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Energy Efficiency of Downlink Transmission Strategies for Cloud Radio Access Networks

Binbin Dai, Wei Yu

arXiv:1601.01070v2cs.IT

TL;DR

Downlink C-RAN must balance BS-side savings against the additional energy consumed by CP–BS backhaul, raising the question of whether data-sharing or compression is more efficient. The paper formulates joint total-power minimization under user-rate constraints and develops convergent approximations for both strategies. Simulations show that both outperform non-optimized CoMP, with data-sharing favored at low rates and compression at high rates as data-sharing backhaul power grows.

  • Problem

    The paper asks which downlink C-RAN strategy, data-sharing or compression, is more energy efficient when BS activation, transmission, and backhaul energy are all included.

  • Method

    The paper minimizes total network power under user-rate constraints using BS and linear rate-dependent backhaul power models, reweighted ℓ1 minimization, and successive convex approximation.

  • Results

    Both optimized strategies provide much improved energy efficiency over non-optimized CoMP; data-sharing is superior at low user rates, whereas compression may be preferred at high rates.

  • Takeaways & Limitations

    Strategy selection should depend on the target-rate regime because data-sharing backhaul power increases significantly as user rate increases.

Abstract

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This paper studies the energy efficiency of the cloud radio access network (C-RAN), specifically focusing on two fundamental and different downlink transmission strategies, namely the data-sharing strategy and the compression strategy. In the data-sharing strategy, the backhaul links connecting the central processor (CP) and the base-stations (BSs) are used to carry user messages -- each user's messages are sent to multiple BSs; the BSs locally form the beamforming vectors then cooperatively transmit the messages to the user. In the compression strategy, the user messages are precoded centrally at the CP, which forwards a compressed version of the analog beamformed signals to the BSs for cooperative transmission. This paper compares the energy efficiencies of the two strategies by formulating an optimization problem of minimizing the total network power consumption subject to user target rate constraints, where the total network power includes the BS transmission power, BS activation power, and load-dependent backhaul power. To tackle the discrete and nonconvex nature of the optimization problems, we utilize the techniques of reweighted $\ell_1$ minimization and successive convex approximation to devise provably convergent algorithms. Our main finding is that both the optimized data-sharing and compression strategies in C-RAN achieve much higher energy efficiency as compared to the non-optimized coordinated multi-point transmission, but their comparative effectiveness in energy saving depends on the user target rate. At low user target rate, data-sharing consumes less total power than compression, however, as the user target rate increases, the backhaul power consumption for data-sharing increases significantly leading to better energy efficiency of compression at the high user rate regime.

I. INTRODUCTION

The paper evaluates energy efficiency in downlink C-RAN by jointly accounting for BS and backhaul power, comparing data-sharing with compression under user-rate constraints. It develops convergent optimization methods and finds that the preferred strategy depends on the target-rate regime.

  • Motivation: C-RAN can improve energy efficiency through low-power radio heads, joint precoding, and resource allocation that places idle BSs into sleep mode.These benefits reduce BS-side energy use, but the paper emphasizes that increased CP–BS backhaul consumption must also be included.
  • Research question: The study asks which of data-sharing or compression is more energy efficient when BS transmit, activation, and backhaul power are jointly considered.The strategies differ in how backhaul rate is determined, creating an interdependent tradeoff among cooperation, BS activation, transmit power, and backhaul power.
  • Formulation: The optimization minimizes total network power subject to user rate or QoS constraints, extending prior work beyond data-sharing to include compression.Backhaul power is modeled as a linear function of backhaul rate, while BS consumption uses a piecewise-linear model with sleep and active modes.
  • Methods: Reweighted ℓ1 minimization approximates nonconvex BS activation and data-sharing backhaul costs, reducing the problem to convex transmit-power minimization with convergence guarantees.The resulting convex problem can be addressed through uplink-downlink duality or SOCP transformation, and the reweighting is connected to MM algorithms.
  • Methods: For compression, successive convex approximation handles nonconvex backhaul power expressed as a difference of logarithmic functions, together with reweighted ℓ1 BS-activation approximation.The combined procedure belongs to the MM class and has a convergence guarantee.
  • Findings: Optimized data-sharing and compression provide much improved energy efficiency over non-optimized CoMP, while their relative advantage changes with user target rate.Data-sharing is superior at low rates; its backhaul power rises significantly with user rate, so compression may be preferred at high rates.

C. Paper Organization and Notations

The paper models downlink C-RAN with CP-connected BSs and compares communication-energy implications across transmission strategies. It accounts for BS and backhaul power while using a single-antenna system model and defined notation.

  • The paper organizes its analysis around the C-RAN system model, data-sharing and compression strategies, simulations, and conclusions.
  • A downlink C-RAN comprises L BSs serving K users, with BSs connected to a CP through backhaul links.User messages are jointly processed at the CP before being forwarded to BSs.
  • The model assumes single antennas at BSs and users, while noting that the algorithms can be generalized to multi-antenna BSs.
  • The received signal consists of the combined BS transmit signals through the users’ channel gains plus Gaussian noise, and each user decodes its own message.
  • Total network power includes BS transmission, BS hardware and operating components, and power consumed by C-RAN backhaul links.The paper emphasizes that transmit power alone does not fully characterize BS and network energy consumption.

2) Backhaul Power Consumption:

The paper models backhaul power as load-dependent and incorporates it into total C-RAN power minimization under fixed user-rate operating points. Energy efficiency reflects the tradeoff among transmission, BS activation, and backhaul traffic.

  • 2) Backhaul Power Consumption:: Backhaul links are modeled as communication channels with capacity C_l and associated power dissipation.
  • 2) Backhaul Power Consumption:: The backhaul power model scales with the traffic R_l^BH between each BS and the CP, using a factor related to maximum backhaul power and capacity.
  • 2) Backhaul Power Consumption:: The total C-RAN power combines the adopted BS power model with the backhaul power model.
  • 2) Backhaul Power Consumption:: Three energy-saving mechanisms are considered jointly: reducing transmit power, placing BSs in sleep mode, and decreasing backhaul traffic.Deactivating BSs can reduce cooperation capability and increase transmit power needed to maintain QoS.
  • 2) Backhaul Power Consumption:: C-RAN energy efficiency is defined as achievable sum rate divided by total consumed power.
  • 2) Backhaul Power Consumption:: The optimization minimizes total power while satisfying fixed target rates r_k for scheduled users.The resulting minimum power characterizes an operating point, while maximizing energy efficiency requires searching across operating points.

D. Data-Sharing versus Compression

Data-sharing forwards user messages to serving BS clusters for joint beamforming, whereas compression centrally precodes signals and forwards compressed versions. The data-sharing formulation jointly selects beamformers and serving clusters under rate and power constraints.

  • D. Data-Sharing versus Compression: Data-sharing routes each scheduled user’s message to a BS cluster, while compression centrally precodes before forwarding compressed signals to BSs.
  • D. Data-Sharing versus Compression: Data-sharing backhaul rate depends on user message rate and cluster size, whereas compression backhaul cost depends on compression resolution.
  • D. Data-Sharing versus Compression: At low user rates and small clusters, data-sharing can be more efficient than compression because compression suffers from quantization noise.
  • D. Data-Sharing versus Compression: The data-sharing transmit signal is formed from beamforming coefficients and user messages, with zero coefficients indicating BSs outside a user’s serving cluster.
  • D. Data-Sharing versus Compression: User rates are obtained from SINR expressions determined by the network beamformers and the received signals.
  • D. Data-Sharing versus Compression: For data-sharing, serving BSs receive user messages and beamforming coefficients, while the modeled backhaul excludes CSI and beamformer-sharing overhead.
  • D. Data-Sharing versus Compression: The data-sharing formulation is discrete and nonconvex because indicator functions represent BS activation and cluster membership.
  • D. Data-Sharing versus Compression: The optimization chooses beamformers and implicitly serving clusters to minimize total power while satisfying user QoS constraints.

B. Proposed Algorithm

The proposed data-sharing algorithm replaces nonconvex indicator terms with reweighted ℓ1 approximations and repeatedly solves convex weighted transmit-power problems. Its reweighting promotes BS sleep modes and smaller user-serving clusters, and the resulting procedure converges to a stationary point of an approximation.

  • B. Proposed Algorithm: Indicator functions are treated as scalar ℓ0 norms and approximated using convex reweighted ℓ1 minimization.
  • B. Proposed Algorithm: Small current BS or user-beamforming powers receive larger subsequent weights, encouraging further power reduction.
  • B. Proposed Algorithm: The BS weight promotes sleep-mode activation, while the user-specific weight controls serving-cluster size and associated backhaul consumption.
  • B. Proposed Algorithm: The reweighting function connects the approximation to majorization-minimization and supports convergence analysis for the proposed algorithms.
  • B. Proposed Algorithm: Each iteration fixes the weights, solves for beamforming coefficients, and updates the weights until convergence.
  • B. Proposed Algorithm: The reweighted approximation converts the nonconvex problem into a weighted transmit-power minimization problem solvable by uplink-downlink duality or SOCP.

C. Convergence Analysis

The convergence analysis shows that the reweighted algorithm is guaranteed to converge under a particular reweighting function, while alternative functions may also work in other setups.

  • C. Convergence Analysis: Algorithm 1 alternates between updating reweighting weights and solving a weighted transmit-power minimization problem.The inner problem can be formulated as an SOCP and solved with an interior-point method.
  • C. Convergence Analysis: A suitable reweighting function makes Algorithm 1 a special case of the MM algorithm and guarantees convergence.
  • C. Convergence Analysis: The reweighting function in equation (19) is not unique, and other approximations may perform similarly in inducing sparsity.
  • C. Convergence Analysis: The algorithm has overall complexity order O(T1 (L + K) (LK)^3) under the stated interior-point implementation.Restricting each user’s candidate serving cluster to nearby BSs reduces complexity with negligible performance loss.

E. Generalization to the Multi-Antenna System

The data-sharing algorithm extends to multiple transmit antennas and to multiple receive antennas when the receive beamformer is fixed; the compression formulation models centralized precoding, independent signal compression, and quantization effects.

  • E. Generalization to the Multi-Antenna System: With multiple transmit antennas, each scalar beamforming coefficient becomes a beamforming vector for the antennas at each BS.The remaining optimization parameters are extended accordingly.
  • E. Generalization to the Multi-Antenna System: With multiple receive antennas, the algorithm uses an effective channel gain when the receive beamformer is fixed.Joint transmit- and receive-beamformer design is more complicated and may be handled iteratively using an MMSE receiver.
  • E. Generalization to the Multi-Antenna System: In compression transmission, the CP centrally precodes user messages, independently compresses each precoded signal, and forwards the compressed signals to the BSs.Each BS transmits its received compressed beamformed signal to the users.
  • E. Generalization to the Multi-Antenna System: Quantization noise adds to BS transmit power and creates an additional noise term at each user receiver.Lower quantization noise requires higher backhaul rate, and practical quantizers are modeled with a gap to the rate-distortion limit.
  • E. Generalization to the Multi-Antenna System: The compression strategy’s total-power problem is nonconvex because of the activation indicator and backhaul-rate expression.

B. Proposed Algorithm

The proposed compression-strategy algorithm combines reweighted ℓ1 minimization with successive convex approximation, producing a convex subproblem at each iteration and guaranteed convergence.

  • B. Proposed Algorithm: Reweighted ℓ1 minimization approximates the BS-activation indicator through iteratively updated weights.The weights are updated using the current beamforming and quantization variables.
  • B. Proposed Algorithm: Successive convex approximation replaces the nonconvex logarithmic term in the backhaul rate with a convex quadratic approximation.The approximation is updated iteratively through the auxiliary variables λ_l.
  • B. Proposed Algorithm: Algorithm 2 repeatedly solves the convex subproblem and updates β_l and λ_l until convergence.
  • B. Proposed Algorithm: For fixed β_l and λ_l, the resulting problem is a convex optimization problem with SOC-reformulated SINR constraints.It can be solved efficiently using a standard convex optimization solver with polynomial complexity.
  • B. Proposed Algorithm: The sequence generated by Algorithm 2 is guaranteed to converge from any initial point under the specified reweighting function.The algorithm has complexity order O(T2 (L + K) (LK + L)^3).

C. Generalization to the Multi-Antenna System

The multi-antenna extension assumes independent compression across transmit antennas, while fixed receive beamformers permit a straightforward receive-side generalization; joint beamformer design remains more difficult.

  • C. Generalization to the Multi-Antenna System: Algorithm 2 extends to multiple transmit antennas when the CP independently compresses the signal for each antenna.
  • C. Generalization to the Multi-Antenna System: The simulation topology contains 7 cells with 4 RRHs per cell, represented by 28 BSs in total.
  • C. Generalization to the Multi-Antenna System: Joint compression across antennas may improve performance but leads to a different optimization problem.
  • C. Generalization to the Multi-Antenna System: The receive-side extension is straightforward with a fixed receive beamformer, whereas joint transmit- and receive-beamformer design requires additional effort.

V. NUMERICAL EVALUATION OF ENERGY EFFICIENCY

The numerical evaluation compares optimized data-sharing and compression against reference schemes in a 7-cell, 28-BS C-RAN network. Both optimized strategies improve energy efficiency over non-optimized CoMP, but the preferable strategy depends on user target rate.

  • Simulation setup: The evaluation uses a wrapped-around 7-cell network with 4 RRHs per cell, totaling 28 BSs.Each point in Fig. 6 is averaged over 100 channel realizations.
  • Algorithm behavior: At 20 Mbps per user, active-BS counts decrease across iterations for both strategies as the algorithms optimize BS activation.More scheduled users require more BSs to remain active.
  • Algorithm behavior: Data-sharing converges within 30 iterations, whereas compression requires up to 50 iterations in the worst case.Both algorithms’ objective values monotonically decrease and converge.
  • Power comparison: Optimized data-sharing and compression consume substantially less power than non-optimized Per-Cell CoMP, which keeps all BSs active.Other optimized large-cluster CoMP schemes may reduce transmission power while retaining high overall power consumption when all BSs remain active.
  • Power comparison: Neither strategy dominates across all target rates: data-sharing uses less power below 30 Mbps in Fig. 6(b), while compression becomes better after 40 Mbps.Data-sharing’s power rises sharply with target rate because its backhaul consumption increases significantly.
  • Power breakdown: Data-sharing has lower backhaul power at low rates, but compression’s backhaul grows gradually and eventually becomes lower as target rate increases.BS power consumption is similar between the strategies, making backhaul power the determining factor.

APPENDIX A PROOF FOR THEOREM 3.1

Appendix A establishes convergence of Algorithm 1 by relating its reweighted approximation to an MM procedure. The proof uses convex upper-bound subproblems satisfying standard MM convergence conditions.

  • Problem approximation: Algorithm 1 is shown to converge to a stationary point of a logarithmically approximated problem.The approximation replaces the original ℓ0-norm terms with logarithmic functions.
  • MM construction: The logarithmic objective is nonconvex, but its majorizing surrogate is a convex quadratic function in the beamforming variables.This enables solving a sequence of convex optimization problems.
  • Convergence guarantee: MM convergence requires a continuous surrogate that tightly upper-bounds the objective and matches its first-order derivative at the tight point.The appendix verifies that the proposed surrogate satisfies these sufficient conditions.
  • Convergence guarantee: Therefore, Algorithm 1, which is equivalent to the MM procedure, converges to stationary-point solutions.

APPENDIX B PROOF FOR THEOREM 4.1

Appendix B proves convergence of Algorithm 2 through an MM treatment of its logarithmic approximation. The method iteratively solves convex upper-bound problems and satisfies the sufficient conditions for convergence.

  • Problem approximation: Algorithm 2 converges to a stationary point of a logarithmic approximation to the original compression-strategy problem.
  • MM construction: The approximated problem is nonconvex because its objective contains logarithmic functions.An MM algorithm replaces this objective with an upper bound and solves a sequence of convex problems.
  • Algorithm equivalence: The MM parameters are updated iteratively, and the resulting procedure is equivalent to Algorithm 2 with the specified reweighting function.
  • Convergence guarantee: The majorizing function satisfies the sufficient MM conditions, so Algorithm 2 is guaranteed to converge.
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