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Algorithms for Enhanced Inter Cell Interference Coordination (eICIC) in LTE HetNets

Supratim Deb, Pantelis Monogioudis, Jerzy Miernik, James P. Seymour

arXiv:1302.3784v1cs.NI

TL;DR

LTE HetNets must jointly determine macro resources offered to picos and UE association to manage interference and avoid pico underutilization. The paper develops a topology-, load-, and interference-aware eICIC algorithm using ABS and CSB, with provable guarantees and real-network evaluation. The algorithm performs within 90% of the optimal in typical settings and improves throughput percentiles over fixed eICIC configurations.

  • Problem

    LTE HetNets need joint decisions about macro resource sharing and UE association because macro interference and highest-signal association can limit pico performance.

  • Method

    The paper jointly optimizes ABS allocations and UE association, accounting for cell-specific load, propagation, macro-pico interference maps, and network topology.

  • Results

    The algorithm is typically within 90% of the optimal, improves the 5th, 10th, and 25th percentile throughput by 30−40% over Fixed-(15/40, 15 dB), and exceeds a local optimal heuristic by more than 80% for pico-footprint UEs.

  • Takeaways & Limitations

    eICIC gains are concentrated among edge UEs, with far-edge gains exceeding 200% and edge gains of 40−55% versus no-eICIC schemes.

Abstract

from arXiv · show

The success of LTE Heterogeneous Networks (HetNets) with macro cells and pico cells critically depends on efficient spectrum sharing between high-power macros and low-power picos. Two important challenges in this context are, {(i)} determining the amount of radio resources that macro cells should {\em offer} to pico cells, and {(ii)} determining the association rules that decide which UEs should associate with picos. In this paper, we develop a novel algorithm to solve these two coupled problems in a joint manner. Our algorithm has provable guarantee, and furthermore, it accounts for network topology, traffic load, and macro-pico interference map. Our solution is standard compliant and can be implemented using the notion of Almost Blank Subframes (ABS) and Cell Selection Bias (CSB) proposed by LTE standards. We also show extensive evaluations using RF plan from a real network and discuss SON based eICIC implementation.

I. INTRODUCTION

LTE HetNets combine high-power macros with low-power picos to improve coverage and capacity, but macro interference and signal-strength association can underuse picos. The paper jointly optimizes resource sharing and UE association through LTE-standard eICIC mechanisms.

  • Macro transmissions can severely interfere with pico downlink UEs, while higher macro signal strength can steer potential pico users toward macros.
  • The paper addresses two coupled questions: how macros should share downlink resources with picos and which UEs should associate with picos.
  • eICIC uses Almost Blank Subframes to reduce macro interference and Cell Selection Bias to influence UE association toward or away from picos.
  • The proposed framework accounts for UE locations and load, propagation maps, macro-pico interference maps, and network topology, with a provable constant-factor guarantee and linear scaling in cell count.
  • ICIC shares resources in the frequency and power-spectral-density domains, whereas eICIC shares them in time; CoMP mitigates interference through coordinated multi-cell transmission.

C. Related Work

The paper models LTE HetNet downlink interference using macro-pico relationships, UE-specific rates, and network topology. It distinguishes eICIC's time-domain coordination from related frequency-domain ICIC and coordinated-transmission approaches.

  • The system contains macro and pico eNBs, with macros providing broad coverage and picos filling coverage holes or enhancing capacity in hotspot locations.
  • The framework focuses on downlink transmissions and assumes no CoMP deployment, leaving CoMP-aware optimization for future work.
  • For each pico, the macro-pico interference set identifies macros that must remain silent during the pico's usable ABS subframes.
  • Pico UEs can still experience pico-pico interference during both ABS and non-ABS subframes, while macro-pico interference is restricted to non-ABS subframes.
  • The model considers static UEs with candidate macros and picos, RSRP-based selection, and average PHY rates under ABS and non-ABS subframes.

IV. PROBLEM STATEMENT AND COMPUTATIONAL HARDNESS

The paper formulates eICIC as a joint optimization of UE association and macro-pico time sharing. It uses weighted proportional fairness to balance throughput, fairness, LTE scheduling compatibility, and service differentiation.

  • The optimization jointly chooses UE association and the ABS subframes reserved for interfered picos over an ABS-period of typically Nsf = 40 subframes.
  • Macro variables specify transmitting subframes, while pico airtime variables distinguish ABS and regular subframes; Ru denotes each UE's average throughput.
  • Each UE associates with either its candidate macro or candidate pico, and its throughput cannot exceed the rate supported by the allocated airtime.
  • ABS constraints require all macros interfering with a pico to offer the pico's ABS subframes, while total-airtime constraints limit aggregate allocations.
  • The weighted proportional-fair objective maximizes P_u w_u ln R_u, balancing system throughput and UE-throughput fairness while allowing service differentiation through w_u.

OPT-ABS

OPT-ABS uses UE-specific macro and pico rates, the macro-pico interference graph, and an ABS-period to jointly determine ABS allocations, macro airtime, association, and throughput. The formulation can incorporate frequency-domain ICIC through modified input rates and interference data.

  • Inputs include candidate parent cells, ABS and non-ABS PHY rates, the macro-pico interference graph, and the total subframe count Nsf.
  • The optimization computes each pico's ABS subframes, each macro's remaining non-ABS subframes, UE association decisions, and UE throughputs.
  • The system utility is the weighted log-throughput objective represented as a function of the UE throughput vector R.
  • With ICIC, low- and high-power subcarrier bands alter spectral efficiencies and rates, while the interference graph and pico non-ABS rates also change.
  • The framework assumes no CoMP; supporting CoMP would require modified association, throughput, and total-airtime constraints.

A. Computational hardness

The optimal ABS problem is computationally hard, motivating a constant-factor approximation based on relaxing selected constraints and then recovering a feasible solution through rounding. A dual-based solution to the relaxed problem supports decomposition and distributed implementation.

  • Computational hardness: The OPT-ABS problem is NP-hard even with a single pico and a single interfering macro.The hardness follows by reducing SUBSET-SUM to OPT-ABS.
  • Approximation strategy: The proposed response to hardness is an algorithm with a constant-factor worst-case guarantee, reported to achieve at least 90% of the optimum in many practical scenarios.The paper motivates approximation because exact optimization is computationally hard.
  • Relaxation and recovery: The relaxed NLP ignores integrality constraints on A_p and N_m and temporarily allows a UE to receive resources from both macro and pico.The relaxed objective maximizes Util(R) subject to constraints (4)-(8).
  • Relaxation and recovery: Integer rounding converts the relaxed optimization output into a feasible solution for the original problem.Rounding addresses both fractional resource variables and the original exclusive-association requirement.
  • Dual solution: A dual-based approach decomposes the relaxed problem, reducing algorithmic complexity and making distributed implementation possible.The method uses subgradient-style dual updates with step-size γ and projection onto the non-negative orthant.

A. Greedy Primal Update: Decomposition Based Approach

The greedy primal update decomposes the relaxed Lagrangian maximization into independent UE, macro, and pico subproblems. Each component selects its corresponding resource or association variables using current dual prices.

  • Decomposition: The Lagrangian maximization decomposes into UE, macro, and pico subproblems that are each straightforward to compute.This decomposition is the basis of the greedy primal update.
  • User primal update: Each UE update chooses its rate R_u to maximize the UE-specific function F_u(p^t,R_u).The update is performed for every UE at iteration t+1.
  • Macro primal update: Each macro update chooses N_m by maximizing its macro-specific function G_m using the current primal and dual variables.The macro also computes the best candidate UE before assigning x_u values.
  • Pico primal update: Each pico update chooses A_p by maximizing its pico-specific function H_p over the current pico-associated variables.The pico computes candidate UE values y_u and breaks ties randomly.

B. Overall Algorithm for RELAXED-ABS

The overall RELAXED-ABS algorithm alternates greedy primal updates with dual-price updates for UEs, macros, and picos. It then averages the iterates to obtain the relaxed NLP solution.

  • Overall algorithm: Algorithm 1 initializes primal and dual variables, repeatedly performs primal and dual updates, and averages the iterates to obtain the optimal NLP values.The primal update uses the UE, macro, and pico update rules defined earlier.
  • Convergence parameters: The paper next derives the step-size and sufficient iteration count required by the RELAXED-ABS procedure.These parameters are analyzed in terms of problem parameters.

C. Step-size and Iteration Rule using Convergence Analysis

Convergence analysis characterizes the step size and iteration count using network parameters and bounds on the optimal dual variables. Disjoint interference-graph components can be solved independently, potentially in parallel.

  • Convergence analysis: The convergence analysis characterizes step size and iteration count in terms of ABS-RELAXED problem parameters rather than only generic convex-program quantities.The analysis adapts a generic dual-based convergence result to the structure of ABS-RELAXED.
  • Algorithmic execution: Algorithm 1 iterates the primal and dual updates for T iterations before averaging the iterates.UE, macro, and pico dual variables are updated during the loop.
  • Convergence analysis: The bound on the optimal dual-variable norm enables explicit step-size and iteration rules for RELAXED-ABS.This distinguishes the analysis from results expressed through a generic Slater vector.
  • Step-size and iteration rule: The iteration count depends on the maximum number of UEs in any cell rather than the overall number of UEs.The stated rule uses γ = O(ϵ/N^2_max U_max/ϵ^2 r_min) with maximum interferers typically small.
  • Step-size and iteration rule: Disjoint macro-pico interference-graph components can run RELAXED-ABS independently, possibly in parallel, using the prescribed component-level step-size and iteration rule.This can reduce the number of iterations required for the overall network.

VII. INTEGER ROUNDING OF RELAXED-ABS

The rounding procedure converts the relaxed ABS solution into a feasible integer solution by assigning each UE to one cell and rounding ABS allocations. Its guarantee depends on the optimization iterations and step-size, with evaluations typically reaching within 90% of optimal.

  • Rounding motivation: The rounding step addresses exclusive UE association and small feasibility violations in the relaxed solution.In the original problem, each UE receives resources from either a macro or a pico, while the relaxed solution may violate feasibility slightly.
  • UE association: Each UE associates with the macro or pico offering higher throughput in the relaxed solution.The resulting macro and pico UE sets are then used for subsequent ABS rounding and throughput computation.
  • ABS rounding: ABS rounding uses the association decisions to obtain feasible integer ABS and non-ABS subframe allocations.The algorithm then computes final macro and pico utilization and throughput values.
  • Guarantees: Algorithm 2 produces a feasible solution to OPT-ABS, with its worst-case guarantee determined by the iterations and step-size used beforehand.Proposition 3 states the guarantee for any δ > 0 after sufficiently many iterations.
  • Guarantees: The worst-case approximation factor is close to 2, while evaluations on several real topologies typically perform within 90% of optimal.The paper recommends the step-size and iteration count given by equation (22) in practice.

VIII. COMPUTING CELL SELECTION BIAS AND ABS PATTERNS

The paper converts optimized UE associations into LTE-compatible cell-selection biases and converts ABS counts into implementable subframe patterns. Biases are chosen to approximate the optimized association when exact realization is infeasible.

  • Implementation: The implementation computes CSB-based UE association and converts ABS numbers into ABS patterns for eICIC realization.These computations connect the joint optimization output to standard-compliant deployment mechanisms.
  • Cell Selection Bias: LTE association selects the cell maximizing received signal strength plus its cell-selection bias.The biases are designed so this rule reproduces the associations derived by the optimization algorithm.
  • Cell Selection Bias: When exact association cannot be achieved, the proposed bias computation minimizes association error relative to the optimized association.Macro biases are set to zero, and pico biases are selected by minimizing mean square error in the UE-association vector.
  • Bias constraints: Operator-imposed minimum and maximum pico biases are handled by restricting the bias search to [bp,min, bp,max].The procedure first fixes associations that remain unchanged at the minimum or maximum bias, then performs constrained bias determination.

B. Converting ABS numbers into ABS patterns

ABS counts are translated into consistent subframe patterns across the evaluated LTE network. The evaluation uses a real New York City RF plan, synthetic UE traffic, and comparisons across eICIC configurations.

  • ABS pattern conversion: A macro that leaves out k of Nsf subframes designates the first k consistently indexed subframes as ABS subframes.This simple conversion works when macros share the same permissible subframe set.
  • Evaluation framework: The evaluation combines an operational New York City LTE deployment with propagation maps, a macro-pico interference graph, and synthetic UE placements.Synthetic hotspots were created around Pico-10, Pico-3, Pico-5, and Pico-9.
  • Evaluation framework: The tested network uses 45 dBm macro transmit power, pico powers of 36, 30, and 27 dBm, 10 MHz bandwidth, and Nsf = 40.The setup uses 2 × 2 MIMO, with pico heights around 30 feet and macros typically higher than 100 feet.

B. Comparative eICIC Schemes

The proposed eICIC jointly configures ABS and CSB using network-specific information, outperforming fixed and local heuristic schemes while typically remaining within 90% of optimal.

  • The proposed eICIC jointly applies an algorithm, rounding scheme, and CSB procedure, whereas alternatives use fixed network-wide settings or a local heuristic.Fixed patterns include (ABS, CSB) combinations from (5/40, 5 dB) through (15/40, 15 dB).
  • 30−40%: the proposed scheme improves the 5th, 10th, and 25th percentile throughput over Fixed-(15/40, 15 dB) for all system UEs.For specific macros without interfering hotspot picos, the improvement exceeds 50%.
  • More than 80%: the proposed eICIC outperforms the local optimal heuristic for UEs in the pico-footprint area.Overall system performance is also better with the proposed scheme.
  • Typically within 90% of optimal: the algorithm achieves this across evaluated macro UE densities and pico transmission powers.The optimality gap compares the final algorithm with the RELAXED-ABS upper-bound solution.
  • More than 200%: proposed eICIC gains over no-eICIC pico deployment for far-edge UEs, reaching around 300% over no-pico deployment at the 5th percentile.Compared with no eICIC, edge-UE gains are 40−55% at the 5th−10th percentiles.
  • Optimal ABS and CSB settings vary by pico because they depend on traffic load and the number of macro interferers, explaining fixed schemes’ poorer performance.Pico-5 receives 4/40 ABS subframes despite a hotspot, while Pico-1 receives 6/40 without one.

X. SON AND EICIC: CHALLENGES AND DISCUSSION

The proposed SON architecture combines centralized eICIC optimization with RAN-provided measurements and network-planning inputs, while also outlining distributed computation. Its implementation must balance solution quality against reporting and X2 communication latency.

  • Architecture: A hybrid SON architecture combines a network planning tool with an engine that computes optimal eICIC configurations.The prototype operates alongside an operational wireless network.
  • Centralized optimization: The prototype executes the main optimization centrally at the OSS, using input distributions supplied and processed from RAN measurements.Centralization is described as offering a globally optimal solution when data inputs are accurate and timely.
  • RAN monitoring: eICIC requires RAN statistics on path loss, traffic load, and SINR, with periodic or event-based reporting trading latency against accuracy.The prototype can flexibly use these monitoring inputs.
  • Network-planning inputs: Network-planning inputs aggregate topology, calibrated path-loss models, and traffic-intensity information for generating optimization data.Traffic maps and SINR distributions can generate sample UE-location snapshots translated into PHY-layer rates with and without ABS.
  • Configuration from network data: Average-load inputs can support ABS and CSB configuration by generating multiple system-wide UE-location snapshots from traffic maps and SINR distributions.The method relies on downlink PHY-layer rates between UEs and macro or pico cells, with and without ABS.
  • Distributed implementation: Distributed eICIC computation is feasible through local network-element resources and X2 messaging, but X2 latency and asynchrony remain key challenges.The distributed approach trades centralized computation's communication latency profile against signaling and communication overhead.
  • Evaluation and implication: Using actual topology, propagation data, and traffic load, joint ABS and UE-association optimization is reported to produce substantial gains on a real RF plan.The paper argues that wireless networks should be optimized using real network data.
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