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
*Dept.
Signal Processing, KTH Royal Institute of Technology, Sweden
§Dip.
Ingegneria dell’Informazione, University of Pisa, Pisa, Italy
†Bell
2013-11-07
Chair on Flexible Radio, Supélec, France
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
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: http://arxiv.org/abs/1310.3843.
• 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!
2013-11-07
Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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Introduction
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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
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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)
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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!
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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 =
bits
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 reasonable power consumption model
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Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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System Model:
Average Sum Throughput
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Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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Time-Division Duplex (TDD) Protocol
Assumption:
Perfect estimation
• Coherence Period: 𝑇 [channel uses]
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Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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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 : Independent random variables, 𝑓λ (𝑥)
• Achievable Rate of User 𝑘:
Average over channels and user selection
Signal-to-interference+noise ratio
(SINR)
Cost of estimation
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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?
- Precoding (vector directions and power allocations)
- “Optimal” precoding: Extensive computations – Not efficient
• Notation
- Matrix form: 𝐕 = [𝐯1 , … , 𝐯𝐾 ], 𝐇 = [𝐡1 , … , 𝐡𝐾 ]
- Total radiated power: Ptrans = tr(𝐕𝐻 𝐕)
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
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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 2 1 + 𝜌 𝑀 − 𝐾
- Scaling parameter 𝜌 ≥ 0 can be optimized
Lemma 1
Consider ZF precoding and the user rates above,
the average radiated power is
Ptrans = E{tr 𝐕𝐻 𝐕) = 𝐾𝜌𝐴λ
where 𝐴λ = E
𝜎2
λ
depends on UE distribution, propagation, etc.
• Consequence:
- We use ZF in analysis and other precoding for simulation
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Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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System Model:
Power Consumption
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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
P
η trans
- 𝑃trans = Average radiated transmit power
-η
= Efficiency of power amplifier at BS
• Transceiver Chains: 𝑀 ∙ 𝑃𝑡𝑥 +𝑃𝑠𝑦𝑛 + 𝐾 ∙ 𝑃𝑟𝑥
- 𝑃𝑡𝑥 = Circuit power / BS antenna (converters, mixers, filters)
- 𝑃𝑠𝑦𝑛 = Power of common oscillator at BS
- 𝑃𝑟𝑥 = Circuit power / UE (oscillator, converters, mixer, filters)
• Coding and Decoding: 𝐾(𝑃𝑐𝑜𝑑 + 𝑃𝑑𝑒𝑐 )
- 𝑃𝑐𝑜𝑑 = Power for coding at BS / user
- 𝑃𝑑𝑒𝑐 = Power for decoding at each user
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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:
𝐶precoding
𝐿∙𝑇
- Only once per coherence period
- Depends on precoding: 𝐶precoding
2𝐾𝑀
for MRT
= 3𝐾 2 𝑀 + 2𝐾𝑀 + 2 𝐾 3 for ZF
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• Architectural Costs: 𝑃0
- Control signaling, backhaul infrastructure,
load-independent processing, etc.
2013-11-07
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:
1
η
𝑃total = Ptrans +
3
𝑖
𝐶
𝐾
𝑖,0
𝑖=0
+
2
𝑖𝑀
𝐶
𝐾
𝑖,1
𝑖=0
for some parameters 0 < η ≤ 1 and 𝐶𝑖,𝑗 ≥ 0.
Energy Efficiency for ZF
User rate: 1 −
𝐾
𝑇
log 2 1 + 𝜌 𝑀 − 𝐾
Radiated power: Ptrans = 𝐾𝜌𝐴λ
Average Sum Throughput
𝐸𝐸 =
=
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
Design parameters: 𝑀, 𝐾, and 𝜌
2013-11-07
Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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Optimize System Parameters
for Energy Efficiency
2013-11-07
Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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Preliminaries
• Our Goal:
- 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:
2013-11-07
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:
𝐾
𝐾 1 − 𝑇 log 2 1 + 𝜌 𝑀 − 𝐾
maximize
𝑀: 𝑀 ≥ 𝐾 1
η 𝐾𝜌𝐴λ +
3
𝑖
𝑖=0 𝐶𝑖,0 𝐾
+
2
𝑖
𝑖=0 𝐶𝑖,1 𝐾 𝑀
Theorem 1 (Optimal 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
2013-11-07
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:
𝐾
𝐾 1 − 𝑇 log 2 1 + 𝜌 𝑀 − 𝐾
maximize
𝜌≥0 1
η 𝐾𝜌𝐴λ +
3
𝑖
𝑖=0 𝐶𝑖,0 𝐾
+
2
𝑖
𝑖=0 𝐶𝑖,1 𝐾 𝑀
Theorem 2 (Optimal 𝜌)
• 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
2013-11-07
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:
𝐾
𝐾 1 − 𝑇 log 2 1 + 𝜌tot 𝛽 − 1
maximize
𝐾 ≥ 0 1 tot
η 𝜌 𝐴λ +
where 𝜌tot = 𝜌𝐾 and 𝛽 =
𝑀
𝐾
3
𝑖
𝑖=0 𝐶𝑖,0 𝐾
+
2
𝑖+1
𝑖=0 𝐶𝑖,1 𝛽𝐾
are fixed.
Theorem 3 (Optimal 𝐾)
Solution is a root to a quartic polynomial:
Closed-form but very large expressions
• Observations
- Decreases with circuit power coefficients multiplied with 𝑀 or 𝐾
- Increases with the static hardware power 𝐶0,0
- Increases with the propagation parameter 𝐴λ
2013-11-07
Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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Numerical Illustrations
2013-11-07
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
2013-11-07
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
2013-11-07
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
2013-11-07
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
Only 2x
difference
in EE
100x
difference
in throughput
• More results: RZF≈ZF, same trends under imperfect CSI
2013-11-07
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
Essentially
linear
growth
• Intuition: More Circuit Power  Use More Transmit Power
2013-11-07
Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
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Conclusions
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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!
2013-11-07
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: http://arxiv.org/abs/1310.3843
2013-11-07
Greentouch Open Forum, Designing Multi-User MIMO for Energy Efficiency, E. Björnson (Supélec & KTH)
30