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

When is Massive MIMO the Answer? Emil Björnson‡*, Luca Sanguinetti‡§, Jakob Hoydis†, and Mérouane Debbah‡ ‡Alcatel-Lucent Chair on Flexible Radio, Supélec, France *Dept. Signal Processing, KTH, and Linköping University, Linköping, Sweden §Dip. Ingegneria dell’Informazione, University of Pisa, Pisa, Italy †Bell Laboratories, Alcatel-Lucent, Stuttgart, Germany Best Paper Award WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Introduction: 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 subcarrier Multi-Antenna Precoding Spatially directed signals Signal improved by array gain Adaptive control of interference Serve multiple users in parallel K users, M antennas WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**What if We Design for Energy Efficiency?**

Cell: Area with user location and pathloss distribution Pick 𝐾 users randomly and serve with rate 𝑅 Some UE Distribution Clean-Slate Design Select (𝑀,𝐾,𝑅) to maximize EE! WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**How to Measure Energy Efficiency?**

Energy Efficiency (EE) in bit/Joule 𝐸𝐸= Average Sum Throughput bit 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 detailed power consumption model WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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System Model WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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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 from some distribution 𝑓 λ (𝑥) Achievable Rate of User 𝑘: TDD mode, perfect channel estimation (coherence time 𝑇) Average over channels and user locations Signal-to-interference+noise ratio (SINR) Cost of estimation WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Average Sum Throughput (2)**

How to Select Precoding? The same rate 𝑅= 𝑅 𝑘 for all users “Optimal” precoding: Extensive computations – Not efficient Notation Matrix form: 𝐕=[ 𝐯 1 ,…, 𝐯 𝐾 ], 𝐇=[ 𝐡 1 ,…, 𝐡 𝐾 ] Power allocation: 𝑃 1 ,…, 𝑃 𝐾 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 WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Detailed Power Consumption Model**

Many Things that Consume Power Radiated transmit power tr( 𝐕 𝐻 𝐕) Baseband processing (e.g., precoding) Active circuits (e.g., converters, mixers, filters) Generic Power Consumption E{tr 𝐕 𝐻 𝐕) η + 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 𝑀 𝐾 2 Circuit power per transceiver chain Cost of channel estimation and precoding computation Power amplifier (η is efficiency) Fixed power (control signals, load-independ. processing, backhaul infrastructure) Coding/decoding data streams Nonlinear function of 𝑀 and 𝐾 WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Problem Formulation Define power parameter 𝜌**

Rate per user: 𝑅 𝜌 = 𝑅 𝑘 = 1− 𝐾 𝑇 log 𝜌 𝑀−𝐾 Lemma 1 (Average radiated power with ZF) E{tr 𝐕 𝐻 𝐕) =𝐾𝜌 𝐴 λ where 𝐴 λ =E 𝜎 2 λ depends on UE distribution, propagation, etc. Simple expression ZF in analysis Other precoding in simulations Maximize Energy Efficiency for ZF 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 Maximize with respect to 𝑀, 𝐾, and 𝜌 WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Overview of Analytic Results**

WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Analytic Results and Observations**

Optimization Results EE is quasi-concave function of (𝑀,𝐾,𝜌) Closed-form optimal 𝑀, 𝐾, or 𝜌 when other two are fixed Increases with Decreases with Antennas 𝑀 Power 𝜌, coverage area 𝐴 λ , and 𝑀-independent circuit power 𝑀-related circuit power Users 𝐾 Fixed circuit power 𝐶 0,0 and coverage area 𝐴 λ 𝐾-related circuit power Transmit power 𝐾𝜌 𝐴 λ Circuit power, coverage area 𝐴 λ , antennas 𝑀, and users 𝐾 - Reveals how variables are connected Large Cell More antennas, users, power More Circuit Power Use more transmit power Limits of 𝑀, 𝐾 Circuit power that scales with 𝑀,𝐾 More Antennas Use more transmit power WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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Numerical Examples WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Simulation Scenario Main Characteristics Realistic Modeling Parameters**

Circular cell with radius 250 m Uniform user distribution with 35 m minimum distance Uncorrelated Rayleigh fading, typical 3GPP pathloss model Realistic Modeling Parameters See the paper for details! WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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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 WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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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 WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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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 WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Energy Efficient to Use More Power?**

Recall: Transmit power increases with 𝑀 Figure shows EE-maximizing power for different 𝑀 Different from recent 1/𝑀 scaling laws Power per antennas decreases, but only logarithmically Almost linear growth WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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Conclusions WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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

Contributions General power consumption model Closed-form results for ZF: Optimal number of antennas Optimal number of 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, huge difference in throughput! WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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**Thank You for Listening!**

Questions? More details and multi-cell results: E. Björnson, L. Sanguinetti, J. Hoydis, M. Debbah, “Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?,” Submitted to IEEE Trans. Wireless Communications, Mar. 2014 Matlab code available for download! Best Paper Award WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

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