Mathematical Scientific Challenges of 5G Mrouane Debbah - PowerPoint PPT Presentation

The unclear 5G technologies The term 5G is sometimes used to encapsulate these technologies Network Function Virtualisation (NFV),  Software Defined Networks (SDN),  Fixed Access Technologies  “Typesetting Standard”. It is important to clarify that these technological advancements are continuing independently of 5G but will have a great impact on 5G. Page 32 HUAWEI TECHNOLOGIES CO., LTD. Huawei Proprietary - Restricted Distribution

Fixed Access breakthroughs are required “Typesetting Standard”. Page 33 HUAWEI TECHNOLOGIES CO., LTD. Huawei Proprietary - Restricted Distribution

“Typesetting Standard”. Page 34 HUAWEI TECHNOLOGIES CO., LTD. Huawei Proprietary - Restricted Distribution

Copper Access: History and Future Trend: Continuous Innovations Keep Exploring the Potential of Copper Year Bandwidth 10G NGB 2020- 1G-NG B 1G 200M-1G G.fast 2015 - 2017 100-300M VDSL3 100M 2012 50-100M Vectoring G.993.5 50M 2004-2011 VDSL2 G.993.2 20M 2003 ADSL2+ G.992.5 10M 6M 2002 ADSL2 G.992.3/4 1M 1999 1M ADSL G.992.1/2 6Km 3Km 1.5Km 800m 400m <100m Loop FTTD CO FTTC/B FTTdp Length VDSL3 VDSL2 Vectoring G.fast NGBB • • Bandwidth:100-300Mbps • • • Bandwidth:50100 Mbps Bandwidth:30-50Mbps Bandwidth:200M-1Gbps Bandwidth:1-NGbps • • Distance300-1200m • • • Distance:300-800m Distance:~1000m Distance:<400m Distance:<100m • • • Scenario: FTTC • • Scenario: FTTC Scenario: FTTC Scenario: FTTB/D/dp Scenario: FTTD/F • • Available:2016-2017 • Mature • • Mature Available: 2015-2016 Multi-pair MIMO? • Available: 2020- HUAWEI TECHNOLOGIES Co., Ltd. HUAWEI Confidential

Optical Access Trend Much more flexible OAN will be the Future trend. New technologies such as DSP , SDN and NFV will be involved. Bandwidth NGPON3?? DSP, SDN and NFV >=80G enabled, full Services. Part 2: PtP WDM-PON (AWG or Splitter based) Huawei: SD FlexPON Part1: TWDM-PON NGPON2 40G NGEPON XG-PON 10G 10G EPON GPON With bandwidth up to 10-40G, how to leverage the huge bandwidth to 1G EPON provide diversified value-added and services using a uniform optical access network for operators to generate more revenue become more important. A/BPON 622M Yr 2002 2005 2009 2010 2012 2014 2016 2017 HUAWEI TECHNOLOGIES Co., Ltd. HUAWEI Confidential

Cable Access Network Trend Future Soon NG2 Cable (40Gbps):  Spectrum: 5M~6GHz;  Network: FTTLA, N+1 Now NG Cable (10Gbps): Coax, 100~200HHP;  Spectrum: 5M~1.7GHz; Past  Technology: 40G Cable  Network: Digital optical fiber, Current Cable (1Gbps): (20G DOCSIS + 20G N+3 Coax, 500~1000HHP;  Spectrum: 5~860MHz; wireless front haul),  Technology: D3.1(LDPC+  Network: Analog optical iCoax(Remote PNM OFDM/OFDMA), PNM; fiber, N+5 Coax,  Architecture: DCA (Distribute diagnose); 500~1000HHP; CCAP Architecture), Remote  Architecture: Cable 2.0  Technology: D2.0/D3.0, PHY or Remote MAC and PHY. (Virtual CCAP, and Virtual Channel bonding (32DS+8US);  Architecture: I-CCAP, CPE). Integrate video and DOCSIS data. 2015 2019 2025 HUAWEI TECHNOLOGIES Co., Ltd. HUAWEI Confidential

Common Trend of various access technologies Data rate faster & faster Data rate Now Soon Future Copper (dedicated) 100 MBPS 1 GBPS 5-10 GBPS Cable (shared) 1 GBPS 10 GBPS 40 GBPS Optical (shared) 2.5 GBPS 10 GBPS 40~400 GBPS Spectrum wider & wider Frequency Spectrum Now Soon Future Copper (dedicated) 30 MHz 100 MHz >200 MHz Cable (shared) 860 MHz 1.7 GHz 6 GHz Optical (shared) 1 lambda x2.5G 4 lambda x 10G more lambda x >10G Loops shorter & shorter Loop length Now Soon Future Copper (dedicated) 300-1000m 100-300m <100m Cable (shared) 1000-2000m 500-1000m <200m HUAWEI TECHNOLOGIES Co., Ltd. HUAWEI Confidential

20 Advanced Mathematical Tools for 5G Engineering  Discipline of Random Matrix Theory  Discipline of Free Probability Theory  Discipline of Stochastic Geometry  Discipline of Discrete Mathematics  Discipline of Statistics  Discipline of Game Theory  Discipline of Mean Field Theory  Discipline of Information Theory  Discipline of Signal Processing  Discipline of Queuing Theory  Discipline of Estimation Theory  Discipline of Decision theory  Discipline of Probability Theory “Typesetting  Discipline of Optimization Theory Standard”.  Discipline of Statistical Mechanics  Discipline of Factor Graphs  Discipline of Control Theory  Discipline of Learning theory  Discipline on Partial Differential Equations Theory  Discipline of Optimal Transport Theory Page 39 HUAWEI TECHNOLOGIES CO., LTD. Huawei Proprietary - Restricted Distribution

Part 1: Architecture Design of 5G: General Mathematical Problem Formulation “Typesetting Standard”. Page 40 HUAWEI TECHNOLOGIES CO., LTD. Huawei Proprietary - Restricted Distribution

Where to start from? • Tons of Plenary Talks and Overview Articles - Fulfilling dream of ubiquitous wireless connectivity • Expectation: Many Metrics Should Be Improved in 5G - Higher user data rates - Higher area throughput - Great scalability in number of connected devices - Higher reliability and lower latency - Better coverage with more uniform user rates - Improved energy efficiency • These are Conflicting Metrics! - Higher user data rate 41

The clean slate approach 42

How to optimally deploy your antennas? 43

What if we are only interested in the average throughput per UT? 44

What if we are only interested in the average throughput per UT? 45

What if we are only interested in the average throughput per UT? 46

What if we are only interested in the average throughput per UT? 47

What if we are only interested in the average throughput per UT? 48

What if we are only interested in the average throughput per UT? 49

What if we are only interested in the average throughput per UT? 50

What if we are only interested in the average throughput per UT? 51

What if we are only interested in the average throughput per UT? 52

Part 2: Architecture Design of 5G: Optimization of Energy Efficiency “Typesetting Standard”. Page 53 HUAWEI TECHNOLOGIES CO., LTD. Huawei Proprietary - Restricted Distribution

Let us know focus on two metrics … • Expectation: Many Metrics Should Be Improved in 5G - Higher user data rates - Higher area throughput - Great scalability in number of connected devices - Higher reliability and lower latency - Better coverage with more uniform user rates - Improved energy efficiency • These are Conflicting Metrics! - Difficult to maximize theoretically all metrics simultaneously - Our goal: High energy efficiency (EE) with uniform user rates 54

How to Measure Energy-Efficiency? • Energy-Efficiency (EE) in bit/Joule Average Sum Rate bit/s/cell Power Consumption Joule/s/cell 𝐹𝐹 = • Conventional Academic Approaches: - Maximize rates with fixed power - Minimize transmit power for fixed rates New Problem: Balance rates and power consumption Important to account for overhead signaling and circuit power! 55

Single-Cell: Optimizing for Energy-Efficiency • Clean Slate Design - Single Cell: One base station (BS) with 𝑁 antennas - Geometry: Random distribution for user locations and pathlosses - Multiple users: Pick 𝐿 users randomly and serve with some rate 𝑆 Problem Next Step Formulation Find expression: Select ( 𝑁 , 𝐿 , 𝑆 ) EE as a function to maximize EE! of 𝑁 , 𝐿 , 𝑆 . 56

System Model: Protocol • Time-Division Duplex (TDD) Protocol - Uplink and downlink separated in time - Uplink fraction ζ (ul) and downlink fraction ζ (dl) • Coherence Block - 𝐶 Hz bandwidth = 𝐶 “channel uses” per second (symbol time 1/𝐶 ) - Channel stays fixed for 𝑉 channel uses (symbols) = Coherence block - Determines how often we send pilot signals to estimate channels Assumption: Perfect channel estimation (relaxed later) 57

System Model: Channels • Flat-Fading Channels 𝐢 2 𝐢 1 - Channel between BS and User 𝑙 : h 𝑙 ∈ ℂ 𝑁 - Rayleigh fading: h 𝑙 ~ 𝐷𝑂(𝟏, λ 𝑙 𝐉) - Channel variances λ 𝑙 : Random variables, pdf 𝑔 λ (𝑦) • Uplink Transmission - User 𝑙 transmits signal 𝑡 𝑙 with power 𝔽 |𝑡 𝑙 | 2 = p 𝑙 (ul) [Joule/channel use] Signals from other users - Received signal at BS: (interference) 𝐿 + 𝐨 𝒛 = h 𝑙 𝑡 𝑙 + h 𝑗 𝑡 𝑗 Signal of User 𝑙 Noise ~ 𝐷𝑂(𝟏, 𝜏 2 𝐉) 𝑗=1, 𝑗≠𝑙 𝐼 𝒛 : - Recover 𝑡 𝑙 by receive beamforming 𝐡 𝑙 as 𝐡 𝑙 2 𝑡 𝑙 2 𝐡 𝑙 𝐼 h 𝑙 (ul) |𝐡 𝑙 𝔽 𝐼 h 𝑙 | 2 p 𝑙 (ul) = 2 SINR 𝑙 2 = 2 (ul) |𝐡 𝑙 + 𝜏 2 𝐡 𝑙 𝑡 𝑗 2 𝐡 𝑙 𝐼 h 𝑗 | 2 𝐼 h 𝑗 𝐼 𝐨 p 𝑗 𝔽 + 𝔽 𝐡 𝑙 𝑗≠𝑙 𝑗≠𝑙 58

System Model: Channels (2) • Flat-Fading Channels - Channel between BS and User 𝑙 : h 𝑙 ∈ ℂ 𝑁 - Rayleigh fading: h 𝑙 ~ 𝐷𝑂(𝟏, λ 𝑙 𝐉) - Channel variances λ 𝑙 : Random variables, pdf 𝑔 λ (𝑦) • Downlink Transmission - BS transmits 𝑒 𝑙 to User 𝑙 with power 𝔽 |𝑒 𝑙 | 2 = p 𝑙 (dl) [Joule/channel use] - Spatial directivity by beamforming vector 𝐰 𝑙 Signals from other users - Received signal at User 𝑙 : (interference) 𝐿 𝐼 𝐰 𝑙 𝐼 𝐰 𝑗 + 𝑜 𝑙 𝑧 𝑙 = 𝐢 𝑙 𝑒 𝑙 + 𝐢 𝑙 𝑒 𝑗 Signal to User 𝑙 𝐰 𝑙 𝐰 𝑗 Noise ~ 𝐷𝑂(0, 𝜏 2 ) 𝑗=1, 𝑗≠𝑙 - Recover 𝑒 𝑙 at User 𝑙 : (dl) |𝐢 𝑙 𝐼 v 𝑙 | 2 / 𝐰 𝑙 2 p 𝑙 (dl) = 2 + 𝜏 2 SINR 𝑙 (dl) |𝐢 𝑙 𝐼 v 𝑗 | 2 p 𝑗 / 𝐰 𝑗 59 𝑗≠𝑙

System Model: How Much Transmit Power? • Design Parameter: Gross rate 𝑆 (ul) ) for all 𝑙 in uplink - Make sure that 𝑆 = 𝐶 log 2 (1 + SINR 𝑙 (dl) ) for all 𝑙 in downlink 𝐶 log 2 (1 + SINR 𝑙 (ul) and p 𝑙 (dl) - Select beamforming 𝐡 𝑙 and 𝐰 𝑙 , adapt transmit power p 𝑙 - Gives 𝐿 Equations: ul 𝐡 𝑙 2 𝐼 h 𝑙 | 2 = (2 𝑆/𝐶 − 1)( + 𝜏 2 𝐡 𝑙 (ul) |𝐡 𝑙 𝐼 h 𝑗 2 ) for 𝑙 = 1, … , 𝐿 p 𝑙 p 𝑗 𝑗≠𝑙 2 2 𝐼 v 𝑙 𝐼 v 𝑗 𝐢 𝑙 𝐰 𝑙 2 = (2 𝑆/𝐶 − 1)( 𝐢 𝑙 dl dl + 𝜏 2 ) for 𝑙 = 1, … , 𝐿 p 𝑙 p 𝑗 𝑗≠𝑙 𝐰 𝑗 2 - Linear equations in transmit powers  Solve by Gaussian elimination! Total Transmit Power [Joule/s] for 𝐡 𝑙 = 𝐰 𝑙 2 𝐼 v 𝑙 𝐢 𝑙 (2 𝑆/𝐶 −1) 𝐰 𝑙 2 for 𝑙 = 𝑚 Uplink energy/symbol: 𝜏 2 𝐄 −𝐼 𝟐 where 𝐄 𝑙,𝑚 = 2 𝐼 v 𝑚 Downlink energy/symbol: 𝜏 2 𝐄 −1 𝟐 𝐢 𝑙 − 𝐰 𝑚 2 for 𝑙 ≠ 𝑚 Same total power: 𝑄 trans = 𝐶𝔽 𝜏 2 𝟐 𝐼 𝐄 −1 𝟐 = 𝐶𝔽 𝜏 2 𝟐 𝐼 𝐄 −𝐼 𝟐 60

System Model: How Much Transmit Power? (2) • What did we Derive? - Optimal power allocation for fixed beamforming vectors • Different Beamforming - Notation: 𝐇 = 𝐡 1 , … , 𝐡 𝐿 𝐖 = [𝐰 1 , … , 𝐰 𝐿 ] , 𝐈 = [𝐢 1 , … , 𝐢 𝐿 ] , ul , … , p 𝐿 𝐐 (ul) = diag(p 1 (ul) ) Minimize Maximize interference signal - Maximum ratio trans./reception (MRT/MRC): 𝐇 = 𝐖 = 𝐈 𝐇 = 𝐖 = 𝐈 𝐈 𝐼 𝐈 −1 - Zero-forcing (ZF) beamforming: 𝐇 = 𝐖 = 𝜏 2 𝐉 + 𝐈 𝐐 (ul) 𝐈 𝐼 −1 𝐈 - Optimal beamforming: Balance signal and interference (iteratively!) 61

System Model: How Much Transmit Power? (3) • Simplified Expressions for ZF ( 𝑁 ≥ 𝐿 + 1 ) - Main property: 𝐈 𝐼 𝐖 = 𝐈 𝐼 𝐈 𝐈 𝐼 𝐈 −1 = 𝐉 2 𝐼 v 𝑙 𝐢 𝑙 Property (2 𝑆/𝐶 −1) 𝐰 𝑙 2 for 𝑙 = 𝑚 1 (2 𝑆/𝐶 −1) 𝐰 𝑙 2 for 𝑙 = 𝑚 - Hence: 𝐄 𝑙,𝑚 = = of Wishart 2 𝐼 v 𝑚 𝐢 𝑙 0 for 𝑙 ≠ 𝑚 matrices − 𝐰 𝑚 2 for 𝑙 ≠ 𝑚 - Total transmit power: 𝑄 trans = 𝔽 𝐶𝜏 2 𝟐 𝐼 𝐄 −1 𝟐 = 𝐶𝜏 2 (2 𝑆/𝐶 − 1) 𝔽 2 𝐰 𝑙 𝑙 𝐈 𝐼 𝐈 −1 𝑁 − 𝐿 𝔽 1 𝐿 Call this 𝒯 λ = tr = 𝐶𝜏 2 (2 𝑆/𝐶 − 1) λ (depends on cell) Summary: Transmit Power with ZF Parameterize gross rate as 𝑆 = 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) for some 𝛽 Total transmit power: 𝑄 trans = 𝛽𝐶𝜏 2 𝒯 λ 𝐿 [Joule/s] 62

Detailed Power Consumption Model • What Consumes Power? - Not only radiated transmission power - Circuits, signal processing, backhaul, etc. - Must be specified as functions of 𝑁, 𝐿, 𝑆 • Power Amplifiers - Amplifier efficiencies: η (ul) , η (dl) ∈ (0,1] 𝑄 trans Summary: ζ (ul) ζ (dl) η 1 - Average inefficiency: η η (ul) + η (dl) = • Active Transceiver Chains - 𝑄 FIX = Fixed power (control signals, oscillator at BS, standby, etc.) - 𝑄 BS = Circuit power / BS antenna (converters, mixers, filters) - 𝑄 UE = Circuit power / user (oscillator, converters, mixer, filters) Summary: 𝑄 FIX + 𝑁 ∙ 𝑄 BS + 𝐿 ∙ 𝑄 UE 63

Detailed Power Consumption Model (2) • Signal Processing - Channel estimation and beamforming - Efficiency: 𝑀 BS , 𝑀 UE arithmetic operations / Joule 2τ (ul) 𝑁𝐿 2 + 4τ (dl) 𝐿 2 • Channel Estimation: 𝐶 𝑉 𝑀 BS 𝑀 UE - Once in uplink/downlink per coherence block - Pilot signal lengths: τ (ul) 𝐿, τ (dl) 𝐿 for some τ (ul) , τ (dl) ≥ 1 τ ul +τ ul 𝐷 beamforming 𝐶 𝐿 2𝑁𝐿 • Linear Processing (for 𝐇 = 𝐖 ): 𝑀 BS + 𝐶 1 − 𝑉 𝑀 BS 𝑉 - Compute beamforming vector once per coherence block - Use beamforming for all 𝐶(1 − τ ul + τ ul 𝐿/𝑉) symbols 3𝑁𝐿 for MRT/MRC 3𝑁𝐿 2 + 𝑁𝐿 + 1 3 𝐿 3 for ZF - Types of beamforming: 𝐷 beamforming = Number of iterations 𝑅(3𝑁𝐿 2 + 𝑁𝐿 + 1 3 𝐿 3 ) for Optimal 64

Detailed Power Consumption Model (3) • Coding and Decoding: 𝑆 sum (𝑄 DEC ) COD + 𝑄 - 𝑄 COD = Energy for coding data / bit - 𝑄 DEC = Energy for decoding data / bit τ ul 𝐿 τ dl 𝐿 - Sum rate: 𝑆 sum = 𝐿 ζ (ul) − 𝑆 + 𝐿 ζ (dl) − 𝑆 𝑉 𝑉 = 𝐿 1 − (τ ul + τ dl )𝐿 𝑆 𝑉 • Backhaul Signaling: 𝑄 BT BH + 𝑆 sum 𝑄 - 𝑄 BH = Load-independent backhaul power - 𝑄 BT = Energy for sending data over backhaul / bit 65

Detailed Power Consumption Model: Summary • Many Things Consume Power - Parameter values (e.g., 𝑄 BS , 𝑄 UE ) change over time - Structure is important for analysis Fixed power Generic Power Model 𝑄 trans + 𝐷 0,0 + 𝐷 0,1 𝑁 + 𝐷 1,0 𝐿 + 𝐷 1,1 𝑁𝐿 + 𝐷 2,0 𝐿 2 + 𝐷 3,0 𝐿 3 + 𝐷 2,1 𝑁𝐿 2 η + 𝐵𝐿 1 − (τ ul + τ dl )𝐿 Circuit power per 𝑆 Cost of signal processing Coding/decoding/ 𝑉 Transmit transceiver chain backhaul with amplifiers • Observations for some parameters 𝐷 𝑚,𝑛 and 𝐵 - Polynomial in 𝑁 and 𝐿  Increases faster than linear with 𝐿 - Depends on cell geometry only through 𝑄 trans 66

Finally: Problem Formulation Average Sum Rate bit/s/cell • Maximize Energy-Efficiency: 𝐿 1 − (τ ul + τ dl )𝐿 𝑆 maximize 𝑉 𝑁, 𝐿, 𝑆 + 𝐵𝐿 1 − (τ ul + τ dl )𝐿 𝑄 trans 𝟒 𝟑 + 𝐷 𝑗,0 𝐿 𝑗 + 𝐷 𝑗,1 𝑁𝐿 𝑗 𝑆 η 𝑉 𝒋=𝟏 𝒋=𝟏 Power Consumption Joule/s/cell Closed Form Expressions with ZF Recall: 𝑆 = 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) for some 𝛽 and 𝑄 trans = 𝛽𝐶𝜏 2 𝒯 λ 𝐿 Define: τ = τ ul + τ dl 𝐿 1 − τ𝐿 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) maximize 𝑉 𝑁, 𝐿, 𝛽 𝛽𝐶𝜏 2 𝒯 λ 𝐿 + 𝐵𝐿 1 − τ𝐿 𝟒 𝟑 𝐷 𝑗,0 𝐿 𝑗 𝐷 𝑗,1 𝑁𝐿 𝑗 + + 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) η 𝑉 𝒋=𝟏 𝒋=𝟏 Simple ZF expression: Used for analysis, other beamforming by simulation 67

Why Such a Detailed/Complicated Model? • Simplified Model  Unreliable Optimization Results - Two examples based on ZF - Beware: Both has appeared in the literature! • Example 1: Fixed circuit power and no coding/decoding/backhaul 𝐿 1 − τ𝐿 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) maximize 𝑉 𝑁, 𝐿, 𝛽 𝛽𝐶𝜏 2 𝒯 λ 𝐿 + 𝐷 0,0 η - If 𝑁 → ∞ , then log 2 (1 + 𝛽(𝑁 − 𝐿)) → ∞ and thus EE → ∞ ! • Example 2: Ignore pilot overhead and signal processing 𝐶 log 2 (1 + 𝛽𝐿(𝑁 𝐿 − 1)) 𝐿𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) maximize 𝑁, 𝐿, 𝛽 = + 𝐷 0,0 𝛽𝐶𝜏 2 𝒯 λ 𝐿 𝛽𝐶𝜏 2 𝒯 λ 𝐿 + 𝐷 1,0 + 𝐷 0,1 𝑁 + 𝐷 0,0 + 𝐷 1,0 𝐿 + 𝐷 0,1 𝑁 η η 𝐿 𝑁 𝑁 - If 𝑁, 𝐿 → ∞ with 𝐿 = constant > 1 , then log 2 (1 + 𝛽𝐿( 𝐿 − 1)) → ∞ and EE → ∞ ! 68

Optimization of Energy-Efficiency 69

Preliminaries • Our Goal - Optimize number of antennas 𝑁 For ZF processing - Optimize number of active users 𝐿 - Optimize the (normalized) transmit power 𝛽 • Outline - Optimize each variable separately - Devise an alternating optimization algorithm Definition (Lambert 𝑋 function) Lambert 𝑋 function, 𝑋(𝑦) , solves equation 𝑋(𝑦)𝑓 𝑋(𝑦) = 𝑦 • The function is increasing and satisfies 𝑋(0) = 0 • 𝑓 𝑋(𝑦) behaves as a linear function (i.e., 𝑓 𝑋(𝑦) ≈ 𝑦 ): • 70

Solving Optimization Problems • How to Solve an Optimization Problem? - Simple if the function is “nice”: Quasi-Concave Function For any two points on the graph of the function, the line between the points is below the graph Property: Goes up and then down Examples: −𝑦 2 , log(𝑦) • Maximization of a Quasi-Concave Function 𝜒(𝑦) : 𝑒 1. Compute the first derivative 𝑒𝑦 𝜒(𝑦) 𝑒 2. Find switching point by setting 𝑒𝑦 𝜒 𝑦 = 0 3. Only one solution  It is the unique maximum! 71

Optimal Number of BS Antennas • Find 𝑁 that maximizes EE with ZF: 𝐿 1 − τ𝐿 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) maximize 𝑉 𝑁 ≥ 𝐿 + 1 𝛽𝐶𝜏 2 𝒯 λ 𝐿 + 𝐵𝐿 1 − τ𝐿 𝟒 𝟑 + 𝐷 𝑗,0 𝐿 𝑗 + 𝐷 𝑗,1 𝑁𝐿 𝑗 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) η 𝑉 𝒋=𝟏 𝒋=𝟏 Theorem 1 (Optimal 𝑁 ) EE is quasi-concave w.r.t. 𝑁 and maximized by 𝟒 𝑋 𝛽(𝐶𝜏 2 𝒯 λ 𝐿/η+ 𝐷 𝑗,0 𝐿 𝑗 ) +𝛽𝐿−1 𝒋=𝟏 +1 𝑓 𝟑 𝐷 𝑗,1 𝐿 𝑗 𝑓 𝑁 ∗ = 𝑓 + 𝛽𝐿 − 1 𝒋=𝟏 𝛽 • Observations - Increases with circuit coefficients independent of 𝑁 (e.g., 𝑄 FIX , 𝑄 UE ) - Decreases with circuit coefficients multiplied with 𝑁 (e.g., 𝑄 BS , 1/𝑀 𝐶𝑇 ) - Independent of cost of coding/decoding/backhaul 𝛽 - Increases with power 𝛽 approx. as log 𝛽 (almost linear) 26 August 2014 72

Optimal Transmit Power • Find 𝛽 that maximizes EE with ZF: 𝐿 1 − τ𝐿 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) maximize 𝑉 𝛽 ≥ 0 𝛽𝐶𝜏 2 𝒯 λ 𝐿 + 𝐵𝐿 1 − τ𝐿 𝟒 𝟑 + 𝐷 𝑗,0 𝐿 𝑗 + 𝐷 𝑗,1 𝑁𝐿 𝑗 𝐶 log 2 (1 + 𝛽(𝑁 − 𝐿)) η 𝑉 𝒋=𝟏 𝒋=𝟏 Theorem 2 (Optimal 𝛽 ) EE is quasi-concave w.r.t. 𝛽 and maximized by 𝟒 𝟑 𝐷 𝑗,0 𝐿 𝑗 𝐷 𝑗,1 𝑁𝐿 𝑗 (𝑁−𝐿)( + ) η −1 𝒋=𝟏 𝒋=𝟏 𝑋 𝑓 +1 𝐶𝜏 2 𝒯 λ 𝑓 𝛽 ∗ = 𝑓 − 1 𝑁 − 𝐿 • Observations - Increases with all circuit coefficients (e.g., 𝑄 FIX , 𝑄 BS , 𝑄 UE , 1/𝑀 𝐶𝑇 ) - Independent of cost of coding/decoding/backhaul More circuit power  𝑁 - Increases with 𝑁 approx. as log 𝑁 (almost linear) More transmit power 73

Optimal Number of Users • Find 𝐿 that maximizes EE with ZF: 𝐿 1 − τ𝐿 𝐶 log 2 (1 + 𝛽 (𝛾 − 1)) maximize 𝑉 𝐿 ≥ 0 𝐶𝜏 2 𝒯 λ 𝛽 + 𝐵𝐿 1 − τ𝐿 𝟒 𝟑 + 𝐷 𝑗,0 𝐿 𝑗 + 𝐷 𝑗,1 𝛾 𝐿 𝑗+1 𝐶 log 2 (1 + 𝛽 (𝛾 − 1)) η 𝑉 𝒋=𝟏 𝒋=𝟏 𝑁 where 𝛽 = 𝛽𝐿 and 𝛾 = 𝐿 are fixed Theorem 3 (Optimal 𝐿 ) EE is quasi-concave w.r.t. 𝐿 Maximized by the root of a quartic polynomial: Closed form for 𝐿 ∗ but very “large” expressions • Observations - Increases with fixed circuit power (e.g., 𝑄 FIX ) - Decreases with circuit coefficients multiplied with 𝑁 or 𝐿 ( 𝑄 BS , 𝑄 UE , 1/ 𝑀 𝐶𝑇 ) 74

Impact of Cell Size • Are Smaller Cells More Energy Efficient? 1 - Recall: 𝒯 λ = 𝔽 λ - Smaller cells  λ is larger  𝒯 λ is smaller • For any given parameters 𝑁, 𝛽, 𝐿 - Smaller 𝒯 λ  smaller transmit power 𝛽𝐶𝜏 2 𝒯 λ 𝐿 - Higher EE! • Expressions for 𝑁 ∗ , 𝛽 ∗ , 𝐿 ∗ Smaller cells: Less hardware and fewer users per cell - 𝑁 ∗ and 𝐿 ∗ increases with 𝒯 λ Use shorter distances to reduce power - 𝛽 ∗ decreases with 𝒯 λ Dependence on Other Parameters Many other observations can be made Example: Impact of bandwidth 𝐶 , coherence block length 𝑉 , etc. 75

Alternating Optimization Algorithm • Joint EE Optimization - EE is a function of 𝑁, 𝛽, and 𝐿 - Theorems 1-3 optimize one parameter, when the other two are fixed - Can we optimize all of them? Algorithm: Alternating Optimization 1. Assume that an initial set (𝑁, 𝛽, 𝐿) is given 2. Update number of users 𝐿 (and implicitly 𝑁 and 𝛽 ) using Theorem 3 3. Update number of antennas 𝑁 using Theorem 1 4. Update transmit power ( 𝛽 ) using Theorem 2 5. Repeat 2.-5. until convergence Theorem 4 Disclaimer The algorithm convergences 𝑁 and 𝐿 should be integers to a local optimum to the Theorems 1 and 3 give real joint EE optimization problem numbers  Take one of the 2 closest integers 76

Single-Cell Simulation Scenario • Main Characteristics - Circular cell with radius 250 m - Uniform user distribution - Uncorrelated Rayleigh fading - Typical 3GPP pathloss model • Many Parameters in the System Model - We found numbers from ≈ 2012 in the literature: 77

Optimal Single-Cell System Design: ZF Beamforming Optimum 𝑁 = 165 𝐿 = 104 α = 0.87 User rates: ≈64 -QAM Massive MIMO! Name for multi-user MIMO with very many antennas 78

Optimal Single-Cell System Design: “Optimal” Beamforming 𝑅 = 3 Optimum 𝑁 = 145 𝐿 = 95 α = 0.91 User rates: ≈64 -QAM Not optimal! Gives optimal beamforming but computations are too costly 79

Optimal Single-Cell System Design: MRT/MRC Beamforming Optimum 𝑁 = 81 𝐿 = 77 α = 0.24 User rates: ≈2 -PSK Observation Lower EE than with ZF Also Massive MIMO setup Low rates 80

Multi-Cell Scenarios and Imperfect Channel Knowledge • Limitations in Previous Analysis - Perfect channel knowledge - No interference from other cells • Consider a Symmetric Multi-Cell Scenario: Assumptions All cells look the same  Jointly optimized All cells transmit in parallel Fractional pilot reuse: Divide cells into clusters Uplink pilot length τ (ul) 𝐿 for τ (ul) ∈ {1,2,4} 81

Multi-Cell Scenarios and Imperfect Channel Knowledge (2) • Inter-Cell Interference - λ 𝑘𝑚 = Channel attenuation between a random user in cell 𝑚 and BS 𝑘 λ 𝑘𝑚 - ℐ = is relative severity of inter-cell interference 𝔽 𝑚≠𝑘 λ 𝑘𝑘 Lemma (Achievable Rate) Consider same transmit power as before: 𝑄 trans = 𝛽𝐶𝜏 2 𝒯 λ 𝐿 Achievable rate under ZF and pilot-based channel estimation: 𝑆 = 𝐶 log 2 1 𝛽(𝑁 − 𝐿) 1 + 𝛽𝐿ℐ − 𝛽𝐿(1 + ℐ PC 2 ) + 1 𝛽 𝑁 − 𝐿 ℐ PC + 1 + ℐ PC + 𝛽𝐿τ ul 2 Intra/inter-cell interference Pilot contamination (PC) λ 𝑘𝑚 λ 𝑘𝑚 where ℐ PC = and ℐ PC = 𝔽 𝔽 𝑚≠𝑘 only in cluster 𝑚≠𝑘 only in cluster λ 𝑘𝑘 (Weaker) λ 𝑘𝑘 (Strong interference) 82

Multi-Cell Scenarios and Imperfect Channel Knowledge (3) • Multi-Cell Rate Expression not Amenable for Analysis - No closed-form optimization in multi-cell case - Numerical analysis still possible • Similarities and Differences - Power consumption is exactly the same - Rates are smaller: Upper limited by pilot contamination: 𝛽(𝑁−𝐿) 1 𝑆 = 𝐶 log 2 1 + 1+𝛽𝐿ℐ −𝛽𝐿(1+ℐ PC2 ) ≤ 𝐶 log 2 1 + ℐ PC 1 𝛽 𝑁−𝐿 ℐ PC + 1+ℐ PC + 𝛽𝐿τ ul - Overly high rates not possible (but we didn’t get that…) - Clustering (fractional pilot reuse) might be good to reduce interference 83

Optimal Multi-Cell System Design: ZF Beamforming Optimum 𝑁 = 123 𝐿 = 40 α = 0.28 τ (ul) = 4 User rates: ≈4 -QAM Massive MIMO! Many BS antennas Note that 𝑁/𝐿 ≈ 3 84

Different Pilot Reuse Factors Higher Pilot Reuse Higher EE and rates! Controlling inter-cell interference is very important! Area Throughput We only optimized EE Achieved 6 Gbit/s/km 2 over 20 MHz bandwidth METIS project mentions 100 Gbit/s/km 2 as 5G goal  Need higher bandwidth! 85

Energy Efficient to Use More Transmit Power? • Recall from Theorem 2: Transmit power increases 𝑁 - Figure shows EE-maximizing power for different 𝑁 Essentially linear growth Power per antenna decreases • Intuition: More Circuit Power  Use More Transmit Power - Different from 1/ 𝑁 scaling laws in recent massive MIMO literature - Power per antennas decreases, but only logarithmically 86

Part 3: Architecture Design of 5G: Beyond Energy Efficiency Optimization “Typesetting Standard”. Page 87 HUAWEI TECHNOLOGIES CO., LTD. Huawei Proprietary - Restricted Distribution

Optimize more than Energy-Efficiency • Recall: Many Metrics in 5G Discussions - Average rate (Mbit/s/active user) - Average area rate (Mbit/s/km 2 ) - Energy-efficiency (Mbit/Joule) - Active devices (per km 2 ) - Delay constraints (ms) • So Far: Only cared about EE - Ignored all other metrics Optimize Multiple Metrics We want efficient operation w.r.t. all objectives Is this possible? For all at the same time? 88

Multi-Objective Network Optimization 89

Basic Assumptions: Multi-Objective Optimization • Consider 𝑂 Performance Metrics - Objectives to be maximized - Notation: 𝑕 1 𝐲 , 𝑕 2 𝐲 , … , 𝑕 𝑂 𝐲 - Example: individual user rates, area rates, energy-efficiency • Optimization Resources - Resource bundle: - Example: power, resource blocks, network architecture, antennas, users - Feasible allocation: 90

Single or Multiple Performance Metrics • Conventional Optimization • Multi-Objective Optimization - Pick one prime metric: 𝑕 1 𝐲 - Consider all 𝑂 metrics - Turn 𝑕 1 𝐲 , 𝑕 2 𝐲 , … , 𝑕 𝑂 𝐲 - No order or preconceptions! into constraints - Optimization problem: [𝑕 1 𝐲 , 𝑕 2 𝐲 , … , 𝑕 𝑂 𝐲 ] - Optimization problem: Solution: Pareto 𝑕 2 𝐲 ≥ 𝐷 2 , … , 𝑕 𝑂 𝐲 ≥ 𝐷 𝑂 . A set Boundary Improve a metric  Degrading - Solution: A scalar number another metric - Cons: Is there a prime 91 metric?

Why Multi-Objective Optimization? • Study Tradeoffs Between Metrics - When are metrics aligned or conflicting? - Common in engineering and economics – new in communication theory A Posteriori Approach Generate region (computationally demanding!) Look at region and select operating point Highly Relatively conflicting aligned 92

A Priori Approach • No Objectively Optimal Solution - Utopia point outside of region  Only subjectively “good” solutions exist • System Designer Selects Utility Function 𝑔 ∶ ℝ 𝑂 → ℝ - Describes subjective preference (larger is better) Aggregate metric • Examples: Sum performance: Proportional fairness: Fairness Harmonic mean: of metrics Max-min fairness: We obtain a simplified problem: - Solution: A scalar number (Gives one Pareto optimal point) 𝑔(𝑕 1 𝐲 , 𝑕 2 𝐲 , … , 𝑕 𝑂 𝐲 ) - Takes all metrics into account! 93

Example: Optimization of 5G Networks • Design Cellular Network - Symmetric system - 16 base stations (BSs) - Select: 𝑁 = # BS antennas 𝐿 = # users 𝑄 = power/antenna • Resource bundle: 500 20 W

Example: Optimization of 5G Networks (2) • Downlink Multi-Cell Transmission - Each BS serves only its own 𝐿 users - Coherence block length: 𝑉 - BS knows channels within the cell (cost: 𝐿/𝑉 ) - ZF beamforming: no intra-cell interference - Interference leaks between cells • Average User Rate Array gain Power/user 𝑄 𝐿 (𝑁 − 𝐿) 𝑆 average = 𝐶 1 − 𝐿 𝑉 log 2 1 + 𝒯 λ 𝜏 2 + ℐ Bandwidth (10 MHz) CSI estimation Noise / Relative inter-cell overhead ( 𝑉 = 1000 ) pathloss interference 2 July 2014 ( 1.72 ∙ 10 −4 ) ( 0.54 )

Example: Optimization of 5G Networks (3) • What Consumes Power? - Transmit power (+ losses in amplifiers) - Circuits attached to each antenna - Baseband signal processing - Fixed load-independent power • Total Power Consumption 𝐶𝐷 beamforming 𝑄 total = 𝑄 trans + 𝐷 0,0 + 𝐷 1,0 𝐿 + 𝐷 0,1 𝑁 + η 𝑉 𝑀 BS Fixed power Amplifier Circuit power ( 10 W ) Computing efficiency per antenna ZF beamforming ( 0.31 ) ( 1 W ) Circuit power ( 2.3 ∙ 10 −6 ∙ 𝑁𝐿 2 ) per user ( 0.3 W )

Example: Results 1. Average user rate 3 Objectives 2. Total area rate 3. Energy-efficiency Observations Area and user rates are conflicting objectives Only energy efficient at high area rates Different number of users

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

Summary • Multi-Objective Optimization - Rigorous way to study problems with multiple performance metrics • 5G Characterized by Multiple Metrics - Calls for multi-objective network design - Framework to derive interplay between EE and other performance metrics - A way to make informed decisions! Further Reading E. Björnson, E. Jorswieck, M. Debbah, B. Ottersten, “ Multi-Objective Signal Processing Optimization: The Way to Balance Conflicting Metrics in 5G Systems ,” IEEE SPM, Nov. 2014. 99

Conclusion 100

Conclusions • What if a Cellular Network is Designed for High Energy-Efficiency? Average Sum Rate bit/s/cell - Energy-efficiency [bit/Joule] = Power Consumption Joule/s / cell - Necessary: Accurate expressions for rate and power consumption - Design parameters: Number of users, BS antennas, transmit power, BS density, and pilot reuse factor • Analytical and Numerical Results - Tractable problem formulation was developed - Fundamental interplay between system parameters obtained by analysis - Network densification is the way to high EE - Small cells and Massive MIMO have complementary benefits - Feasible to combine these techniques: Massive MIMO ≠ large size • Multi-Objective Optimization - Framework to jointly optimize energy-efficiency and other 5G metrics 101