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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