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Energy-Efficient Resource Assignment and Power Allocation in Heterogeneous Cloud Radio Access Networks

Mugen Peng, Kecheng Zhang, Jiamo Jiang, Jiaheng Wang, Wenbo Wang

arXiv:1412.3788v1cs.IT

TL;DR

The paper addresses energy-efficient resource allocation in H-CRANs while accounting for RRH/HPN association and inter-tier interference. It enhances S-FFR, reformulates the non-convex problem, and applies Lagrange dual decomposition to jointly allocate RBs and transmit power. Simulations report significant energy-efficiency gains for H-CRANs and the proposed allocation solution.

  • Problem

    H-CRANs lack straightforward energy-efficiency solutions that jointly optimize RRH/HPN association, RB assignment, and power allocation under inter-tier interference.

  • Method

    The paper enhances S-FFR, reformulates the non-convex optimization as an equivalent convex feasibility problem, and applies Lagrange dual decomposition.

  • Results

    H-CRANs achieve significant energy-efficiency gains over traditional C-RAN/HetNet architectures, while the proposed iterative solution outperforms two baseline algorithms.

  • Takeaways & Limitations

    Joint association-aware resource allocation and enhanced S-FFR provide an energy-efficient solution for OFDMA-based H-CRANs.

Abstract

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Taking full advantages of both heterogeneous networks (HetNets) and cloud access radio access networks (CRANs), heterogeneous cloud radio access networks (H-CRANs) are presented to enhance both the spectral and energy efficiencies, where remote radio heads (RRHs) are mainly used to provide high data rates for users with high quality of service (QoS) requirements, while the high power node (HPN) is deployed to guarantee the seamless coverage and serve users with low QoS requirements. To mitigate the inter-tier interference and improve EE performances in H-CRANs, characterizing user association with RRH/HPN is considered in this paper, and the traditional soft fractional frequency reuse (S-FFR) is enhanced. Based on the RRH/HPN association constraint and the enhanced S-FFR, an energy-efficient optimization problem with the resource assignment and power allocation for the orthogonal frequency division multiple access (OFDMA) based H-CRANs is formulated as a non-convex objective function. To deal with the non-convexity, an equivalent convex feasibility problem is reformulated, and closedform expressions for the energy-efficient resource allocation solution to jointly allocate the resource block and transmit power are derived by the Lagrange dual decomposition method. Simulation results confirm that the H-CRAN architecture and the corresponding resource allocation solution can enhance the energy efficiency significantly.

I. INTRODUCTION

H-CRANs combine C-RAN and HetNet capabilities to improve coverage, capacity, and energy efficiency, but require association and interference-aware resource optimization. This paper proposes enhanced S-FFR and joint resource-block assignment and power allocation for OFDMA-based H-CRANs.

  • Motivation: HetNets face constrained backhaul for CoMP signaling and excessive energy consumption from densely deployed LPNs.These challenges motivate combining HetNet coverage with C-RAN processing and coordination.
  • Problem: Strongest-received-power association is not always efficient because RRHs and HPNs differ in transmit power and experience difficult inter-tier interference.Inter-RRH interference can be coordinated centrally, whereas inter-tier interference between RRHs and HPNs is severe and harder to mitigate.
  • Problem: The paper investigates joint RB assignment and power allocation under RRH/HPN association and inter-tier interference constraints to maximize energy efficiency.The optimization is formulated for OFDMA-based H-CRANs.
  • Architecture: H-CRANs combine low-energy RRHs for high-rate, high-QoS users with HPNs for seamless coverage and lower-QoS users.The architecture integrates RRHs with centralized BBU processing while retaining HPN functionality for coverage and coordination.
  • Resource coordination: Enhanced S-FFR divides the frequency band into exclusive RRH resources and shared RRH/HPN resources for users with different rate-constrained QoS requirements.Exclusive RBs serve high-rate-constrained users, while shared RBs serve low-rate-constrained users.
  • Optimization: The non-convex optimization is transformed into an equivalent convex feasibility problem and solved with an iterative outer- and inner-loop algorithm.The proposed solution uses Lagrange dual decomposition to obtain energy-efficient resource allocation.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The proposed H-CRAN model combines enhanced S-FFR with RRH/HPN association, OFDMA resource assignment, and power allocation to improve energy efficiency while controlling inter-tier interference.

  • Enhanced S-FFR: Enhanced S-FFR divides resources into Ω1 for high-rate RUEs and Ω2 shared by low-rate RUEs and HUEs.The two-set design supports both inband and outband strategies while trading performance gains against implementation complexity.
  • Resource model: The system assigns different resource blocks to UEs using OFDMA, with K total RBs of bandwidth B0 partitioned into Ω1 and Ω2.Ω1 serves high-rate RUEs, while Ω2 serves low-rate RUEs and HUEs.
  • Resource model: Binary indicators an,k specify RB assignment, while pn,k specifies transmit power for RUE n on RB k.The corresponding HPN variables at,m and pt,m describe HUE RB assignment and transmit power.
  • Problem formulation: The optimization maximizes energy efficiency subject to QoS, inter-tier interference, RB allocation, and maximum transmit-power constraints.The interference constraint limits RRH power on reused RBs to protect HUEs.
  • Problem formulation: The resulting mixed-integer fractional problem is non-convex, and its computational complexity increases exponentially with the number of binary variables.Classical convex optimization methods cannot solve it directly.

III. ENERGY-EFFICIENT RESOURCE ALLOCATION OPTIMIZATION

The paper develops an effective optimization approach that first transforms the nonlinear fractional energy-efficiency objective and then solves the resulting problem iteratively.

  • Optimization framework: Non-linear fractional programming is used to convert the original energy-efficiency objective before developing an iterative maximization algorithm.The method targets the resource-allocation problem defined for H-CRANs.
  • Optimization framework: The transformed formulation enables an iterative solution procedure for the energy-efficiency maximization problem.The passage characterizes this as an effective method for solving Problem 1.

A. Optimization Problem Reformulation

The fractional objective is reformulated through a parameterized subtractive function, yielding a tractable feasibility problem solved by nested iterations with global convergence guarantees.

  • Optimization Problem Reformulation: The reference RRH’s energy efficiency is represented by a non-negative parameter γ, with the optimum denoted γ*.This parameter supports reformulation of the fractional objective.
  • Optimization Problem Reformulation: At γ*, maximizing C(a,p) − γ*P(a,p) over feasible allocations yields zero, establishing equivalence with the original problem.The equivalence holds for feasible solutions satisfying constraints (9)–(13).
  • Optimization Problem Reformulation: The algorithm updates γ iteratively while maintaining feasibility, converting the fractional objective into a subtractive form.The transformed problem is described as a tractable feasibility problem.
  • Proposed Iterative Algorithm: The outer loop updates γ using the previous iteration’s data rate and power consumption, while the inner loop solves the corresponding resource-allocation problem.The procedure initializes γ and checks a convergence condition based on C(a,p) − γP(a,p).
  • Proposed Iterative Algorithm: Algorithm 1 converges to the global optimal solution of Problem 3.This guarantee is stated explicitly in Theorem 2.
  • Proposed Iterative Algorithm: When the number of resource blocks is sufficiently large, the duality gap between Problem 3 and its dual is nearly zero.The stated relation is D* − EE* ≈ 0.

C. Lagrange Dual Decomposition Method

Lagrange dual decomposition separates the inner resource-allocation problem across resource blocks and derives power and RB policies from dual variables.

  • Lagrangian formulation: The Lagrangian introduces multipliers for minimum-rate, inter-tier-interference, and total-transmit-power constraints.β handles rate constraints, λ handles interference constraints, and ν handles total power.
  • Dual decomposition: The dual optimization problem is convex and decomposes into K independent resource-block problems.This follows because the dual function is the maximum of linear functions of the dual variables.
  • Power allocation: For a fixed RB assignment, the power subproblem is concave in transmit power and can be solved using Karush-Kuhn-Tucker conditions.The resulting expression uses a nonnegative projection and an optimal water-filling level.
  • Dual decomposition: Substituting the optimal power allocation into each decomposed problem produces the objective used to determine the resource assignment.This completes the inner-loop dual-decomposition procedure.
  • RB assignment: The optimal RB allocation indicator is expressed in terms of the dual variables, and sub-gradient updates solve the resulting dual problem.The dual variables are updated using positive step sizes during inner-loop iterations.

IV. RESULTS AND DISCUSSIONS

The simulations evaluate H-CRAN energy efficiency under varied user configurations and specified channel, power, and circuit-consumption assumptions.

  • Simulation setup: Each RRH contains 10 high-rate-constrained RUEs on exclusive RB set Ω1, while M low-rate-constrained RUEs are varied and may share resources with HUEs.When M = 0, no inter-tier interference occurs.
  • Simulation setup: The simulation uses K = 25 RBs, 5 MHz bandwidth, 43 dBm HPN transmit power, and 1000 snapshots.The path-loss model differs across RRH-to-RUE, HPN-to-RUE, and RRH-to-HUE links.
  • Power assumptions: RRH and HPN circuit-power, amplifier-efficiency, fronthaul, and backhaul-consumption assumptions are included in the evaluation.The fronthaul and HPN-to-BBU backhaul power consumptions are each assumed to be 0.2 W.

A. H-CRAN Performance Comparisons

The evaluation compares H-CRAN energy efficiency with 1-tier HPN, 2-tier HetNet, and 1-tier C-RAN baselines under defined RB-sharing and allocation policies.

  • Baseline policies: The 1-tier HPN baseline allocates Ω1 and Ω2 to cell-center and cell-edge UEs, using water-filling power allocation and maximum-SINR scheduling.The number of cell-center UEs is 10, while low-rate-constrained cell-edge UEs vary from 1 to 10.
  • Baseline policies: The overlaid HetNet uses orthogonal RB sets for PBSs and HPNs, whereas the underlaid HetNet fully shares Ω1 and Ω2 within the overlapping coverage areas.The overlaid configuration therefore has no inter-tier interference between PBS and HPN allocations.
  • H-CRAN policy: In H-CRAN, Ω1 is exclusive to RUEs and Ω2 is shared by cell-edge RUEs and HUEs under the proposed association and interference-mitigation solution.The 1-tier C-RAN instead fully shares all RBs among RUEs.
  • Results: H-CRAN achieves the best EE among the evaluated scenarios, while 1-tier C-RAN is slightly worse because it lacks the HPN architecture's advantages.The underlaid HetNet outperforms the overlaid HetNet because spectrum reuse and interference are optimized.

B. Convergence of the Proposed Iterative Algorithm

The proposed resource-allocation solution is evaluated against fixed-power and sequential-RB baselines across convergence, SINR-threshold, transmit-power, and RB-ratio settings.

  • Convergence: The optimal EE solution is compared with fixed-power and sequential-RB algorithms using the same system constraints.The evaluation places 12 uniformly spaced RRHs around a reference HPN.
  • Convergence: EE performance generally converges within 3 iterations, while the baselines converge faster because the proposed solution has higher computing complexity.The comparison varies allowed inter-tier interference thresholds and iteration numbers.
  • SINR thresholds: With ηHUE below 10 dB, EE is nearly stable for increasing HUE SINR thresholds; baseline EE declines above 10 dB, whereas the proposed solution deteriorates only above 14 dB.The proposed solution is reported to sustain more inter-tier interference and provide higher HUE bit rates than the baselines.
  • Transmit power: When RRH maximum transmit power is not large, EE increases almost linearly with P_Rmax; for P_Rmax ≥22 dBm, SE and total power consumption also increase almost linearly.The sequential-RB algorithm often exceeds fixed power, while the proposed solution achieves the best EE through joint RB assignment and power allocation.
  • RB partitioning: EE increases almost linearly with the Ω1-to-ΩT ratio because more exclusive RRH RBs reduce shared-RB inter-tier interference and improve RUE SINRs.The results also show EE increasing with the maximum allowed RRH transmit power.
  • RB partitioning: Optimizing EE alone favors allocating more radio resources to Ω1, but fairness requires retaining RBs for HUEs and cell-edge RUEs.The paper identifies joint fairness and EE support as a challenging open issue for real H-CRANs.

V. CONCLUSIONS

The paper jointly optimizes H-CRAN resource allocation and reports significant EE gains, while identifying advanced S-FFR design as future work.

  • Conclusions: The paper jointly optimizes RB assignment and power allocation subject to inter-tier interference mitigation and RRH/HPN association.The optimization uses a non-convex fractional formulation and a Lagrange dual decomposition method.
  • Conclusions: H-CRANs achieve significant EE gains over traditional HetNets and C-RANs, and the proposed optimal solution outperforms two baseline algorithms.The conclusion attributes further improvement to researching advanced S-FFR schemes and designing optimal ratios among RB sets.

APPENDIX A PROOF OF THEOREM 1

Theorem 1 is established by proving sufficient and necessary conditions for equivalence between the original energy-efficiency problem and its transformed objective. The transformed optimum satisfies the same optimality condition as the original problem.

  • The proof defines the maximum energy-efficiency value γ∗ using optimal resource-block and power allocation policies.
  • The sufficient condition follows because γ∗P(a, p) = 0 is achievable by the optimal policies a∗ and p∗.
  • For the transformed objective, the optimal policies ˆa∗ and ˆp∗ satisfy C(ˆa∗, ˆp∗) − γ∗P(ˆa∗, ˆp∗) = 0.
  • The necessary condition shows that the transformed-objective optimum ˆa∗ and ˆp∗ is also optimal for the original objective.
  • F(γ) is strictly decreasing in γ, supporting the equivalence argument through the transformed objective.

APPENDIX C PROOF OF THEOREM 2

Theorem 2 establishes convergence of the outer-loop update for energy efficiency. Each non-optimal iteration increases γ, while the transformed objective decreases toward zero at the maximum achievable value γ∗.

  • The updated energy-efficiency value cannot exceed the maximum achievable value γ∗.
  • F(γ(i)) = P(a(i), p(i))(γ(i+1) − γ(i)) > 0 implies γ(i+1) > γ(i) when power consumption is positive.
  • Because γ increases monotonically, F(γ) decreases across outer-loop iterations.
  • When γ reaches γ∗, F(γ∗) = 0 and the algorithm derives the global optimal resource-block and power solutions.

APPENDIX D PROOF OF THEOREM 3

Theorem 3 proves zero duality gap by showing that the perturbation function v(H) is concave. This follows from a time-sharing construction that combines feasible power allocations across carrier fractions in the OFDMA H-CRAN system.

  • Problem reformulation: The transformed objective and constraints are expressed as functions of the power-allocation variables p_n,k and a perturbation vector H.
  • Problem reformulation: The perturbation function v(H) is introduced to analyze the duality gap between the primal problem and its dual.
  • Time-sharing condition: The time-sharing condition combines optimal solutions for H1 and H2 through a feasible allocation associated with H3 = αH1 + (1 −α)H2.
  • Concavity proof: The constructed allocation makes the relevant constraints linear combinations of the allocations used for H1 and H2, proving concavity of v(H).
  • Duality result: For the OFDMA-based H-CRAN system, time sharing is satisfied as the number of carriers approaches infinity, so the duality gap is zero.
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