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**Designing Multi-User MIMO for Energy Efficiency**

When is Massive MIMO the Answer? Emil Björnson‡* Joint work with: Luca Sanguinetti‡§, Jakob Hoydis†, and Mérouane Debbah‡ ‡Alcatel-Lucent Chair on Flexible Radio, Supélec, France *Dept. Signal Processing, KTH Royal Institute of Technology, Sweden §Dip. Ingegneria dell’Informazione, University of Pisa, Pisa, Italy †Bell Laboratories, Alcatel-Lucent, Stuttgart, Germany Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Outline Presentation is based on Main Question Conclusions**

E. Björnson, L. Sanguinetti, J. Hoydis, M. Debbah, “Designing Multi-User MIMO for Energy Efficiency: When is Massive MIMO the Answer?,” Submitted IEEE WCNC Preprint available on arXiv: Main Question How should a single-cell downlink system be designed to maximize energy efficiency? Optimization variables: Number of base station antennas Number of active user equipments Data rate guaranteed per user Conclusions Result depends strongly on physical layer precoding scheme Unconventionally many users and antennas can be optimal! Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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Introduction Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**What are the Expectations?**

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! Impossible to maximize all metrics simultaneously Our goal: High energy efficiency (EE) with uniform user rates Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Multi-User MIMO System**

Multi-User Multiple-Input Multiple-Output (MIMO) One base station (BS) with array of 𝑀 antennas 𝐾 single-antenna user equipments (UEs) Downlink: Transmission from BS to UEs Share a flat-fading carrier Multi-Antenna Precoding Spatially directed signals Signal improved by array gain Adaptive control of interference Serve multiple users in parallel Space-division multiple access (SDMA) Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Multi-User MIMO System (2)**

Cell: Area with user location and pathloss distribution Scheduling: Pick users randomly, with random location Some UE Distribution Clean-Slate Design Select 𝑀 and 𝐾 to maximize EE! Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**How to Measure Energy Efficiency?**

Energy Efficiency in bits/Joule 𝐸𝐸= Average Sum Throughput bits channel use Power Consumption Joule channel use Conventional Academic Approaches Maximize throughput with fixed power Minimize transmit power for fixed throughput New Problem: Balance throughput and power consumption Crucial: Account for overhead signaling Crucial: Use reasonable power consumption model Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**System Model: Average Sum Throughput**

Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Time-Division Duplex (TDD) Protocol**

Coherence Period: 𝑇 [channel uses] Assumption: Perfect estimation Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Average Sum Throughput**

𝐡 1 𝐡 2 System Model Precoding vector of User 𝑘: v 𝑘 Channel vector of User 𝑘: h 𝑘 ~ 𝐶𝑁(𝟎, λ 𝑘 𝐈) Random User Selection, Channel variances λ 𝑘 : Independent random variables, 𝑓 λ (𝑥) Achievable Rate of User 𝑘: Signal-to-interference+noise ratio (SINR) Average over channels and user selection Cost of estimation Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Impact of Precoding What Determines User Rates? Notation**

Precoding (vector directions and power allocations) “Optimal” precoding: Extensive computations – Not efficient Notation Matrix form: 𝐕=[ 𝐯 1 ,…, 𝐯 𝐾 ], 𝐇=[ 𝐡 1 ,…, 𝐡 𝐾 ] Total radiated power: P trans =tr( 𝐕 𝐻 𝐕) Heuristic Closed-Form Precoding Maximum ratio transmission (MRT): v 𝑘 = 𝑃 𝑘 h 𝑘 Zero-forcing (ZF) precoding: 𝐕=𝐇 𝐇 𝐻 𝐇 −1 diag( 𝑃 1 ,…, 𝑃 𝐾 ) Regularized ZF (RZF) precoding: 𝐕=𝐇 𝜎 2 𝐈+ 𝐇 𝐻 𝐇 −1 𝜎 2 𝐈+ 𝐇 𝐻 𝐇 −1 diag( 𝑃 1 ,…, 𝑃 𝐾 ) Maximize signal Minimize interference Balance signal and interference Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Uniform User Performance**

Assumption: Uniform user performance Same rate at every user: 1− 𝐾 𝑇 log 𝜌 𝑀−𝐾 Scaling parameter 𝜌≥0 can be optimized Consequence: We use ZF in analysis and other precoding for simulation Lemma 1 Consider ZF precoding and the user rates above, the average radiated power is P trans =E{tr 𝐕 𝐻 𝐕) =𝐾𝜌 𝐴 λ where 𝐴 λ =E 𝜎 2 λ depends on UE distribution, propagation, etc. Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**System Model: Power Consumption**

Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Reasonable Power Consumption Model**

What Consumes Power? Examples will motivate our model Transmit Power: 1 η P trans 𝑃 trans = Average radiated transmit power η = Efficiency of power amplifier at BS Transceiver Chains: 𝑀 ∙𝑃 𝑡𝑥 + 𝑃 𝑠𝑦𝑛 +𝐾∙ 𝑃 𝑟𝑥 𝑃 𝑡𝑥 = Circuit power / BS antenna (converters, mixers, filters) 𝑃 𝑠𝑦𝑛 = Power of common oscillator at BS 𝑃 𝑟𝑥 = Circuit power / UE (oscillator, converters, mixer, filters) Coding and Decoding: 𝐾( 𝑃 𝑐𝑜𝑑 + 𝑃 𝑑𝑒𝑐 ) 𝑃 𝑐𝑜𝑑 = Power for coding at BS / user 𝑃 𝑑𝑒𝑐 = Power for decoding at each user Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Reasonable Power Consumption Model (2)**

Computational Efficiency: 𝐿 operations per Joule Uplink Channel Estimation: 𝐾∙𝑀 𝐿∙𝑇 Only once per coherence period 𝑀 channel components per user, processed separately Precoding: 𝐶 precoding 𝐿∙𝑇 Depends on precoding: 𝐶 precoding = 2𝐾𝑀 for MRT 3 𝐾 2 𝑀+2𝐾𝑀 𝐾 for ZF Architectural Costs: 𝑃 0 Control signaling, backhaul infrastructure, load-independent processing, etc. Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Reasonable Power Consumption Model (3)**

Summary General model of power consumption: 𝑃 total = 1 η P trans + 𝑖=0 3 𝐶 𝑖,0 𝐾 𝑖 + 𝑖=0 2 𝐶 𝑖,1 𝐾 𝑖 𝑀 for some parameters 0<η≤1 and 𝐶 𝑖,𝑗 ≥0. Energy Efficiency for ZF User rate: 1− 𝐾 𝑇 log 𝜌 𝑀−𝐾 Radiated power: P trans =𝐾𝜌 𝐴 λ 𝐸𝐸= Average Sum Throughput Power Consumption = 𝐾 1− 𝐾 𝑇 log 𝜌 𝑀−𝐾 η 𝐾𝜌 𝐴 λ + 𝑖=0 3 𝐶 𝑖,0 𝐾 𝑖 + 𝑖=0 2 𝐶 𝑖,1 𝐾 𝑖 𝑀 Design parameters: 𝑀, 𝐾, and 𝜌 Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Optimize System Parameters for Energy Efficiency**

Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Preliminaries Our Goal: Definition Optimize number of antennas 𝑀**

Optimize the (normalized) transmit power 𝜌 Optimize number of active UEs 𝐾 Definition 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 almost as linear: Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Optimal Number of BS Antennas**

Find 𝑀 that maximizes EE with ZF precoding: maximize 𝑀:𝑀≥𝐾 𝐾 1− 𝐾 𝑇 log 𝜌 𝑀−𝐾 η 𝐾𝜌 𝐴 λ + 𝑖=0 3 𝐶 𝑖,0 𝐾 𝑖 + 𝑖=0 2 𝐶 𝑖,1 𝐾 𝑖 𝑀 Observations Increases sublinearly with power 𝜌 but linearly at high 𝜌 Increases with circuit power coefficients independent of 𝑀 Decreases with circuit power coefficients multiplied with 𝑀 Theorem 1 (Optimal 𝑀) Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Optimal Transmit Power**

Find 𝜌 that maximizes EE with ZF precoding: maximize 𝜌≥0 𝐾 1− 𝐾 𝑇 log 𝜌 𝑀−𝐾 η 𝐾𝜌 𝐴 λ + 𝑖=0 3 𝐶 𝑖,0 𝐾 𝑖 + 𝑖=0 2 𝐶 𝑖,1 𝐾 𝑖 𝑀 Observations Increases power with number of antennas as 𝑀/ log 𝑀 Opposite to recent claim: Power should decrease as 1/ 𝑀 Intuition: Higher circuit power Use more transmit power Theorem 2 (Optimal 𝜌) Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Optimal Number of Active UEs**

Find 𝐾 that maximizes EE with ZF precoding: maximize 𝐾≥0 𝐾 1− 𝐾 𝑇 log 𝜌 tot 𝛽− η 𝜌 tot 𝐴 λ + 𝑖=0 3 𝐶 𝑖,0 𝐾 𝑖 + 𝑖=0 2 𝐶 𝑖,1 𝛽𝐾 𝑖+1 where 𝜌 tot =𝜌𝐾 and 𝛽= 𝑀 𝐾 are fixed. Observations Decreases with circuit power coefficients multiplied with 𝑀 or 𝐾 Increases with the static hardware power 𝐶 0,0 Increases with the propagation parameter 𝐴 λ Theorem 3 (Optimal 𝐾) Solution is a root to a quartic polynomial: Closed-form but very large expressions Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Numerical Illustrations**

Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Simulation Scenario Main Characteristics**

Circular cell with radius 250 m Uniform user distribution with 35 m minimum distance Uncorrelated Rayleigh fading, typical 3GPP pathloss model Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Optimal System Design: ZF Precoding**

Optimum 𝑀=165 𝐾=85 𝜌=4.6 User rates: as 256-QAM Massive MIMO! Very many antennas, 𝑀/𝐾≈2 Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Optimal System Design: MRT**

Optimum 𝑀=4 𝐾=1 𝜌=12.7 User rates: as 64-QAM Single-user transmission! Only exploit precoding gain Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Why This Huge Difference?**

Interference is the Limiting Factor ZF: Suppress interference actively MRT: Only indirect suppression by making 𝑀≫𝐾 More results: RZF≈ZF, same trends under imperfect CSI 100x difference in throughput Only 2x difference in EE Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Energy Efficient to Use More Power?**

Recall Theorem 2: Transmit power increases with 𝑀 Figure shows EE-maximizing power for different 𝑀 Intuition: More Circuit Power Use More Transmit Power Essentially linear growth Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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Conclusions Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Conclusions What if a Single-Cell System Designed for High EE?**

Need: Reasonable throughput model Need: Reasonable power consumption model Contributions General power consumption model Closed-form results for ZF: Optimal number of antennas Optimal number of active UEs Optimal transmit power Observations: More circuit power Use more transmit power Numerical Example ZF/RZF precoding: Massive MIMO system is optimal MRT precoding: Single-user transmission is optimal Small difference in EE, but huge difference in throughput! Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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**Thank You for Listening!**

Questions? Main reference: E. Björnson, L. Sanguinetti, J. Hoydis, M. Debbah, “Designing Multi-User MIMO for Energy Efficiency: When is Massive MIMO the Answer?” Submitted IEEE WCNC 2014 Preprint available on arXiv: Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

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