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On the Interactions between Multiple Overlapping WLANs using Channel Bonding

B. Bellalta, A. Checco, A. Zocca, J. Barcelo

arXiv:1412.0929v2cs.NI

TL;DR

Wider, autonomously selected WLAN channels may improve throughput but also increase overlap and competition, creating coupled performance effects. The paper develops and validates a CTMN framework for analyzing these interactions and compares random selection with proportional-fair centralized allocation. Results show substantial channel-bonding gains can coexist with lower throughput, spectrum utilization, and fairness under random selection than under centralized allocation.

  • Problem

    Autonomous selection of channel center frequency and width makes it difficult to understand how channel bonding affects overlapping WLANs and their achievable throughput.

    Source: §I · p. 1

  • Method

    The paper develops and validates a CTMN framework, including WLAN-centric state aggregation and proportional-fair waterfilling allocation, to model and evaluate overlapping WLAN interactions.

    Source: §I · p. 1, §V · p. 7, §VIII · p. 15

  • Results

    Random channel center and width selection yields significantly lower throughput, spectrum utilization, and fairness than the centralized allocation algorithm.

    Source: §VIII · p. 15

  • Takeaways & Limitations

    Channel bonding can provide significant performance gains in dense WLAN scenarios, but smarter decentralized channel-selection algorithms are needed for efficient autonomous spectrum use.

    Source: D. Final Remarks · p. 15, §VIII · p. 15

Abstract

from arXiv · show

Next-generation WLANs will support the use of wider channels, which is known as channel bonding, to achieve higher throughput. However, because both the channel center frequency and the channel width are autonomously selected by each WLAN, the use of wider channels may also increase the competition with other WLANs operating in the same area for the limited available spectrum, thus causing the opposite effect. In this paper, we analyse the interactions between a group of neighboring WLANs that use channel bonding and evaluate the impact of those interactions on the achievable throughput. A Continuous Time Markov Network (CTMN) model that is able to capture the coupled operation of a group of overlapping WLANs is introduced and validated. The results show that the use of channel bonding can provide significant performance gains even in scenarios with high densities of WLANs, though it may also cause unfair situations in which some WLANs cannot access the channel, while others receive most of the transmission opportunities.

I. INTRODUCTION

Channel bonding can increase WLAN throughput by aggregating basic channels, but wider autonomous channel choices also intensify overlap and CSMA/CA coupling. The paper addresses this gap with CTMN-based modeling, interaction analysis, channel allocation, and evaluation of existing analytical and selection approaches.

I. INTRODUCTION

  • Channel bonding aggregates basic channels into wider 40, 80, or 160 MHz channels, potentially increasing throughput but also overlap and competition among nearby WLANs.These effects become more pronounced as IEEE 802.11 amendments support wider channels.Source: §I · p. 1
  • The paper introduces a CTMN model for coupled operation and achievable throughput in overlapping WLANs, including configurations with different traffic, packet, contention, channel, and rate parameters.The model is intended for scenarios where not all nodes can listen to every transmission.Source: §I · p. 1
  • The study reduces model complexity with a WLAN-centric state aggregation, categorizes WLAN interactions, and relates some interactions to single-channel CSMA/CA multi-hop networks.This provides a more compact description of neighboring WLAN behavior.Source: §I · p. 1
  • The paper formulates proportional-fair channel allocation and evaluates random channel center and width selection against the resulting centralized allocation benchmark.The centralized approach uses waterfilling, while the random-selection evaluation varies overlapping WLAN count, available basic channels, and allowed widths.Source: §I · pp. 1–2

A. Channel Bonding

  • Prior work reports throughput gains from channel bonding, but overlapping activity can severely compromise those gains, while existing channel-selection studies often require information exchange or centralized authority.The paper positions its analytical treatment as addressing limitations across channel bonding, selection, and continuous-time CSMA/CA models.Source: A. Channel Bonding · p. 2, B. Channel Selection Algorithms · p. 2, §II · p. 2

III. SYSTEM MODEL

The system models autonomous WLANs selecting contiguous channel subsets and using CSMA/CA with channel-width-dependent sensing and transmission. It adopts simplifying assumptions about collisions, hidden nodes, and retransmissions that make analysis tractable but qualify the results.

A. Network description

  • Each WLAN selects a contiguous subset of available basic channels, and two WLANs overlap when their channel sets intersect while they are within carrier-sense range.A 20 MHz basic channel gives WLAN width W_i = 20 · c_i for c_i assigned basic channels.Source: A. Network description · p. 3, §III · p. 3

B. Node operation

  • Nodes sense their entire allocated channel after DIFS, freeze backoff when any portion is busy, and transmit across the full channel width when the timer expires.Neighboring WLANs defer when they share at least one basic channel with the transmitting node.Source: B. Node operation · p. 3
  • Packet transmission duration depends on channel width, receiver SNR, and payload size, while successful reception is represented by η_i,j and retransmissions are unlimited.The resulting packet departure rate is μ_i,j = E[T_i,j(c_i, γ_i,j, L_i,j)]^-1.Source: B. Node operation · p. 3

C. Implications

  • The model assumes zero collisions among carrier-sensing nodes because of continuous-time backoff and negligible propagation delay, making the reported results potentially optimistic.The authors argue the approximation is reasonable under standard conditions and useful for modeling nodes outside one another’s carrier-sense range.Source: C. Implications · pp. 3–4
  • Hidden nodes are expected to have low impact when carrier-sense range is at least twice data range, but obstacles can create hidden nodes that severely affect performance.The model also assumes infinite retransmissions, which simplifies analysis because retransmission counts need not be tracked.Source: C. Implications · p. 4

IV. THROUGHPUT MODEL

The throughput model represents feasible simultaneous transmissions as a continuous-time Markov process whose stationary behavior determines long-run WLAN activity and throughput. It incorporates channel allocation and packet-error sources, including hidden and external interferers.

A. Continuous Time Markov Networks

  • Throughput is insensitive to the distributions of backoff and packet durations under the Markov network’s insensitivity property, depending only on their expected values.The model initially assumes exponential durations to obtain the Markov representation, then extends the result through insensitivity.Source: §IV · p. 4
  • For a fixed channel allocation, feasible states contain node subsets whose WLANs do not overlap, and each allocation induces its own state space Ω(C).Changing any WLAN’s allocation therefore changes the feasible network states considered by the model.Source: A. Continuous Time Markov Networks · pp. 4–5
  • The CTMN uses node backoff rates ρ_i,jλ_i,j and transmission rates μ_i,j to define transitions for adding or removing transmitting nodes.These transitions remain within the feasible state space Ω(C).Source: A. Continuous Time Markov Networks · p. 5
  • The finite-state process is irreducible, aperiodic, and positive recurrent, so it has a stationary distribution π_s equal to each state’s long-run time fraction.Time reversibility and detailed balance yield a product-form stationary distribution.Source: A. Continuous Time Markov Networks · p. 5

B. Packet Errors, Hidden Nodes & External Interferers

  • Packet-success modeling separates corruption from ambient noise, hidden nodes, and external interferers, whose effects are combined under an independence assumption.Hidden-node characterization is more difficult because the interferer and affected transmission have coupled dynamics.Source: B. Packet Errors, Hidden Nodes &… · p. 5

C. Performance Metrics

The model derives throughput and fairness metrics from the stationary distribution, solves the resulting nonlinear equations iteratively, and illustrates the CTMN construction and validation process for a representative WLAN scenario.

C. Performance Metrics

  • The model computes throughput, proportional fairness, and Jain’s Fairness Index from the stationary distribution.Source: C. Performance Metrics · p. 5

D. Computing the stationary distribution of the Markov network

  • The stationary probabilities depend mutually on the activity ratios, producing a generally nonlinear system without a closed-form solution.Source: D. Computing the stationary… · p. 6
  • An iterative fixed-point procedure updates activity ratios until all node throughputs converge, marking a node saturated when throughput cannot meet its traffic load.Source: D. Computing the stationary… · p. 6

E. Solving the Model

  • For a fixed channel allocation, the solution constructs feasible states, computes stationary probabilities, derives node throughputs, and then evaluates both fairness metrics.Source: E. Solving the Model · p. 6

F. Numerical Example

G. Insensitivity

The paper establishes insensitivity of the CTMN results to distributional details, then aggregates node states into a WLAN-centric model that preserves throughput while reducing computational demands for interaction analysis.

G. Insensitivity

  • Throughput and stationary probabilities depend on backoff and transmission distributions only through their mean ratios, making the analysis insensitive to their exact distributions.Source: G. Insensitivity · p. 7

V. INTERACTIONS BETWEEN OVERLAPPING WLANS

  • The paper characterizes overlapping-WLAN interactions, improves computational efficiency through state aggregation, and validates WLAN-centric throughput predictions against detailed simulations.Source: §V · p. 7

A. WLAN-centric Throughput Analysis

  • The WLAN-centric model aggregates states by active WLAN, assumes saturated WLANs with similar within-WLAN conditions, and represents each WLAN through aggregate activity parameters.Source: A. WLAN-centric Throughput Analysis · p. 7
  • Both node-centric and WLAN-centric models produce the same throughput, while the node-centric model requires substantially more time and computational resources.Source: A. WLAN-centric Throughput Analysis · p. 8

B. Cases of interest

1) To overlap or not to overlap:

The examples show that non-overlapping channel allocations are generally preferable, while overlapping WLANs can exhibit performance anomalies in which different channel widths receive equal throughput.

1) To overlap or not to overlap:

  • When three WLANs use non-overlapping channel groups, they operate independently, whereas complete overlap forces them to compete for transmission opportunities.Source: 1) To overlap or not to overlap · p. 8
  • Protocol overhead prevents overlapping WLANs from outperforming separate non-overlapping channel groups under the stated transmission-time comparison.Source: 1) To overlap or not to overlap · p. 8

2) Performance Anomaly:

  • Different channel widths can nevertheless yield equal throughput for overlapping WLANs, confirming a performance anomaly analogous to multi-rate WLAN behavior.Source: 2) Performance Anomaly · p. 8
  • The anomaly can be mitigated by allowing wider-channel WLANs to send larger packets or by assigning different backoff durations.Source: 2) Performance Anomaly · p. 8
  • A WLAN’s throughput can also be affected by a third WLAN even when the first two WLANs do not overlap directly.Source: 3) Non-direct interactions · p. 8

3) Non-direct interactions:

The analysis shows that overlapping WLANs can interact indirectly through shared competitors, producing unequal throughput and starvation. Numerical examples validate the WLAN-centric model and expose how channel allocation, activity, collisions, and contention windows shape performance.

3) Non-direct interactions:

WLAN B

  • The WLAN-centric throughput model matches the analytical-assumption simulation, while capture raises and collisions lower throughput relative to its predictions.Source: WLAN B · p. 9
  • With equal activity, non-overlapping channels let throughput depend on width, whereas full overlap equalizes throughput and can make one basic channel preferable to eight.Source: WLAN B · p. 9, Figure 7 · p. 10
  • Random allocation can nearly starve the wider WLAN because the other WLANs form two independent competing groups; unequal widths can nevertheless yield equal throughput through a performance anomaly.Source: WLAN B · p. 9, Figure 8 · p. 10
  • Increasing active stations raises a WLAN's activity factor and changes both its throughput and interactions with neighboring networks.Source: WLAN B · p. 10
  • Increasing the contention window reduces WLAN A's starvation but severely lowers the throughput of the other three WLANs.Source: WLAN B · p. 10

VI. CHANNEL ALLOCATION SCHEMES

The paper models autonomous channel allocation as decentralized random selection, including both arbitrary contiguous groups and IEEE 802.11ac channelisation. It contrasts these autonomous choices with controlled allocation aimed at quantifying lost capacity.

VI. CHANNEL ALLOCATION SCHEMES

  • Autonomous WLANs independently choose their channel groups, reflecting separate administrative domains and typically unavailable spectrum-occupancy information.Source: §VI · pp. 10–11, A. Decentralised approaches · p. 11
  • The evaluation compares arbitrary random selection and IEEE 802.11ac channelisation against an optimal centralized proportional-fair strategy to estimate capacity lost without controlled allocation.Source: §VI · p. 11

1) Random Channel Selection:

B. Centralised approach

The centralized approach formulates proportional-fair channel allocation over channel configurations and uses waterfilling to obtain efficient allocations. It extends the method to partial interference graphs, while noting computational and optimality limitations.

B. Centralised approach

1) Proportional Fair Channel Allocation:

VII. PERFORMANCE EVALUATION

The evaluation studies how neighboring-WLAN count, available basic channels, and supported channel widths affect system performance.

VII. PERFORMANCE EVALUATION

  • The evaluation varies neighboring-WLAN density, the number of available basic channels, and the channel widths available to each WLAN.Source: §VII · p. 13

A. Increasing the number of channels

With more available basic channels, channel allocation can improve spectrum use, throughput, and fairness, while random wide-channel choices become advantageous only under favorable density or spectrum conditions. As WLAN density rises, interactions increase spectrum utilization but generally reduce throughput and fairness, with rare starvation under large maximum widths.

A. Increasing the number of channels

  • The waterfilling algorithm maximizes spectrum utilization while distributing basic channels evenly, yielding the highest network throughput and fairness.Fairness falls below 1 when channel allocations do not give all WLANs the same channel width.Source: A. Increasing the number of channels · p. 13
  • Large random channel widths improve throughput only with few neighboring WLANs or many available basic channels, and can worsen fairness through overlap.With four WLANs, W = 160 MHz exceeds W = 80 MHz in throughput only when more than 50 basic channels are available.Source: A. Increasing the number of channels · p. 13
  • For six WLANs, the optimal average width is W = 40 MHz at N = 8, yielding 103.21 Mbps, and W = 80 MHz at N = 24, yielding 170.33 Mbps.The throughput histograms show that more basic channels allow more channel combinations and improve overall system performance.Source: A. Increasing the number of channels · p. 13

B. Increasing the number of WLANs

  • Increasing the number of WLANs raises spectrum utilization but generally lowers throughput and fairness as more overlapping interactions become possible.Randomly selecting W creates more interaction combinations; with many WLANs, throughput approaches the Wmax = 20 MHz case while fairness decreases with Wmax.Source: B. Increasing the number of WLANs · pp. 13–14
  • With Wmax = 160 MHz, rare starvation events occur, especially as the number of WLANs increases.Figure 15 compares the ratio between optimal and sampled random-allocation throughput with the waterfilling solution.Source: B. Increasing the number of WLANs · p. 14

C. IEEE 802.11ac channelisation

IEEE 802.11ac channelisation slightly improves aggregate throughput and fairness for large widths by avoiding partial overlaps and non-direct interactions. Overall, random autonomous channel selection performs substantially worse than centralized allocation, motivating smarter decentralized algorithms.

C. IEEE 802.11ac channelisation

  • IEEE 802.11ac channelisation yields slightly higher aggregate throughput and fairness than the alternative decentralized scheme for large channel widths.The stated advantage comes from preventing negative effects of partial overlaps and non-direct interactions.Source: C. IEEE 802.11ac channelisation · p. 14

D. Final Remarks

  • With 10 WLANs, waterfilling provides almost 100% higher expected single-WLAN throughput than random selection with Wmax = 40 MHz.Waterfilling also achieves significantly higher fairness and spectrum utilization because random selection leaves some basic channels shared and others empty.Source: D. Final Remarks · pp. 14–15

VIII. CONCLUSIONS

  • The paper identifies a substantial gap between centralized channel allocation and autonomous random channel selection.The conclusion reports lower throughput, spectrum utilization, and fairness for random center-frequency and width selection.Source: D. Final Remarks · p. 15, §VIII · p. 15

D. Final Remarks

  • A proposed response is decentralized channel selection that adapts to inferred spectrum occupancy and neighboring WLAN behavior.A cloud database is another suggested option, but it cannot force existing WLANs to reduce channel width as demand rises.Source: D. Final Remarks · p. 15

VIII. CONCLUSIONS

  • The framework evaluates interactions across WLAN density, available basic channels, and allowed widths, while waterfilling provides a proportional-fair global allocation or best suboptimal discrete allocation.The analytical framework is based on a developed and validated CTMN model.Source: §VIII · p. 15

APPENDIX A SYSTEM PARAMETERS AND SCENARIO CONSIDERATIONS

The evaluation assumes IEEE 802.11ac WLANs in the 5 GHz band with 20–160 MHz bonded channels, specified transmission parameters, negligible packet errors, and scenario averaging. A COST-based simulator reproduces slotted backoff, collisions, and capture effects for model validation.

APPENDIX A SYSTEM PARAMETERS AND SCENARIO CONSIDERATIONS

  • The scenario uses IEEE 802.11ac in the 5 GHz ISM band, with 20, 40, 80, or 160 MHz channels composed of 1, 2, 4, or 8 basic channels.Unless otherwise stated, each WLAN has two nodes and uses rates associated with the number of bonded basic channels.Source: Appendix A · p. 16, Table VI · p. 16, Table VII · p. 17

TPHY +

  • Nodes use at least two antennas for two single-user MIMO spatial streams, with packet aggregation of 64 packets per transmission.The transmission-time model includes PHY, MAC, delimiter, tail, and block-ACK components.Source: Appendix A · pp. 16–17, TPHY + · p. 17
  • The model assumes negligible packet errors because stations are located near their access points.This assumption applies to all WLANs in the considered scenario.Source: TPHY + · p. 17

APPENDIX A SYSTEM PARAMETERS AND SCENARIO CONSIDERATIONS

  • Unless otherwise stated, each plotted point averages 2000 randomly generated global channel-allocation scenarios, with the sample-mean error’s standard deviation relative to true computed throughput below 10 Mbps.Source: TPHY + · p. 17

A. Simulation Tool

  • A COST-based simulator reproduces slotted backoff, collisions, and capture effects to compare against the analytical model.The comparison is used to assess model accuracy and the impact of construction assumptions.Source: A. Simulation Tool · p. 17
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