Signal Processing for Optimal Radio Resource Management: Fundamentals and Recent Multi-Cell Advances Emil Björnson Dept. of Signal Processing, KTH Royal Institute of Technology, Stockholm, Sweden Alcatel-Lucent Chair on Flexible Radio, Supélec, Gif-sur-Yvette, France 20 March 2014

Biography: Emil Björnson 1983: Born in Malmö, Sweden 2007: Master of Science in Engineering Mathematics, Lund University, Sweden 2011: PhD in Telecommunications, KTH, Stockholm, Sweden Advisors: Björn Ottersten, Mats Bengtsson 2012-2014: International Postdoc Grant from Sweden. Work with Prof. Mérouane Debbah at Supélec on “Optimization of Green Small-Cell Networks” 2014: Assistant Professor in Communication Systems, Linköping University, Sweden Signal processing for optimal radio resource management 20 March 2014

Optimal Resource Allocation in Coordinated Multi-Cell Systems Book Reference Tutorial is Partially based on a Book: 270 pages E-book for free (from our homepages) Printed book: Special price $35, use link: https://ecommerce.nowpublishers.com/shop/add_to_cart?id=1595 Matlab code is available online Visit: http://flexible-radio.com/emil-bjornson Optimal Resource Allocation in Coordinated Multi-Cell Systems Research book by E. Björnson and E. Jorswieck Foundations and Trends in Communications and Information Theory, Vol. 9, No. 2-3, pp. 113-381, 2013 Signal processing for optimal radio resource management 20 March 2014

Covered by in second 90 min General Outline Introduction Problem formulation and general system model Optimal Single-Objective Resource Management Which problems are practically solvable and why? Multi-Objective Network Optimization Definitions and potential applications Generalizations and Specific Properties How does optimal solutions look like? Handling imperfect channel knowledge Distributed resource management Handling hardware impairments Fundamentals Covered by in first 90 min Recent advances Covered by in second 90 min Signal processing for optimal radio resource management 20 March 2014

Part 1 Fundamentals Signal processing for optimal radio resource management 20 March 2014

Outline: Part 1 – Fundamentals Introduction Multi-cell structure, system model, performance measure Problem Formulation Resource management: Multi-objective optimization problem Subjective Resource Management Utility functions, different computational complexity Multi-Objective Network Optimization What are the future potentials of this theory? Signal processing for optimal radio resource management 20 March 2014

Section Introduction Signal processing for optimal radio resource management 20 March 2014

Introduction Wireless Connectivity Rapid Network Traffic Growth A natural part of our lives Text messages Voice call Social networks Video streaming Web browsing Gaming Rapid Network Traffic Growth 61% annual data traffic growth Exponential increase! Extrapolation: 20x until 2020 200x until 2025 2000x until 2030 Signal processing for optimal radio resource management 20 March 2014

Introduction: Evolving Networks for Higher Traffic Increasing Network Capacity [bit/s/Area] Consider a given area How to handle 1000x more data traffic? Formula for Network Capacity: Capacity bit/s in area = Spectral efficiency bit/s/Hz/Cell ∙ Cell density Cell/Area ∙ Available spectrum in Hz Spectral efficiency Cell density Spectrum Total History (1965-2010) 25x 1600x 1 000 000x Spectral efficiency Cell density Spectrum Total History (1965-2010) 25x 1600x 1000000x Future: Nokia 10x 1 000x Future: SK Telecom 6x 56x 3x Considered in this lecture Signal processing for optimal radio resource management 20 March 2014

Introduction: Preliminary Definitions Problem Formulation (vaguely): Transfer information wirelessly to users Divide radio resources among users (time, frequency, space) Downlink Cellular System Many transmitting base stations (BSs) Many receiving users Multiple-input multiple-output (MIMO) Sharing a Frequency Band All signals reach everyone! Limiting Factor Inter-user interference Signal processing for optimal radio resource management 20 March 2014

Introduction: Multi-Antenna Transmission Traditional Ways to Manage Interference Avoid and suppress in time and frequency domain Results in orthogonal access techniques: TDMA, OFDMA, etc. Multi-Antenna Transmission Beamforming: Spatially directed signals Adaptive control of interference Serve multiple users: Space-division multiple access (SDMA) Main difference from classical resource management! Signal processing for optimal radio resource management 20 March 2014

Introduction: Multi-Antenna Transmission (2) With channel knowledge: beamforming or precoding Direct signal towards intended receiver – some interference leaks! Beamforming Design Easy for one user Difficult for multiple users, due to interference Signal processing for optimal radio resource management 20 March 2014

Introduction: From Single-Cell to Multi-Cell Naïve Multi-Cell Extension Divide BS into disjoint clusters SDMA within each cluster Avoid inter-cluster interference Fractional frequency-reuse Coordinated Multi-Cell Transmission SDMA in multi-cell: All BSs collaborate Frequency-reuse one: Interference managed by beamforming Many names: co-processing, coordinated multi-point (CoMP), network MIMO, multi-cell processing Almost as One Super-Cell But: Different data knowledge, channel knowledge, power constraints! Signal processing for optimal radio resource management 20 March 2014

Basic Multi-Cell Coordination Structure General Multi-Cell Coordination Adjacent base stations coordinate interference Some users served by multiple base stations Dynamic Cooperation Clusters Inner Circle : Serve users with data Outer Circle : Suppress interference Outside Circles: Negligible impact Impractical to acquire information Difficult to coordinate decisions E. Björnson, N. Jaldén, M. Bengtsson, B. Ottersten, “Optimality Properties, Distributed Strategies, and Measurement-Based Evaluation of Coordinated Multicell OFDMA Transmission,” IEEE Trans. on Signal Processing, 2011. Signal processing for optimal radio resource management 20 March 2014

Example: Ideal Joint Transmission All Base Stations Serve All Users Jointly = One Super Cell Signal processing for optimal radio resource management 20 March 2014

Example: Wyner Model Abstraction: User receives signals from own and neighboring base stations One or Two Dimensional Versions Joint Transmission or Coordination between Cells Signal processing for optimal radio resource management 20 March 2014

Example: Coordinated Beamforming One Base Station Serves Each User Interference Coordination Across Cells Special Case Interference channel Signal processing for optimal radio resource management 20 March 2014

Example: Soft-Cell Coordination Heterogeneous Deployment Conventional macro BS overlaid by short-distance small BSs Interference coordination and joint transmission between layers Signal processing for optimal radio resource management 20 March 2014

Example: Cognitive Radio Secondary System Borrows Spectrum of Primary System Underlay: Interference limits for primary users Other Examples Spectrum sharing between operators Physical layer security Signal processing for optimal radio resource management 20 March 2014

Optimizing Resource Management: First Definition 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 knowledge Centralized optimization Ideal transceiver hardware Relaxed in Part 2 Signal processing for optimal radio resource management 20 March 2014

Multi-Cell System Model 𝐾 𝑟 Users: Channel vector to User 𝑘 from all BSs 𝑁 𝑗 Antennas at 𝑗th BS (dimension of h 𝑗𝑘 ) – small or large 𝑁= 𝑗 𝑁 𝑗 Antennas in Total (dimension of h 𝑘 ) One System Model for All Multi-Cell Scenarios! Signal processing for optimal radio resource management 20 March 2014

Multi-Cell System Model: Dynamic Cooperation Clusters How are D 𝑘 and C 𝑘 Defined? Consider User 𝑘: Interpretation: Block-diagonal matrices D 𝑘 has identity matrices for BSs that send data C 𝑘 has identity matrices for BSs that can/should coordinate interference Signal processing for optimal radio resource management 20 March 2014

Multi-Cell System Model: Dynamic Cooperation Clusters (2) Example: Coordinated Beamforming This is User 𝑘 Beamforming: D 𝑘 v 𝑘 Data only from BS1: Effective channel: C 𝑘 h 𝑘 Interference from all BSs: Signal processing for optimal radio resource management 20 March 2014

Multi-Cell System Model: Power Constraints Need for Power Constraints Limit radiated power according to regulations Protect dynamic range of amplifiers Manage cost of energy expenditure Control interference to certain users 𝐿 General Power Constraints: All at the same time! Weighting matrix (Positive semi-definite) Limit (Positive scalar) Signal processing for optimal radio resource management 20 March 2014

Multi-Cell System Model: Power Constraints (2) Recall: Example 1, Total Power Constraint: Example 2, Per-Antenna Constraints: Example 3, Control Interference to User 𝑖 Signal processing for optimal radio resource management 20 March 2014

Introduction: How to Measure User Performance? Mean Square Error (MSE) Difference: transmitted and received signal Easy to Analyze Far from User Perspective? Bit/Symbol Error Probability (BEP/SEP) 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 Anyway closest to reality? All improves with SINR: Signal Interference + Noise Signal processing for optimal radio resource management 20 March 2014

Introduction: Generic Measure User Performance Generic Model Any function of signal-to-interference-and-noise ratio (SINR): Increasing and continuous function For simplicity: 𝑔 𝑘 0 =0 Simple Examples: Information rate: MSE: Complicated Function Depends on all beamforming vectors v 1 ,…, v 𝐾 𝑟 for User 𝑘 User Specific Measure user’s satisfaction Signal processing for optimal radio resource management 20 March 2014

Section: Introduction Questions? Signal processing for optimal radio resource management 20 March 2014

Problem Formulation Section Signal processing for optimal radio resource management 20 March 2014

Problem Formulation General Formulation of Optimal Resource Management: Multi-Objective Optimization Problem Generally impossible to maximize for all users! Must divide power and cause inter-user interference Signal processing for optimal radio resource management 20 March 2014

Performance Region Definition: Achievable Performance Region Contains all feasible combinations Feasible = Achieved by some {v 1 ,…, v 𝐾 𝑟 } under power constraints Care about user 2 Pareto Boundary Cannot improve for any user without degrading for other users Balance between users Part of interest: Pareto boundary Other Names Rate Region Capacity Region MSE Region, etc. 2-User Performance Region Care about user 1 Signal processing for optimal radio resource management 20 March 2014

Performance Region (2) Definitions of Pareto Boundary Strong Pareto point: Improve for any user  Degrade for other user Weak Pareto point: Cannot simultaneously improve for all users Weak Definition is More Convenient Boundary is compact and simply-connected Optimality Condition 1 Sending one stream per user is sufficient (assumed earlier) Optimality Condition 2 At least one power constraint is active (=holds with equality) X. Shang, B. Chen, H. V. Poor, “Multiuser MISO Interference Channels With Single-User Detection: Optimality of Beamforming and the Achievable Rate Region,” IEEE Trans. on Information Theory, 2011. R. Mochaourab and E. Jorswieck, “Optimal Beamforming in Interference Networks with Perfect Local Channel Information,” IEEE Trans. on Signal Processing, 2011. Signal processing for optimal radio resource management 20 March 2014

Upper corner in region, everything inside region Performance Region (3) Can the region have any shape? No! Can prove that: Compact set Normal set Upper corner in region, everything inside region Signal processing for optimal radio resource management 20 March 2014

Performance Region (4) Some Possible Shapes User-Coupling Weak: Convex Strong: Concave Scheduling Time-sharing for strongly coupled users Select multiple points Hard: Unknown region Signal processing for optimal radio resource management 20 March 2014

Performance Region (5) Which Pareto Optimal Point to Choose? Tradeoff: Aggregate performance vs. fairness Utilitarian point (Max sum performance) Utopia point (Combine user points) No Objective Answer Utopia point outside of region Only subjective answers exist! Single user point Egalitarian point (Max fairness) Performance Region Single user point Signal processing for optimal radio resource management 20 March 2014

Section: Problem Formulation Questions? Signal processing for optimal radio resource management 20 March 2014

Subjective Resource Management Section Subjective Resource Management Signal processing for optimal radio resource management 20 March 2014

Known as A Priori Approach Subjective Approach System Designer Selects Utility Function Describes subjective preference Increasing and continuous function Examples: Sum performance: Proportional fairness: Harmonic mean: Max-min fairness: Put different weights to move between extremes Known as A Priori Approach Select utility function before optimization Signal processing for optimal radio resource management 20 March 2014

Subjective Approach (2) Utilities Functions Has Different Shapes Curve: 𝑓 g =constant Optimal constant: Curve intersects optimum Symmetric region: Same point Asymmetric region: Different points Signal processing for optimal radio resource management 20 March 2014

Subjective Approach (3) Utility Function gives Single-Objective Optimization Problem: This is the Starting Point of Many Researchers Although selection of is Inherently subjective Affects the solvability Should always have a motivation in mind! Pragmatic Approach Try to Select Utility Function to Enable Efficient Optimization Signal processing for optimal radio resource management 20 March 2014

Complexity of Single-Objective Optimization Problems Classes of Optimization Problems Different scaling with number of parameters and constraints Main Classes Convex: Polynomial time solution Monotonic: Exponential time solution Arbitrary: More than exponential time Practically solvable Approximations needed Hard to even approximate Signal processing for optimal radio resource management 20 March 2014

Complexity of Resource Management Problems What is a Convex Problem? Recall definitions: Convex Function For any two points on the graph of the function, the line between the points is above the graph Examples: Convex Problem Convex if objective 𝑓 0 and constraints 𝑓 1 ,…, 𝑓 𝑀 are convex functions Signal processing for optimal radio resource management 20 March 2014

Complexity of Resource Management Problems (2) When is the Resource Management a Convex Problem? Original problem: Rewritten problem (replace SINR 𝑘 with variable ): Can be selected to be convex SINR constraints: Main complication! Convex power constraints Signal processing for optimal radio resource management 20 March 2014

Classification of Resource Management Problems Classification of Three Important Problems The “Easy” problem Weighted max-min fairness Weighted sum performance We will see: These have Different Complexities Difficulty: Too many spatial degrees of freedom Convex problem only if search space is particularly limited Monotonic problem in general Signal processing for optimal radio resource management 20 March 2014

Complexity Example 1: The “Easy” Problem Given Any Point ( 𝑔 1 ,…, 𝑔 𝐾 𝑟 ) or SINRs ( 𝛾 1 ,…, 𝛾 𝐾 𝑟 ) Find beamforming v 1 ,…, v 𝐾 𝑟 that attains this point Fixed SINRs make the constraints convex: Global solution in polynomial time – use CVX, Yalmip Second order cone: Convex M. 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. Björnson, G. Zheng, M. Bengtsson, B. Ottersten, “Robust Monotonic Optimization Framework for Multicell MISO Systems,” IEEE Trans. on Signal Processing, 2012. Total Power Constraints Per-Antenna Constraints General Constraints Signal processing for optimal radio resource management 20 March 2014

Complexity Example 2: Max-Min Fairness How to Classify Weighted Max-Min Fairness? Property: Solution makes 𝑤 𝑘 𝑔 𝑘 the same for all 𝑘 Solution is on this line Line in direction ( 𝑤 1 ,…, 𝑤 𝐾 𝑟 ) Signal processing for optimal radio resource management 20 March 2014

Complexity Example 2: Max-Min Fairness (2) Simple Line-Search: Bisection Iteratively Solving Convex Problems (i.e., quasi-convex) Find start interval Solve the “easy” problem at midpoint If feasible: Remove lower half Else: Remove upper half Iterate Subproblem: Convex optimization Line-search: Linear convergence One dimension (independ. #users) Signal processing for optimal radio resource management 20 March 2014

Complexity Example 2: Max-Min Fairness (3) Classification of Weighted Max-Min Fairness: Quasi-convex problem (belongs to convex class) Polynomial complexity in #users, #antennas, #constraints Might 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. Björnson, 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 uncertainty Signal processing for optimal radio resource management 20 March 2014

Complexity Example 3: Weighted Sum Performance How to Classify Weighted Sum Performance? Geometrically: 𝑤 1 𝑔 1 + 𝑤 2 𝑔 2 = opt-value is a line Opt-value is unknown! Distance from origin is unknown Line  Hyperplane (dim: #user – 1) Harder than max-min fairness Non-convex problem Signal processing for optimal radio resource management 20 March 2014

Complexity Example 3: Weighted Sum Performance (2) Classification of Weighted Sum Performance: Non-convex problem Power constraints: Convex Utility: Monotonically increasing or decreasing in beamforming vectors Therefore: 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. Signal processing for optimal radio resource management 20 March 2014

Complexity Example 3: Weighted Sum Performance (3) Are Monotonic Problems Impossible to Solve? No, not for small problems! Monotonic Optimization Algorithms Improve Lower/upper bounds on optimum: Continue until Subproblem: Essentially weighted max-min fairness problem Monotonic optimization Early works Polyblock algorithm BRB algorithm 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. Björnson, G. Zheng, M. Bengtsson, B. Ottersten, “Robust Monotonic Optimization Framework for Multicell MISO Systems,” IEEE Trans. on Signal Processing, 2012. Signal processing for optimal radio resource management 20 March 2014

Complexity Example 3: Weighted Sum Performance (4) Branch-Reduce-and-Bound (BRB) Algorithm Cover performance region with a box Divide the box into two sub-boxes Remove parts with no solutions in Search for solutions to improve bounds Continue with sub-box with largest value End when bounds are tight enough: Accuracy Signal processing for optimal radio resource management 20 March 2014

Complexity Example 3: Weighted Sum Performance (5) BRB Algorithm Global convergence Accuracy ε>0 in finitely many iterations Exponential complexity only in #users ( 𝐾 𝑟 ) Polynomial complexity in other parameters (#antennas, #constraints) Signal processing for optimal radio resource management 20 March 2014

Complexity Example 3: Weighted Sum Performance (6) Maximizing Sum Performance has High Complexity Under linear beamforming Other Shortcomings Not all Pareto points are attainable Weights have no clear interpretation Not robust to perturbations Signal processing for optimal radio resource management 20 March 2014

Summary: Complexity of Resource Management Problems General Sum Performance NP-hard Max-Min Fairness Quasi-Convex “Easy” Problem Convex General Zero Forcing Single Antenna Sum Performance NP-hard Convex Max-Min Fairness Quasi-Convex “Easy” Problem Linear Proportional Fairness Harmonic Mean What about other utility functions? Recall: The SINR constraints are complicating factor Three conditions that simplify: Fixed SINRs (“easy” problem) Allow no interference (called: zero-forcing) Multiplication  Addition (change of variable, single antenna BSs) Signal SINR Interference Signal processing for optimal radio resource management 20 March 2014

Summary: Complexity of Resource Management (2) Recall: All Utility Functions are Subjective Pragmatic approach: Select to enable efficient optimization Good Choice: Any Problem with Polynomial complexity Example: Weighted max-min fairness Use weights to adapt to other system needs Bad Choice: Weighted Sum Performance Generally NP-hard: Exponential complexity (in #users) Should be avoided – Sometimes needed (virtual queuing techniques) General Zero Forcing Single Antenna Sum Performance Convex Max-Min Fairness Quasi-Convex “Easy” Problem Linear Proportional Fairness Harmonic Mean Signal processing for optimal radio resource management 20 March 2014

Summary: Complexity of Resource Management (3) Complexity Analysis for Any Dynamic Cooperation Clusters Same optimization algorithms! Extra characteristics can sometime simplify Multi-antenna transmission: Higher complexity, higher performance Ideal Joint Transmission Coordinated Beamforming Underlay Cognitive Radio Signal processing for optimal radio resource management 20 March 2014

Section: Subjective Resource Management Questions? Signal processing for optimal radio resource management 20 March 2014

Multi-Objective Network Optimization Section Multi-Objective Network Optimization Signal processing for optimal radio resource management 20 March 2014

Many Network Performance Metrics How to Improve Network Performance? Higher user rates Balance user satisfaction/fairness Other possible metrics: Higher total area rate More active users (per area) Higher energy efficiency Considered so far Can be any performance metrics Multi-Objective Optimization Study conflict/alignment of any metrics Common tool in engineering/economics Signal processing for optimal radio resource management 20 March 2014

Basic Properties Multiple Resources Multiple Objectives Resource bundle Feasible resource allocation: Multiple Objectives Performance metrics: Subjective utility: 𝑓(∙) Performance Region Compact set Can be non-normal Can be non-convex Signal processing for optimal radio resource management 20 March 2014

Visualization Performance Region is Generally Unknown Sample points can be computed numerically Helps to visualize tradeoffs/possibilities Compare 2-3 metrics Algorithm Maximize sequence of 𝑓() Points out different directions from the origin A Posteriori Approach Look at region at select operating point Signal processing for optimal radio resource management 20 March 2014

Example: Optimization of Future Networks Design Cellular Network Symmetric system Select: 𝑁 = # BS antennas 𝐾 = # users 𝑃 = power/antenna Resource bundle: 500 20 W Signal processing for optimal radio resource management 20 March 2014

Example: Optimization of Future Networks (2) Coordinated beamforming Each BS serves only its own 𝐾 users Channels fixed for 𝑇 channel uses BS knows channels within the cell (cost: 𝐾/𝑇) Zero-forcing beamforming: no intra-cell interference Interference leaks between cells Average User Rate Array gain Power/user Bandwidth (10 MHz) CSI estimation overhead (𝑇=1000) Noise · pathloss (1.72∙ 10 −4 ) Relative intercell interference (0.54) Signal processing for optimal radio resource management 20 March 2014

Example: Optimization of Future Networks (3) What Consumes Power? Transmit power (+ losses in amplifiers) Circuits attached to each antenna Baseband computations Coding/decoding Backhaul/control signaling, cooling etc. Total Power Consumption Fixed power (10 W) Amplifier efficiency (0.31) Circuit power per antenna (1 W) Circuit power per user (0.3 W) Computing zero-forcing (2.3∙ 10 −6 ∙𝑁 𝐾 2 ) Signal processing for optimal radio resource management 20 March 2014

Example: Results Average user rate Total area rate 3 Objectives Energy efficiency 3 Objectives Low user rates, High area rates Observations Area and user rates are conflicting objectives Different number of users High user rates, Low area rates Signal processing for optimal radio resource management 20 March 2014

Example: Results (2) Energy Efficiency vs. User Rates Utility functions normalized by utopia point Observations Aligned for small user rates Conflicting for high user rates Signal processing for optimal radio resource management 20 March 2014

Summary Multi-Objective Optimization Network Design and Optimization Rigorous way to study problems with multiple performance metrics Metrics are generally conflicting, but can be aligned Network Design and Optimization Metrics can be: User rates, total area rates, energy-efficiency, etc. A posteriori approach: Visualize tradeoffs  Make decision Open problems: How to use framework for design of future networks? L. Zadeh, “Optimality and non-scalar-valued performance criteria,” IEEE Trans. on Autom. Control, 1963. R.T. Marler and J.S. Arora, “Survey of multi-objective optimization methods for engineering,” Structural and Multidisciplinary Optimization, 2004. E. Björnson, L. Sanguinetti, J. Hoydis, and M. Debbah, “Designing multi-user MIMO for energy efficiency: When is massive MIMO the answer?,” in Proc. IEEE WCNC, 2014. E. Björnson, E. Jorswieck, M. Debbah, and Björn Ottersten, “Multi-Objective Signal Processing Optimization: The Way to Balance Conflicting Metrics In 5G Systems,” IEEE Signal Processing Magazine, to appear. Signal processing for optimal radio resource management 20 March 2014

Section: Multi-Objective Network Optimization Questions? Signal processing for optimal radio resource management 20 March 2014

Summary: Part 1 Signal processing for optimal radio resource management 20 March 2014

Summary: Part 1 Resource Management in Multi-Antenna Multi-Cell Systems 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 Multi-antenna transmission: More possibilities – higher complexity Pragmatic approach: Select to enable efficient optimization Polynomial complexity: Weighted max-min fairness etc. Not solvable in practice: Weighted sum performance etc. Multi-Objective Network Optimization Practical optimization problems may have more than one metric General framework: Study tradeoff between metrics A posterior approach: Visualize the tradeoff and make decisions Signal processing for optimal radio resource management 20 March 2014

Coffee Break Thank you for listening! Questions? After the Break: Part 2 Recent Advances Imperfect channel knowledge Structure of optimal beamforming Distributed resource management Handling hardware impairments Signal processing for optimal radio resource management 20 March 2014

Part 2 Recent Advances Signal processing for optimal radio resource management 20 March 2014

Outline: Part 2 – Recent Advances Imperfect Channel Knowledge Resource management with channel uncertainty Structure of Optimal Beamforming Beamforming parametrization and its applications Distributed Resource Management Decompose system-wide problem into user-specific subproblems Handling Hardware Impairments Can we model and adapt to practical hardware? Signal processing for optimal radio resource management 20 March 2014

Imperfect Channel Knowledge Section Imperfect Channel Knowledge Signal processing for optimal radio resource management 20 March 2014

Robustness to Imperfect Channel Knowledge Perfect versus Imperfect Channel State Information (CSI) Resource management framework developed with perfect CSI Practical systems: Uncertainty of h 𝑘 Causes: estimation errors, feedback quantization, delays, etc. What is the Expected Impact? Small loss in signal power 100+100=200, 98+92=190 Larger interference leakage 100−100=0, 98−92=6 Goal: Robustness to Uncertainty How to define it? Perfect CSI Imperfect CSI Signal processing for optimal radio resource management 20 March 2014

Modeling Imperfect CSI Shape of Channel Estimation Errors Send: Known “pilot” information Apply: Optimal channel estimator Obtain: Unlimited support: Cannot handle all errors! Ellipsoidal Uncertainty Sets at BSs Cut out part of estimation errors Definition: Signal processing for optimal radio resource management 20 March 2014

Robust Resource Management Robust User Performance User k achieves an SINR 𝛾 𝑘 using v 1 ,…, v 𝐾 𝑟 if where 𝐒 𝑖 = 𝐯 𝑖 𝐯 𝑖 𝐻 is outer product of beamforming vectors Robust Performance Region Feasible points { 𝛾 1 ,…, 𝛾 𝐾 𝑟 } Achieved by v 1 ,…, v 𝐾 𝑟 under power constraints Good points: On upper boundary Different system utilities = different points Unknown shape, but compact and normal 2-User Performance Region Signal processing for optimal radio resource management 20 March 2014

Robust Resource Management (2) Formulated as search in robust performance region: Subjective Utility Functions: Sum performance: Proportional fairness: Harmonic mean: Max-min fairness: Recall We can solve any such problem if the “easy” problem is solvable Signal processing for optimal radio resource management 20 March 2014

Robust Resource Management (3) Robust “Easy” Problem (with 𝐒 𝑘 = 𝐯 𝑘 𝐯 𝑘 𝐻 ): Infinitely many constraints! Should have contained: rank 𝐒 𝑘 =1 Lemma The solution to the robust “easy” has always rank one. U. L. Wijewardhana, M. Codreanu, M.Latva-aho, and A. Ephremides, “A Robust Beamformer Design for Underlay Cognitive Radio Networks Using Worst Case Optimization,” EURASIP J. Wireless Communications and Networking, 2014. Signal processing for optimal radio resource management 20 March 2014

S-Procedure Application Lemma: S-Procedure Uncertainty set SINR ≥ Value Signal processing for optimal radio resource management 20 March 2014 81 Application Replace each uncertainty set with one linear matrix inequality Signal processing for optimal radio resource management 20 March 2014

Solving Robust “Easy” Problem Proof: Based on S-procedure. Intuition: Uncertainty sets replaced by new parameters λ 1 ,…, λ 𝐾 𝑟 Theorem A point is in the robust region if and only if the following convex feasibility problem is feasible: Signal processing for optimal radio resource management 20 March 2014

Simulation Examples Robust Performance Region Radius of uncertainty region: ξ Region shrinks with ξ : Particularly when both users are served Signal processing for optimal radio resource management 20 March 2014

Simulation Examples (2) Robust Performance Region Radius of uncertainty region: ξ Region shrinks with ξ : Particularly when both users are served Can even turn convex  non-convex Signal processing for optimal radio resource management 20 March 2014

Summary: Robust Resource Management Channel Uncertainty in Practical Systems Robust to compact uncertainty sets Shrinks the performance region - less beneficial to share resources Robust Resource Management “Easy” problem is still convex Consequence: Same problem classifications as with perfect CSI More optimization parameters  higher complexity G. Zheng, K.-K.Wong, and T.-S. Ng, “Robust linear MIMO in the downlink: A worst-case optimization with ellipsoidal uncertainty regions,” EURASIP J. on Adv. in Signal Process., 2008. E. Björnson, G. Zheng, M. Bengtsson, B. Ottersten, “Robust Monotonic Optimization Framework for Multicell MISO Systems,” IEEE Trans. on Signal Processing, 2012. C. Shen, T.-H. Chang, K.-Y. Wang, Z. Qiu, and C.-Y. Chi, “Distributed robust multicell coordinated beamforming with imperfect CSI: An ADMM approach,” IEEE Trans. on Signal Processing, 2012. U. L. Wijewardhana, M. Codreanu, M.Latva-aho, and A. Ephremides, “A Robust Beamformer Design for Underlay Cognitive Radio Networks Using Worst Case Optimization,” EURASIP J. Wireless Communications and Networking, 2014. Signal processing for optimal radio resource management 20 March 2014

Section: Imperfect Channel Knowledge Questions? Signal processing for optimal radio resource management 20 March 2014

Structure of Optimal Beamforming Section Structure of Optimal Beamforming Signal processing for optimal radio resource management 20 March 2014

Line-of-Sight and Non-Line-of-Sight Transmission Adapt signal phases at antennas Steer beam towards receiving user Not a perfect beam: interference Non-Line-of-Sight Multipath propagation Add components coherently Signal processing for optimal radio resource management 20 March 2014

Structure of Optimal Beamforming Goal: Derive Simple Beamforming Parametrization For any resource management problem Step 1: Consider “Easy” Problem ( C 𝑘 = D 𝑘 = 𝐈 𝑁 , 𝐾 users for brevity): Lagrangian satisfies Karush-Kuhn-Tucker (KKT) conditions: Convex problem! Lagrange multiplier Signal processing for optimal radio resource management 20 March 2014

Structure of Optimal Beamforming (2) Stationarity KKT Condition: Beamforming direction parameterized by λ 1 ,…, λ 𝐾 Signal processing for optimal radio resource management 20 March 2014

Structure of Optimal Beamforming (3) Power Allocation Based on SINR constraints Beamforming Parametrization In terms of Lagrange multipliers λ 1 ,…, λ 𝐾 Optimal parameters: (Fixed-point iteration) Signal processing for optimal radio resource management 20 March 2014

Structure of Optimal Beamforming: Summary Optimal Beamforming for “Easy” Problem: with Consider Any Resource Management Problem: Has 𝐾𝑁 complex optimization variables Note: Solution coincides with “Easy” problem for some 𝛾 1 ,…, 𝛾 𝐾 Parameterization from above: 𝐾 –1 positive parameters Equal to 𝑃 Signal processing for optimal radio resource management 20 March 2014

Asymptotic Behavior: Signal-to-noise ratio (SNR) Recall: Low SNR: 𝜎 2 →∞ Inverse  Identity: Transmit in channel direction Name: Maximum ratio transmission (MRT) Maximizes signal gain, ignores interference Complexity: Prop. to 𝑀𝐾 High SNR: 𝜎 2 →0 Inverse  Project orthogonal to co-users Name: Zero-forcing beamforming (ZFBF) Minimizes interference Under this condition: Signal as large as possible Complexity: Prop. to 𝑀 𝐾 2 Intended user Signal processing for optimal radio resource management 20 March 2014

Geometric Interpretation Special Case: 𝐾=2 Beamforming: Linear combination of channel and zero-forcing direction Tradeoff Maximize signal vs. minimize interference Hard to find optimal tradeoff Signal processing for optimal radio resource management 20 March 2014

Heuristic Beamforming at any SNR Select parameters heuristically Interpretation: λ 1 ,…, λ 𝐾 are user priorities Large: High performance requirement or weak channel gain Small: Low performance requirement or strong channel gain One Common Heuristic Approach Set all parameters equal: λ 𝑘 = 𝑃 𝐾 Proposed many times (since 1995): Transmit Wiener/MMSE filter, Regularized zero-forcing, Signal-to-leakage beamforming, Virtual SINR beamforming, Virtual-uplink MVDR beamforming, etc. Does it Perform Well? Symmetric scenarios: Yes, no reason to give different priorities! Asymmetric scenarios: Okay, but can be improved Signal processing for optimal radio resource management 20 March 2014

Heuristic Beamforming at any SNR (2) Observations MRT good at low SNR ZFBF good at high SNR Transmit MMSE always good Example: One BS with 4 antennas 4 single-antenna users Maximize sum information rate Beamforming Schemes Optimal beamforming (BRB algorithm) Transmit MMSE filter (regularized ZFBF) ZFBF MRT Signal processing for optimal radio resource management 20 March 2014

Asymptotic Behavior: Massive MIMO Many Antennas: 𝑁→∞ (𝐾 fixed) Behavior depends on channel model Suppose: h 1 ,…, h 𝐾 ~ 𝐶𝑁(𝟎, 𝐈 𝑁 ) Asymptotics: 𝐸{ 𝐡 𝑘 2 }=𝑁 and 𝐸{ |𝐡 𝑖 𝐻 𝐡 𝑘 |}≤ 𝑁 Inverse  Project orthogonal to co-users Once again: Zero-forcing beamforming (ZFBF) Note User channels become orthogonal Consequence: Interference vanish as 𝑁→∞ also with MRT But: MRT is not asymptotically optimal! Signal processing for optimal radio resource management 20 March 2014

Asymptotic Behavior: Massive MIMO (2) Example: 10 users, SNR is 15 dB Beamforming: Transmit MMSE (regularized ZF), ZFBF, and MRT Multi-cell case: Pilot contamination is 30 dB weaker Large difference between ZF/MMSE and MRT! Single-cell case Multi-cell case Constant gap 4-5x Vanishing gap Signal processing for optimal radio resource management 20 March 2014

Extension: Any Dynamic Cooperation Clusters Any Resource Management Problem is Solved by Parameters Priority of User 𝑘: 𝜆 𝑘 Impact of Constraint 𝑙: 𝜇 𝑙 Total: 𝐾 𝑟 +𝐿–2 positive parameters (due to sum constraints) Lagrange multipliers of “Easy” problem Signal processing for optimal radio resource management 20 March 2014

Summary Structure of Optimal Beamforming Heuristic Beamforming Simple parametrization – balance signal and interference Described by 𝐾 𝑟 +𝐿 –2 positive parameters Will not make it easier to solve an NP-hard problem! Heuristic Beamforming MRT: Good at low SNR and lower complexity ZFBF: Good at high SNR and many antennas Transmit MMSE/regularized ZFBF: Good at all SNRs/antennas Good for analysis! Best in practice! Early work State-of- the-art Tutorial E. A. Jorswieck, E. G. Larsson, D. Danev, “Complete characterization of the Pareto boundary for the MISO interference channel,” IEEE Trans. on Signal Processing, 2008. E. Björnson, M. Bengtsson, B. Ottersten, “Pareto Characterization of the Multicell MIMO Performance Region With Simple Receivers,” IEEE Trans. on Signal Processing, 2012. E. Björnson, M. Bengtsson, B. Ottersten, “Optimal Multi-User Transmit Beamforming: Difficult Problem with a Simple Solution Structure,” IEEE Signal Proces. Mag., to appear. Signal processing for optimal radio resource management 20 March 2014

Section: Structure of Optimal Beamforming Questions? Signal processing for optimal radio resource management 20 March 2014

Distributed Resource Management Section Distributed Resource Management Signal processing for optimal radio resource management 20 March 2014

Centralized vs. Distributed Deployments Centralized Deployment Assumed in Part 1 Example: Cloud-RAN (China Mobile) Pro: Highest performance? Con: Expensive infrastructure Distributed Deployment BSs exchange information Pro: Inexpensive approach (exploit local functionality) Con: Loss in performance? Exchange what information? Signal processing for optimal radio resource management 20 March 2014

Distributed Optimization Coupling Between Users Users “compete” for resources Cause inter-user interference Distributed Optimization Approach: Represent coupling by coupling variables (CVs) Make local copies of CVs Local optimization of resources for fixed CVs Update CVs iteratively Popular Techniques Classical: Dual decomposition Robustification: Alternating direction method of multipliers (ADMM) Very essence of radio resource management! Signal processing for optimal radio resource management 20 March 2014

Example: Dual Decomposition Consider “Easy” Problem Achieve points { 𝛾 1 ,…, 𝛾 𝐾 𝑟 } Centralized problem: Add Auxiliary Variables Interference from User 𝑖 to User 𝑘: Believed: True: Power for User 𝑘: Signal processing for optimal radio resource management 20 March 2014

Example: Dual Decomposition (2) How to remove decouple? Partial Lagrangian for coupling constraints Lagrange multipliers Interference: 𝑦 𝑖𝑘 Power: 𝑧 𝑙 Change objective Remove coupling constraints Problem is decoupled! One problem per user (for fixed Lagrange multipliers) Signal processing for optimal radio resource management 20 March 2014

Example: Dual Decomposition (3) Subproblem: User 𝑘 Convex problem Requires: Local CSI Allowed interference leakage Master problem Update Lagrange multipliers Complicated structure Subgradient update Solutions to subproblems Signal processing for optimal radio resource management 20 March 2014

Example: Max-Min Fairness Iterative Algorithm Solve subproblems Update multipliers (step size 𝜉) Update best achieved point Iterate Signal processing for optimal radio resource management 20 March 2014

Summary: Distributed Resource Management Distributed Optimization Global problem can be decomposed Proof-of-concept: Dual decomposition Exchange control variables (interference level, power usage) – no CSI! Complexity: Can actually be greatly reduced! Will it Converge to Optimum? At least for convex problems! D. Palomar and M. Chiang, “A tutorial on decomposition methods for network utility maximization,” IEEE J. Selected Areas in Communications, 2006. A. Tölli, H. Pennanen, and P. Komulainen, “Decentralized minimum power multi-cell beamforming with limited backhaul signaling,” IEEE Trans. Wireless Communications, 2011. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Foundations and Trends in Machine Learning, 2011. C. Shen, T.-H. Chang, K.-Y. Wang, Z. Qiu, and C.-Y. Chi, “Distributed robust multicell coordinated beamforming with imperfect CSI: An ADMM approach,” IEEE Trans. on Signal Processing, 2012. Signal processing for optimal radio resource management 20 March 2014

Section: Distributed Resource Management Questions? Signal processing for optimal radio resource management 20 March 2014

Handling Hardware Impairments Section Handling Hardware Impairments Signal processing for optimal radio resource management 20 March 2014

Adapting to Transceiver Hardware Impairments Physical Hardware is Non-Ideal Phase noise, I/Q-imbalance, non-linearities, etc. Expensive vs. cheap hardware Impact reduced by calibration/compensation (not fully removed!) Exact Characterization is Very Complicated Many types of impairments and mitigation algorithms Depends on signal waveform (OFDM, single-carrier, etc.) Only the combined impact is needed! Signal processing for optimal radio resource management 20 March 2014

Non-Linear Systems Generalized System Model: Bussgang theorem: Assume: Gaussian input signal (codebook and/or OFDM-signal) Bussgang theorem: OFDM systems: 𝑐 equal over subcarriers (can be tracked) 𝑉 is proportional to signal (inter-carrier interference) W. Zhang, “A general framework for transmission with transceiver distortion and some applications,” IEEE Trans. Commun., 2012. Signal processing for optimal radio resource management 20 March 2014

Orthogonal frequency-division multiplexing (OFDM) Source: Wikipedia Transmitter Receiver Signal processing for optimal radio resource management 20 March 2014

Definition and Interpretation Transmitter distortion Receiver distortion Received Signal at User 𝑘 Gaussian Distortion Noise Independent between antennas Depends on beamforming Error Vector Magnitude (EVM) Proportional to signal power Quality of transceivers: LTE requirements: 0≤EVM≤0.17 (smaller  higher rates) 𝑘 𝑟 at receiver Signal processing for optimal radio resource management 20 March 2014

Resource Management with Hardware Impairments Generalization of “Easy” Problem: Signal processing for optimal radio resource management 20 March 2014

Resource Management with Hardware Impairments Generalization of “Easy” Problem: Picks out signal at 𝑛th antenna Auxiliary variables for distortion magnitudes EVM constraints Lemma This is a convex problem if 𝑘 𝑡 and 𝑘 𝑟 are constant. E. Björnson, P. Zetterberg, and M. Bengtsson, “Optimal coordinated beamforming in the multicell downlink with transceiver impairments,” in IEEE GLOBECOM, 2012. Signal processing for optimal radio resource management 20 March 2014

Resource Management with Hardware Impairments (2) Recall We can solve any resource management problem if the “easy” problem is solvable Performance region Reduces with impairments Strong users more sensitive Signal processing for optimal radio resource management 20 March 2014

Resource Management with Hardware Impairments (3) Performance Degradation as Function of SNR Distortion noise power is proportional to signal power High SNR  Distortions dominate over “regular” noise Upper bound on achievable user rates Simulation User rate as function of transmit power Impact increases with power and imperfections Signal processing for optimal radio resource management 20 March 2014

Summary Transceiver Hardware Impairments Can be reduced but not avoided Negligible impact at low SNR Limits performance at high SNR What is the Point of This Analysis? Model and adapt beamforming to impairments Achieve higher performance with same hardware Achieve same performance with less expensive hardware T. Schenk, “RF Imperfections in High-Rate Wireless Systems: Impact and Digital Compensation”. Springer, 2008 M. Wenk, “MIMO-OFDM Testbed: Challenges, Implementations, and Measurement Results”. Hartung-Gorre, 2010 E. Björnson, P. Zetterberg, M. Bengtsson, and B. Ottersten, “Capacity limits and multiplexing gains of MIMO channels with transceiver impairments,” IEEE Commun. Letters, 2013. Books on modeling Fundamental Capacity Behaviors Signal processing for optimal radio resource management 20 March 2014

Section: Handling Hardware Impairments Questions? Signal processing for optimal radio resource management 20 March 2014

Summary: Part 2 Signal processing for optimal radio resource management 20 March 2014

Summary Framework 1 can be Extended to Practical Conditions Imperfect channel knowledge Distributed resource management Handling hardware impairments Optimal Beamforming Balance between signal gain and low interference Simple beamforming structure MRT and ZFBF are good for analysis Transmit MMSE (regularized ZF) has better performance Signal processing for optimal radio resource management 20 March 2014

Many Open Problems Extension to Multi-Hop Networks Including AF/DF relaying and/or physical layer network coding Distributed Resource Management using Game Theory Reach “good” operating points non-cooperatively or cooperatively Use of More Detailed System Models Consider imperfect CSI, impairments, etc. at the same time For amplifiers, hardware imperfections, energy efficiency, etc. Impact on resource management (e.g., beamforming, power allocation) Context-Aware Resource Management Exploit time dimension (e.g., delay constraints, predictable behaviors) Define and optimize quality-of-experience Interference and Load Management in Coordinated Multi-Tier Networks Signal processing for optimal radio resource management 20 March 2014

Thank You! Thank You For Listening! More Details in Our book More parametrizations and structural insights Guidelines for scheduling and forming clusters Multi-casting, Multi-carrier Multi-antenna users, etc. Cognitive radio and physical layer security 300 references to articles in these areas E-book and code available for free download! All papers are available: http://flexible-radio.com/emil-bjornson Signal processing for optimal radio resource management 20 March 2014