Massive MIMO: Bringing the Magic of Asymptotic Analysis to ...
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Bringing the Magic of Asymptotic Analysis to Wireless Networks Massive MIMO
Dr. Emil Björnson Department of Electrical Engineering (ISY) Linköping University, Linköping, Sweden International Workshop on Computer-Aided Modeling Analysis and Design of Communication Links and Networks (CAMAD) December 1, 2014
Biography
• 1983: Born in Malmö, Sweden
• 2007: Master of Science in Engineering Mathematics, Lund, Sweden
• 2011: PhD in Telecommunications, KTH, Stockholm, Sweden
• 2012-2014: International Postdoc Grant Worked at Supélec, Paris, France
• 2014: Assistant Professor Division of Communication Systems, Electrical Engineering, Linköping University, Sweden
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Optimal Resource Allocation in Coordinated Multi-Cell Systems
Book by Emil Björnson, Eduard Jorswieck FnT in Communications and Information Theory
Outline
• Introduction • Expectation on future cellular networks
• What is Massive MIMO?
• Basic Motivation: Asymptotic Properties • Theoretical results meet measurements
• Bringing the Magic of Asymptotic Analysis to Wireless Networks • Anticipated implementation and performance gains
• Recent Results: More Magic from Asymptotic Analysis • Hardware design, coordination, hardware utilization all get easier/better
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WHAT CAN THE PAST TELL US ABOUT THE FUTURE?
Introduction
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Incredible Success of Wireless Communications
• Last 45 years: 1 Million Increase in Wireless Traffic
5 Source: Wikipedia
Martin Cooper Inventor of handheld cellular phones
Source: Personal Communications in 2025, Martin Cooper
Martin Cooper’s law
The number of simultaneous voice/data connections has doubled
every 2.5 years (+32% per year) since the beginning of wireless
Predictions for the Future
• Wireless Connectivity • A natural part of our lives
• Rapid Network Traffic Growth • 61% annual data traffic growth
• Faster than in the past!
• Exponential increase
• Extrapolation: 20x until 2020 200x until 2025 2000x until 2030
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210 MB/month/person
2.2 GB/person/month
Video streaming
Voice calls
Next killer app?
Gaming
Social networks
Evolving Networks for Higher Traffic
• Increase Network Throughput [bit/s] • Consider a given area
• Simple Formula for Network Throughput:
Throughputbit/s in area
= Available spectrumin Hz
∙ Cell densityCell/Area
∙ Spectral efficiencybit/s/Hz/Cell
• Ways to achieve 1000x improvement:
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More spectrum Higher cell density Higher spectral efficiency
Nokia (2011) 10x 10x 10x
SK Telecom (2012) 3x 56x 6x
New regulations, cognitive radio,
higher frequencies
Smaller cells, heterogeneous deployments
Massive MIMO (Topic of this talk)
?x
MASSIVE MIMO Introduction to
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Higher Spectral Efficiency
• Spectral Efficiency of Point-to-Point Transmission • Governed by Shannon’s capacity limit:
log2 1 +Received Signal Power
Interference Power + Noise Power [bit/s/Hz/User]
• Cannot do much: 4 bit/s/Hz 8 bit/s/Hz costs 17 times more power!
• Many Parallel Transmissions: Spatially focused to each desired user
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Multi-User MIMO (Multiple-input Multiple-output)
• Multi-Cell Multi-User MIMO • Base stations (BSs) with 𝑁 antennas
• Parallel uplink/downlink for 𝐾 users
• Channel coherence block: 𝑇 symbols
• Theory: Hardware is Limiting • Spectral efficiency roughly prop. to
min 𝑁,𝐾, T 2
• 2x improvement = 2x antennas and users (since 𝑇 ∈ [100,10000])
• Practice: Interference is Limiting • Multi-user MIMO in LTE-A: Up to 8 antennas
• Small gains since: Hard to learn users’ channels Hard to coordinate BSs
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End of the MIMO road? No reason to add
more antennas/users?
Taking Multi-User MIMO to a New Level
• Network Architecture: Massive MIMO • Use large arrays at BSs; e.g., 𝑁 ≈ 200 antennas, 𝐾 ≈ 40 users
• Key: Excessive number of antennas, 𝑁 ≫ 𝐾
• Very narrow beamforming
• Little interference leakage
• 2013 IEEE Marconi Prize Paper Award Thomas Marzetta, “Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas,” IEEE Trans. Wireless Communications, 2010.
• Analysis based on asymptotics: 𝑁 → ∞
• Concept applicable at any 𝑁
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Spectral efficiency prop. to number of users!
min 𝑁,𝐾,T 2
≈ 𝐾
What is the Key Difference from Today?
• Number of Antennas? • 3G/UMTS: 3 sectors x 20 element-arrays = 60 antennas
• 4G/LTE-A: 4-MIMO x 60 = 240 antennas
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Typical vertical array: 10 antennas x 2 polarizations
Only 1-2 antenna ports
3 sectors, 4 vertical arrays per sector Image source: gigaom.com
Massive MIMO Characteristics
Active antennas: Many antenna ports Coherent beamforming to tens of users
160 antenna elements, LuMaMi testbed, Lund University
No, we already have many antennas!
Massive MIMO Deployment
• When to Deploy Massive MIMO? • The future will tell, but it can
1. Improve wide-area coverage
2. Handle super-dense scenarios
• Co-located Deployment • 1D, 2D, or 3D arrays
• One or multiple sectors
• Distributed Deployment • Remote radio heads
• Cloud RAN
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ASYMPTOTIC PROPERTIES Basic Motivation
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Asymptotic Channel Orthogonality
• Example: Uplink with Isotropic/Rayleigh Fading • Two users, i.i.d. channels: 𝐡1,𝐡2 ~ 𝐶𝑁(𝟎, 𝐈𝑁)
• Signals: 𝑠1, 𝑠2 with power 𝑃
• Noise: 𝐧 ~ 𝐶𝑁(𝟎, 𝐈𝑁)
• Received: 𝐲 = 𝐡1𝑠1 + 𝐡2𝑠2 + 𝐧
• Linear Processing for User 1: 𝑦�1 = 𝐰1𝐻𝐲 = 𝐰1
𝐻𝐡1𝑠1 + 𝐰1𝐻𝐡2𝑠2 + 𝐰1
𝐻𝐧
• Matched filter: 𝐰1 = 1𝑁𝐡1
• Signal remains: 𝐰1𝐻𝐡1 = 1
𝑁| 𝐡1 |2
𝑁→∞ E |ℎ11|𝟐 = 1
• Interference vanishes: 𝐰1𝐻𝐡2 = 1
𝑁𝐡1𝐻𝐡2
𝑁→∞ E[ℎ11𝐻 ℎ21] = 0
• Noise vanishes: 𝐰1𝐻𝐧 = 1
𝑁𝐡1𝐻𝐧
𝑁→∞ E[ℎ11𝐻 𝑛1] = 0
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𝐡1 𝐡2
Asymptotically noise/interference-free communication: 𝑦�1𝑁→∞
𝑠1
Is this Result Limited to Isotropic Fading?
• Assumptions in i.i.d. Rayleigh Fading • No dominant directivity
• Very many scattering objectives
• Example: Line-of-Sight Propagation • Uniform linear array
• Random user angles
• 𝑁 observations: • Stronger signal
• Suppressed noise
• What is 𝐡1𝐻𝐡2 = ?
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Less true as 𝑁 → ∞
|𝐡1𝐻𝐡2|2
𝐡1 2 𝐡2 2 ≈1𝑁𝐡1𝐻𝐡2
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Main difference: How quickly interference is suppressed
Does This Hold for Practical Channels?
• Initial Measurements: Show similar results
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Source: J. Hoydis, C. Hoek, T. Wild, and S. ten Brink, “Channel Measurements for Large Antenna Arrays,” ISWCS 2012
|𝐡1𝐻𝐡2|𝐡1 𝐡2
≈1𝑁𝐡1𝐻𝐡2
|𝐡1𝐻𝐡2|2
𝐡1 2 𝐡2 2 ≈1𝑁𝐡1𝐻𝐡2
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Source: X. Gao, O. Edfors, F. Rusek, and F. Tufvesson, “Linear Pre-Coding Performance in Measured Very-Large MIMO Channels,“ VTC 2011.
Spectral Efficiency
Only 10-20% lower than with isotropic fading
Favorable Propagation
• Favorable Propagation • Definition: 𝐡1𝐻𝐡2 = 0 for any users
• No interference leakage Everyone gets “the whole cake”
• Asymptotic Favorable Propagation • Definition: 1
𝑁𝐡1𝐻𝐡2 → 0 as 𝑁 → ∞
• Achieved in Rayleigh fading and line-of-sight – two extremes!
• Same behavior expected and seen in practice
• Computer-Aided Design Requires Models With • Line-of-sight and spherical wavefronts
• Scattering less “rich”: Other random distributions
• Spatial correlation: Directivity and user-correlation 18
Affect if 1𝑁𝐡1𝐻𝐡2 → 0
and convergence in mean and variance
There are no experimentally verified massive MIMO channel models
BRINGING THE MAGIC OF ASYMPTOTIC ANALYSIS TO WIRELESS NETWORKS
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Channel Acquisition
• Asymptotic Favorable Propagation • 𝑁 → ∞: Interference vanishes using linear matched filtering
• Finite 𝑁: Reject remaining interference with zero-forcing filtering
• Requires channel state information (CSI) at BSs
• Pilot-based CSI Estimation • Frequency-division duplex (FDD): Two-way estimation and feedback
• Time-division duplex (TDD): Only one-way estimation (exploits reciprocity)
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Estimation overhead ≈ 𝑂(𝐾) Estimation overhead ≈ 𝑂(𝑁)
Natural choice: TDD
Much less overhead!
Example parameters: 𝑁 = 100, 𝐾 = 20, 𝑇 = 200
Massive MIMO Transmission Protocol
• Basic TDD Frame Structure • Dimensioned to have fixed channels
• Coherence time: 𝑇𝑐 s
• Coherence bandwidth: 𝐵𝑐 Hz
• Depends on mobility and environment
• Block length: 𝑇 = 𝑇𝑐𝐵𝑐 symbols
• Typically: 𝑇 ∈ [100,10000]
• Processing Tasks per Frame • Channel estimation
• Linear processing of data signals
• Fourier transforms (in OFDM)
• Computing processing filter
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Complexity: • Increase linearly with 𝑁 and 𝐾 • Straightforward to parallelize
Scales as 𝑁𝐾 with matched filter 𝑁𝐾2 with zero-forcing filter
Limited Pilot Resources
• Limiting Factor: Coherence Block 𝑇 • Not more than 𝑇 orthogonal pilots
• CSI errors: Act as noise and are suppressed
• Multi-cell: Must reuse pilots across cells
• Pilot Contamination • BS cannot tell difference between users
• Channel estimates are correlated
• This interference doesn’t vanish as 𝑁 → ∞
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Will Pilot Contamination Kill Massive MIMO?
No, but treat it with much respect!
Make: Target SINR ≪ Pathloss2 from transmitter∑ Pathloss2from interferers
Limited Pilot Resources (2)
• Solution: Smart Pilot Allocation • Cannot be based on current CSI
• Simple: Pilot reuse factor β
• Advanced: Exploit spatial statistics
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Pilot reuse: 𝜷 = 𝟏
Design Tradeoff High β: Less contamination Higher user performance
Low β: More users/cell, up to T 2β, can give higher area performance
Different statistical angles of arrival Pilot reuse: 𝜷 = 𝟑
Pilot reuse: 𝜷 = 𝟒
Anticipated Area Spectral Efficiency
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Simulation
LTE-like system parameters
Coherence block: 𝑇 = 500
SNR 5 dB, i.i.d. Rayleigh fading
Observations
Baseline: 3 bit/s/Hz/cell (IMT-Advanced)
Massive MIMO, 𝑁 = 100: x20 gain
Massive MIMO, 𝑁 = 200: x30 gain
Per scheduled user: ≈ 2 bit/s/Hz
MORE MAGIC FROM ASYMPTOTIC ANALYSIS
Recent Results
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Capitalizing on Excessive Degrees of Freedom
• Benefits from Coherent Transmit/Receive Filtering • Desired signals amplified by a factor 𝑁
• Undesired signals are not amplified
• Noise and hardware distortions are not amplified
• Ways to Sacrifice Degrees of Freedom • Cancel interference at undesired receivers
• Cancel interference in spatial areas
• Simplifying hardware design
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Distortions from Hardware Impairments
• Real Hardware is Non-Ideal • Hardware impairments: Phase noise, I/Q-imbalance, non-linearities, etc.
• Impact reduced by calibration/compensation (not fully removed!)
• Simple Hardware Model:
• Bussgang’s Theorem:
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Power loss (can be tracked)
Additive distortion noise
Key Property: Distortion noise is suppressed just as other noise
Tolerate larger impairments Cheap and energy-efficient hardware
OFDM signal
• Well-designed Systems are Energy Efficient [bit/Joule]
• 𝐸𝐸 = Average Sum Rate bit/sTransmit Power + Circuit Power Joule/s
• What if we optimize over 𝑁, 𝐾, and rate per user?
• Use state-of-the-art models with recent parameters
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Efficient Hardware Utilization Large array gain
Many simultaneous users
Transmit Power Total: Slightly lower than today
Per antenna: Much smaller
Key Property: Massive MIMO gives high energy efficiency
Energy Efficient Hardware Utilization
Cancel Interference to Other Systems
• Simple Coordination Protocol • Estimate received interference subspace
• Transmit orthogonal to the 𝑀 dominating interferers
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Key Property: Distributed Coordination
𝑁 large: Subspace dimension 𝑀 ≪ 𝑁
Small signal loss, much less interference
Helps coexistence with legacy systems
Fully Distributed
Use only local information
No feedback or exchange
Scalable!
Massive MIMO
Not Massive MIMO
Hardware-Friendly Signal Shaping
• Downlink Transmission • Received signal: 𝑦 = 𝐡𝐻𝐰 + 𝑛
• How to pick 𝐰 so that 𝑠 = 𝐡𝐻𝐰 ?
• Matched filter: 𝐰 ∝ 𝐡𝐡𝑠
• Pro: Minimize transmit power 𝐰 2 • Con: x10 power variations over antennas/time, inefficient amplifiers
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Effective Signal 𝑠
Noise Channel
Key Property: Constant Envelope Precoding
• Elements in 𝐰: |𝑤1|2 = ⋯ = |𝑤𝑁|2 for all 𝑠
• Pro: No power variations, much simpler amplifier design
• Con: More radiated power, same total power when 𝑁 is large
SUMMARY
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Summary
• Massive MIMO: A technique to increase spectral efficiency • Massive multi-user MIMO: >20x gain over IMT-Advanced are foreseen
• High spectral efficiency per cell, not per user
• Many potential deployment strategies and propagation environments
• Many Base Station Antennas • Near favorable propagation
• Resilience to hardware impairments
• High energy efficiency
• Distributed coordination with other systems
• Hardware-friendly signal shaping
• Important: Channel coherence block • Limits multiplexing gain and per-user performance
• Pilot contamination mitigated by smart pilot allocation 32
Magic brought by asymptotic analysis
Bringing the Magic to Reality
• FP7 MAMMOET project (Massive MIMO for Efficient Transmission) • Bridge gap between “theoretical and conceptual” massive MIMO
• Develop: Flexible, effective and efficient solutions
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QUESTIONS?
Dr. Emil Björnson
Visit me online: http://www.commsys.isy.liu.se/en/staff/emibj29
Main References
1. T. Marzetta, “Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas,” IEEE Trans. Wireless Communications, 2010.
2. H. Huh, G. Caire, H. C. Papadopoulos, and S. A. Ramprashad, “Achieving ‘Massive MIMO’ Spectral Efficiency with a Not-so-Large Number of Antennas,” IEEE Trans. Wireless Communications, 2012.
3. S.K. Mohammed, Erik G. Larsson, “Per-Antenna Constant Envelope Precoding for Large Multi-User MIMO Systems,” IEEE Transactions on Communications, 2013.
4. J. Hoydis, K. Hosseini, S. ten Brink, and M. Debbah, “Making Smart Use of Excess Antennas: Massive MIMO, Small Cells, and TDD,” Bell Labs Technical Journal, 2013.
5. F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, “Scaling up MIMO: Opportunities and Challenges with Very Large Arrays,” IEEE Signal Proces. Mag., vol. 30, no. 1, pp. 40-46, 2013.
6. E. Björnson, E. G. Larsson, M. Debbah, “Optimizing Multi-Cell Massive MIMO for Spectral Efficiency: How Many Users Should Be Scheduled?,” Proc. IEEE GlobalSIP, 2014.
7. E.G. Larsson, F. Tufvesson, O. Edfors, and T. L. Marzetta, “Massive MIMO for Next Generation Wireless Systems,” IEEE Commun. Mag., vol. 52, no. 2, pp. 186-195, 2014.
8. E. Björnson, J. Hoydis, M. Kountouris, M. Debbah, “Massive MIMO Systems with Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits,” To appear in IEEE Trans. Information Theory.
9. 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.
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