Designing Multi-User MIMO
for Energy Efficiency
When is Massive MIMO the Answer?
Emil Björnson‡*,
Luca Sanguinetti‡§, Jakob Hoydis†, and Mérouane Debbah‡
‡Alcatel-Lucent
*Dept.
Chair on Flexible Radio, Supélec, France
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
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
1
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
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
2
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!
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
3
How to Measure Energy Efficiency?
• Energy Efficiency (EE) in bit/Joule
𝐸𝐸 =
bit
channel use
Joule
Power Consumption
channel use
Average Sum Throughput
• 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
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
4
System Model
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
5
Average Sum Throughput
𝐡1
• System Model
𝐡2
- Precoding vector of User 𝑘: v𝑘
- Channel vector of User 𝑘: h𝑘 ~ 𝐶𝑁(𝟎, λ𝑘 𝐈)
• Random User Selection
- Channel variances λ𝑘 from some distribution 𝑓λ (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
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
6
Average Sum Throughput (2)
• How to Select Precoding?
- The same rate 𝑅 = 𝑅𝑘 for all users
- “Optimal” precoding: Extensive computations – Not efficient
• Notation
- Matrix form: 𝐕 = [𝐯1 , … , 𝐯𝐾 ], 𝐇 = [𝐡1 , … , 𝐡𝐾 ]
- Power allocation: 𝑃1 , … , 𝑃𝐾
Maximize
signal
Minimize
interference
• Heuristic Closed-Form Precoding
- Maximum ratio transmission (MRT): v𝑘 =
- Zero-forcing (ZF) precoding: 𝐕 = 𝐇 𝐇 𝐻 𝐇
- Regularized ZF (RZF) precoding:
𝑃𝑘 h𝑘
−1 diag(𝑃 , … , 𝑃 )
1
𝐾
𝐕 = 𝐇(𝜎 2 𝐈 +
Balance signal and interference
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
7
Detailed Power Consumption Model
• Many Things that Consume Power
- Radiated transmit power tr(𝐕𝐻 𝐕)
- Baseband processing (e.g., precoding)
- Active circuits (e.g., converters, mixers, filters)
• Generic Power Consumption
E{tr 𝐕𝐻 𝐕)
+ 𝐶0,0 + 𝐶0,1 𝑀 + 𝐶1,0 𝐾 + 𝐶1,1 𝑀𝐾 + 𝐶2,0 𝐾 2 + 𝐶3,0 𝐾 3 + 𝐶2,1 𝑀𝐾 2
η
Power amplifier
(η is efficiency)
Circuit power per
transceiver chain
Cost of channel estimation
and precoding computation
Fixed power
(control signals,
Coding/decoding
load-independ. processing, data streams
backhaul infrastructure)
2014-04-07
Nonlinear
function of 𝑀 and 𝐾
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
8
Problem Formulation
• Define power parameter 𝜌
- Rate per user: 𝑅 𝜌 = 𝑅𝑘 = 1 −
𝐾
𝑇
log 2 1 + 𝜌 𝑀 − 𝐾
Lemma 1 (Average radiated power with ZF)
E{tr 𝐕𝐻 𝐕) = 𝐾𝜌𝐴λ
where 𝐴λ = E
Simple
expression
ZF in analysis
Other precoding
in simulations
2014-04-07
𝜎2
λ
depends on UE distribution, propagation, etc.
Maximize Energy Efficiency for ZF
𝐸𝐸 =
Average Sum Throughput
=
1
Power Consumption
𝐾
𝐾 1 − 𝑇 log 2 1 + 𝜌 𝑀 − 𝐾
η 𝐾𝜌𝐴λ +
3 𝐶 𝐾𝑖
𝑖=0 𝑖,0
+
2 𝐶 𝐾𝑖𝑀
𝑖=0 𝑖,1
Maximize with respect to 𝑀, 𝐾, and 𝜌
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
9
Overview of Analytic Results
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
10
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
Antennas 𝑀
Reveals how
variables are
connected
Users 𝐾
Transmit
power 𝐾𝜌𝐴λ
Large Cell
More antennas,
users, power
2014-04-07
Increases with
Decreases with
Power 𝜌, coverage area 𝐴λ , and
𝑀-independent circuit power
𝑀-related circuit power
Fixed circuit power 𝐶0,0 and
coverage area 𝐴λ
𝐾-related circuit power
Circuit power, coverage area 𝐴λ ,
antennas 𝑀, and users 𝐾
-
More Circuit
Power
Use more
transmit power
Limits of 𝑀, 𝐾
More Antennas
Circuit power that
scales with 𝑀,𝐾
Use more
transmit power
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
11
Numerical Examples
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
12
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
• Realistic Modeling Parameters
- See the paper for details!
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
13
Optimal System Design: ZF Precoding
Optimum
𝑀 = 165
𝐾 = 85
ߩ = 4.6
User rates:
as 256-QAM
Massive
MIMO!
Very many
antennas,
𝑀/𝐾 ≈ 2
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
14
Optimal System Design: MRT
Optimum
𝑀=4
𝐾=1
ߩ = 12.7
User rates:
as 64-QAM
Single-user
transmission!
Only exploit
precoding gain
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
15
Why This Huge Difference?
• Interference is the Limiting Factor
- ZF: Suppress interference actively
- MRT: Only indirect suppression by making 𝑀 ≫ 𝐾
Only 2x
difference
in EE
100x
difference
in throughput
• More results: RZF≈ZF, same trends under imperfect CSI
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
16
Energy Efficient to Use More Power?
• Recall: Transmit power increases with 𝑀
- Figure shows EE-maximizing power for different 𝑀
Almost
linear
growth
- Different from recent 1/𝑀 scaling laws
- Power per antennas decreases, but only logarithmically
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
17
Conclusions
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
18
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!
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
19
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
2014-04-07
WCNC 2014, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec, KTH, Linköping)
20