PaperlayerView exact revision on arXiv

Source-linked AI summary

Optimality Properties, Distributed Strategies, and Measurement-Based Evaluation of Coordinated Multicell OFDMA Transmission

Emil Björnson, Niklas Jaldén, Mats Bengtsson, Björn Ottersten

arXiv:1209.2138v1cs.ITmath.IT

TL;DR

Multicell coordination can improve performance, but its backhaul and computational demands complicate resource allocation. The paper proposes dynamic cooperation clusters and derives optimality properties to build centralized and distributed strategies. On measured channels, the strategies perform close to their respective benchmarks, while joint transmission is sensitive to synchronization errors.

  • Problem

    Inter-cell interference limits multicell performance, while coordination can require substantial backhaul signaling and computational resources.

    Source: §I · p. 1

  • Method

    The paper introduces dynamic cooperation clusters and derives optimality properties used to construct low-complexity centralized and distributed resource-allocation strategies.

    Source: §I · p. 2

  • Results

    Measured-channel evaluation finds substantial gains over single-cell processing, with CVSINR close to optimal and DVSINR close to expected distributed-scheme performance.

    Source: §VII · p. 13

  • Takeaways & Limitations

    The measured-channel results show that multicell coordination improves average terminal performance, while the distributed strategy offers a practical alternative when centralized iterative solutions are unavailable.

    Source: §I · p. 2, §VII · p. 13

    Joint transmission and CVSINR are very sensitive to synchronization errors because they rely on coherent interference cancellation.

    Source: B. Results for Evaluation Scenario B · p. 13

Abstract

from arXiv · show

The throughput of multicell systems is inherently limited by interference and the available communication resources. Coordinated resource allocation is the key to efficient performance, but the demand on backhaul signaling and computational resources grows rapidly with number of cells, terminals, and subcarriers. To handle this, we propose a novel multicell framework with dynamic cooperation clusters where each terminal is jointly served by a small set of base stations. Each base station coordinates interference to neighboring terminals only, thus limiting backhaul signalling and making the framework scalable. This framework can describe anything from interference channels to ideal joint multicell transmission. The resource allocation (i.e., precoding and scheduling) is formulated as an optimization problem (P1) with performance described by arbitrary monotonic functions of the signal-to-interference-and-noise ratios (SINRs) and arbitrary linear power constraints. Although (P1) is non-convex and difficult to solve optimally, we are able to prove: 1) Optimality of single-stream beamforming; 2) Conditions for full power usage; and 3) A precoding parametrization based on a few parameters between zero and one. These optimality properties are used to propose low-complexity strategies: both a centralized scheme and a distributed version that only requires local channel knowledge and processing. We evaluate the performance on measured multicell channels and observe that the proposed strategies achieve close-to-optimal performance among centralized and distributed solutions, respectively. In addition, we show that multicell interference coordination can give substantial improvements in sum performance, but that joint transmission is very sensitive to synchronization errors and that some terminals can experience performance degradations.

I. INTRODUCTION

The paper addresses inter-cell interference and the complexity of multicell coordination with a framework that limits each base station’s coordination to selected terminals. It formulates resource allocation broadly and derives optimality properties used by centralized and distributed strategies, evaluated on measured channels.

II. GENERAL MULTICELL SYSTEM MODEL

  • The system model combines OFDMA with SDMA/MIMO, and assumes single-user detection so receivers treat co-terminal interference as noise.The model assumes perfect channel knowledge for coordinated terminals and synchronous joint transmission.Source: §I · p. 1, §II · p. 3

I. INTRODUCTION

  • The framework targets inter-cell interference and coordination overhead, which make practical centralized multicell optimization difficult in large networks.Fixed clusters remain exposed to out-of-cluster interference, while a dynamic approach described in prior work assumed global coordination.Source: §I · pp. 1–2
  • The resource-allocation problem jointly optimizes precoding and scheduling using arbitrary monotonic SINR-based utilities and arbitrary linear power constraints.The utilities can represent measures such as data rates, error rates, or mean square errors.Source: §I · p. 2, §II · p. 3
  • The authors propose centralized and distributed low-complexity resource-allocation strategies and evaluate them using measured channel vectors from a typical urban macro-cell environment.The evaluation considers average and fixed-location performance and studies robustness to synchronization imperfections.Source: §I · p. 2

II. GENERAL MULTICELL SYSTEM MODEL

  • Dynamic cooperation clusters let each base station coordinate interference toward C_j terminals while serving data to the subset D_j, spanning scenarios from interference channels to ideal network MIMO.Terminals outside the coordination set are treated as experiencing negligible interference from that base station.Source: §II · p. 2, §I · p. 2

A. Examples: Two Simple Multicell Scenarios

The paper illustrates its framework with ideal network MIMO and a two-user interference channel, then formulates multicell resource allocation through general utility maximization and a convex QoS feasibility problem. The latter offers an efficient analysis route but requires individual QoS targets.

A. Examples: Two Simple Multicell Scenarios

  • Ideal network MIMO has every transmitter serve and coordinate interference to every terminal, whereas the two-user interference channel has each base station serve one terminal while coordinating interference to the other.The examples use total-power constraints for network MIMO and per-transmitter power constraints for the interference channel.Source: A. Examples: Two Simple Multicell… · p. 3, 2) Two-user Interference Channel · p. 3

III. PROBLEM FORMULATION

  • The main problem maximizes system utility over resource allocation, with terminal and system performance modeled by strictly increasing functions of SINRs.The utility can represent weighted max-min or weighted-sum performance.Source: §III · p. 4
  • Problem (P1) jointly optimizes resource allocation and is generally non-convex and NP-hard.The paper also considers (P2), a QoS-constrained formulation with predefined SINR targets.Source: §III · p. 4
  • With fixed power constraints, (P2) is convex and can be solved efficiently, and solutions meeting the optimal SINRs are also optimal for (P1).The convex formulation requires individual QoS targets, whose optimal values are generally unknown.Source: §III · pp. 4–5

IV. PROPERTIES OF OPTIMAL RESOURCE ALLOCATION

The paper derives three properties of optimal resource allocation: single-stream beamforming, conditions for full power usage, and a parametrization of optimal precoding. These properties reduce the search space and inform the proposed low-complexity strategies.

IV. PROPERTIES OF OPTIMAL RESOURCE ALLOCATION

  • Single-stream beamforming is an optimality property of the resource-allocation solution.Source: §IV · p. 5
  • The analysis derives conditions under which the optimal solution uses full available power.Source: §IV · p. 5
  • Optimal precoding strategies can be parametrized, reducing the search space and supporting the low-complexity strategies evaluated in the paper.Source: §IV · p. 5

A. Optimality of Single-Stream Beamforming

For (P1) and (P2), rank-one signal correlation matrices suffice for optimality; higher-rank solutions can match but not outperform them. This reduces the search space and simplifies implementation.

A. Optimality of Single-Stream Beamforming

  • A rank-one solution is sufficient even under the stated general utility functions and power constraints, although higher-rank solutions may achieve the same performance.The paper’s toy example illustrates why rank one is not a necessary condition for every optimum.Source: A. Optimality of Single-Stream… · p. 5
  • If the problem is feasible, it has a single-stream beamforming solution with rank(S_kc) ≤ 1 for every terminal and subcarrier.The result is sufficiency, not a claim that every optimal solution must have rank one.Source: A. Optimality of Single-Stream… · p. 5
  • Restricting the search to rank-one matrices reduces the solution space and simplifies implementation, since higher-rank transmission requires vector coding or successive interference cancellation.The result generalizes earlier single-stream optimality results to the paper’s general multicell framework and arbitrary linear power constraints.Source: A. Optimality of Single-Stream… · p. 5

B. Conditions for Full Power Usage

With general linear power constraints, full power need not be optimal because signal gains must be balanced against co-terminal interference. The paper gives conditions for when power constraints are active or a transmitter should use full power.

B. Conditions for Full Power Usage

  • In the two-user example, only BS2 uses full power at the max-min optimum, with SINR1 = SINR2 = 10/3.Increasing BS1’s power would decrease SINR2 and degrade performance in this example.Source: B. Conditions for Full Power Usage · p. 5
  • At least one power constraint is active in some optimal solution, but general linear constraints do not require every transmitter or antenna to use full power.The paper frames this as a balance between increasing signal gains and limiting co-terminal interference.Source: B. Conditions for Full Power Usage · pp. 5–6
  • With only per-transmitter power constraints, BS_j should use full power when |C_j| ≤ N_j.The condition also holds when fewer than N_j terminals in C_j are allocated to some subcarrier.Source: B. Conditions for Full Power Usage · p. 6

C. Parametrization of Optimal Precoding Strategies

The optimal allocation can be parameterized directly by a small set of values between zero and one, governing both precoding and subcarrier scheduling. This structure applies across the stated strictly increasing utility and quality functions.

C. Parametrization of Optimal Precoding Strategies

  • The parameters determine a transmit strategy directly, without requiring an optimization problem to be solved for each parameter choice.The theorem gives the optimal solution through power allocations and beamforming vectors, with parameters ω_l and λ_kc in [0, 1].Source: C. Parametrization of Optimal… · pp. 6–7
  • The optimal precoding and scheduling can be expressed using K_rK_c + L real-valued parameters between zero and one.The parameter count is much smaller than the search over K_rK_c positive semidefinite transmit correlation matrices.Source: C. Parametrization of Optimal… · pp. 6–7
  • The parameterization applies to any strictly monotonically increasing outer utility and terminal quality functions.It includes one parameter per terminal and subcarrier, even when multiple base stations participate.Source: C. Parametrization of Optimal… · p. 7
  • Compared with prior parametrizations, the method generally uses fewer parameters, with linear rather than quadratic growth in the cited MISO interference-channel example.The paper notes an exception: prior parametrizations are superior when K_t = K_r = 2 because they consider only per-transmitter power constraints.Source: C. Parametrization of Optimal… · p. 7
  • Theorem 3’s parameters can be searched iteratively or selected heuristically; SLNR beamforming corresponds to one such heuristic selection.The paper says fine-tuning the parameters can achieve better performance than those heuristic strategies.Source: C. Parametrization of Optimal… · p. 7

V. LOW-COMPLEXITY OFDMA RESOURCE ALLOCATION

The proposed low-complexity strategies exploit the optimality properties to allocate OFDMA resources. The centralized approach uses global information, while the distributed approach uses local channel knowledge and sequential allocation steps.

V. LOW-COMPLEXITY OFDMA RESOURCE ALLOCATION

  • The resource allocation problem is generally NP-hard, motivating low-complexity strategies that exploit the derived optimality properties.The paper reports close-to-optimal performance in its measurement-based evaluation and optimal multiplexing gain in certain scenarios.Source: §V · p. 7

A. Centralized Resource Allocation

  • The centralized CVSINR strategy schedules terminals on subcarriers, selects parameters heuristically, calculates single-stream beamforming, and rescales to meet power constraints.Its heuristic parameter choices use the weighted-sum weights and transmitter power limits.Source: A. Centralized Resource Allocation · p. 7

B. Distributed Resource Allocation

  • Centralized allocation requires global CSI and joint processing, creating substantial backhaul-signaling and computational demands in large systems.This motivates a distributed CVSINR version based on local CSI, with lower performance but more reasonable system requirements.Source: B. Distributed Resource Allocation · pp. 7–8
  • The distributed strategy assigns subcarriers, power, and beamforming sequentially using local CSI, with limited signaling to coordinate interference.Each terminal is served by one base station per subcarrier; this reduces synchronization requirements, with small or no performance loss reported in Section VI.Source: B. Distributed Resource Allocation · p. 8

C. Step 1: Subcarrier Allocation

Subcarrier scheduling is performed independently because subcarriers are coupled only through power constraints. The distributed strategy adapts prior-slot schedules while coordinating interference toward terminals served by other transmitters.

C. Step 1: Subcarrier Allocation

D. Step 2: Power Allocation

Distributed power allocation uses zero-forcing simplifications to address unknown interference powers, while beamforming selection uses a parametrized structure with heuristic parameter choices. The allocation can favor strong subcarriers and highly weighted terminals, and the beamforming scheme reduces to SLNR under equal weights and noise terms.

D. Step 2: Power Allocation

  • The power-allocation step assumes zero-forcing to handle unknown interference powers, relying on scheduling to keep served and protected terminals within N_j.Source: D. Step 2: Power Allocation · p. 9
  • Exact SER can be used, but its derivative has no closed-form inverse for the allocation procedure.Source: D. Step 2: Power Allocation · p. 9
  • For the listed quality functions, power allocation has waterfilling behavior, favoring strong subcarriers and terminals with large weights.Terminals allocated zero or negligible power below threshold τ should be removed from the schedule, with adjacent base stations informed to adjust coordination sets.Source: D. Step 2: Power Allocation · p. 9

E. Step 3: Beamforming Selection

  • The optimal beamforming structure is stated for disjoint scheduled sets and per-transmitter power constraints; its parametrization requires heuristic parameter choices.The parameters reflect virtual-uplink SNR and normalized user priorities adjusted for noise power.Source: E. Step 3: Beamforming Selection · pp. 9–10
  • With identical user weights and noise terms, the proposed beamforming scheme reduces to SLNR beamforming.Source: E. Step 3: Beamforming Selection · p. 10

F. Final Strategy

The proposed strategies are evaluated on measured multicell channels, with centralized CVSINR close to optimal and distributed strategies improving on single-cell processing. CVSINR and DVSINR also achieve optimal multiplexing gain under the stated scheduling condition, with bounded absolute performance losses at high transmit power.

F. Final Strategy

  • DVSINR is a distributed resource-allocation strategy based on optimizing virtual SINRs, and in certain single-carrier scenarios it reduces to the DVSINR beamforming scheme in.CVSINR and DVSINR are suboptimal, but achieve the stated asymptotic multiplexing gain for a given subcarrier scheduling.Source: F. Final Strategy · p. 10
  • With |Sc ∩ Cj| ≤ Nj for every cell and subcarrier, CVSINR and DVSINR achieve multiplexing gain equal to the total number of scheduled terminals.At high transmit power, weighted sum rate grows as the scheduled-terminal count times log2(P), so absolute power offsets are bounded and relative loss vanishes.Source: F. Final Strategy · p. 10

VI. MEASUREMENT-BASED PERFORMANCE EVALUATION

  • The measured-channel evaluation considers a single subcarrier because the measurements are flat-fading, with results expected to represent general OFDMA systems.The authors note that subcarriers in weighted-sum-rate optimization are coupled only through power constraints and OFDMA systems typically have nearly flat power allocation across subcarriers.Source: §VI · p. 10
  • CVSINR is close to optimal, while distributed strategies reach about half the centralized performance; all studied strategies improve over single-cell processing.The distributed gap reflects inability to achieve coherent interference cancellation, rather than simply serving each terminal from one transmitter.Source: A. Results for Evaluation Scenario A · p. 12
  • For randomly located terminals, CVSINR is especially close to optimal at high output power, and both CVSINR and DVSINR improve individual rates over single-cell processing.Moving terminals benefit on average, while fixed-location terminals in Scenario B may experience performance degradations.Source: A. Results for Evaluation Scenario A · p. 12

B. Results for Evaluation Scenario B

On measured channels, the proposed strategies achieve substantial gains over single-cell processing, with centralized CVSINR close to optimal and DVSINR near the expected range for distributed schemes. The evaluation also finds sensitivity to synchronization errors and performance losses for some terminals.

B. Results for Evaluation Scenario B

  • In Scenario B, CVSINR provides close-to-optimal average weighted sum rate, while the gap to distributed approaches reflects their fewer degrees of freedom for interference cancellation.The difference between DVSINR and optimal joint transmission is 5–10 dB; the major gain over single-cell processing comes from interference cancellation for terminals in Cj.Source: B. Results for Evaluation Scenario B · p. 12
  • With multicell coordination, increased weighted sum rate does not monotonically improve every terminal’s rate: Terminal 3 gains substantially with almost equally strong channels from both base stations, while Terminal 2’s performance decreases below 10 dBm.The decrease is explained by BS1 modifying its precoding to avoid interference at Terminals 3 and 4.Source: B. Results for Evaluation Scenario B · pp. 12–13
  • The optimal solution and CVSINR are very sensitive to synchronization errors, whereas DVSINR and coordinated ZF are unaffected; tight synchronization is required to gain from centralized joint transmission.The evaluation emulates mismatches through random phase deviations in the actual channels, with zero phase standard deviation representing perfect synchronization.Source: B. Results for Evaluation Scenario B · p. 13

VII. CONCLUSION

  • The framework combines single-stream beamforming, full-power conditions, and a bounded-parameter precoding form to reduce the search space for resource allocation.It supports arbitrary monotonic SINR utilities and linear power constraints, and underlies centralized CVSINR and distributed DVSINR strategies.Source: §VII · p. 13
  • On measured urban macro-cell channels, CVSINR is close to optimal and DVSINR performs closely to what can be expected from distributed schemes, while both substantially outperform single-cell processing.The evaluation also finds that joint transmission is very sensitive to synchronization errors and that terminals in some cell locations can experience performance degradation.Source: §VII · p. 13

APPENDIX A PROOF OF LEMMA 4

The proof restricts the search to rank-one precoding solutions and uses convex feasibility and duality arguments. It also derives active SINR constraints and a relationship between the primal and auxiliary beamformers.

APPENDIX A PROOF OF LEMMA 4

  • By Theorem 1, it is sufficient to consider rank-one solutions of (P2) of the form S_kc = w_kc w_kc^H, with a nonzero beamformer.For these solutions, the denominator is nonzero.Source: Appendix A · p. 13
  • After choosing the phase of w_kc so that h_kc^H D_k w_kc > 0, the feasibility problem (P2) can be expressed in the stated form.The passage identifies the QoS constraints as second-order cones and the power constraints as semidefinite, making the problem convex with strong duality.Source: Appendix A · p. 13
  • At the optimum, all SINR constraints are active, so the proof replaces the inequalities with equalities to obtain (D2).This follows because otherwise some λ_kc could be increased, raising the cost function.Source: Appendix A · p. 14
  • The proof uses the Lagrangian stationary condition to relate the optimal auxiliary beamformer to w_kc, with the auxiliary beamformer identified up to scaling.The derivation also forms a Lagrange dual problem by setting w_kc = 0.Source: Appendix A · p. 14
Loading 1209.2138v1…