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Downlink and Uplink Energy Minimization Through User Association and Beamforming in Cloud RAN

Shixin Luo, Rui Zhang, Teng Joon Lim

arXiv:1402.4238v2cs.IT

TL;DR

The paper addresses energy minimization through joint DL and UL MU-AP association and beamforming, motivated by increasingly important high-bandwidth UL transmission. It uses UL-DL duality to convert the joint problem into an equivalent DL formulation and proposes two algorithms that improve network reliability/feasibility and energy-related tradeoffs.

  • Problem

    The paper studies joint DL and UL MU-AP association and beamforming for energy minimization as UL transmission becomes more important.

  • Method

    The approach establishes a virtual DL transmission for UL, converts the joint optimization into an equivalent DL problem with two inter-related subproblems, and applies GSO- and RIP-based algorithms.

  • Results

    The proposed algorithms improve network reliability/feasibility and energy efficiency and power-consumption tradeoffs between APs and MUs compared with existing methods.

  • Takeaways & Limitations

    UL-DL duality supports computationally efficient joint DL and UL association and beamforming design in C-RAN.

Abstract

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The cloud radio access network (C-RAN) concept, in which densely deployed access points (APs) are empowered by cloud computing to cooperatively support mobile users (MUs), to improve mobile data rates, has been recently proposed. However, the high density of active ("on") APs results in severe interference and also inefficient energy consumption. Moreover, the growing popularity of highly interactive applications with stringent uplink (UL) requirements, e.g. network gaming and real-time broadcasting by wireless users, means that the UL transmission is becoming more crucial and requires special attention. Therefore in this paper, we propose a joint downlink (DL) and UL MU-AP association and beamforming design to coordinate interference in the C-RAN for energy minimization, a problem which is shown to be NP hard. Due to the new consideration of UL transmission, it is shown that the two state-of-the-art approaches for finding computationally efficient solutions of joint MU-AP association and beamforming considering only the DL, i.e., group-sparse optimization and relaxed-integer programming, cannot be modified in a straightforward way to solve our problem. Leveraging on the celebrated UL-DL duality result, we show that by establishing a virtual DL transmission for the original UL transmission, the joint DL and UL optimization problem can be converted to an equivalent DL problem in C-RAN with two inter-related subproblems for the original and virtual DL transmissions, respectively. Based on this transformation, two efficient algorithms for joint DL and UL MU-AP association and beamforming design are proposed, whose performances are evaluated and compared with other benchmarking schemes through extensive simulations.

I. INTRODUCTION

This paper formulates joint DL and UL MU-AP association and beamforming for C-RAN energy minimization, motivated by interference, AP energy use, and growing UL demands. It addresses the resulting NP-hard problem through a virtual-DL transformation and efficient algorithms based on GSO and RIP.

  • Motivation: Dense AP deployment increases interference and energy consumption, motivating network-wide energy optimization for both DL and UL transmissions.The paper targets energy consumed by active APs and the transport network while accounting for DL and UL QoS requirements.
  • Problem formulation: The proposed optimization jointly assigns MUs to active APs, selects the active AP subset, and designs transmit powers and beamforming vectors.The objective is a weighted sum-power minimization subject to given DL and UL QoS requirements.
  • Motivation: DL-only association and AP-selection methods can yield inefficient or infeasible UL transmit power under DL–UL asymmetries and stringent UL applications.The paper cites high-bandwidth applications such as 1080p Skype video calling, requiring about 20 Mbps upload speed.
  • Contributions: The paper presents a unified DL–UL framework and evaluates two efficient algorithms through extensive simulations against benchmarking schemes.The stated direction combines association, active-AP selection, and coordinated transmission to address energy tradeoffs.
  • Challenges: The joint problem is NP hard, and existing GSO and RIP approaches for DL-only designs cannot be applied directly because of UL-specific scaling issues.The paper therefore develops methods specifically for the joint DL–UL setting.
  • Proposed approach: UL-DL duality enables a virtual DL representation of UL transmission, producing an equivalent DL problem with two inter-related transmission subproblems.The transformed formulation supports extensions of GSO and RIP, while a price-based iterative method further optimizes active APs under per-MU power constraints.

II. SYSTEM MODEL

The system models a densely deployed C-RAN in which centralized processing coordinates multi-antenna APs and single-antenna mobile users for both DL and UL communications. Channel, duplexing, fading, and beamforming assumptions define the joint transmission setting.

  • The C-RAN contains N distributed APs jointly supporting K mobile users for DL and UL communications.
  • The BBU jointly designs linear DL precoding and UL decoding with perfect channel knowledge; APs have multiple antennas, while users have one each.
  • A BBU pool centrally performs baseband processing and scheduling for APs connected through high-capacity, low-latency backhaul links.
  • Centralized processing coordinates transmission and reception among APs and can adapt coordination to traffic demand.
  • The model assumes quasi-static fading and defines DL and UL channel vectors between every AP and mobile user.
  • With TDD, UL and DL channels are assumed reciprocal; without that assumption, the channel vectors may differ.

A. DL Transmission

The transmission model represents DL as cooperative multi-AP single-stream beamforming and UL as user transmission with network-wide receive beamforming. Per-AP and per-user power limits and SINR expressions characterize both links.

  • In DL, all APs cooperatively transmit one single stream to each mobile user using an aggregate beamforming vector.
  • Each AP’s DL signal is formed from its local components of the users’ aggregate beamforming vectors.
  • The DL model imposes a maximum transmit-power constraint at every AP and evaluates each user’s SINR with interference treated as noise.
  • Receiver noises are modeled as zero-mean CSCG variables, with scalar noise at users and a noise vector at the APs.
  • In UL, each single-antenna mobile user transmits an information-bearing signal with its own transmit power and power limit.
  • All APs jointly receive UL signals, and each user’s UL SINR is evaluated after applying a network-wide receive beamforming vector.

C. Energy Consumption Model

The energy model combines AP transmit and static power, transport-network consumption, and MU transmit power, while allowing APs and links to sleep. The resulting joint optimization minimizes weighted DL and UL power under QoS and hardware constraints.

  • C. Energy Consumption Model: Total C-RAN energy includes AP and MU transmit power together with static power consumed by active APs and the transport network.
  • C. Energy Consumption Model: High-capacity backhaul makes transport-network power non-negligible, and the PON model separates OLT power from per-AP ONU and link power.
  • C. Energy Consumption Model: APs and associated transport links may enter sleep mode with negligible power consumption, saving each active AP’s static power contribution.
  • C. Energy Consumption Model: Users may connect to different AP sets for DL and UL, while an AP can sleep only when it serves no user.
  • III. PROBLEM FORMULATION AND TWO SOLUTION APPROACHES: The objective minimizes a weighted sum-power that trades energy consumption between active APs and mobile users.
  • III. PROBLEM FORMULATION AND TWO SOLUTION APPROACHES: The joint problem is non-convex because indicator functions introduce implicit integer programming, and its feasibility can be checked through separate DL and UL problems.
  • III. PROBLEM FORMULATION AND TWO SOLUTION APPROACHES: The formulation addresses DL–UL asymmetries in channels, traffic, and hardware while trading power between grid-powered APs and battery-powered users.

A. GSO based Solution

The GSO approach promotes AP selection through group-sparse beamforming, but direct application to the joint DL–UL problem fails because UL receive beamformers can shrink without changing UL SINR. Consequently, DL-only sparsity cannot ensure UL QoS or select APs jointly.

  • A. GSO based Solution: Because AP static power dominates transmit power, energy minimization favors solutions whose concatenated beamforming vectors have few nonzero AP blocks.
  • A. GSO based Solution: The mixed ℓ1,2 norm provides a convex approximation to ℓ0 and is used to encourage group sparsity across AP-associated beamforming blocks.
  • A. GSO based Solution: The paper focuses on ℓ1,2 and compares its performance with the potentially sparser ℓ1,∞ norm through simulations.
  • A. GSO based Solution: Replacing the objective with a group-sparsity penalty does not make the joint problem convex because the DL and UL constraints remain non-convex.
  • A. GSO based Solution: UL receive beamformers can be scaled arbitrarily toward zero without changing UL SINR, causing direct penalty minimization to drive them to zero.
  • A. GSO based Solution: The resulting DL-only active-AP selection neither lets UL contribute to AP selection nor guarantees UL QoS, so GSO cannot solve the joint problem directly.

B. RIP based Solution

The RIP-based formulation introduces binary AP activity variables and relaxes them to obtain a convex SOCP, but joint DL–UL constraints create limitations absent in the DL-only case.

  • RIP formulation: A DL-only incentive heuristic cannot be directly extended because selecting APs jointly for DL and UL requires an incentive measure reflecting both transmissions.The paper identifies this difficulty as arising from the relaxed RIP variables and the scaling behavior of UL receive beamforming.
  • RIP formulation: Binary variables ρ_n indicate whether each AP is active or sleeping in the reformulated problem.The active-sleep constraints use a big-M construction to couple AP activity with beamforming variables.
  • RIP formulation: The binary formulation is equivalent to the original problem, while the continuous relaxation provides a lower bound for its non-relaxed counterpart.The formulation is transformed into a convex SOCP after relaxing the binary variables.
  • RIP formulation: For the joint DL–UL problem, relaxing ρ_n to continuous values no longer yields a convex formulation because of the associated constraints.The relaxed indicator can also become decoupled from the virtual UL beamforming variables because of their scaling invariance.

IV. PROPOSED SOLUTION

The proposed solution converts the UL into a virtual DL transmission using UL–DL duality, then develops GSO- and RIP-based algorithms for joint DL–UL AP association and beamforming.

  • Overview: Two efficient approximate algorithms are proposed for the joint DL and UL problem, based on group-sparse optimization and relaxed-integer programming.Both approaches address AP selection and beamforming design after the UL-to-virtual-DL transformation.
  • UL–DL transformation: The UL transmission is represented by a virtual DL transmission, converting the joint optimization into inter-related original-DL and virtual-DL subproblems.This transformation follows from UL–DL duality and supports joint AP selection.
  • GSO-based solution: For the GSO approach, an equivalent DL-only problem preserves the optimal value and optimal DL/UL beamforming vectors of the infinite-power formulation.The resulting DL-only problem retains a group-sparse structure suitable for approximate solution.
  • GSO-based solution: The method replaces UL receive beamforming vectors with equivalent virtual-DL transmit vectors to resolve the receive-beamforming scaling issue.The virtual-DL SINR becomes non-scaling-invariant with respect to the replacement beamforming vectors.
  • GSO-based solution: The GSO algorithm iteratively identifies active APs, recomputes beamforming vectors, and obtains UL transmit powers through a linear program.Small entries in the AP activity variables are driven toward zero using an MM-style iterative update.

2) Per-AP and Per-MU Power Constraints:

With per-AP and per-MU power constraints, the algorithms add feasibility checks and AP-selection updates to ensure that the selected AP set can support the UL requirements.

  • Constraint handling: Per-AP power constraints are convex, so adding them does not require altering the preceding formulation.Per-MU constraints require separate treatment because the prior equivalent DL construction cannot directly handle them.
  • Constraint handling: The candidate AP set is first obtained under a UL sum-power constraint, after which feasibility is checked against individual MU power limits.If infeasible, additional APs are activated for the UL transmission.
  • AP selection: When MU power limits are violated, a price-based iterative method activates APs according to weighted channel gains normalized by static power consumption.The price weights reflect each MU’s required additional power relative to its power limit.
  • Complexity: The GSO algorithm has overall complexity approximately O(M^3.5K^3.5), with MM updates converging in approximately 10–15 iterations in simulations.The dominant computation is solving the SOCP subproblem.

B. Proposed Algorithm for (P1) based on RIP

The RIP algorithm relaxes AP activity variables, uses their optimized values as incentives for AP removal, and repeatedly checks feasibility while reducing weighted power.

  • RIP formulation: The RIP formulation introduces virtual-DL terms and relaxes binary AP activity variables to continuous values, yielding a convex SOCP.Separate coupled active-sleep constraints are used for the actual and virtual DL transmissions.
  • Incentive-based AP selection: The relaxed activity value ρ̌_n serves as an incentive measure for deciding which AP should be switched to sleep mode.Smaller values indicate APs more suitable for removal from the active set.
  • Incentive-based AP selection: The algorithm starts with all APs active and removes the AP with the smallest ρ̌_n while the weighted sum-power can still be reduced and feasibility is maintained.The process stops when the objective cannot improve or one of the relevant problems becomes infeasible.
  • Complexity: The RIP algorithm has overall complexity O(NM^3.5K^3.5), combining SOCP solution cost with O(N) worst-case AP-removal iterations.The computation is dominated by solving the SOCP problem.

V. NUMERICAL RESULTS

The numerical evaluation tests feasibility, power saving, and active-AP/MU power tradeoffs under homogeneous and heterogeneous C-RAN configurations.

  • The evaluation examines feasibility, network power saving, and active-AP/MU power-consumption tradeoffs.These are the three stated perspectives for assessing the proposed algorithms.
  • Homogeneous setup: The homogeneous setup assigns every AP static power consumption Pc,n = 2W and maximum DL transmit power P^DL_n,max = 1W.
  • Heterogeneous setup: The heterogeneous setup models HAPs with 50W static power and 20W transmit power, versus 2W and 1W for LAPs.
  • Simulation assumptions: Simulations use APs with two antennas, single-antenna MUs, and MU UL transmit-power limits of P^UL_i,max = 0.5W.
  • Simulation assumptions: The channel model uses pathloss exponent α = 3, Rayleigh fading, and receiver noise power σ2 = −50dBm.

A. Feasibility Performance

The proposed algorithms select active APs using joint DL/UL considerations and improve feasibility relative to reference-signal and DL-only schemes, especially under heterogeneous conditions.

  • Algorithms I and II select the same active AP set as exhaustive search in the heterogeneous example with 2 HAPs, 8 LAPs, and 8 MUs.Both DL and UL SINR targets are 8dB in this example.
  • The APIRSS scheme activates both HAPs, because their stronger transmit power makes them provide most MUs’ strongest DL reference signals.
  • MUIRSS selects APs closer to the MUs, whereas PAw/oUL selects only two LAPs because it optimizes AP selection from the DL perspective.
  • Across homogeneous and heterogeneous tests, APIRSS, MUIRSS, and PAw/oUL produce many more infeasible cases than the proposed algorithms.Feasibility requires all MUs’ DL and UL SINR constraints to be satisfied.
  • PAw/oUL performs best when DL requirements dominate but worst when UL requirements are stringent, which can make MU UL transmit powers infeasible.
  • Under heterogeneous conditions, APIRSS performs worse than MUIRSS at high UL SINR targets because HAP association can place MUs farther from serving APs.This imbalanced association can require higher MU transmit powers or cause UL infeasibility.

B. Sum-Power Minimization

The proposed joint-association algorithms approach exhaustive-search power performance, outperform joint processing benchmarks, and expose the tradeoff between active-AP and MU power.

  • Benchmarks: Exhaustive search provides the optimal active-AP set but has exponentially growing complexity in the number of APs.It is therefore practical only for C-RANs with a small number of APs.
  • Sum-power minimization: The proposed algorithms achieve power consumption similar to optimal exhaustive search and significant savings compared with joint processing.This pattern is reported for sum-power comparisons versus MU count and AP static power.
  • Algorithm comparison: The ℓ1,2- and ℓ1,∞-norm sparsity penalties have little effect on performance, while Algorithm I consistently outperforms Algorithm II.
  • Power tradeoff: As λ increases, active-AP power consumption increases while total MU power consumption decreases for all considered algorithms.
  • Power tradeoff: Algorithm I achieves a more favorable active-AP/MU power tradeoff than the compared algorithms.
  • Approach: The study jointly optimizes DL and UL MU-AP association and beamforming by converting UL transmission into a virtual DL transmission through UL-DL duality.The resulting equivalent DL problem contains inter-related subproblems for original and virtual DL transmissions.
  • Approach: Two efficient algorithms based on group-sparse optimization and relaxed-integer programming are proposed for the transformed problem.
  • Overall findings: Extensive simulations show improved network reliability and feasibility, energy efficiency, and active-AP/MU power-consumption tradeoffs over existing methods.
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