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Energy-Efficient, Large-scale Distributed-Antenna System (L-DAS) for Multiple Users

Jingon Joung, Yeow Khiang Chia, Sumei Sun

arXiv:1312.1870v2cs.IT

TL;DR

The paper addresses unclear energy-efficiency behavior in large-scale distributed-antenna systems amid substantial computational, signaling, and energy costs. It models total power and decomposes EE optimization using antenna selection, user clustering, precoding, and power control. Simulations find that full-antenna MU-MIMO can be inefficient with processing overhead, more antennas do not always improve EE, and the proposed design outperforms the compared L-DAS and colocated systems.

  • Problem

    L-DAS energy-efficiency behavior is unclear because total transmit power omits transmitter overhead, while large scale creates major signaling, computational, and energy burdens.

  • Method

    The paper models L-DAS power consumption including overhead, formulates EE maximization, and uses channel-gain-based antenna selection with interference-based user clustering to create parallel cluster subproblems.

  • Results

    The proposed L-DAS design improves EE over non-clustering L-DAS and colocated antenna systems, while full-antenna MU-MIMO can be inefficient with nonnegligible processing overhead.

  • Takeaways & Limitations

    More distributed antennas do not necessarily produce higher EE, so antenna use and MU-MIMO processing overhead must be considered jointly.

  • Takeaways & Limitations

    Accurate measurement of the model parameters is outside the paper's scope.

Abstract

from arXiv · show

Large-scale distributed-antenna system (L-DAS) with very large number of distributed antennas, possibly up to a few hundred antennas, is considered. A few major issues of the L-DAS, such as high latency, energy consumption, computational complexity, and large feedback (signaling) overhead, are identified. The potential capability of the L-DAS is illuminated in terms of an energy efficiency (EE) throughout the paper. We firstly and generally model the power consumption of an L-DAS, and formulate an EE maximization problem. To tackle two crucial issues, namely the huge computational complexity and large amount of feedback (signaling) information, we propose a channel-gain-based antenna selection (AS) method and an interference-based user clustering (UC) method. The original problem is then split into multiple subproblems by a cluster, and each cluster's precoding and power control are managed in parallel for high EE. Simulation results reveal that i) using all antennas for zero-forcing multiuser multiple-input multiple-output (MU-MIMO) is energy inefficient if there is nonnegligible overhead power consumption on MU-MIMO processing, and ii) increasing the number of antennas does not necessarily result in a high EE. Furthermore, the results validate and underpin the EE merit of the proposed L-DAS complied with the AS, UC, precoding, and power control by comparing with non-clustering L-DAS and colocated antenna systems.

I. INTRODUCTION

The paper studies energy efficiency in large-scale distributed-antenna systems, where increasing scale creates uncertain cost-benefit tradeoffs and substantial computational, signaling, and energy burdens. It models L-DAS power consumption and decomposes EE optimization through antenna selection, user clustering, precoding, and power control.

  • Motivation: L-DAS extends distributed-antenna systems toward very large scale, but its energy-efficiency behavior remains unclear because network costs grow with size.The paper evaluates the tradeoff between L-DAS benefits and overhead energy consumption rather than relying only on spectral efficiency.
  • Problem formulation: The paper models transmitter power consumption including overhead and formulates EE maximization under per-antenna transmit-power and per-user-rate constraints.The optimization jointly selects distributed antennas, designs MU precoding, and controls transmit power.
  • Decomposition strategy: Channel-gain-based antenna selection and interference-based user clustering split the computationally intractable problem into cluster-based subproblems.The resulting subproblems support parallel processing and reduce computational complexity and signaling overhead.
  • Cluster-level design: Each cluster receives EE-aware precoding and per-cluster optimal or heuristic power control, with additional antenna assignment and clustering-threshold adaptation used to improve EE.The paper generalizes precoding and power-control results for L-DAS and evaluates average EE across clustering thresholds, user counts, and network sizes.
  • Results: Using all distributed antennas for MU-MIMO can be energy-inefficient when MU-MIMO processing has nonnegligible overhead power consumption.The result identifies processing overhead as a condition under which full-antenna use is not energy efficient.
  • Results: Increasing the number of distributed antennas does not necessarily yield high EE, while the proposed L-DAS design improves EE over non-clustering L-DAS and colocated antenna systems.The comparison combines antenna selection, user clustering, precoding, and power control.

II. L-DAS SYSTEM AND ITS ISSUES

The L-DAS connects a BBU to many distributed antennas through wired optical fronthaul, but its scale creates processing, fronthaul, propagation, signaling, and energy challenges. The proposed AS and UC enable parallel cluster processing to reduce complexity and signaling overhead while targeting energy efficiency.

  • System architecture: An L-DAS uses a BBU with baseband and RF modules connected to distributed antenna ports through optical fronthaul.Each antenna path converts signals between electrical and optical forms before RF transmission, and module power consumption is modeled explicitly.
  • System issues: Its large number of distributed antennas creates centralized computational delay and substantial MU-MIMO channel-state-information feedback overhead.The feedback burden grows because the number of distributed antennas can greatly exceed the number of users.
  • Proposed response: AS and UC permit parallel processing per cluster, reducing computational complexity, processing delay, feedback information, and signaling overhead.The paper leaves complete resolution of synchronization and remaining delay issues outside its scope.
  • System issues: Optical fronthaul and nearby distributed antennas can mitigate fronthaul and propagation delays under the stated deployment assumptions.The paper cites optical-fiber delay around 5 µs/km, residual tuning up to 15 ns, and 25–900 antennas with 30–200 m neighboring-antenna distances.
  • System issues: The paper focuses on unclear L-DAS energy-consumption behavior by characterizing energy efficiency and proposing energy-improving baseband algorithms.Activating many distributed antennas is expected to increase energy or power consumption, motivating the EE analysis.

III. EE MAXIMIZATION PROBLEM FORMULATION

The paper formulates L-DAS energy efficiency as throughput normalized by modeled transmitter power, then maximizes it over antenna selection, precoding, and power allocation under system constraints. The model separates transmit-power-dependent and power-independent consumption while acknowledging possible infeasibility and the limits of exhaustive optimization.

  • Signal model: The system models single-antenna UEs, an MU-MIMO channel matrix, transmit signals, precoding, power allocation, and additive white Gaussian noise.The received SINR determines each user's throughput through a logarithmic rate expression.
  • Power model: Total power consumption is divided into transmit-power-dependent and transmit-power-independent components.The independent component includes RF-circuit, baseband signal-processing, network-signaling, and fixed power terms.
  • EE objective: Energy efficiency is defined from system throughput and total transmitter power, with optimization variables S, W, and P.The formulation includes antenna selection, precoding, and power allocation as joint design variables.
  • Constraints: The optimization imposes per-antenna power, per-user rate, power-allocation, and antenna-selection constraints.The per-user rate constraints provide QoS requirements, while per-antenna limits reflect PA capability and radio regulations.
  • Feasibility: The problem may be infeasible because upper per-antenna power limits and lower rate requirements may conflict.Using all antennas can worsen infeasibility by increasing channel-matrix dimension and the likelihood of ill-conditioning under ZF precoding.

IV. ANTENNA SELECTION AND USER CLUSTERING

The proposed AS and UC methods decompose the original EE optimization into cluster-level subproblems. Clustering uses an SINR threshold to keep inter-cluster interference sufficiently small, enabling parallel computation and feedback.

  • Cluster decomposition: AS and UC decompose the original EE optimization into multiple subproblems organized by cluster.The decomposition is presented as a suboptimal strategy for addressing the complexity of solving the full problem.
  • User clustering: UEs, or equivalently selected DAs, are clustered using an SINR threshold that keeps inter-cluster interference sufficiently small.This interference condition supports splitting the original optimization problem across clusters.
  • Benefits: Cluster-based parallel computation and feedback reduce computational complexity and signaling information.The resulting parallel management makes the L-DAS more scalable for the targeted large-system setting.

A. Antenna Selection (AS) Algorithms

The paper motivates channel-aware AS because all-antenna ZF MU-MIMO can create ill-conditioned channels and excessive power requirements. It replaces high-complexity greedy selection with simpler algorithms that determine each UE's assigned DAs and the selection matrix.

  • Motivation: AS is motivated by the SE–EE tradeoff and the possibility that all-antenna ZF MU-MIMO increases power or causes infeasibility.An ill-conditioned channel can raise transmit power, while a power-limit violation can force all coupled ZF transmit powers downward.
  • Proposed AS: The proposed algorithms avoid this high complexity and determine the DA set M_u assigned to each UE together with the AS matrix S.The paper frames these as simple-yet-effective AS algorithms for large-size networks.
  • Optimization difficulty: The full EE optimization remains non-convex after continuous relaxation, lacks a computable upper bound, and therefore does not support BnC methods.This limitation reinforces the need for alternative selection procedures.

1) Channel-Gain-Based (CGB)-Greedy AS Algorithm:

The CGB-greedy AS algorithm assigns distributed antennas to users using channel-gain information, reducing the combinatorial allocation burden and signaling requirements. Users are then clustered using an SINR-derived distance metric so strongly interfering users can receive MU-MIMO support.

  • Antenna selection: RSSI can provide the channel-gain metric without additional resources, while location-based MDB-greedy AS can omit RSSI detection when user locations are available.
  • Antenna selection: CGB-greedy AS pairs each user with an available distributed antenna having the strongest channel gain, repeating until each user receives its predetermined number of antennas.Assigned antennas and users are removed from subsequent allocation steps.
  • Antenna selection: Full CSI is unnecessary for AS, and the original allocation problem has O(2^MU) combinatorial complexity.
  • Antenna selection: The greedy AS algorithm requires O(U) time plus O(MU log(MU)) sorting, substantially reducing complexity relative to existing greedy algorithms.
  • User clustering: The UC algorithm treats SINR as a distance metric, merging nearby users with strong inter-user interference into clusters for MU-MIMO precoding.

C. Cluster-based Subproblems

Cluster-based decomposition partitions the original optimization into independently solvable cluster subproblems, reducing CSI feedback and enabling parallel processing. The threshold γ controls the trade-off between interference, complexity, and decomposition optimality.

  • Threshold trade-off: Typical γ values between 20 dB and 30 dB are described as supporting negligible inter-cluster interference and short propagation distances under the paper’s assumptions.
  • Decomposition: Cluster-based subproblems can be solved in parallel over clusters, significantly reducing the computational complexity of the original problem.
  • Feedback reduction: The required CSI is reduced from MU complex values for the full channel matrix to ΣℓMℓUℓ complex values for the cluster channel matrices.Only columns corresponding to antennas assigned through AS are needed for each cluster.
  • Feedback reduction: In the illustrated cases, CSI requires 48 or 160 complex values, compared with 8,000 values for a system without AS and UC.
  • Threshold trade-off: Increasing γ enlarges clusters and reduces their number, while decreasing γ increases the number of clusters and can introduce optimality loss.

D. Adaptive Algorithms for Mu and γ

The adaptive algorithms tune antenna assignments and the clustering threshold to balance throughput, processing complexity, latency, and energy efficiency. Numerical results support an optimal γ, while adaptation frequency is constrained by network complexity and latency requirements.

  • Adaptive framework: The proposed framework combines AS, UC, precoding, and power control, with precoding and power control performed after the adaptive assignment and clustering steps.
  • Adaptive γ: Increasing γ enlarges clusters and reduces their number, increasing throughput through reduced inter-cluster interference but also increasing processing complexity.Larger clusters produce larger MU-MIMO matrices.
  • Adaptive γ: Decreasing γ creates smaller, more numerous clusters that reduce processing complexity through parallel processing but may decrease throughput because of increased actual inter-cluster interference.
  • Adaptive γ: Numerical results show an optimal γ, and adapting γ can manage actual inter-cluster interference to improve EE.
  • Adaptive γ: The number of γ adaptations is limited by network requirements for computational complexity and latency.
  • Adaptive Mu: The AS adaptation algorithm increases a user’s antenna count when power control is infeasible, selecting an additional antenna for the user with the weakest channel gain.

VI. POWER CONTROL

The paper develops cluster-based power control for both single-user and multi-user clusters, including optimal and heuristic methods. The optimal MU procedure converts the problem into repeated convex-feasibility checks within a bisection search, but its complexity motivates a non-iterative alternative.

  • Power-control methods: Per-cluster optimal power control methods are proposed for SU and MU clusters, alongside a simple heuristic method for MU clusters.
  • Optimal MU power control: For fixed ξ, the reformulated power-control constraints are convex or linear, so feasibility can be checked through a convex feasibility problem.
  • Optimal MU power control: The MU power-control problem is quasi-convex, allowing the optimal ξ to be found through bisection with sequential convex-feasibility solves.
  • Complexity: The complexity of Algorithm 5 for cluster ℓ is approximately O(M^3.5) per iteration.
  • Complexity: The number of iterations needed to reach within ε of optimal energy efficiency is log 1/ε, motivating a non-iterative method to avoid high complexity.

B. Heuristic(Optimal) Power Control for MU(SU) Cluster

The paper develops optimal and heuristic per-cluster power control by scaling users’ relative powers under power and quality-of-service constraints. The heuristic maximizes an EE lower bound to obtain a tractable closed-form solution, with marginal performance loss and no optimality loss for SU clusters.

  • Heuristic power control: The power-control matrix assigns each UE a relative power portion based on its minimum power requirement for the target rate.The relative factors satisfy the cluster power-limit and QoS constraints after scaling by a common factor α_ℓ.
  • Heuristic power control: The common scaling factor α_ℓ is bounded by lower and upper limits derived from the power and QoS constraints.These bounds define the feasible region for the power-control solution.
  • Heuristic power control: The heuristic method maximizes an EE lower bound, replacing the original objective with a tractable surrogate based on the minimum user rate.The lower bound is described as tight in the cited discussion.
  • Optimal power control: The resulting objective is quasi-concave in α_ℓ, so the unconstrained maximizer is projected onto the feasible interval to obtain the optimal feasible scaling.The procedure first sets the derivative to zero, then applies the feasibility bounds.
  • Performance and complexity: The heuristic solution has a tractable closed form, with marginal performance degradation and no optimality loss for an SU cluster.The paper attributes the SU result to the EE lower bound being identical to the SU-cluster EE.
  • Performance and complexity: The heuristic power-control method has O(M_ℓ^3) complexity because it includes multiplication of two M_ℓ-dimensional matrices.This provides a lower-complexity alternative to the per-cluster optimal procedure.

VII. PERFORMANCE EVALUATION AND DISCUSSION

The evaluation examines average EE under practical L-DAS power-consumption assumptions and varying clustering thresholds. It shows that MU-processing overhead, clustering, and colocated-system path loss strongly shape the energy-efficiency trade-offs.

  • Evaluation setup: The simulations evaluate average EE over clustering threshold, user count, and network size using practical parameter settings.The evaluation includes different power-consumption models and compares L-DAS behavior with a colocated antenna system.
  • Power-consumption assumptions: The simulation models TPI power consumption as dominant over TPD because distributed antennas transmit at low power.With c = 2.63, TPD accounts for less than 3% of TPI power consumption in the simulation.
  • Clustering-threshold effects: MU-MIMO-processing power consumption significantly decreases EE, creating an optimal clustering threshold γ* beyond which EE declines.When the MU-processing penalty increases, the optimal threshold decreases and high EE favors more SU clusters.
  • Clustering-threshold effects: The optimal clustering threshold depends on U, M, and the power-consumption model, making it difficult to determine analytically.The paper therefore evaluates threshold behavior numerically.
  • Power-control comparison: The EE gap between per-cluster optimal and heuristic power control is negligible near the maximum-EE point when MU-precoding power has a nonnegligible penalty.This supports using the tractable heuristic method in the evaluated setting.
  • L-DAS versus L-CAS: The colocated antenna system has very poor EE because its large path losses require high power consumption.Its comparison uses a 60% PA efficiency and increased signal-processing power in the simulation.

B. Average EE over Number of Users

The user-count evaluation shows that the best clustering strategy depends on MU-processing overhead, while network-size scaling creates an EE optimum under nonzero signaling power. The paper concludes that AS and UC reduce computational and signaling burdens while supporting EE gains.

  • Average EE over number of users: For β = 0.5, full MU achieves higher EE than full SU under heuristic power control because its throughput advantage outweighs MU-processing overhead.As the number of UEs increases, the fixed γ = 22 dB clustering scheme overtakes full MU because MU-processing power becomes dominant; full MU is better below nine UEs.
  • Average EE over number of users: Adaptive antenna assignment and clustering can improve EE across user counts, while per-cluster optimal power control provides an additional improvement.The simulations use iterative adaptation of the assigned antennas and clustering threshold.
  • Average EE over network size: As the network size M increases, average EE first rises and then falls because antenna-selection freedom reduces path loss while signaling power increases.With Psig = 50 nW/Hz, the observed optimal network size is around M = 400.
  • Conclusion: The proposed channel-gain-based AS and SINR-threshold-based UC reduce precoding and power-control complexity together with signaling overhead.Iterative adaptation of assigned antennas and clustering threshold is also considered.
  • Conclusion: Remaining L-DAS issues include deployment, synchronization, CSI-error robustness, optical-fronthaul infrastructure cost, and quantitative L-DAS–L-CAS comparisons including capital and operating expenditures.These topics are identified as directions for further work.
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