Handoff Rate and Coverage Analysis in Multi-tier Heterogeneous Networks

• Multi-tier heterogeneous access is expected to support growing handheld applications, making mobility management important as users move between access points.Source: §I · p. 2
• Media streams tolerate interruptions up to 200 msec, while longer interruptions cause perceptible and unacceptable delays.Source: §I · p. 2
• Handoffs should limit excessive delays and call drops, but skipping a handoff can increase interference when a user enters another access point’s service area.Source: §I · p. 2

• Existing multi-tier algorithms assign users to lower or upper tiers using resources, estimated sojourn time, or velocity and direction; some approaches target large cells or prevent ping-pong handoffs.Source: A. Related Work · pp. 2–3
• Prior handoff-rate and dwell-time analyses generally assume deterministic access-point locations on regular grids, unlike irregular small-cell deployments.Source: A. Related Work · p. 3
• PPP analyses of heterogeneous networks commonly evaluate a stationary user, while PPP coverage predictions can bound real-world 4G results and model cell-edge interference relatively closely,.Source: A. Related Work · pp. 3–5
• Prior work uses biased received power or biased SINR for flexible tier association, and studies load, rate, and interference under different spectrum-allocation approaches –.Source: A. Related Work · pp. 3–4
• Lin et al. analyzed handoff rate and sojourn time for a single-tier PPP network, finding handoff rate proportional to the square root of access-point density and slightly pessimistic predictions versus a 4G network.Source: A. Related Work · p. 5

• The paper defines handoff rate as the probability of crossing into the next cell during one movement period, using a mobility model different from modified random waypoint.Source: B. Our Contributions · p. 5
• The PPP-based handoff-rate expression is simplified using mild approximations, and simulations show reliable results across a broad range of system parameters.Source: B. Our Contributions · p. 6
• For mobile users, coverage analysis assumes a fraction of handoffs cause connection failure, modeled as outage probability linearly related to handoff rate; service degradation decreases as the SIR threshold increases when desired resources are allocated.Source: B. Our Contributions · p. 6
• In fully loaded multi-tier networks with orthogonal spectrum allocation, mobility-aware bias adjustment can improve coverage and system performance by changing tier association.Source: B. Our Contributions · p. 6

• The downlink network has K tiers, each modeled as an independent homogeneous PPP with tier-specific transmit power, access-point density, and SIR threshold.Source: §II · p. 7
• Coverage uses received SIR with constant path loss exponent and Rayleigh fading; the model ignores thermal noise and shadowing and assumes orthogonal spectrum between tiers.Source: §II · p. 7
• Tier association selects the tier with maximum biased average received power, and within that tier the user connects to the nearest access point.Source: §II · pp. 7–8
• The movement model places the user a distance v from its initial location, with direction θ relative to the serving connection; it is suited to constant speed or small speed variation.Source: §II · p. 8

III. HANDOFF RATE IN A SINGLE TIER NETWORK

• The handoff rate Hk(v, λk) is the probability of handoff for a user connected to tier k moving distance v in a unit of time.A handoff occurs when another AP is closer to the user at the new location than the serving AP.Source: §III · pp. 8–9
• For radial motion, the handoff rate has a closed-form expression, while the general uniformly distributed-angle case has no closed form and is approximated when v ≪ R.The general-case approximation is based on displacement being much smaller than connection distance.Source: §III · pp. 10–11
• Simulations match the radial-motion expression exactly, and the general-case approximation is accurate at reasonable speeds and AP densities but deviates when displacement approaches connection distance.Handoff rate increases with user displacement and AP density.Source: §III · p. 12, Figure 2 · p. 12

IV. COVERAGE PROBABILITY WITH HANDOFFS

• Without handoffs, SIR-based coverage is independent of AP density, but for mobile users increasing AP density raises handoff rate and can negatively affect system performance.The coverage probability also represents the fraction of users in coverage at a given time.Source: §IV · p. 13
• Mobile-user coverage decreases as handoff rate increases, with a more noticeable reduction when the handoff-failure fraction β is large.β measures the system's sensitivity to handoffs; at β → 0, coverage reduces to the stationary expression.Source: §IV · pp. 14, 16
• The coverage gap between high- and low-density networks is more noticeable at lower SIR thresholds or when β is large.Although the SIR distribution remains the same regardless of AP density, frequent handoffs reduce coverage in denser networks.Source: §IV · p. 16

V. MOBILITY-AWARE TIER ASSOCIATION

• With equal SIR thresholds, equal tier-association probabilities maximize coverage for a stationary user.The stated maximum coverage is independent of tier AP density and transmit power in this case.Source: §V · pp. 18, 19, 23
• For any nonzero tier-association probabilities, the corresponding bias factors are uniquely determined by a linear system.The paper attributes this one-to-one relationship to the system matrix being full-rank.Source: §V · pp. 19–20
• Mobile multi-tier coverage incorporates handoff-sensitive connection success; for stationary users or β = 0, it reduces to the stationary coverage expression.The mobile expression uses a linear handoff cost, combining coverage without handoff and coverage when a handoff does not occur.Source: §V · pp. 20–21
• The authors conjecture that mobile multi-tier coverage is concave in tier-association probabilities, based on numerical concavity over the parameters considered.This conjecture supports use of standard optimization solvers, although it does not yield a closed-form solution.Source: §V · pp. 22–23
• Mobility-aware biasing improves coverage by steering fast-moving users toward higher tiers with lower AP densities.The two-tier simulations compare mobility-aware biasing with stationary-user biasing and Max-SIR association.Source: §V · p. 23

VI. CONCLUSIONS

• The handoff-rate analysis matches numerical simulations across a broad range of AP densities and user speeds.AP locations in each tier are modeled by a homogeneous PPP.Source: §VI · p. 23
• The dependence of handoff rate on AP density and its associated cost motivates assigning users to tiers based on velocity.Source: §VI · p. 23
• With equal SIR thresholds in the stated two-tier setup, overall coverage is maximized at A1 = A2 = 0.5.Source: Figure 6 · p. 24
• Optimizing bias factors is shown to improve coverage, and the authors conjecture that the optimization is concave.The analysis is for orthogonal spectrum allocation among tiers.Source: §VI · p. 24

APPENDIX A

• The probability of no handoff depends on whether another AP lies closer than the user's new distance R, with the Poisson null probability used for the area test.The relevant area is the excess area swept as the user moves between locations.Source: Appendix A · pp. 24, 26
• By symmetry, the movement angle need only be considered uniformly over [0, π).Source: Appendix A · p. 26
• The handoff rate is based on the probability of a handoff conditioned on the initial geometry and movement direction.The text then gives the handoff-rate expression and notes use of the distribution of the AP distance Rk.Source: Appendix A · p. 27

APPENDIX B

• The proof uses induction, with K = 2 as its base case and a block-matrix form for K > 2.Source: Appendix B · p. 28
• The block representation identifies U as a square matrix of size K − 2, V as a column vector, and W as a row vector.Source: Appendix B · p. 28
• The proof uses reciprocal off-diagonal entries and the relation aikakj = aij for i ≠ j, then concludes that A has a non-zero determinant and is full rank.Source: Appendix B · p. 28