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Group Sparse Beamforming for Green Cloud-RAN

Yuanming Shi, Jun Zhang, Khaled B. Letaief

arXiv:1310.0234v1cs.IT

TL;DR

Cloud-RAN centralizes baseband processing but makes transport-link power consumption significant. This paper jointly selects RRHs and minimizes coordinated-beamforming power, using greedy selection and weighted group sparse beamforming; simulations and analysis report near-optimal, substantially reduced network power. The study leaves several large-scale and transport-link challenges for future work.

  • Problem

    The paper addresses minimizing Cloud-RAN network power, including transport and radio-access consumption, subject to per-user QoS constraints.

  • Method

    It combines backward greedy RRH selection with weighted group sparse beamforming, using mixed-norm minimization to identify RRHs that can be switched off.

  • Results

    The greedy algorithm provides near-optimal performance, while the GSBF framework substantially outperforms conventional unweighted mixed-norm algorithms and reduces network power.

  • Takeaways & Limitations

    Considering transport-link power and jointly selecting RRHs with coordinated beamforming can significantly reduce Cloud-RAN network power, especially in low-QoS regimes.

  • Takeaways & Limitations

    The study leaves very-large-scale beamforming, limited-capacity transport-link compression, joint user scheduling, and effective CSI acquisition for future work.

Abstract

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A cloud radio access network (Cloud-RAN) is a network architecture that holds the promise of meeting the explosive growth of mobile data traffic. In this architecture, all the baseband signal processing is shifted to a single baseband unit (BBU) pool, which enables efficient resource allocation and interference management. Meanwhile, conventional powerful base stations can be replaced by low-cost low-power remote radio heads (RRHs), producing a green and low-cost infrastructure. However, as all the RRHs need to be connected to the BBU pool through optical transport links, the transport network power consumption becomes significant. In this paper, we propose a new framework to design a green Cloud-RAN, which is formulated as a joint RRH selection and power minimization beamforming problem. To efficiently solve this problem, we first propose a greedy selection algorithm, which is shown to provide near- optimal performance. To further reduce the complexity, a novel group sparse beamforming method is proposed by inducing the group-sparsity of beamformers using the weighted $\ell_1/\ell_2$-norm minimization, where the group sparsity pattern indicates those RRHs that can be switched off. Simulation results will show that the proposed algorithms significantly reduce the network power consumption and demonstrate the importance of considering the transport link power consumption.

I. INTRODUCTION

Cloud-RAN centralizes baseband processing and coordinates distributed RRHs, but its transport links add significant energy costs. The paper formulates joint RRH selection and beamforming methods to reduce total network power while preserving QoS.

  • Motivation: 1000x capacity growth is expected in the following decade, motivating architectures that improve capacity and energy efficiency.Dense small-cell and massive-MIMO alternatives face interference, spacing, deployment, or operating challenges.
  • Architecture: Cloud-RAN separates centralized BBUs from distributed RRHs, enabling coordinated transmission, interference management, and low-cost deployment.The architecture includes a BBU pool, optical transport network, and distributed RRHs.
  • Energy challenge: Transport-link and RRH power consumption becomes important in Cloud-RAN because many low-power RRHs require high-bandwidth optical connections.Prior cellular energy-efficiency studies generally focused on base-station power because conventional backhaul consumption was negligible by comparison.
  • Problem formulation: The paper formulates joint RRH selection and transmit-power-minimization beamforming with per-user QoS constraints as an NP-hard MINLP.The transport power depends on active RRHs, while coordinated beamforming minimizes transmit power.
  • Algorithms: The proposed greedy selection algorithm switches off one RRH per step, while group sparse beamforming uses weighted mixed ℓ1/ℓp minimization to identify switchable RRHs.The weights exploit transport power, amplifier efficiency, and instantaneous effective channel gain.
  • Reported performance: The greedy algorithm is reported as near-optimal, while the three-stage group sparse framework substantially outperforms conventional unweighted mixed-norm methods.The paper positions bi-section GSBF for large networks and iterative GSBF for medium-size networks.

B. Power Model

The power model accounts for active and sleep consumption in RRHs and transport links. It motivates switching both components into sleep mode when traffic and operation permit.

  • Model scope: The Cloud-RAN network power model includes RRH and transport-network consumption, with limited-capacity-link compression left for future work.The paper explicitly identifies limited-capacity transport links as outside the present setting.
  • RRH power: RRH power is modeled empirically as active consumption plus transmit-power-dependent consumption when the RRH is transmitting.The model includes antenna-dependent active power, sleep power, transmit power, and RF power-amplifier efficiency.
  • RRH power: Typical Pico-BS parameters include 4.3W sleep power and η_l = 4, supporting the conclusion that RRHs should sleep when possible.These values are used to motivate the energy benefit of switching off RRHs.
  • Transport power: Transport-link power is modeled with separate active and sleep consumption for the optical network components.The model includes OLT power and ONU or transport-link power in active and sleep modes.

3) Network Power Consumption:

The network-power objective jointly accounts for transmit power and transport-link power while selecting active RRHs under QoS constraints. Fixing an active RRH set yields an SOCP, but exhaustive set search is generally exponential.

  • The power model separates total transmit power from total transport-network power.
  • Reducing transmit power and reducing active RRHs impose conflicting design pressures.More active RRHs can improve beamforming gain, while active transport links increase network power.
  • The optimization jointly selects RRHs and designs transmit beamformers under target SINRs and perfect CSI at the BBU pool.
  • For a fixed active RRH set A, the network-power minimization problem is an SOCP solvable efficiently by interior-point methods.
  • Exhaustively searching all active-RRH subsets is generally exponential in the number of RRHs and impractical for large networks.

C. Group Sparse Beamforming Formulation

The GSBF formulation represents beamformer coefficients in RRH-aligned groups, so group zeros identify RRHs that can be switched off. A mixed norm provides a tractable group-sparsity surrogate for the combinatorial problem.

  • Beamformer coefficients are partitioned into RRH-specific groups whose simultaneous zeros indicate switched-off RRHs.
  • The transport-link power can be expressed through an indicator of whether each RRH group has nonzero support.
  • The sparse formulation is equivalent to the original joint RRH-selection and beamforming problem.
  • Conventional ℓ1 sparsity does not ensure zeros align within one RRH group, so mixed ℓ1/ℓp norms are used instead.
  • Because global optimization is computationally difficult, the paper proposes greedy selection and group-sparsity-based low-complexity algorithms.

IV. GREEDY SELECTION ALGORITHM

The backward greedy algorithm progressively switches off RRHs while re-optimizing beamforming for the remaining active set. It chooses the feasible removal that yields the lowest resulting network power.

  • The algorithm iteratively selects one active RRH to switch off and re-optimizes coordinated beamforming for the remaining set.
  • The procedure initializes with all RRHs active, permanently moves selected RRHs to the inactive set, and solves the fixed-set problem at each iteration.
  • At each iteration, the selected RRH minimizes network power after its removal among feasible candidates.
  • Switching off an RRH reduces transport-network power but can increase total transmit power.
  • The final active set is chosen from the recorded feasible iterations as the one with minimum optimized network power.

B. Complexity Analysis

The greedy method requires a number of SOCP solves that grows quadratically with RRH count, motivating GSBF alternatives with logarithmic or linear growth. These methods induce RRH-aligned group sparsity using weighted norms and then select active RRHs.

  • Complexity Analysis: The greedy algorithm solves |A[i]| SOCPs per iteration, with each SOCP having complexity O((K sum_l∈A N_l)^3.5).
  • Complexity Analysis: Because iterations are bounded by L, the greedy algorithm’s total number of SOCP solves grows quadratically with L.
  • GSBF Algorithms: Bi-section and iterative GSBF reduce the overall SOCP-solve growth to logarithmic and linear in L, respectively.
  • GSBF Algorithms: Weighted mixed ℓ1/ℓ2 minimization induces group sparsity, while reweighting iteratively enhances sparsity for the iterative GSBF method.
  • Three-Stage Framework: The three-stage framework first induces sparsity, then orders RRH switch-off priorities using the sparse beamformer and system parameters, and finally selects the active set and performs coordinated beamforming.
  • Weighted Relaxation: The weighted norm is a convex SOCP-relaxation surrogate whose weights incorporate system parameters such as transport-link consumption and amplifier efficiency.

2) RRH Ordering:

The RRH ordering criterion combines beamforming and system-level parameters to prioritize RRHs for switching off. It then supports selecting a feasible active set through coefficient sorting and search.

  • RRH Ordering: The initial ordering based only on smaller beamforming coefficients is reported to degrade performance.A smaller coefficient may reflect lower beamforming gain, but that alone is not a sufficient switching criterion.
  • RRH Ordering: The ordering accounts for channel power gain because higher κ_l contributes more to Cloud-RAN sum capacity and should not be prioritized for deactivation.The capacity argument uses equal power allocation and an upper bound based on total receive SNR.
  • RRH Ordering: A smaller θ_l prioritizes an RRH for switching off when it has lower beamforming gain, lower channel power gain, lower amplifier efficiency, and higher transport-link power consumption.The criterion is designed to incorporate system parameters rather than relying only on beamformer sparsity.
  • RRH Ordering: The bi-section GSBF procedure sorts θ_l ascending, sets the smallest coefficients to zero, and uses feasibility tests to determine the maximum number of switchable RRHs.It then solves the optimization problem for the resulting active RRH set.

C. Iterative GSBF Algorithm

The iterative GSBF algorithm enhances group sparsity through reweighted mixed-norm minimization. It uses system-aware initialization, updates weights iteratively, and then applies the RRH ordering criterion.

  • Iterative GSBF Algorithm: A nonzero minimum group coefficient can bias estimates of which RRHs should be switched off, so an MM-based procedure is used to enhance group sparsity.The iterative method is motivated by the need to obtain a more reliable sparse beamformer.
  • Iterative GSBF Algorithm: The method replaces the convex ℓ1 relaxation with a log-sum-based surrogate whose concavity enables an MM majorization step.The log-sum penalty is described as potentially more sparsity-encouraging than the weighted mixed norm.
  • Iterative GSBF Algorithm: The reweighted GSBF method updates mixed ℓ1/ℓ2-norm weights using the beamformer estimated at the previous minimization step.This iterative reweighting is intended to encourage group sparsity more strongly than the initial convex relaxation.
  • Iterative GSBF Algorithm: Initialization uses channel power gain and system parameters so RRHs with higher transport power, lower amplifier efficiency, and lower channel gain receive heavier penalties.This differs from starting with an unweighted sparsity solution.
  • Iterative GSBF Algorithm: The algorithm typically converges within 20 iterations in simulation and applies the ordering criterion afterward to determine the final active RRH set.The simulations set the maximum iteration count to m_max = L.

2) Iterative Search Procedure:

The iterative search procedure evaluates feasible active-RRH sets rather than assuming that maximizing RRH deactivation minimizes total network power. Simulations compare the proposed approach with coordinated, exact, sparse, and relaxed optimization baselines.

  • Iterative Search Procedure: Minimizing transport-network power alone may not minimize total network power, so the procedure searches across candidate active-RRH sets.This is a conservative alternative to the bi-section strategy, which switches off as many RRHs as possible.
  • Iterative Search Procedure: The search evaluates P*(A[i]) for progressively larger inactive sets and requires no more than L SOCP solves.The selected set minimizes network power among the feasible candidates.
  • Iterative Search Procedure: The iterative GSBF algorithm updates weights until convergence or a maximum iteration count, then tests candidate RRH deactivations and chooses the minimum-power feasible set.The final step jointly obtains the optimal RRH set and beamformers.
  • Simulation Setup: Each simulation point averages 50 randomly generated network realizations under a standard cellular channel model.The channel model includes path loss, shadowing, antenna gain, and small-scale fading.
  • Simulation Setup: The comparisons include all-active coordinated beamforming, globally optimal MINLP for small networks, conventional sparsity, and relaxed MINLP baselines.Their stated complexities differ: MINLP grows exponentially, while relaxed MINLP grows linearly with L.

A. Network Power Consumption versus Target SINR

The simulations compare average network power across target SINR, transport-link power, and user-count settings. The proposed greedy and group-sparse beamforming methods provide strong power reductions with complexity-dependent performance tradeoffs.

  • Target SINR: The proposed schemes reduce network power consumption by 40% in the low QoS regime and by 20% in the high QoS regime.These reductions are reported for the target-SINR comparison.
  • Target SINR: The greedy algorithm achieves global optimum in the target-SINR experiment, matching the MINLP solution.This supports the effectiveness of its RRH selection rule.
  • Transport-link power: Both the greedy and iterative GSBF algorithms significantly outperform other algorithms when transport-link power consumption is high.The bi-section GSBF method is close to RMINLP while using lower complexity.
  • Number of mobile users: With O(L^2) complexity, greedy selection has the best low-complexity performance, while iterative GSBF with O(L) complexity outperforms RMINLP at the same complexity.The comparisons are reported for varying numbers of mobile users.
  • Number of mobile users: With O(log(L)) complexity, bi-section GSBF nearly matches RMINLP and outperforms conventional SP, making it attractive for large-scale Cloud-RAN.The conclusion recommends bi-section GSBF for large-scale deployments and iterative GSBF for medium-size networks.

APPENDIX A PROOF OF PROPOSITION 1

The appendix derives a tight positively homogeneous lower bound for the relevant objective and characterizes its convex formulation through matrix and dual-norm constructions.

  • Lower-bound derivation: The proof begins by deriving the tightest positively homogeneous lower bound of p(w).The bound is developed as the starting point for Proposition 1.
  • Lower-bound derivation: The lower bound is obtained by optimizing the scalar parameter λ, whose minimizing value is expressed using F(T(w)) and T(w).The resulting objective combines two terms multiplicatively.
  • Convex characterization: The convex-envelope construction introduces diagonal matrices U and V and evaluates the conjugate using indexed submatrices and vectors.The dual norm Ω*(y) is used in this characterization.
  • Proof identities: The proof invokes the Cauchy-Schwarz inequality and a second equality to establish the stated identities.These steps support the proposition’s equality relations.
  • Proof conclusion: The appendix states that the upper bound holds with equality, completing the key bound characterization.This equality is reported directly after the convex lower-bound result.

APPENDIX B PRELIMINARIES ON MAJORIZATION-MINIMIZATION ALGORITHMS

The appendix introduces majorization-minimization as an iterative surrogate-minimization method and explains why its objective values decrease monotonically.

  • MM framework: Majorization-minimization finds a local optimum by iteratively minimizing a surrogate function that majorizes the objective.The method is described as widely used in statistics and machine learning.
  • MM framework: For minimizing f(x) over F, the method constructs a majorization function g(x|x[m]) satisfying equality at the current iterate.The surrogate replaces the original objective during each iteration.
  • Iterative update: Each iteration minimizes the surrogate over F to obtain the next iterate x[m+1].The update is defined as the minimizer of g(x|x[m]) at iteration m.
  • Convergence property: The MM procedure decreases f(x) monotonically after each iteration.This property follows from the majorization definitions.
  • Convergence property: The decreasing property gives MM algorithms numerical stability.The appendix identifies this as a notable consequence of the iterative procedure.
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