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Joint Downlink Cell Association and Bandwidth Allocation for Wireless Backhauling in Two-Tier HetNets with Large-Scale Antenna Arrays

Ning Wang, Ekram Hossain, Vijay K. Bhargava

arXiv:1501.00078v1cs.NIcs.IT

TL;DR

The paper addresses joint cell association and wireless backhaul bandwidth allocation in two-tier HetNets where small cells use in-band wireless backhaul. It proposes reverse-TDD/SFR interference management and optimization algorithms for unified and per-small-cell allocation, finding that system load matters more than small-cell density and that CRE is inefficient under wireless-backhaul constraints.

  • Problem

    The paper studies joint downlink cell association and wireless backhaul bandwidth allocation under in-band wireless-backhaul constraints in a two-tier HetNet.

  • Method

    The paper combines co-channel reverse TDD and dynamic SFR with relaxed hierarchical optimization, GAMS solutions, and fast heuristics for unified and per-small-cell WBBA.

  • Results

    System load has more impact than small-cell density on sum log-rate and per-user rate, while the optimal load is approximately the macro BS antenna-array size.

  • Takeaways & Limitations

    CRE, effective with perfect backhauling, is inefficient when small cells use in-band wireless backhauling.

  • Takeaways & Limitations

    The study assumes a 5 dB transmit and receive antenna gain for small cells.

Abstract

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The problem of joint downlink cell association (CA) and wireless backhaul bandwidth allocation (WBBA) in two-tier cellular heterogeneous networks (HetNets) is considered. Large-scale antenna array is implemented at the macro base station (BS), while the small cells within the macro cell range are single-antenna BSs and they rely on over-the-air links to the macro BS for backhauling. A sum logarithmic user rate maximization problem is investigated considering wireless backhauling constraints. A duplex and spectrum sharing scheme based on co-channel reverse time-division duplex (TDD) and dynamic soft frequency reuse (SFR) is proposed for interference management in two-tier HetNets with large-scale antenna arrays at the macro BS and wireless backhauling for small cells. Two in-band WBBA scenarios, namely, unified bandwidth allocation and per-small-cell bandwidth allocation scenarios, are investigated for joint CA-WBBA in the HetNet. A two-level hierarchical decomposition method for relaxed optimization is employed to solve the mixed-integer nonlinear program (MINLP). Solutions based on the General Algorithm Modeling System (GAMS) optimization solver and fast heuristics are also proposed for cell association in the per-small-cell WBBA scenario. It is shown that when all small cells have to use in-band wireless backhaul, the system load has more impact on both the sum log-rate and per-user rate performance than the number of small cells deployed within the macro cell range. The proposed joint CA-WBBA algorithms have an optimal load approximately equal to the size of the large-scale antenna array at the macro BS. The cell range expansion (CRE) strategy, which is an efficient cell association scheme for HetNets with perfect backhauling, is shown to be inefficient when in-band wireless backhauling for small cells comes into play.

I. INTRODUCTION

The paper studies joint cell association and wireless backhaul bandwidth allocation in a two-tier HetNet with large-scale antenna arrays at the macro BS and in-band backhauling for small cells. It proposes interference-management and optimization approaches for unified and per-small-cell bandwidth allocation.

  • Motivation: In-band wireless backhauling offers low-cost, fast small-cell deployment but introduces interference that affects cell association and resource allocation.The approach supports plug-and-play small cells using over-the-air links to macro BSs.
  • System model: The system uses large-scale antenna arrays at macro BSs and single-antenna small cells relying on in-band over-the-air backhaul links.Macro BSs have wired high-capacity backhaul, while the macro tier hubs wireless backhaul connections for small cells.
  • Problem formulation: Two joint CA-WBBA scenarios are investigated: unified WBBA and per-small-cell WBBA.The scenarios allocate a common backhaul bandwidth factor or adjust backhaul bandwidth locally at each small cell.
  • Interference management: A reverse-TDD and dynamic-SFR duplex and spectrum-sharing framework is proposed to manage interference in the HetNet.The framework is designed to facilitate large-scale MIMO at the macro BS and in-band wireless backhauling.
  • Algorithms: Relaxed optimization and hierarchical decomposition are used for the unified-WBBA MINLP, while separate iterative designs and fast heuristics address per-small-cell WBBA.The paper also uses GAMS to solve the sum log-rate maximization problem.
  • Cell association: SINR-based association can overload macro cells, motivating joint association and resource allocation rather than association based only on radio signal quality.The paper frames optimal association as coupled with scheduling and radio resource allocation, creating a combinatorial optimization problem.

B. Wireless Backhauling

Wireless backhauling is important for scalable two-tier HetNets, but its constraints must be incorporated into cell association and radio-resource design. The paper addresses the previously uninvestigated combination of in-band backhauling, large-scale macro-BS antenna arrays, and cell association.

  • Prior HetNet studies insufficiently examined how small-cell backhauling affects radio-resource management and cell-association design.
  • In-band wireless backhauling connects small cells to macro-BS hubs over over-the-air links, enabling fast and cost-efficient large-scale 5G deployment.
  • The paper studies cell association under in-band wireless-backhauling constraints with large-scale antenna arrays at the macro BS, a combination not previously investigated in the literature.
  • Large-scale MIMO can support macro users and in-band small-cell backhaul without separate backhaul spectrum or hardware.
  • The localized interference pattern of large-scale MIMO must be considered jointly with cell association and wireless-backhaul resource allocation.

III. SYSTEM MODEL

The modeled network contains one large-array macro BS, multiple single-antenna small cells, and mobile terminals that each associate with one cell. Joint association and bandwidth allocation maximize proportional-fairness-oriented downlink utility under wireless-backhaul constraints.

  • The HetNet comprises a single macro BS with a large antenna array, small cells within its range, and mobile terminals.
  • The macro BS has beamforming group size Ng ≪ NT, with Ng greater than NS and NU much greater than Ng.
  • Each mobile terminal selects either the macro cell or a small cell, while the objective maximizes the sum of logarithmic rates.
  • The study investigates unified WBBA with one backhaul fraction β and per-small-cell WBBA with fractions βj for individual small cells.
  • The channel model retains large-scale fading, using macro-to-terminal gain H̄k and corresponding small-cell and backhaul gains.

C. Interference Management Considerations for Wireless Backhauling of Small Cells

Wireless backhauling creates self-interference and cross-link interference because small-cell access and backhaul share network nodes and spectrum. Reverse-TDD and soft frequency reuse coordinate duplexing and bandwidth to control these effects.

  • Reverse-TDD reverses small-cell and macro-BS DL/UL configurations so small cells can receive backhaul and serve users without conflicting duplex roles.
  • A small cell receives backhaul during a macro downlink slot and serves its users during a macro uplink slot, using orthogonal frequency channels for simultaneous functions.
  • Universal frequency reuse is excluded because small-cell uplink backhaul can interfere with its downlink users, while user uplink can interfere with backhaul reception.
  • Soft frequency reuse is used as a compromise between spectral efficiency and interference control.
  • Backhaul bandwidth is not reused for user transmissions either globally in u-WBBA or locally in p-WBBA.
  • Large-scale MIMO assumes NT much greater than simultaneously served nodes and uses joint FDMA-SDMA with beamforming groups of size Ng.

B. Relaxed Optimization and Hierarchical Decomposition

The relaxed mixed-integer optimization is decomposed hierarchically into outer bandwidth allocation and inner cell association problems. Convexity, dual decomposition, and strong duality support iterative solution of the unified-WBBA formulation.

  • Relaxing binary association indicators yields a convex inner problem for cell association and an outer problem for unified wireless-backhaul allocation.
  • The two subproblems are solved iteratively until convergence through upper-level primal decomposition.
  • The outer problem reduces to finding the smallest feasible backhaul fraction β satisfying the wireless-backhaul constraint.
  • Because the number of small cells is limited by beamforming group size Ng, the globally optimal β can be identified with low evaluation complexity.
  • A lower-level dual decomposition enables distributed solution of the inner association problem while avoiding complex inter-tier coordination.
  • Slater’s condition holds for the linear-constraint relaxation, so strong duality makes the primal association problem equivalent to its dual.

C. Distributed Joint CA-WBBA Method With Unified WBBA

The unified-WBBA method uses hierarchical decomposition to alternate cell association and a shared backhaul bandwidth factor. Dual updates solve the inner association problem, while outer iterations update the shared factor until convergence.

  • Inner association: Each user selects the base station maximizing its association utility under the current dual variables and unified factor.The method assigns binary association indicators directly rather than relaxing them.
  • Outcome: The hierarchical approach provides an exact solution to the MINLP for joint CA-WBBA with unified WBBA.The distributed design specifies operations for the macro BS, small cells, and mobile terminals.
  • Inner association: The nonsmooth Lagrangian dual is solved with sub-gradient multiplier updates using diminishing step sizes.With appropriate step sizes, the dual solution is guaranteed to converge; alternating primal and dual updates yields the association solution.
  • Hierarchical decomposition: Hierarchical decomposition separates the unified-WBBA problem into inner cell association and outer bandwidth-factor updates.The association solution feeds the outer problem, whose updated factor is passed back to the next inner iteration.

V. JOINT CA-WBBA WITH PER-SMALL CELL WIRELESS BACKHAUL BANDWIDTH ALLOCATION

Per-small-cell WBBA allows different small cells to adapt their backhaul bandwidth factors to local channel and load conditions. This flexibility is motivated by potential spectral-efficiency gains over a unified factor.

  • Motivation: The unified WBBA factor is constrained by the maximum of the smallest feasible per-small-cell ratios.Different channel and load conditions can make these minimum ratios vary substantially across small cells.
  • Motivation: Per-small-cell WBBA lets each small cell adapt its bandwidth factor to local channel and load conditions.The authors investigate this scheme because adaptive factors can achieve better spectral efficiency.

A. Problem Formulation

The per-small-cell formulation assigns each small cell its own backhaul bandwidth factor and jointly optimizes association and allocation. Unlike the unified case, the resulting MINLP contains nonseparable and nonlinear coupling that motivates distributed and heuristic solutions.

  • Bandwidth allocation: Per-small-cell WBBA assigns β_j ∈ [0, 1] to wireless backhaul, with the remaining bandwidth serving small-cell users.The small-cell-specific factor affects both backhaul capacity and user rates, including macro-cell user rates through the joint formulation.
  • Problem formulation: The joint per-small-cell CA-WBBA problem P2 is formulated as a mixed-integer nonlinear program.The formulation maximizes the system sum of logarithmic mobile-terminal rates under per-small-cell allocation and backhaul constraints.
  • Problem formulation: P2 is difficult because its objective is nonlinear, non-convex, and nonseparable in bandwidth and association variables.Its wireless backhaul constraint is also a nonlinear non-convex coupling constraint.
  • Solution methods: The proposed solutions include a distributed algorithm, centralized fast heuristics, and BONMIN optimization through GAMS for numerical benchmarks.The distributed method uses Lagrangian dual decomposition for the association subproblem with per-small-cell factors.
  • Solution structure: With fixed association, each small cell can determine its optimal bandwidth factor locally by making its backhaul constraint active.Distributed association can then update user assignments, while centralized association can use a macro-BS or RNC scheduler.

C. Macro BS Offloading and Small Cell Load Balancing

The per-small-cell setting motivates load-balancing heuristics because SINR-based association can overload the macro BS while leaving some small-cell backhaul underused. The proposed offloading procedure targets utility improvement, but extra small-cell balancing provides negligible numerical gain.

  • Motivation and limitations: Per-small-cell WBBA increases message passing and creates practical overhead for distributed implementation.The separation of association and bandwidth allocation is sub-optimal and is not based on decoupling the variables as in the unified case.
  • Load balancing: SINR-based association can overload the macro BS while leaving some small cells lightly loaded or unable to use available backhaul resources.These imbalances motivate a load-balancing heuristic for the two-tier network.
  • Macro-BS offloading: The macro-BS offloading heuristic sequentially tests macro-associated users and retains moves that improve the sum log-rate utility.Its stated complexity is O(N_UN_S).
  • Small-cell balancing: The supplementary small-cell load-balancing procedure adds overall complexity O(N_UN_S^2).It repeatedly applies offloading to non-empty small cells after macro-BS offloading.
  • Outcome: The numerical studies found negligible improvement from the extra small-cell load-balancing procedure.The heuristic is therefore positioned as a performance–overhead/complexity compromise rather than an exact solution.

VI. NUMERICAL RESULTS AND DISCUSSION

The numerical evaluation uses randomized two-tier HetNet deployments to compare joint cell-association and bandwidth-allocation strategies under varied small-cell and user densities.

  • Simulation setup: Simulations place one large-scale MIMO macro BS at the center of a 350 m-radius cell, with small cells and mobile terminals uniformly randomized.An example uses N_S = 10 small cells and N_U = 100 mobile terminals.
  • Simulation setup: Results are averaged over a sufficiently large number of simulation trials for each system setting.This averaging supports comparisons across the examined association and allocation strategies.

A. Joint CA-WBBA With Unified WBBA Factor

Under unified and per-small-cell WBBA, simulations compare association strategies using rate distributions, QoS indicators, and sum log-rate objectives. Joint methods generally improve rates, while per-small-cell allocation improves performance at higher complexity.

  • Unified WBBA: The distributed joint CA-WBBA algorithm significantly shifts MT-rate CDFs toward higher rates and improves QoS indicators in most unified-WBBA scenarios.The reported QoS-indicator improvement is consistently around 60% in most examined scenarios.
  • Unified WBBA: Up to 77% improvement in R0.5 and 87% improvement in R0.9 is achieved over SINR-based association under unified WBBA.R0.5 is the median MT rate, while R0.9 is attained by 90% of MTs.
  • Unified WBBA: CRE provides negligible improvement over SINR-based association and is inefficient when small-cell in-band wireless-backhaul constraints apply.This pattern appears in both rate CDFs and corresponding R_p values.
  • Per-small-cell WBBA: Per-small-cell WBBA generally improves MT rates and objective values over unified WBBA, but increases system complexity.The distributed joint and macro-BS-offloading heuristics offer complementary fairness and median-rate advantages.
  • Per-small-cell WBBA: Under per-small-cell WBBA, distributed joint CA-WBBA achieves the best fairness for 90% MT rate, while macro-BS offloading achieves the best median MT rate.The GAMS BONMIN solution attains the best objective value but sacrifices fairness by leaving more MTs in the very low-rate region.

VII. CONCLUSION

The paper combines reverse-TDD and soft frequency reuse with joint cell association and wireless-backhaul bandwidth allocation in a two-tier HetNet. Its evaluations show gains from per-small-cell allocation, load sensitivity near the macro array size, and CRE weakness under backhaul constraints.

  • System and interference management: The model uses a large-scale-antenna macro BS and single-antenna small cells relying on in-band wireless links to the macro BS for backhauling.The macro BS acts as the wireless-backhaul hub for the small-cell tier.
  • System and interference management: Reverse-TDD and soft frequency reuse are introduced to manage interference in the two-tier HetNet.The framework supports the joint downlink scheduling problem with wireless-backhaul constraints.
  • Optimization framework: The joint scheduling problem maximizes the sum of logarithmic MT rates and is formulated as a nonlinear mixed-integer programming problem.The study considers unified and per-small-cell backhaul bandwidth allocation scenarios.
  • Optimization framework: A two-level hierarchical decomposition method exploits separability in the unified-WBBA objective, enabling distributed cell-association algorithms.Fast heuristic and solver-based approaches are also studied for per-small-cell WBBA.
  • Main findings: Per-small-cell WBBA achieves improved spectral efficiency and network utility compared with unified allocation, with higher system complexity.This conclusion is stated for the proposed extension and the associated allocation scenarios.
  • Main findings: Algorithm performance is not sensitive to small-cell density, while the observed optimal associated-user load is approximately equal to the number of macro-BS antennas.The optimal load is linked to the large-scale antenna array rather than small-cell density.
  • Main findings: CRE fails to provide good performance when wireless-backhaul constraints are included in cell association.The conclusion concerns in-band wireless backhauling for the small-cell tier.
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