Optimal Resource Allocation in Coordinated Multi-Cell Systems

Optimal Resource Allocation in Coordinated Multi-Cell SystemsEmil Bjrnson

Assistant Professor

Div. of Communication Systems, ISY, Linkping University, Linkping, Sweden

Ericsson, Linkping, 20 October 2014

1Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 20142Biography: Emil Bjrnson1983: Born in Malm, Sweden

2007: Master of Science inEngineering Mathematics,Lund University, Sweden

2011: PhD in Telecommunications,KTH, Stockholm, SwedenAdvisors: Bjrn Ottersten, Mats Bengtsson

2012-2014: Postdoc at SUPELEC, Gif-sur-Yvette, France,Recipient of International Postdoc Grant from Sweden

2014: Assistant Professor at Linkping UniversityTopics: Massive MIMO, energy-efficiency, network optimization

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 20143Book ReferenceSeminar Based on Our Recent Book:

270 pagesE-book for free (from our homepages)Printed book: Special price $35, use link:https://ecommerce.nowpublishers.com/shop/add_to_cart?id=1595Matlab code is available online

Check out: http://www.commsys.isy.liu.se/en/staff/emibj29Optimal Resource Allocation in Coordinated Multi-Cell SystemsResearch book by E. Bjrnson and E. JorswieckFoundations and Trends in Communications and Information Theory, Vol. 9, No. 2-3, pp. 113-381, 2013Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 20144OutlineIntroductionMulti-cell structure, system model, performance measure

Problem FormulationResource allocation: Multi-objective optimization problem

Subjective Resource AllocationUtility functions, different computational complexity

Structural InsightsBeamforming parametrization

Extensions to Practical ConditionsHandling non-idealities in practical systems

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 20145SectionIntroductionBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 20146IntroductionProblem Formulation (vaguely):Transfer information wirelessly to usersDivide radio resources among users (time, frequency, space)

Downlink Coordinated Multi-Cell SystemMany transmitting base stations (BSs)Many receiving users

Sharing a Frequency BandAll signals reach everyone!

Limiting FactorInter-user interference

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 20147Introduction: Multi-Antenna Single-Cell TransmissionTraditional Ways to Manage InterferenceAvoid and suppress in time and frequency domainResults in orthogonal single-cell access techniques: TDMA, OFDMA, etc.

Multi-Antenna TransmissionBeamforming: Spatially directed signalsAdaptive control of interferenceServe multiple users: Space-division multiple access (SDMA)

Main difference from classical resource allocation!Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 20148Introduction: From Single-Cell to Multi-CellNave Multi-Cell ExtensionDivide BS into disjoint clustersSDMA within each clusterAvoid inter-cluster interferenceFractional frequency-reuse

Coordinated Multi-Cell TransmissionSDMA in multi-cell: Cooperation between all BSsFull frequency-reuse: Interference managed by beamformingMany names: co-processing, coordinated multi-point (CoMP), network MIMO, multi-cell processing

Almost as One Super-CellBut: Different data knowledge, channel knowledge, power constraints!

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 20149Basic Multi-Cell Coordination StructureGeneral Multi-Cell CoordinationAdjacent base stations coordinate interferenceSome users served by multiple base stations

Dynamic Cooperation Clusters

Inner Circle : Serve users with dataOuter Circle : Suppress interferenceOutside Circles:Negligible impactImpractical to acquire informationDifficult to coordinate decisions

E. Bjrnson, N. Jaldn, M. Bengtsson, B. Ottersten, Optimality Properties, Distributed Strategies, and Measurement-Based Evaluation of Coordinated Multicell OFDMA Transmission, IEEE Trans. on Signal Processing, 2011.Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201410Example: Ideal Joint TransmissionAll Base Stations Serve All Users Jointly = One Super Cell

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201411Example: Wyner ModelAbstraction: User receives signals from own and neighboring base stations

One or Two Dimensional VersionsJoint Transmission or Coordination between Cells

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201412Example: Coordinated BeamformingOne Base Station Serves Each UserInterference Coordination Across Cells

Special Case

Interference channelBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201413Example: Soft-Cell CoordinationHeterogeneous DeploymentConventional macro BS overlaid by short-distance small BSsInterference coordination and joint transmission between layers

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201414Example: Cognitive RadioSecondary System Borrows Spectrum of Primary SystemUnderlay: Interference limits for primary users

Other Examples

Spectrum sharing between operators

Physical layer securityBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201415Resource Allocation: First DefinitionProblem Formulation (imprecise):Select beamforming to maximize system utilityMeans: Allocate power to users and in spatial dimensionsSatisfy: Physical, regulatory & economic constraints

Some Assumptions:Linear transmission and receptionPerfect synchronization (whenever needed)Flat-fading channels (e.g., using OFDM)

Perfect channel knowledgeIdeal transceiver hardwareCentralized optimization

Relaxed at the endBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201416Multi-Cell System Model

One System Model for All Multi-Cell Scenarios!

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201417Multi-Cell System Model: Dynamic Cooperation Clusters (2)

Example: Coordinated BeamformingBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201418Multi-Cell System Model: Power ConstraintsWeighting matrix(Positive semi-definite)Limit(Positive scalar)

All at the same time!Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201419Multi-Cell System Model: Power Constraints (2)Recall:

Example 1, Total Power Constraint:

Example 2, Per-Antenna Constraints:

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201420Introduction: How to Measure User Performance?Mean Square Error (MSE)Difference: transmitted and received signalEasy to AnalyzeFar from User Perspective?

Bit/Symbol Error Probability (BEP/SEP)Probability of error (for given data rate)Intuitive interpretationComplicated & ignores channel coding

Information RateBits per channel useMutual information: perfect and long codingAnyway closest to reality?

All improveswith SINR:

SignalInterference + NoiseBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201421Introduction: Generic Measure User Performance

User Specific

Measure users satisfaction Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201422SectionProblem FormulationBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201423Problem FormulationGeneral Formulation of Resource Allocation:

Multi-Objective Optimization ProblemGenerally impossible to maximize for all users!Must divide power and cause inter-user interference

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201424Performance Region

2-UserPerformanceRegionCare aboutuser 2Care aboutuser 1BalancebetweenusersPart of interest:Pareto boundaryPareto Boundary

Cannot improve for any user without degrading for other usersOther Names

Rate RegionCapacity RegionMSE Region, etc.Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201425Performance Region (2)Can the region have any shape?

No! Can prove that:Compact setNormal set

Upper corner in region, everything inside regionBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201426Performance Region (3)Some Possible Shapes

User-Coupling

Weak: ConvexStrong: ConcaveScheduling

Time-sharing for strongly coupled users

Select multiple pointsHard: Unknown regionUtopia point(Combine user points)

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201427Performance Region (4)Which Pareto Optimal Point to Choose?Tradeoff: Aggregate Performance vs. Fairness

PerformanceRegionUtilitarian point(Max sum performance)

Egalitarian point(Max fairness)

Single user point

Single user point

No Objective Answer

Utopia point outside of region

Only subjective answers exist!Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201428SectionSubjective Resource AllocationBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201429Subjective ApproachSystem Designer Selects Utility FunctionDescribes subjective preferenceIncreasing and continuous function

Examples:

Sum performance:Proportional fairness:Harmonic mean:Max-min fairness:

Known as A Priori Approach

Select utility function before optimizationPut different weights to move betweenextremesBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201430Subjective Approach (2)Utility Function gives Single-Objective Optimization Problem:

This is the Starting Point of Many ResearchersAlthough selection of is Inherently subjectiveAffects the solvabilityShould always have a motivation in mind!

Pragmatic Approach

Try to Select Utility Function to Enable Efficient OptimizationBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201431Complexity of Single-Objective Optimization ProblemsClasses of Optimization ProblemsDifferent scaling with number of parameters and constraints

Main ClassesConvex: Polynomial time solutionMonotonic: Exponential time solutionArbitrary: More than exponential time Approximations neededPractically solvable Hard to even approximate

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201432Classification of Resource Allocation ProblemsClassification of Three Important ProblemsThe Easy problemWeighted max-min fairnessWeighted sum performance

We will see: These have Different ComplexitiesDifficulty: Too many spatial degrees of freedom Convex problem only if search space is particularly limitedMonotonic problem in generalBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201433Complexity Example 1: The Easy ProblemM. Bengtsson, B. Ottersten, Optimal Downlink Beamforming Using Semidefinite Optimization, Proc. Allerton, 1999.A. Wiesel, Y. Eldar, and S. Shamai, Linear precoding via conic optimization for fixed MIMO receivers, IEEE Trans. on Signal Processing, 2006.W. Yu and T. Lan, Transmitter optimization for the multi-antenna downlink with per-antenna power constraints, IEEE Trans. on Signal Processing, 2007.E. Bjrnson, G. Zheng, M. Bengtsson, B. Ottersten, Robust Monotonic Optimization Framework for Multicell MISO Systems, IEEE Trans. on Signal Processing, 2012.

Total PowerConstraints

Per-AntennaConstraints

General Constraints

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201434Complexity Example 2: Max-Min Fairness

Solution is on this lineBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201435Complexity Example 2: Max-Min Fairness (2)Simple Line-Search: BisectionIteratively Solving Convex Problems (i.e., quasi-convex)

Find start intervalSolve the easy problem at midpointIf feasible: Remove lower halfElse: Remove upper halfIterate

Subproblem: Convex optimizationLine-search: Linear convergenceOne dimension (independ. #users)Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201436Complexity Example 2: Max-Min Fairness (3)Classification of Weighted Max-Min Fairness:Quasi-convex problem (belongs to convex class)Polynomial complexity in #users, #antennas, #constraintsMight be feasible complexity in practice

T.-L. Tung and K. Yao, Optimal downlink power-control design methodology for a mobile radio DS-CDMA system, in IEEE Workshop SIPS, 2002.M. Mohseni, R. Zhang, and J. Cioffi, Optimized transmission for fading multiple-access and broadcast channels with multiple antennas, IEEE Journal on Sel. Areas in Communications, 2006.A. Wiesel, Y. Eldar, and S. Shamai, Linear precoding via conic optimization for fixed MIMO receivers, IEEE Trans. on Signal Processing, 2006.E. Bjrnson, G. Zheng, M. Bengtsson, B. Ottersten, Robust Monotonic Optimization Framework for Multicell MISO Systems, IEEE Trans. on Signal Processing, 2012.

Early work

Main references

Channel uncertaintyBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201437Complexity Example 3: Weighted Sum Performance

Opt-value is unknown!Distance from origin is unknownLine Hyperplane (dim: #user 1)Harder than max-min fairnessNon-convex problemBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201438Complexity Example 3: Weighted Sum Performance (2)Classification of Weighted Sum Performance:Non-convex problemPower constraints: ConvexUtility: Monotonic increasing/decreasing in beamforming vectorsTherefore: Monotonic problem

Can There Be a Magic Algorithm?No, provably NP-hard (Non-deterministic Polynomial-time hard)Exponential complexity but in which parameters?(#users, #antennas, #constraints)

Z.-Q. Luo and S. Zhang, Dynamic spectrum management: Complexity and duality, IEEE Journal of Sel. Topics in Signal Processing, 2008.Y.-F. Liu, Y.-H. Dai, and Z.-Q. Luo, Coordinated beamforming for MISO interference channel: Complexity analysis and efficient algorithms, IEEE Trans. on Signal Processing, 2011.Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201439Complexity Example 3: Weighted Sum Performance (3)Are Monotonic Problems Impossible to Solve?No, not for small problems!Monotonic Optimization AlgorithmsImprove Lower/upper bounds on optimum:Continue untilSubproblem: Essentially weighted max-min fairness problem

H. Tuy, Monotonic optimization: Problems and solution approaches, SIAM Journal of Optimization, 2000.L. Qian, Y. Zhang, and J. Huang, MAPEL: Achieving global optimality for a non-convex wireless power control problem, IEEE Trans. on Wireless Commun., 2009.E. Jorswieck, E. Larsson, Monotonic Optimization Framework for the MISO Interference Channel, IEEE Trans. on Communications, 2010.W. Utschick and J. Brehmer, Monotonic optimization framework for coordinated beamforming in multicell networks, IEEE Trans. on Signal Processing, 2012.E. Bjrnson, G. Zheng, M. Bengtsson, B. Ottersten, Robust Monotonic Optimization Framework for Multicell MISO Systems, IEEE Trans. on Signal Processing, 2012.

Monotonicoptimization

Early works

PolyblockalgorithmBRBalgorithmBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201440Complexity Example 3: Weighted Sum Performance (4)

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201441Summary: Complexity of Resource Allocation ProblemsRecall: All Utility Functions are SubjectivePragmatic approach: Select to enable efficient optimization

Good Choice: Any Problem with Polynomial complexityExample: Weighted max-min fairnessUse weights to adapt to other system needs

Bad Choice: Weighted Sum PerformanceGenerally NP-hard: Exponential complexity (in #users)Should be avoided Sometimes needed (virtual queuing techniques)

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201442Summary: Complexity of Resource Allocation Problems (2)Complexity Analysis for Any Dynamic Cooperation ClustersSame optimization algorithms!Extra characteristics can sometime simplifyMulti-antenna transmission: Higher complexity, higher performance

Ideal Joint TransmissionCoordinated BeamformingUnderlay Cognitive RadioBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201443SectionStructural InsightsBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201444Parametrization of Optimal BeamformingLagrange multipliers of Easy problem

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201445Parametrization of Optimal Beamforming (2)Geometric Interpretation:

Heuristic Parameter SelectionKnown to work remarkably wellMany Examples (since 1995): Transmit Wiener filter, Regularized Zero-forcing, Signal-to-leakage beamforming, Virtual SINR beamforming, etc.

E. Bjrnson, M. Bengtsson, B. Ottersten, Optimal Multiuser Transmit Beamforming: A Difficult Problem with a Simple Solution Structure, IEEE Signal Processing Magazine, 2014.Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201446SectionExtensions to Practical ConditionsBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201447Robustness to Channel UncertaintyPractical Systems Operate under UncertaintyDue to estimation, feedback, delays, etc.

Robustness to UncertaintyMaximize worst-case performanceCannot be robust to any error

Ellipsoidal Uncertainty SetsEasily incorporated in system modelSame classifications More variablesDefinition:

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201448Distributed Resource AllocationInformation and Functionality is DistributedLocal channel Knowledge and computational resourcesOnly limited backhaul for coordination

Distributed ApproachDecompose optimizationExchange control signalsIterate subproblems

Convergence to Optimal Solution?At least for convex problems

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201449Adapting to Transceiver Hardware ImpairmentsPhysical Hardware is Non-IdealPhase noise, IQ-imbalance, non-linearities, etc.Reduced calibration/compensation: Residual distortion remains!Non-negligible performance degradation at high SNRs

Model of Residual Transmitter Distortion:Additive noiseVariance scales with signal power

Same Classifications Hold under this ModelEnables adaptation: Much larger tolerance for impairments

Bjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201450SummaryBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201451SummaryMulti-Cell Multi-Antenna Resource AllocationDivide power between users and spatial directionsSolve a multi-objective optimization problemPareto boundary: Set of efficient solutionsSubjective Utility FunctionSelection has fundamental impact on solvabilityMulti-antenna transmission: More possibilities higher complexityPragmatic approach: Select to enable efficient optimizationPolynomial complexity: Weighted max-min fairnessNot solvable in practice: Weighted sum performanceParametrization of Optimal BeamformingPractical ExtensionsChannel uncertainty, Distributed optimization, Hardware impairmentsBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201452Main Reference: Our BookThorough Resource Allocation FrameworkMore parametrizations and structural insightsGuidelines for scheduling and forming clustersMatlab code distributed for algorithms

Other Convex Problems and Optimization Algorithms:

Further Extensions:Multi-cast, Multi-carrier, Multi-antenna users, etc.

GeneralSum PerformanceNP-hardMax-Min FairnessQuasi-ConvexEasy ProblemConvexGeneralZero ForcingSingle AntennaSum PerformanceNP-hardConvexNP-hardMax-Min FairnessQuasi-ConvexQuasi-ConvexQuasi-ConvexEasy ProblemConvexConvexLinearProportional FairnessNP-hardConvexConvexHarmonic MeanNP-hardConvexConvexBjrnson: Optimal Resource Allocation in Coordinated Multi-Cell Systems20 October 201453Questions?

My papers and presentations are available online:http://www.commsys.isy.liu.se/en/staff/emibj29