Optimal Resource Allocation in Coordinated Multi-Cell Systems Emil Björnson Post-Doc Alcatel-Lucent...
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Optimal Resource Allocation in Coordinated Multi-Cell Systems Emil Björnson Post-Doc Alcatel-Lucent Chair on Flexible Radio, Supélec, France & Signal Processing Lab, KTH Royal Institute of Technology, Sweden Seminar at Alcatel-Lucent, Stuttgart, 2013-02-06 2013-02-06 Emil Björnson, Post-Doc at SUPELEC and KTH 1
Optimal Resource Allocation in Coordinated Multi-Cell Systems Emil Björnson Post-Doc Alcatel-Lucent Chair on Flexible Radio, Supélec, France & Signal Processing
Optimal Resource Allocation in Coordinated Multi-Cell Systems
Emil Bjrnson Post-Doc Alcatel-Lucent Chair on Flexible Radio,
Suplec, France & Signal Processing Lab, KTH Royal Institute of
Technology, Sweden Seminar at Alcatel-Lucent, Stuttgart, 2013-02-06
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH1
Slide 2
Biography: Emil Bjrnson 1983: Born in Malm, Sweden 2007: Master
of Science in Engineering Mathematics, Lund University, Sweden
2011: PhD in Telecommunications, KTH, Stockholm, Sweden 2012:
Recipient of International Postdoc Grant from Sweden. Work with
Prof. Mrouane Debbah at Suplec for 2 years. 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH2 Optimal Resource Allocation in
Coordinated Multi-Cell Systems Research book by E. Bjrnson and E.
Jorswieck Foundations and Trends in Communications and Information
Theory, Vol. 9, No. 2-3, pp. 113-381, 2013
Slide 3
Outline Introduction -Multi-Cell Structure, System Model,
Performance Measure Problem Formulation -Resource Allocation:
Multi-Objective Optimization Problem Subjective Resource Allocation
-Utility Functions, Different Computational Complexity Structural
Insights -Beamforming Parametrization Extensions to Practical
Conditions -Handling Non-Idealities in Practical Systems
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH3
Slide 4
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH4
Introduction
Slide 5
Problem Formulation (vaguely): -Transfer Information Wirelessly
to Devices Downlink Coordinated Multi-Cell System -Many
Transmitting Base Stations (BSs) -Many Receiving Users -Sharing a
Common Frequency Band -Limiting Factor: Inter-User Interference
Multi-Antenna Transmission -Beamforming: Spatially Directed Signals
-Can Serve Multiple Users (Simultaneously) 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH5
Slide 6
Introduction: Basic Multi-Cell Structure Multiple Cells with
Base Stations -Adjacent Base Stations Coordinate Interference -Some
Users Served by Multiple Base Stations Dynamic Cooperation Clusters
-Inner Circle: Serve Users with Data -Outer Circle: Avoid
Interference -Outside Circles: Negligible Impact (Impractical to
Coordinate) 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and
KTH6
Slide 7
Example: Ideal Joint Transmission All Base Stations Serve All
Users Jointly 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and
KTH7
Slide 8
Example: Wyner Model Abstraction: User receives signals from
own and neighboring base stations One or Two Dimensional Versions
Joint Transmission or Coordination between Cells 2013-02-06Emil
Bjrnson, Post-Doc at SUPELEC and KTH8
Slide 9
Example: Coordinated Beamforming One base station serves each
user Interference coordination across cells 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH9
Slide 10
Example: Cognitive Radio Secondary System Borrows Spectrum of
Primary System Underlay: Interference Limits for Primary Users
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH10 Other
Examples Spectrum Sharing between Operators Physical Layer
Security
Slide 11
Introduction: Resource Allocation Problem Formulation
(imprecise): -Select Beamforming to Maximize System Utility -Means:
Allocate Power to Users and in Spatial Dimensions -Satisfy:
Physical, Regulatory & Economic Constraints Some Assumptions:
-Linear Transmission and Reception -Perfect Synchronization
(whenever needed) -Flat-fading Channels (e.g., using OFDM) -Perfect
Channel State Information -Ideal Transceiver Hardware -Centralized
Optimization 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH11
Will be relaxed
Slide 12
Introduction: Multi-Cell System Model 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH12
Slide 13
Introduction: Power Constraints 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH13 Weighting Matrix (Positive
semi-definite) Limit (Positive scalar)
Slide 14
Introduction: User Performance Measure Mean Square Error (MSE)
-Difference: transmitted and received signal -Easy to Analyze -Far
from User Perspective? Bit/Symbol Error Rate (BER/SER) -Probability
of Error (for given data rate) -Intuitive Interpretation
-Complicated & Ignores Channel Coding Information Rate -Bits
per Channel Use -Mutual Information: perfect and long coding -Still
Closest to Reality? 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and
KTH14 All improves with SINR: Signal Interf + Noise
Slide 15
Introduction: User Performance Measure 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH15
Slide 16
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH16 Problem
Formulation
Slide 17
General Formulation of Resource Allocation: Multi-Objective
Optimization Problem -Generally Impossible to Maximize For All
Users! -Must Divide Power and Cause Inter-User Interference
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH17
Slide 18
Definition: Performance Region R -Contains All Feasible
Performance Region 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and
KTH18 2-User Performance Region Care about user 2 Care about user 1
Balance between users Part of interest: Pareto boundary Pareto
Boundary Cannot Improve for any user without degrading for other
users
Slide 19
Performance Region (2) Can it have any shape? No! Can prove
that: -Compact set -Simply connected (No holes) -Nice upper
boundary 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH19
Normal set Upper corner in region, everything inside region
Slide 20
Performance Region (3) Some Possible Shapes 2013-02-06Emil
Bjrnson, Post-Doc at SUPELEC and KTH20 User-Coupling Weak: Convex
Strong: Concave Shape is Unknown Scheduling Time-sharing between
strongly coupled users
Slide 21
Performance Region (4) Which Pareto Optimal Point to Choose?
-Tradeoff: Aggregate Performance vs. Fairness 2013-02-06Emil
Bjrnson, Post-Doc at SUPELEC and KTH21 Performance Region
Utilitarian point (Max sum performance) Egalitarian point (Max
fairness) Single user point No Objective Answer Only subjective
answers exist!
Slide 22
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH22
Subjective Resource Allocation
Slide 23
Subjective Approach System Designer Selects Utility Function f
: R R -Describes Subjective Preference -Increasing and Continuous
Function Examples: Sum Performance: Proportional Fairness: Harmonic
Mean: Max-Min Fairness: 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC
and KTH23
Slide 24
Subjective Approach (2) Gives Single-Objective Optimization
Problem: This is the Starting Point of Many Researchers -Although
Selection of f is Inherently Subjective Affects the Solvability
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH24 Pragmatic
Approach Try to Select Utility Function to Enable Efficient
Optimization
Slide 25
Subjective Approach (3) Characterization of Optimization
Problems Main Categories of Resource Allocation -Convex: Polynomial
time solution -Monotonic: Exponential time solution 2013-02-06Emil
Bjrnson, Post-Doc at SUPELEC and KTH25 Approx. Needed Practically
Solvable
Slide 26
Subjective Approach (4) When is the Problem Convex? -Most
Problems are Non-Convex -Necessary: Search Space must be
Particularly Limited Classification of Three Important Problems
-The Easy Problem -Weighted Max-Min Fairness -Weighted Sum
Performance 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and
KTH26
Slide 27
The Easy Problem 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC
and KTH27 Total Power Constraints Per-Antenna Constraints General
Constraints, Robustness
Slide 28
Subjective Approach: Max-Min Fairness 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH28 Solution is on this line
Slide 29
Subjective Approach: Max-Min Fairness (2) 2013-02-06Emil
Bjrnson, Post-Doc at SUPELEC and KTH29 Simple Line-Search:
Bisection -Iteratively Solving Convex Problems (i.e., quasi-convex)
1.Find start interval 2.Solve the easy problem at midpoint 3.If
feasible: Remove lower half Else: Remove upper half 4.Iterate
Subproblem: Convex optimization Line-search: Linear convergence One
dimension (independ. #users)
Slide 30
Subjective Approach: Max-Min Fairness (3) Classification of
Weighted Max-Min Fairness: -Quasi-Convex Problem (belongs to convex
class) If Subjective Preference is Formulated in this Way -Resource
Allocation Solvable in Polynomial Time 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH30
Slide 31
Subjective Approach: Sum Performance 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH31 Opt-value is unknown! -Distance from
origin is unknown -Line Hyperplane (dim: #user 1) -Harder than
max-min fairness -Provably NP-hard!
Slide 32
Subjective Approach: Sum Performance (2) Classification of
Weighted Sum Performance: -Monotonic Problem If Subjective
Preference is Formulated in this Way -Resource Allocation Solvable
in Exponential Time Algorithm for Monotonic Optimization -Improve
Lower/Upper Bounds on Optimum: -Continue Until -Subproblem:
Essentially weighted max-min fairness 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH32
Slide 33
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH33
Subjective Approach: Sum Performance (3)
Slide 34
Pragmatic Resource Allocation Recall: All Utility Functions are
Subjective -Pragmatic Approach: Select to enable efficient
optimization Bad Choice: Weighted Sum Performance -NP-hard:
Exponential complexity (in #users) Good Choice: Weighted Max-Min
Fairness -Quasi-Convex: Polynomial complexity 2013-02-06Emil
Bjrnson, Post-Doc at SUPELEC and KTH34 Pragmatic Resource
Allocation Weighted Max-Min Fairness (select weights to enhance
throughput)
Slide 35
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH35
Structural Insights
Slide 36
Parametrization of Optimal Beamforming 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH36
Slide 37
Parametrization of Optimal Beamforming Geometric
Interpretation: Heuristic Parameter Selection -Known to Work
Remarkably Well -Many Examples (since 1995): Transmit Wiener/MMSE
filter, Regularized Zero-forcing, Signal-to-leakage beamforming,
virtual SINR/MVDR beamforming, etc. 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH37
Slide 38
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH38
Extensions to Practical Conditions
Slide 39
Robustness to Channel Uncertainty Practical Systems Operate
under Uncertainty -Due to Estimation, Feedback, Delays, etc.
Robustness to Uncertainty -Maximize Worst-Case Performance -Cannot
be Robust to Any Error Ellipsoidal Uncertainty Sets -Easily
Incorporated in the Model -Same Classifications More Variables
-Definition: 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and
KTH39
Slide 40
Distributed Resource Allocation Information and Functionality
is Distributed -Local Channel Knowledge and Computational Resources
-Only Limited Backhaul for Coordination Distributed Approach
-Decompose Optimization -Exchange Control Signals -Iterate
Subproblems Convergence to Optimal Solution? -At Least for Convex
Problems 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH40
Slide 41
Adapting to Transceiver Impairments Physical Hardware is
Non-Ideal -Phase Noise, IQ-imbalance, Non-Linearities, etc.
-Non-Negligible Performance Degradation at High SNR Model of
Transmitter Distortion: -Additive Noise -Variance Scales with
Signal Power Same Classifications Hold under this Model -Enables
Adaptation: Much larger tolerance for impairments 2013-02-06Emil
Bjrnson, Post-Doc at SUPELEC and KTH41
Slide 42
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH42
Summary
Slide 43
Resource Allocation -Divide Power between Users and Spatial
Directions -Solve a Multi-Objective Optimization Problem -Pareto
Boundary: Set of efficient solutions Subjective Utility Function
-Selection has Fundamental Impact on Solvability -Pragmatic
Approach: Select to enable efficient optimization -Weighted Sum
Performance: Not solvable in practice -Weighted Max-Min Fairness:
Polynomial complexity Parametrization of Optimal Beamforming
Extensions: Channel Uncertainty, Distributed Optimization,
Transceiver Impairments 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC
and KTH43
Slide 44
Main Reference 270 Page Tutorial, Published in Jan 2013 -Other
Convex Problems and General Algorithms -More Parametrizations and
Structural Insights -Guidelines for Scheduling and Forming Dynamic
Clusters -Extensions: multi-cast, multi-carrier, multi-antenna
users, etc. Matlab Code Available Online 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH44 Promotion Code: EBMC-01069
Slide 45
2013-02-0645Emil Bjrnson, Post-Doc at SUPELEC and KTH Thank You
for Listening! Questions? All Papers Available:
http://flexible-radio.com/emil-bjornson
Slide 46
2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH46
Additional Slides
Slide 47
Problem Classifications GeneralZero ForcingSingle Antenna Sum
PerformanceNP-hardConvexNP-hard Proportional FairnessNP-hardConvex
Harmonic MeanNP-hardConvex Max-Min FairnessQuasi-Convex QoS/Easy
ProblemConvex Linear 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC
and KTH47
Slide 48
Why is Weighted Sum Performance Bad? Some Shortcomings -Law of
Diminishing Marginal Utility not Satisfied -Not all Pareto Points
are Attainable -Weights have no Clear Interpretation -Not Robust to
Perturbations 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and
KTH48
Slide 49
Further Geometric Interpretations 2013-02-06Emil Bjrnson,
Post-Doc at SUPELEC and KTH49 Utilities has different shapes Same
point in symmetric regions Generally large differences
Slide 50
Computation of Performance Regions Performance Region is
Generally Unknown -Compact and Normal - Perhaps Non-Convex Generate
1: Vary parameters in parametrization Generate 2: Maximize sequence
of utilities f 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and
KTH50
Slide 51
Branch-Reduce-Bound (BRB) Algorithm 1.Cover Region with a Box
2.Divide the Box into Two Sub-Boxes 3.Remove Parts with No
Solutions in 4.Search for Solutions to Improve Bounds (Based on
Fairness-profile problem) 5.Continue with Sub-Box with Largest
Value 2013-02-06Emil Bjrnson, Post-Doc at SUPELEC and KTH51
Monotonic Optimization