Scientific Challenges of 5G

Transcription

1 Scientific Challenges of 5G Mérouane Debbah Huawei, France Joint work with: Luca Sanguinetti * and Emil Björnson * * * University of Pisa, Dipartimento di Ingegneria dell Informazione, Pisa, Italy * * Division of Communication Systems at Linköping University, Sweden 1

2 5g-4g=1g 2

3 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 3

4 20 Advanced Mathematical Tools for 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 Discipline of Optimization Theory 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 4

5 What if we are only interested in the average throughput per UT? 5

6 The clean slate approach 6

7 What if we are only interested in the average throughput per UT? 7

8 How to optimally deploy your antennas? 8

9 What if we are only interested in the average throughput per UT? 9

10 What if we are only interested in the average throughput per UT? 10

11 What if we are only interested in the average throughput per UT? 11

12 What if we are only interested in the average throughput per UT? 12

13 What if we are only interested in the average throughput per UT? 13

14 What if we are only interested in the average throughput per UT? 14

15 What if we are only interested in the average throughput per UT? 15

16 What if we are only interested in the average throughput per UT? 16

17 What if we are only interested in the average throughput per UT? 17

18 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 18

19 How to Measure Energy-Efficiency? Energy-Efficiency (EE) in bit/joule Average Sum Rate bit/s/cell EE = Power Consumption Joule/s/cell 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! 19

20 Single-Cell: Optimizing for Energy-Efficiency Clean Slate Design - Single Cell: One base station (BS) with M antennas - Geometry: Random distribution for user locations and pathlosses - Multiple users: Pick K users randomly and serve with some rate R Problem Formulation Select (M,K,R) to maximize EE! Next Step Find expression: EE as a function of M,K,R. 20

21 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 - B Hz bandwidth = B channel uses per second (symbol time 1/B) - Channel stays fixed for U channel uses (symbols) = Coherence block - Determines how often we send pilot signals to estimate channels Assumption: Perfect channel estimation (relaxed later) 21

22 System Model: Channels Flat-Fading Channels - Channel between BS and User k: h k C M - Rayleigh fading: h k ~ CN(0, λ k I) - Channel variances λ k : Random variables, pdf f λ (x) h 1 h 2 Uplink Transmission - User k transmits signal s k with power E s k 2 = p k (ul) [Joule/channel use] - Received signal at BS: Signal of User k K y = h k s k + h i s i i=1, i k + n - Recover s k by receive beamforming g k as g k H y: E s 2 (ul) k g H k h k SINR k = E s 2 i g H 2 i k k h i + E g H k n 2 = 2 Signals from other users (interference) Noise ~ CN(0, σ 2 I) p k (ul) gk H h k 2 p i (ul) gk H h i 2 i k + σ 2 g k 2 22

23 System Model: Channels (2) Flat-Fading Channels - Channel between BS and User k: h k C M - Rayleigh fading: h k ~ CN(0, λ k I) - Channel variances λ k : Random variables, pdf f λ (x) Downlink Transmission - BS transmits d k to User k with power E d k 2 = p k (dl) [Joule/channel use] - Spatial directivity by beamforming vector v k - Received signal at User k: H y k = h v K k H k d v k + h v Signals from other users i (interference) k d k v i + n k i i=1, i k Signal to User k Noise ~ CN(0, σ 2 ) - Recover d k at User k: (dl) (dl) p H SINR k = k hk v k 2 / v 2 k (dl) i k p H i hk v i 2 / v 2 i + σ 2 23

24 System Model: How Much Transmit Power? Design Parameter: Gross rate R (ul) B log 2 (1 + SINR - Make sure that R = k ) for all k in uplink (dl) B log 2 (1 + SINR k ) for all k in downlink (ul) (dl) - Select beamforming g k and v k, adapt transmit power p k and pk - Gives K Equations: p k (ul) gk H h k 2 = (2 R/B 1)( ul p i g H 2 i k k h i + σ 2 g 2 k ) for k = 1,, K 2 dl h p kh v k = k v 2 (2R/B dl h H 2 1)( p k v i i k k i v 2 + σ 2 ) for k = 1,, K i - Linear equations in transmit powers Solve by Gaussian elimination! Total Transmit Power [Joule/s] for g k = v k Uplink energy/symbol: σ 2 D H 1 Downlink energy/symbol: σ 2 D 1 1 Same total power: P trans = BE σ 2 1 H D 1 1 where D k,l = = BE σ 2 1 H D H 1 h kh v k 2 (2 R/B 1) v k 2 h k H v l 2 v l 2 for k = l for k l 24

25 System Model: How Much Transmit Power? (2) What did we Derive? - Optimal power allocation for fixed beamforming vectors Different Beamforming - Notation: G = g 1,, g K V = [v 1,, v K ], H = [h 1,, h K ], P (ul) = diag(p 1 ul,, p K (ul) ) Minimize interference Maximize signal - Maximum ratio trans./reception (MRT/MRC): G = V = H - Zero-forcing (ZF) beamforming: G = V = H H H H 1 - Optimal beamforming: G = V = σ 2 I + H P (ul) H H 1 H Balance signal and interference (iteratively!) 25

26 System Model: How Much Transmit Power? (3) Simplified Expressions for ZF (M K + 1) - Main property: H H V = H H H H H H 1 = I - Hence: D k,l = - Total transmit power: h kh v k 2 (2 R/B 1) v 2 for k = l k h k H 2 = v l for k l v 2 l 1 (2 R/B 1) v k 2 P trans = E Bσ 2 1 H D 1 1 = Bσ 2 (2 R/B 1) E v k 2 k for k = l 0 for k l Property of Wishart matrices = Bσ 2 (2 R/B K 1) M K E 1 λ = tr H H H 1 Call this S λ (depends on cell) Summary: Transmit Power with ZF Parameterize gross rate as R = B log 2 (1 + α(m K)) for some α Total transmit power: P trans = αbσ 2 S λ K [Joule/s] 26

27 Detailed Power Consumption Model What Consumes Power? - Not only radiated transmission power - Circuits, signal processing, backhaul, etc. - Must be specified as functions of M, K, R Power Amplifiers - Amplifier efficiencies: η (ul), η (dl) (0,1] - Average inefficiency: ζ(ul) ζ(dl) η (ul) + = 1 η (dl) η Summary: P trans η Active Transceiver Chains - P FIX = Fixed power (control signals, oscillator at BS, standby, etc.) - P BS = Circuit power / BS antenna (converters, mixers, filters) - P UE = Circuit power / user (oscillator, converters, mixer, filters) Summary: P FIX + M P BS + K P UE 27

28 Detailed Power Consumption Model (2) Signal Processing - Channel estimation and beamforming - Efficiency: L BS, L UE arithmetic operations / Joule Channel Estimation: B 2τ (ul) MK 2 + 4τ(dl) K 2 U L BS L UE - Once in uplink/downlink per coherence block - Pilot signal lengths: τ (ul) K, τ (dl) K for some τ (ul), τ (dl) 1 Linear Processing (for G = V): B U C beamforming + B 1 τ ul +τ ul K L BS U - Compute beamforming vector once per coherence block - Use beamforming for all B(1 τ ul + τ ul K/U) symbols 3MK - Types of beamforming: C beamforming = Number of iterations 3MK 2 + MK K3 2MK L BS for MRT/MRC for ZF Q(3MK 2 + MK K3 ) for Optimal 28

29 Detailed Power Consumption Model (3) Coding and Decoding: R sum (P COD + P DEC ) - P COD = Energy for coding data / bit - P DEC = Energy for decoding data / bit - Sum rate: R sum = K ζ (ul) τ ul K U R + K = K 1 (τ ul + τ dl )K U ζ (dl) τ dl K U R R Backhaul Signaling: P BH + R sum P BT - P BH = Load-independent backhaul power - P BT = Energy for sending data over backhaul / bit 29

30 Detailed Power Consumption Model: Summary Many Things Consume Power - Parameter values (e.g., P BS, P UE ) change over time - Structure is important for analysis P trans η Fixed power Generic Power Model + C 0,0 + C 0,1 M + C 1,0 K + C 1,1 MK + C 2,0 K 2 + C 3,0 K 3 + C 2,1 MK 2 + AK 1 (τ ul + τ dl )K U R Transmit with amplifiers Circuit power per transceiver chain Cost of signal processing for some parameters C l,m and A Coding/decoding/ backhaul Observations - Polynomial in M and K Increases faster than linear with K - Depends on cell geometry only through P trans 30

31 Finally: Problem Formulation Maximize Energy-Efficiency: maximize M, K, R P trans η K 1 (τ ul + τ dl )K U Average Sum Rate bit/s/cell 3 + i=0 C i,0 K i 2 + i=0 C i,1 MK i + AK 1 (τ ul + τ dl )K U Power Consumption Joule/s/cell R R Closed Form Expressions with ZF Recall: R = B log 2 (1 + α(m K)) for some α and P trans = αbσ 2 S λ K Define: τ = τ ul + τ dl maximize M, K, α αbσ 2 S λ K η K 1 τk U B log 2(1 + α(m K)) 3 + i=0 C i,0 K i 2 + i=0 C i,1 MK i + AK 1 τk U B log 2(1 + α(m K)) Simple ZF expression: Used for analysis, other beamforming by simulation 31

32 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 maximize M, K, α K 1 τk U B log 2(1 + α(m K)) αbσ 2 S λ K η + C 0,0 - If M, then log 2 (1 + α(m K)) and thus EE! Example 2: Ignore pilot overhead and signal processing maximize M, K, α KB log 2 (1 + α(m K)) αbσ 2 = S λ K + C η 0,0 + C 1,0 K + C 0,1 M B log 2 (1 + αk( M K 1)) αbσ 2 S λ η + C 0,0 K + C 1,0 + C 0,1 M K - If M, K with M = constant > 1, then log K 2(1 + αk( M 1)) and EE! K 32

33 Optimization of Energy-Efficiency 33

34 Preliminaries Our Goal - Optimize number of antennas M - Optimize number of active users K - Optimize the (normalized) transmit power α For ZF processing Outline - Optimize each variable separately - Devise an alternating optimization algorithm Definition (Lambert W function) Lambert W function, W(x), solves equation W(x)e W(x) = x The function is increasing and satisfies W(0) = 0 e W(x) behaves as a linear function (i.e., e W(x) x): 34

35 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: x 2, log(x) Maximization of a Quasi-Concave Function φ(x): 1. Compute the first derivative d φ(x) dx 2. Find switching point by setting d φ x dx = 0 3. Only one solution It is the unique maximum! 35

36 Optimal Number of BS Antennas Find M that maximizes EE with ZF: maximize M K + 1 αbσ 2 S λ K η K 1 τk U B log 2(1 + α(m K)) 3 + i=0 C i,0 K i 2 + i=0 C i,1 MK i + AK 1 τk U B log 2(1 + α(m K)) Theorem 1 (Optimal M) EE is quasi-concave w.r.t. M and maximized by M = ew α(bσ 2 S λ K/η+ 3 i=0 C i,0 K i ) e C i,1 K i Observations - Increases with circuit coefficients independent of M (e.g., P FIX, P UE ) - Decreases with circuit coefficients multiplied with M (e.g., P BS, 1/L BS ) - Independent of cost of coding/decoding/backhaul - Increases with power α approx. as α (almost linear) 2 i=0 α log α + αk 1 e +1 + αk 1 26 August

37 Optimal Transmit Power Find α that maximizes EE with ZF: maximize α 0 αbσ 2 S λ K η K 1 τk U B log 2(1 + α(m K)) 3 + i=0 C i,0 K i 2 + i=0 C i,1 MK i + AK 1 τk U B log 2(1 + α(m K)) Theorem 2 (Optimal α) EE is quasi-concave w.r.t. α and maximized by α = ew η (M K)( Bσ 2 S λ 3 i=0 C i,0 K i + C i,1 MK i e M K 2 i=0 ) 1 e +1 1 Observations - Increases with all circuit coefficients (e.g., P FIX, P BS, P UE, 1/L BS ) - Independent of cost of coding/decoding/backhaul - Increases with M approx. as M log M (almost linear) More circuit power More transmit power 37

38 Optimal Number of Users Find K that maximizes EE with ZF: maximize K 0 αbσ 2 S λ η Observations K 1 τk U B log 2(1 + α(β 1)) 3 + i=0 C i,0 K i 2 + i=0 C i,1 β K i+1 + AK 1 τk U B log 2(1 + α(β 1)) where α = αk and β = M K are fixed Theorem 3 (Optimal K) EE is quasi-concave w.r.t. K Maximized by the root of a quartic polynomial: Closed form for K but very large expressions - Increases with fixed circuit power (e.g., P FIX ) - Decreases with circuit coefficients multiplied with M or K (P BS, P UE, 1/L BS ) 38

39 Impact of Cell Size Are Smaller Cells More Energy Efficient? - Recall: S λ = E 1 λ - Smaller cells λ is larger S λ is smaller For any given parameters M, α, K - Smaller S λ smaller transmit power αbσ 2 S λ K - Higher EE! Expressions for M, α, K - M and K increases with S λ - α decreases with S λ Smaller cells: Less hardware and fewer users per cell Use shorter distances to reduce power Dependence on Other Parameters Many other observations can be made Example: Impact of bandwidth B, coherence block length U, etc. 39

40 Alternating Optimization Algorithm Joint EE Optimization - EE is a function of M, α, and K - 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 (M, α, K) is given 2. Update number of users K (and implicitly M and α) using Theorem 3 3. Update number of antennas M using Theorem 1 4. Update transmit power (α) using Theorem 2 5. Repeat until convergence Theorem 4 The algorithm convergences to a local optimum to the joint EE optimization problem Disclaimer M and K should be integers Theorems 1 and 3 give real numbers Take one of the 2 closest integers 40

41 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: 41

42 Optimal Single-Cell System Design: ZF Beamforming Optimum M = 165 K = 104 α = 0.87 User rates: 64-QAM Massive MIMO! Name for multi-user MIMO with very many antennas 42

43 Optimal Single-Cell System Design: Optimal Beamforming Optimum M = 145 K = 95 α = 0.91 Q = 3 User rates: 64-QAM Not optimal! Gives optimal beamforming but computations are too costly 43

44 Optimal Single-Cell System Design: MRT/MRC Beamforming Optimum M = 81 K = 77 α = 0.24 User rates: 2-PSK Observation Lower EE than with ZF Also Massive MIMO setup Low rates 44

45 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) K for τ (ul) {1,2,4} 45

46 Multi-Cell Scenarios and Imperfect Channel Knowledge (2) Inter-Cell Interference - λ jl = Channel attenuation between a random user in cell l and BS j - I = E λ jl l j is relative severity of inter-cell interference λ jj Lemma (Achievable Rate) Consider same transmit power as before: P trans = αbσ 2 S λ K Achievable rate under ZF and pilot-based channel estimation: R = B log where I PC = α(m K) α M K I PC I PC + αkτ ul 1 + αki αk(1 + I PC 2) E λ jl λ jj l j only in cluster and I PC = E λ jl l j only in cluster λ jj 2 Pilot contamination (PC) (Strong interference) Intra/inter-cell interference (Weaker) 46

47 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: R = B log α(m K) α M K I PC + 1+I PC + 1 αkτ ul 1+αKI αk(1+i PC 2) - Overly high rates not possible (but we didn t get that ) B log I PC - Clustering (fractional pilot reuse) might be good to reduce interference 47

48 Optimal Multi-Cell System Design: ZF Beamforming Optimum M = 123 K = 40 α = 0.28 τ (ul) = 4 User rates: 4-QAM Massive MIMO! Many BS antennas Note that M/K 3 48

49 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! 49

50 Energy Efficient to Use More Transmit Power? Recall from Theorem 2: Transmit power increases M - Figure shows EE-maximizing power for different M Essentially linear growth Power per antenna decreases Intuition: More Circuit Power Use More Transmit Power - Different from 1/ M scaling laws in recent massive MIMO literature - Power per antennas decreases, but only logarithmically 50

51 Summary Optimization Results - EE is a quasi-concave function of (M, K, α) - Closed-form optimal M, K, or α for single-cell - Alternating optimization algorithm Increases with Simulations Depends on parameters Download Matlab code to try other values! Decreases with Antennas M Power α, coverage area S λ, and M-independent circuit power M-related circuit power Reveals how variables are connected Users K Transmit power αbσ 2 S λ K Fixed circuit power C 0,0 and coverage area S λ Circuit power, coverage area S λ, antennas M, and users K K-related circuit power - Large Cell More antennas, users, RF power Massive MIMO Appears Naturally Fractional pilot reuse important! More Circuit Power Use more transmit power Limits of M, K Circuit power that scales with M,K 51

52 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? 52

53 Multi-Objective Network Optimization 53

54 Basic Assumptions: Multi-Objective Optimization Consider N Performance Metrics - Objectives to be maximized - Notation: g 1 x, g 2 x,, g N x - Example: individual user rates, area rates, energy-efficiency Optimization Resources - Resource bundle: - Example: power, resource blocks, network architecture, antennas, users - Feasible allocation: 54

55 Single or Multiple Performance Metrics Conventional Optimization - Pick one prime metric: g 1 x - Turn g 1 x, g 2 x,, g N x into constraints - Optimization problem: Multi-Objective Optimization - Consider all N metrics - No order or preconceptions! - Optimization problem: [g 1 x, g 2 x,, g N x ] g 2 x C 2,, g N x C N. - Solution: A scalar number - Cons: Is there a prime metric? How to select constraints? Solution: A set Pareto Boundary Improve a metric Degrading another metric 55

56 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 conflicting Relatively aligned 56

57 A Priori Approach No Objectively Optimal Solution - Utopia point outside of region Only subjectively good solutions exist System Designer Selects Utility Function f R N R - Describes subjective preference (larger is better) Examples: Sum performance: Proportional fairness: Harmonic mean: Max-min fairness: Aggregate metric Fairness of metrics We obtain a simplified problem: f(g 1 x, g 2 x,, g N x ) - Solution: A scalar number (Gives one Pareto optimal point) - Takes all metrics into account! 57

58 Example: Optimization of 5G Networks Design Cellular Network - Symmetric system - 16 base stations (BSs) - Select: M = # BS antennas K = # users P = power/antenna Resource bundle: W

59 Example: Optimization of 5G Networks (2) Downlink Multi-Cell Transmission - Each BS serves only its own K users - Coherence block length: U - BS knows channels within the cell (cost: K/U) - ZF beamforming: no intra-cell interference - Interference leaks between cells Average User Rate Power/user R average = B 1 K U log Array gain P (M K) K S λ σ 2 + I Bandwidth (10 MHz) CSI estimation overhead (U = 1000) Noise / pathloss ( ) Relative inter-cell interference (0.54) 2 July 2014

60 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 P total = P trans η + C 0,0 + C 1,0 K + C 0,1 M + BC beamforming U L BS Amplifier efficiency (0.31) Fixed power (10 W) Circuit power per user (0.3 W) Circuit power per antenna (1 W) Computing ZF beamforming ( MK 2 )

61 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

62 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

63 References L.Sanguinetti, A. L. Moustakas, E. Björnson and M. Debbah, Large System Analysis of the Energy Consumption Distribution in Multi-User MIMO Systems with Mobility, submitted to IEEE Transactions on Wireless Communications, 2014 E. Björnson, J. Hoydis, M. Kountouris and M. Debbah Massive MIMO Systems with Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits, accepted for publication, IEEE Transactions on Information Theory, 2014 E. Björnson, M. Kountouris, and M. Debbah, Massive MIMO and small cells: Improving energy efficiency by optimal soft-cell coordination, in Proc. Int. Conf. Telecommun. (ICT), E. Björnson, L. Sanguinetti, J. Hoydis, M. Debbah, Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?, IEEE Transactions on Wireless Communications, Submitted for publication, 2014 E. Björnson, E. Jorswieck, M. Debbah, B. Ottersten, Multi-Objective Signal Processing Optimization: The Way to Balance Conflicting Metrics in 5G Systems, To Appear in IEEE Signal Processing Magazine, Special Issue on Signal Processing for the 5G Revolution. 63