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Offloading in Heterogeneous Networks: Modeling, Analysis, and Design Insights
Sarabjot Singh, Harpreet S. Dhillon, Jeffrey G. Andrews
TL;DR
Inter-RAT offloading can relieve cellular congestion, but its system-wide performance depends on signal quality, load, and resource conditions. The paper develops a tractable PPP model for multi-RAT, multi-tier networks with weighted association, derives rate coverage, and shows that the offload fraction optimizing SINR coverage generally differs from the one optimizing rate coverage.
Problem
Offloading can overload alternative APs or create load disparity, while existing analyses provide limited tractable understanding of spatial association and rate distributions in heterogeneous networks.
Method
The paper models an M-RAT, K-tier heterogeneous network with PPP-distributed APs and users, Rayleigh fading, and tunable weighted received-power association.
Results
The optimal offload fraction for SINR coverage depends solely on SINR thresholds, whereas rate-coverage optimization also depends on resources, QoS requirements, and RAT density.
Takeaways & Limitations
Offloading should be optimized for rate coverage rather than inferred from SINR coverage alone because the two objectives can prescribe different traffic splits.
Abstract
from arXiv · showhide
Pushing data traffic from cellular to WiFi is an example of inter radio access technology (RAT) offloading. While this clearly alleviates congestion on the over-loaded cellular network, the ultimate potential of such offloading and its effect on overall system performance is not well understood. To address this, we develop a general and tractable model that consists of $M$ different RATs, each deploying up to $K$ different tiers of access points (APs), where each tier differs in transmit power, path loss exponent, deployment density and bandwidth. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. The distribution of rate over the entire network is then derived for a weighted association strategy, where such weights can be tuned to optimize a particular objective. We show that the optimum fraction of traffic offloaded to maximize $\SINR$ coverage is not in general the same as the one that maximizes rate coverage, defined as the fraction of users achieving a given rate.
I. INTRODUCTION
The paper develops a spatially explicit framework for inter-RAT offloading in heterogeneous networks, motivated by congestion, load imbalance, and the difficulty of deriving rate distributions. Weighted association allows traffic routing to be tuned for network-wide objectives.
- Motivation: WiFi APs and femtocells are presented as complementary alternatives to overloaded macro cellular networks amid explosive, video-driven data demand.
- Motivation: Aggressive offloading can reduce effective rates when WiFi APs have strong signals but heavy loads or less effective bandwidth.
- Motivation: Conservative offloading can create load disparity, underutilize resources, and degrade multimedia performance through bursty interference from lightly loaded APs.
- Related work: Existing RAT-selection studies often emphasize flow-level assignment without explicitly modeling AP and user locations or their association effects.
- Model: The model represents each AP class with a homogeneous PPP and uses weighted path-loss association, including nearest-AP, received-power, and biased-received-power special cases.
- Model: Association weights can be tuned to route more traffic through a selected RAT, while optimal weights depend on load, SINR, power, density, bandwidth, and path-loss parameters.
B. Resource Allocation
The resource-allocation model combines link spectral efficiency with AP load, so rate coverage captures both congestion and signal quality under saturated downlink operation.
- Resource allocation: Each AP continuously serves associated users and allocates rate proportional to each link’s spectral efficiency.
- Resource allocation: The rate model captures congestion through load and proximity through SINR.
- Resource allocation: For 4G systems, the allocation model corresponds to fair OFDMA resource scheduling across associated users.
- Rate coverage: Rate coverage is the probability that a randomly chosen user achieves a target rate, equivalently an average fraction of users or area exceeding that rate.
A. Load Characterization
The paper characterizes association areas and AP loads using PPP-based analysis and approximations, then connects association probabilities to traffic offload fractions and rate coverage.
- Load characterization: Load analysis uses typicality, formalized through Palm theory, to characterize users served by representative APs.
- Load characterization: The load of a typical AP is characterized through its probability generating function, with associated users modeled through the AP’s random association area.
- Association probabilities: A typical user’s association probability is proportional to AP density and association weights for each RAT-tier pair.
- Association probabilities: The probability of association with a RAT equals the average fraction of traffic offloaded to that RAT.
- Area approximation: Association-region areas are approximated by a linear scaling based on Poisson-Voronoi areas and validated through rate-coverage analysis.
- Area approximation: The area approximation is exact for a single-tier, single-RAT network and when association weights and path-loss coefficients are equal across classes.
B. SINR Distribution
The paper derives SINR coverage for users associated with each RAT-tier and aggregates it over the heterogeneous network. The tagged-user distance depends on competition from other open-access classes, while interference is generated by APs of the associated RAT.
- Interference for a user associated with RAT i is modeled from APs belonging to RAT i across its tiers, excluding the tagged AP.
- SINR coverage is defined as the probability that a user associated with RAT-tier (i, j) exceeds threshold τij.
- Overall SINR coverage combines the conditional coverage across the network.
- A user’s distance to its tagged AP depends on competing AP classes, not only the serving class.
- The general SINR coverage result requires one numerical integration and a lookup table, and reduces to established single-RAT special cases.
C. Main Result
The paper derives the network-wide rate distribution for the general heterogeneous-network model. The result accounts for rate thresholds, bandwidth, and AP load, with a finite-sum approximation available for computation.
- Theorem 1 gives rate coverage for a randomly located mobile user in the general HetNet setting.
- Rate coverage is derived by evaluating whether the rate requirement is met for users associated with each RAT-tier pair.
- The rate condition depends on the tagged AP’s load, defined as the typical user plus the other associated users.
- The general rate-distribution expression requires one numerical integral, lookup tables for Z and Γ, and a finite summation over AP load.
D. Mean Load Approximation
The paper simplifies rate coverage by replacing each AP’s random load with its mean, and validates the resulting approximations against simulations and deployment models. Association weights can then be tuned to optimize rate coverage or traffic offloading.
- The mean-load approximation simplifies rate coverage by replacing each AP’s load with its mean, at the cost of accuracy.
- Corollary 1 provides rate coverage under the mean-load approximation.
- The approximation eliminates the summation over AP load, and special conditions can also remove the numerical integral.
- Rate distribution is expressed as a function of association weights, enabling optimization of traffic offloaded to each RAT for rate coverage.
- Validation uses PPP, realistic deployment, and square-grid AP locations, with biased received-power association and uniform 10 MHz resources.
- Analytical rate distributions from Theorem 1 and Corollary 1 agree well with simulations in tested multi-RAT, multi-tier settings.
IV. DESIGN OF OPTIMAL OFFLOAD
The paper derives optimal association biases and traffic offload fractions for SIR and rate coverage in a two-RAT setting, revealing substantially different design behavior. SIR optimization admits simpler structural insights, whereas rate-coverage optimization generally requires numerical search because load depends on association bias.
- Design setup: Optimal offloading is analyzed for both SIR coverage and rate coverage in a two-RAT, single-tier network using association biases.The rate-coverage design uses the mean load approximation.
- SIR coverage: The SIR-optimal association bias decreases as the corresponding RAT’s AP density or transmit power increases.Higher density and power increase interference for offloaded users and require less bias to achieve the same offload fraction.
- SIR coverage: For SIR coverage, the optimal offload fraction depends only on the two RATs’ SIR thresholds, not their densities or transmit powers.When the thresholds are equal, offloading half of the user population maximizes SIR coverage.
- Rate coverage: Rate-coverage optimization has no closed-form optimal bias because association bias changes load and therefore the rate threshold.The optimal bias can instead be obtained through linear search using the analytical rate-coverage expression.
- Rate coverage: SIR coverage and rate coverage exhibit considerably different behavior: rate-optimal offloading is expected to increase with second-RAT density as load per AP decreases.For fixed density, rate coverage has an optimal traffic offload fraction.
V. RESULTS AND DISCUSSION
The results examine how association bias and RAT-2 density affect SIR and rate coverage in a macro-plus-low-power-tier setting. Optimal offloading differs across objectives: SIR coverage depends on thresholds, whereas rate coverage also reflects load, resources, and QoS requirements.
- SIR and rate coverage: The study evaluates association bias and traffic offloading between macro RAT-1 and low-power RAT-2 APs.The setting models V = {(1, 1); (2, 3)} and ignores thermal noise.
- SIR coverage: The optimal SIR-coverage bias decreases as the corresponding RAT’s AP density or transmit power increases.Higher density and power increase interference and require less bias to offload the same traffic fraction.
- Rate coverage: Rate coverage increases with RAT-2 AP density because the load per AP decreases, while association bias strongly influences rate coverage.The evaluated configuration uses λu = 200 users/km2, ρmk ≡256 Kbps, Wmk ≡10 MHz, and αk ≡3.5.
- Rate coverage: For rate coverage, optimal bias decreases with AP density but optimal traffic offload fraction increases as RAT-2 load falls.The optimum also depends on the ratio of rate threshold to bandwidth: greater available resources relative to threshold favor offloading to that RAT.
- Design insights: The paper presents a tractable M-RAT K-tier model showing that rate-coverage-optimal offloading depends on QoS requirements and resource conditions as well as signal power and load.The framework is presented as the first study of rate coverage for inter-RAT offload.
APPENDIX A
Appendix A derives association-area and user-load distributions using independent PPP structure, area biasing, and Poisson probability tools.
- The association probability of a typical user is derived using independence among the AP point processes.
- The nearest-AP distance distribution follows the PPP void probability P(Zmk > z) = e−πλmkz2.
- The tagged AP’s association-area distribution is area-biased because users are more likely to lie in larger association regions.
- The number of other users associated with the tagged AP is obtained from the PPP Palm property, its probability generating function, and Poisson moments.
APPENDIX C
Appendix C derives the serving-distance distribution by conditioning the nearest-AP distance on association with a specific RAT-tier pair.
- The distance Yij from a typical user to its tagged serving AP is the conditional distribution of Zij given association with (i, j).
- The conditional survival probability is expressed as P(Yij > y) = P(Zij > y, user is associated with (i, j)) / P(user is associated with (i, j)).
APPENDIX D
Appendix D derives overall SINR coverage by combining conditional coverage for each serving RAT-tier pair with interference MGFs and total-probability aggregation.
- SINR coverage is first formulated for a user associated with a particular RAT-tier pair.
- The interference MGF uses independence of AP processes and fading, the PPP PGFL, and the exponential-fading MGF.
- A change of variables simplifies the interference integrals before producing the interference MGF.
- Combining the interference result with the serving-distance distribution gives conditional coverage, and total probability yields overall SINR coverage.
APPENDIX E
The appendix proves that SIR coverage is strictly quasiconcave in the association bias, yielding a unique optimal bias and corresponding traffic offload fraction. The optimal SIR coverage follows by substituting this bias into the coverage expression.
- The proof formulates SIR coverage in the described setting using the parameterization V = {(1, q), (2, r)}, λ2r = aλ1q, and B2r = bB1q.
- The gradient of SIR coverage with respect to association bias is zero at the optimum.
- For b > bopt the gradient is negative, whereas for b < bopt it is positive, making S strictly quasiconcave in b with bopt as the unique mode.
- The optimal traffic offload fraction is obtained using Lemma 2 after identifying the unique optimal bias.
- The corresponding SIR coverage is obtained by substituting the optimal bias value into equation (68).