1. 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)

2. 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)

3. 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)

4. 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)

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

6. 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)

7. 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)

8. 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)

9. 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)

10. Overview of Analytic Results
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)

11. 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)

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

13. 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)

14. 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)

15. 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)

16. 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)

17. 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)

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

19. 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)

20. 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)