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User Mobility Evaluation for 5G Small Cell Networks Based on Individual Mobility Model
Xiaohu Ge, Junliang Ye, Yang Yang, Qiang Li
TL;DR
The paper asks how user mobility affects 5G small cell networks when traditional models omit human tendency and clustering. It uses IMM to derive mobility and coverage probabilities in a hotspot community, finding distinct mobility behavior from RWP, including higher IMM-based community arrival probability and a pause-probability minimum at Sc/St = 5%.
Problem
The paper addresses the need to evaluate user mobility in 5G small cell networks while accounting for human tendency and clustering behaviors absent from traditional mobility models.
Method
The paper applies the individual mobility model (IMM) to derive pause, arrival, departure, and coverage probabilities for users in a hotspot-type 5G small cell network.
Results
At Sc/St = 5%, IMM user pause probability reaches a minimum, while IMM community arrival probability exceeds the corresponding RWP probability.
Takeaways & Limitations
IMM provides a framework for evaluating how human tendency and clustering behaviors relate to mobility and coverage performance in 5G small cell networks.
Abstract
from arXiv · showhide
With small cell networks becoming core parts of the fifth generation (5G) cellular networks, it is an important problem to evaluate the impact of user mobility on 5G small cell networks. However, the tendency and clustering habits in human activities have not been considered in traditional user mobility models. In this paper, human tendency and clustering behaviors are first considered to evaluate the user mobility performance for 5G small cell networks based on individual mobility model (IMM). As key contributions, user pause probability, user arrival and departure probabilities are derived in this paper for evaluat-ing the user mobility performance in a hotspot-type 5G small cell network. Furthermore, coverage probabilities of small cell and macro cell BSs are derived for all users in 5G small cell networks, respectively. Compared with the traditional random waypoint (RWP) model, IMM provides a different viewpoint to investigate the impact of human tendency and clustering behaviors on the performance of 5G small cell networks.
I. INTRODUCTION
The paper addresses mobility evaluation in 5G small cell networks by incorporating human tendency and clustering behaviors into the individual mobility model (IMM). It derives mobility probabilities and coverage probabilities, contrasting this perspective with traditional simple mobility models.
- Motivation: 5G small cells reduce communication distances to support high transmission rates, making user mobility impacts more significant as cell coverage radii decrease.The paper motivates mobility evaluation through reduced cell coverage and shorter transmission distances.
- Research gap: Existing small cell studies primarily use simple mobility models, while human tendency and clustering behaviors remain insufficiently investigated.The paper identifies limited investigation of IMM in small cell networks as an additional gap.
- Contributions: The paper applies IMM to derive user arrival, departure, and pause probabilities for evaluating mobility performance in community-based 5G small cell networks.These probabilities are developed for a hotspot-type community setting.
- Contributions: Coverage probabilities inside and outside the community are derived for 5G small cell networks using the proposed arrival and departure probabilities.The contribution extends mobility analysis to coverage behavior across community regions.
A. Network Model
The network model represents a finite community embedded in a larger plane, with macro and small cell base stations deployed according to distinct spatial assumptions. Static and mobile users are associated with different network tiers under orthogonal-frequency downlink transmission.
- Spatial setting: A finite rectangular region represents a community where users are concentrated, embedded within a larger finite plane and its complement.The community has area Sc, while the surrounding region and finite plane are represented separately.
- Base-station deployment: Macro cell base stations follow a Poisson point process, while small cell base stations inside and outside the community follow uniform distributions with densities λc,BS and λs,BS.The macro-cell boundaries are obtained through Delaunay triangulation.
- User deployment: Users inside and outside the community follow uniform distributions with densities λs and λc, respectively, with λc > λs and λc,BS > λs,BS.These inequalities encode higher user and small-cell densities in the community.
- Transmission assumptions: Macro and small cell base stations transmit on different frequencies, so interference between the two network types is absent.The model studies downlink transmission and ignores intra-cell co-channel interference under OFDM.
- User association: Static users associate with small cell base stations, whereas mobile users associate with macro cell base stations.The group cell scheme allows static users to associate with multiple small cell base stations when their SINRs meet γ0.
B. Individual Mobility Model
IMM models mobility through repeated jumps that balance exploration of new locations with returns to previously visited locations. It also incorporates human visiting tendencies and heavy-tailed pauses between movements.
- Model motivation: IMM differs from fully random mobility models by incorporating human tendency and clustering behaviors in location visits.Users tend to revisit locations they have visited frequently in the past.
- Jump process: Each user mobility event is defined as one jump, preceded by two potential active modes for the next jump.The two modes are exploration of a new location and return to an old location.
- Location exploration: The probability of visiting a new location depends on fixed habit parameters ρ and γ, the number of previously visited locations S(n), and the jump number n.The supplied passage identifies 0 < ρ ≤ 1 and γ > 0 as parameters related to mobility habits.
- Location revisitation: The alternative mode returns the user to an old location previously visited, capturing revisitation behavior.As S(n) increases, the probability of returning to an old location becomes larger.
- Pause behavior: After completing a jump, the user pauses at the destination for a waiting time whose probability follows P(∆t) ∼|∆t|^-1-β, with 0 < β ≤ 1.The parameter β is measured from empirical data.
III. USER MOBILITY PERFORMANCE
The mobility analysis derives community-entry behavior and time-based mobility probabilities under IMM. It establishes that community-entry probability depends on the community-to-plane area ratio and develops the geometric expectations needed for arrival and pause probabilities.
- Community-entry probability: Under IMM, the probability that a user jumps into the community equals Sc/St and is independent of the jump number n.The result is obtained by summing exploration and old-location return cases.
- Community-entry probability: The proof separates community entry into exploration of a new community location and return to an old community location.These two cases jointly produce the community-entry probability.
- Time accounting: The total time spent in the community combines movement time and pause time across jumps.The model expresses this as tc,in(n) = tc,m(n) + tc,p(n).
- Time accounting: The model defines community-entry jump counts using arrivals from outside and movements remaining inside the community.Specifically, nc,in = no,i + ni,i, while total jumps satisfy n = no,i + ni,i + ni,o + no,o.
- Probability derivation: Arrival and pause probabilities are obtained by substituting expected distances for inside-inside, outside-inside, and outside-outside movements into the derived expressions.The derivation uses rectangle geometry and expected distances between uniformly distributed points.
- Probability derivation: The expected inside-community distance is derived from the distance distribution between two independent uniformly distributed points in the rectangular community.The paper then derives analogous expected distances for inside-outside and outside-outside movements.
- Probability derivation: Substituting the geometric expectations into the analytical expressions yields the user arrival probability πc,in and pause probability πpause.These are the final mobility probabilities obtained from the derivation.
IV. COVERAGE MODEL
The coverage model derives small-cell coverage for static users and macro-cell coverage for moving users under the paper’s association and mobility assumptions. It also derives the expected number of available small-cell BSs for static users.
- Static-user coverage: Static users associate with multiple small-cell BSs when their wireless-link SINRs meet threshold γ0, modeled as independent Bernoulli selections.The associated small-cell count is governed by binomial distributions inside and outside the community.
- Static-user coverage: The small-cell coverage probability accounts for desired signal, co-channel interference, Rayleigh fading, Gaussian noise, equal transmission power, and independently distributed link distances.Coverage is derived separately for small-cell BSs inside and outside the community.
- Available small-cell BSs: The expected number of available small-cell BSs equals the weighted mean associated count multiplied by the user pause probability, and its computation requires iteration.The weighting uses inside- and outside-community coverage probabilities.
- Moving-user coverage: Moving users are covered by macro-cell BSs only when SINR remains at least γ0 throughout movement at average velocity v over period Δtm.The post-movement distance depends on the initial distance, movement distance, and direction angle.
- Moving-user coverage: Macro-cell coverage for moving users is derived using interference and desired-signal Laplace transforms, Poisson-distributed macro-cell BS locations, and a uniformly distributed movement direction.The distance distribution after movement is substituted into the coverage expression.
V. NUMERICAL RESULTS AND DISCUSSIONS
Numerical results examine how IMM mobility parameters and small-cell density affect pause, arrival, available-BS, and coverage probabilities. Results also compare IMM with RWP and show mobility- and threshold-dependent coverage trends for small-cell and macro-cell BSs.
- User mobility: At Sc/St = 5%, IMM user pause probability reaches a minimum as the community-to-plane area ratio varies.With fixed Sc/St, pause probability increases with average user velocity; under RWP, it is constant with respect to Sc/St.
- User mobility: IMM user arrival probability decreases with average user velocity and increases with Sc/St, while exceeding the corresponding RWP probability.Under RWP, arrival probability is independent of average user velocity and increases with Sc/St.
- Available small cell BSs: The number of available small cell BSs decreases with SINR threshold and increases with small cell BS density inside the community.Fig. 4 evaluates Ncover against γ0 and small-cell densities inside and outside the community.
- Coverage probabilities: Small-cell coverage probability inside the community decreases as either SINR threshold or inside-community small-cell density increases.This trend is evaluated for Pc cover in Fig. 5.
- Coverage probabilities: Small-cell coverage probability outside the community decreases as either SINR threshold or outside-community small-cell density increases.This trend is evaluated for Ps cover in Fig. 6.
- Coverage probabilities: Macro-cell coverage probability decreases with both average user velocity and SINR threshold when the other parameter is fixed.Fig. 7 evaluates Pm cover against these two parameters.
VI. CONCLUSION
The paper evaluates 5G small-cell user mobility with IMM in hotspot communities, incorporating human tendency and clustering behaviors. It derives mobility probabilities and coverage probabilities relevant to small-cell deployment.
- VI. CONCLUSION: IMM evaluates user mobility performance in 5G small-cell networks within a community-area hotspot scenario.The model considers human tendency and clustering behaviors.
- VI. CONCLUSION: User pause, arrival, and departure probabilities are derived for evaluating mobility performance.
- VI. CONCLUSION: Coverage probabilities are derived for small-cell BSs inside and outside the community and for macro-cell BSs serving moving users.
- VI. CONCLUSION: The results support investigation of small-cell deployment and BS coverage under human tendency and clustering behaviors.
- VI. CONCLUSION: The paper identifies its work as the first evaluation of 5G small-cell user mobility using IMM with human tendency and clustering behaviors.
APPENDIX A
The appendix simplifies the derivation of the user arrival probability by decomposing the total time over jumps and analyzing limiting series.
- APPENDIX A: Terms in t_c,in(n) are denoted to simplify the derivation.
- APPENDIX A: Equation (10) is rewritten using the notation introduced for t_c,in(n), after which its first term is derived.
- APPENDIX A: The total time over n jumps satisfies lim n→∞ t(n) →∞.
- APPENDIX A: The appendix analyzes Θ1 as the series {ρ^(z−γ), z∈Z+} and relates Θ2 to it as a subseries.
- APPENDIX A: When γ > 1, the series converges to a limited value δ, enabling derivation of the remaining terms and πc,in.
ni,i X
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