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REFIM: A Practical Interference Management in Heterogeneous Wireless Access Networks

Kyuho Son, Soohwan Lee, Yung Yi, Song Chong

arXiv:1105.0738v1cs.NI

TL;DR

Heterogeneous small-cell networks create diverse interference and make practical interference management difficult because centralized optimization is complex and communication-intensive. The paper proposes REFIM, a distributed scheme using reference users, per-base-station decomposition, and reduced feedback. Simulations report improved cell-edge and overall throughput, with performance near that of a centralized near-optimal method.

  • Problem

    Heterogeneous networks need interference management that handles severe cell-edge interference without the high complexity and signaling overhead of existing dynamic approaches.

  • Method

    REFIM approximates neighboring interference with a reference user, decomposes decisions per base station, and reduces temporal and spatial feedback.

  • Results

    REFIM improves low-throughput users by 43% in AET versus EQ, achieves about 95% of the centralized near-optimal algorithm’s performance, and gains 16% GAT and 42% AET in urban deployment.

  • Takeaways & Limitations

    Under effective interference management, spectrum sharing can outperform the best spectrum-splitting policy, while REFIM provides a practical distributed alternative.

Abstract

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Due to the increasing demand of capacity in wireless cellular networks, the small cells such as pico and femto cells are becoming more popular to enjoy a spatial reuse gain, and thus cells with different sizes are expected to coexist in a complex manner. In such a heterogeneous environment, the role of interference management (IM) becomes of more importance, but technical challenges also increase, since the number of cell-edge users, suffering from severe interference from the neighboring cells, will naturally grow. In order to overcome low performance and/or high complexity of existing static and other dynamic IM algorithms, we propose a novel low-complex and fully distributed IM scheme, called REFIM, in the downlink of heterogeneous multi-cell networks. We first formulate a general optimization problem that turns out to require intractable computation complexity for global optimality. To have a practical solution with low computational and signaling overhead, which is crucial for low-cost small-cell solutions, e.g., femto cells, in REFIM, we decompose it into per-BS problems based on the notion of reference user and reduce feedback overhead over backhauls both temporally and spatially. We evaluate REFIM through extensive simulations under various configurations, including the scenarios from a real deployment of BSs. We show that, compared to the schemes without IM, REFIM can yield more than 40% throughput improvement of cell-edge users while increasing the overall performance by 10~107%. This is equal to about 95% performance of the existing centralized IM algorithm that is known to be near-optimal but hard to implement in practice due to prohibitive complexity. We also present that as long as interference is managed well, the spectrum sharing policy can outperform the best spectrum splitting policy where the number of subchannels is optimally divided between macro and femto cells.

I. INTRODUCTION

Heterogeneous networks increase capacity through small-cell deployment but create diverse interference and more vulnerable cell-edge users. REFIM addresses this with a low-complexity, distributed approach based on reference users and reduced feedback.

  • Small cells increase spatial reuse and capacity, but heterogeneous deployments create diverse interference across macro and femto cells.
  • Static interference management is poorly matched to user-controlled small cells that may be deployed or activated dynamically.
  • Dynamic interference management is difficult because power control is nonconvex, coupled with scheduling, and communication-intensive.
  • Spectrum splitting avoids macro-to-femto interference but can waste spectrum, whereas spectrum sharing requires effective interference management.
  • REFIM uses a reference user to approximate neighboring interference, reducing computational and signaling overhead while supporting distributed operation.

A. Network and Traffic Model

The model describes heterogeneous macro, pico, and femto base stations serving users over universally reused subchannels in a slotted downlink. Each base station jointly schedules users and allocates transmit power under power constraints.

  • The network contains macro, pico, and femto base stations, with each user associated with exactly one base station.
  • Subchannels are the basic allocation unit, and all base stations use all subchannels under universal frequency reuse.
  • At every slot, each base station selects a user on each subchannel and determines its allocated transmit power.
  • User scheduling permits at most one associated user per base station on each subchannel.
  • Each base station obeys a total power budget and per-subchannel spectral-mask constraints.

C. Link Model

The link model treats inter-cell interference as noise and formulates weighted long-term utility maximization through slot-by-slot joint scheduling and power allocation. The resulting problem is computationally intractable in general.

  • Interference from other base stations is treated as noise, while the algorithm coordinates multi-channel power allocation to mitigate interference.
  • The formulation excludes signal-level coordination such as CoMP and focuses on spectrum-level coordination.
  • Achievable rates follow Shannon’s formula using received SINR, bandwidth, and an SINR gap parameter Γ.
  • The slot-by-slot optimization jointly chooses scheduling indicators and powers to produce utility-optimal long-term rates.
  • The objective uses user weights derived from marginal utilities; inverse average throughput can implement proportional fairness.
  • The problem is a mixed-integer nonlinear program, and even the fixed-scheduling simplification is computationally intractable for centralized per-slot solution.

III. REFIM: REFERENCE USER BASED INTERFERENCE MANAGEMENT

REFIM decomposes interference management into distributed per-base-station decisions by representing each neighboring subchannel environment with a reference user. It combines sequential scheduling and power allocation with temporal and spatial feedback reduction.

  • User scheduling: For fixed power, user scheduling decomposes into independent base-station and subchannel subproblems.
  • Reference user selection: A reference user is the scheduled neighboring user having the strongest channel gain to the considered base station on a subchannel.
  • Reference-user approximation: Each base station solves a per-base-station power problem using one reference user per subchannel instead of all cochannel users.
  • Power allocation: The taxation term increases when the reference user is more strongly interfered with, causing the base station to lower its power.
  • Computational properties: The modified power problem remains nonconvex, so the stated conditions are necessary rather than sufficient for global optimality.
  • Power allocation: If the taxation term is ignored, the power allocation reduces to selfish water-filling; with taxation, base stations lower their water-filling levels.
  • REFIM algorithm: REFIM executes user scheduling and power allocation sequentially without the general algorithm’s inner and outer loops.

B. Online Reference User Selection Method

REFIM selects one locally dominant victim user per neighboring environment and subchannel as a reference for interference management, avoiding centralized coordination. The paper notes that more elaborate reference-user choices increase complexity without comparable performance gains.

  • Each BS considers one neighboring scheduled user per subchannel rather than all scheduled users when modeling interference.
  • The reference user is the neighboring user most strongly affected by the BS’s transmission on a subchannel.
  • Reference users are selected independently and locally by each BS on each subchannel, so centralized coordination is unnecessary.
  • Alternative choices, including averaged virtual users or multiple reference users, raise complexity without producing similarly high performance improvement.

C. Feedback Reduction

REFIM reduces feedback overhead by separating infrequent user-information updates from per-slot scheduling-index exchange. It further limits feedback spatially, especially for macro edge users and femto cells with unreliable backhauls.

  • Candidate reference users require weight, received signal strength, and noise-plus-interference information, creating substantial backhaul feedback overhead.
  • Temporal feedback reduction: Candidate users average their information over T ≫1 slots and report it infrequently, while BSs exchange only scheduled-user indexes each slot.
  • Spatial feedback reduction: Macro BSs send infrequent reference information only for edge users because center users are unlikely to become reference users.
  • Spatial feedback reduction: Femto BSs avoid per-slot scheduled-user-index feedback because their Internet backhauls provide no guaranteed latency.

D. Initial Power Setting

REFIM initializes each slot’s power allocation using candidate starting rules because its nonconvex optimization can produce different solutions from different initial powers. The previous-power rule preserves performance while the other rules lose performance substantially.

  • Different initial power settings can lead to different solutions and convergence speeds in the nonconvex power-control problem.
  • The uniform rule starts each BS by splitting maximum transmission power equally across subchannels.
  • The random rule selects subchannel powers randomly and scales them to use the total transmission power budget.
  • The previous rule starts each BS from the power used in the preceding slot.
  • The previous rule’s performance likely remains unchanged, whereas uniform and random initialization lose performance substantially.
  • Temporal correlation makes previous-slot initialization function like power-allocation iterations across successive slots, enabling sequential scheduling and power allocation.

E. REFIM: Reference Based Interference Management

The final REFIM algorithm combines previous-slot power initialization, single-reference-user abstraction, and sequential scheduling and power allocation. This design avoids within-slot loops and requires one feedback exchange from each user per slot.

  • REFIM uses previous-slot power for initialization and limits each subchannel’s neighboring-environment abstraction to one reference user.
  • REFIM executes user scheduling and power allocation sequentially without loops.
  • Sequential execution runs quickly in a slot and requires feedback from each user only once per slot.

IV. COMPLEXITY ANALYSIS

REFIM achieves the computational complexity of selfish waterfilling while requiring substantially less complexity than state-of-the-art dynamic interference-management algorithms. Its signaling overhead is reduced through periodic candidate-user feedback and limited per-slot exchange of scheduled-user indexes.

  • Computational complexity: User scheduling has linear complexity O(SK) for all compared algorithms except MC-IIWF.
  • Computational complexity: MC-IIWF's total computational complexity is T1 ·(O(SK) + O(SN)) because it iterates power allocation and user scheduling centrally.
  • Inter-BS signaling complexity: REFIM requires periodic feedback about candidate reference users, while macro BSs exchange only scheduled-user indexes per slot.The periodic feedback is ρ|Kn|AS, with A = 4 required reference-user information items; femto BSs do not require per-slot index feedback.
  • Computational complexity: REFIM's computational complexity is the same as selfish waterfilling and much lower than MGR and MC-IIWF.REFIM's power-allocation complexity is essentially the same as waterfilling, while MGR and MC-IIWF add virtual scheduling or centralized iteration loops.
  • Inter-BS signaling complexity: REFIM's per-slot feedback is limited to scheduled-user indexes exchanged between neighboring macro BSs, reducing signaling overhead.The paper argues that this small exchange can be handled through high-speed dedicated backbones.

V. PERFORMANCE EVALUATION

The evaluation uses extensive simulations across multiple network topologies and compares REFIM with conventional and dynamic interference-management algorithms. Results examine parameter choices, temporal feedback, transmit-power behavior, and throughput performance.

  • Evaluation setup: Extensive simulations evaluate REFIM across a 19-cell two-tier network, a real 3G deployment, and heterogeneous networks with small cells.
  • Evaluation setup: The simulations use logarithmic utility, 16 subchannels, 20 macro-cell users, 4 small-cell users, and maximum transmit powers of 43dBm and 15dBm.
  • Evaluation metrics: GAT measures geometric-average user throughput, while AET measures the average throughput of the bottom 5% of users.
  • Parameter and algorithm choices: 97% of the performance obtained with all six neighbors is achieved by considering one reference user per subchannel.
  • Parameter and algorithm choices: Previous-slot power initialization outperforms the other tested initialization strategies, motivating a REFIM design without iteration loops.
  • Power behavior: REFIM's previous-slot power allocation can emulate iterations across multiple slots when user scheduling remains similar over consecutive slots.
  • Feedback freshness: For nomadic users, GAT degradation remains relatively small with a feedback period of 200 slots, whereas mobile users lose performance as the period increases.

B. Performance Comparison with Other Algorithms

Across real deployment and varied topologies, REFIM improves throughput—especially for cell-edge users—while approaching the performance of a near-optimal centralized algorithm. Its gains are strongest in dense urban and suburban settings and remain substantial under partial deployment.

  • Overall comparison: 43% improvement in AET over EQ is achieved for low-throughput cell-edge users.REFIM improves throughput for all users compared with EQ, WF, and MGR.
  • Overall comparison: REFIM achieves about 95% of near-optimal MC-IIWF performance in GAT, AET, and AAT.MC-IIWF is centralized and difficult to implement because of prohibitive complexity.
  • Evaluation setting: The evaluation uses a real 3G deployment map containing 30 BSs within a 20 × 10 km2 area.The tested topology represents an operational network in Korea, with BS density proportional to user density.
  • Topology effects: 16% GAT and 42% AET gains are obtained in the urban environment.Performance improvements are high in urban and suburban environments, but almost no gain appears in sparse rural topology.
  • Incremental deployment: More than 85% gain is achieved when REFIM is deployed on only 15 of 30 BSs, mainly in urban areas.Unaided boundary BSs automatically reduce to WF, so partial deployment performs at least like WF and better than EQ.

D. Heterogeneous Networks (Macro + Small BSs)

REFIM is evaluated in heterogeneous macro–femto networks under spectrum sharing and splitting. With interference management, spectrum sharing delivers stronger performance, including gains that increase as femto-cell density grows.

  • Heterogeneous evaluation: The study considers macro-to-macro, femto-to-femto, and macro-to-femto interference across heterogeneous deployments.The simulations include cases with one, five, and ten femto BSs per macro cell.
  • Five femto cells per macro cell: With five femto cells per macro cell, spectrum sharing is always better than spectrum splitting because cross-tier interference is small.Even EQ under sharing is higher than or equal to REFIM under optimal splitting at 8/16 subchannels.
  • Ten femto cells per macro cell: With ten femto cells per macro cell, REFIM under spectrum sharing outperforms every spectrum-splitting case.Without appropriate interference management, severe cross-tier interference can degrade macro-user performance as femto density rises.
  • Policy implication: The results support spectrum sharing when interference is managed effectively, rather than relying only on orthogonal spectrum splitting.The paper links this potential gain to more complete spectral-resource reuse under increasing traffic demand.
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