

E. Proof of Theorem 3

  • The dynamic-blockage probability for a BS follows the same expression as the earlier conditional probability when static blockages are absent.The proof uses this equivalence to simplify ζ_d.Source: E. Proof of Theorem 3 · p. 14
  • Theorem 3's proof removes static blockages by simplifying ζ_d, then derives expected dynamic-blockage frequency conditioned on coverage.It first evaluates E[ζ_d|n], then E[ζ_d], before conditioning on C_d.Source: E. Proof of Theorem 3 · p. 14

F. Proof of Lemma 4

  • Lemma 4 derives coverage probability under the assumption that LOS and NLOS links are independent, solving an integral to obtain a closed-form expression.The final coverage calculation follows steps similar to the earlier derivation.Source: F. Proof of Lemma 4 · pp. 14–15
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