1. 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)

2. 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)

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

4. 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)

5. 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)

6. 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)

7. 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)

8. System Model: Average Sum Throughput
Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

9. 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)

10. 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)

11. 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)

12. 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)

13. System Model: Power Consumption
Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)

14. 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)

15. 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)

16. 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)

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

18. 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)

19. 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)

20. 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)

21. 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)

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

23. 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)

24. 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)

25. 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)

26. 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)

27. 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)

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

29. 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)

30. 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)