Comparing Massive MIMO and

mmWave Massive MIMORobert W. Heath Jr.

The University of Texas at Austin Department of Electrical and Computer Engineering

Wireless Networking and Communications Group !

Joint work with Tianyang Bai Some new results of cooperation project

www.profheath.org

Wireless is Big in Texas

Wireless is Big in Texas20 Faculty

Wireless is Big in Texas

150 Graduate Students

20 Faculty

Wireless is Big in Texas

150 Graduate Students

10 Industrial Affiliates20 Faculty

Wireless is Big in Texas

150 Graduate Students$5M

Heavily funded center

10 Industrial Affiliates20 Faculty

Wireless is Big in Texas

150 Graduate Students$5M

Heavily funded center

Affiliates  champion  large  federal  proposals,  provide  technical  input/feedback,  unrestricted  gift  funds

WNCG  provides  pre-­‐prints,  pre-­‐competitive  research  ideas,  vast  expertise,  first  access  to  students

10 Industrial Affiliates20 Faculty

Wireless is Big in Texas

150 Graduate Students$5M

Heavily funded center

Affiliates  champion  large  federal  proposals,  provide  technical  input/feedback,  unrestricted  gift  funds

WNCG  provides  pre-­‐prints,  pre-­‐competitive  research  ideas,  vast  expertise,  first  access  to  students

About  half  of  all  students  intern  for  an  affiliate  or  work  full-­‐time

Affiliates  provide  real  world  context

10 Industrial Affiliates20 Faculty

3

Heath Group in the WNCG @ UT Austin

10 PhD students

millimeter wave for 5G cellular

millimeter wave for tactical ad hoc networks

transportation systems and wireless

cloud radio access networks

centimeter level navigation

device-to-device

3

Heath Group in the WNCG @ UT Austin

10 PhD students

millimeter wave for 5G cellular

millimeter wave for tactical ad hoc networks

transportation systems and wireless

cloud radio access networks

centimeter level navigation

device-to-device

!

!

Introduction to 5G

millimeter wave

Usual 5G Motivation Slide

5

Spectrum

Spectrum Efficiency

Infrastructure (more dense)

macro cell

micro cell

small cell / HetNet

distributed antennas

microwave

MIMO

multiuser MIMO

network MIMO

massive MIMO

hot warm cold

D2D

cognitive

Massive MIMO is a key technology for 5G

millimeter wave

Usual 5G Motivation Slide

5

Spectrum

Spectrum Efficiency

Infrastructure (more dense)

macro cell

micro cell

small cell / HetNet

distributed antennas

microwave

MIMO

multiuser MIMO

network MIMO

massive MIMO

hot warm cold

D2D

cognitive

!

!

Why massive MIMO at mmWave frequencies?

Why Millimeter Wave?

Huge amount of spectrum available in mmWave bands Technology advances make mmWave possible for low cost consumer devices mmWave research is as old as wireless itself, e.g. Bose 1895 and Lebedew 1895

7

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ISM – 40.68 ± .02 MHz

ISM – 24.125 ± 0.125 GHz 30 GHz

ISM – 245.0 ± 1GHzISM – 122.5 ± .500 GHzISM – 61.25 ± .250 GHz

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PLEASE NOTE: THE SPACING ALLOTTED THE SERVICES IN THE SPEC-TRUM SEGMENTS SHOWN IS NOT PROPORTIONAL TO THE ACTUAL AMOUNTOF SPECTRUM OCCUPIED.

AERONAUTICALMOBILE

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ALLOCATION USAGE DESIGNATIONSERVICE EXAMPLE DESCRIPTION

Primary FIXED Capital LettersSecondary Mobi le 1st Capital with lower case letters

U.S. DEPARTMENT OF COMMERCENational Telecommunications and Information AdministrationOffice of Spectrum Management

October 2003

MOBIL

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TRAVELERS INFORMATION STATIONS (G) AT 1610 kHz

59-64 GHz IS DESIGNATED FORUNLICENSED DEVICES

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BANDDESIGNATIONS

ACTIVITIES

FREQUENCY

3 x 107m 3 x 106m 3 x 105m 30,000 m 3,000 m 300 m 30 m 3 m 30 cm 3 cm 0.3 cm 0.03 cm 3 x 105Å 3 x 104Å 3 x 103Å 3 x 102Å 3 x 10Å 3Å 3 x 10-1Å 3 x 10-2Å 3 x 10-3Å 3 x 10-4Å 3 x 10-5Å 3 x 10-6Å 3 x 10-7Å

0 10 Hz 100 Hz 1 kHz 10 kHz 100 kHz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz 100 GHz 1 THz 1013Hz 1014Hz 1015Hz 1016Hz 1017Hz 1018Hz 1019Hz 1020Hz 1021Hz 1022Hz 1023Hz 1024Hz 1025Hz

THE RADIO SPECTRUMMAGNIFIED ABOVE3 kHz 300 GHz

VERY LOW FREQUENCY (VLF)Audible Range AM Broadcast FM Broadcast Radar Sub-Millimeter Visible Ultraviolet Gamma-ray Cosmic-ray

Infra-sonics Sonics Ultra-sonics Microwaves InfraredP L S XC Radar

Bands

LF MF HF VHF UHF SHF EHF INFRARED VISIBLE ULTRAVIOLET X-RAY GAMMA-RAY COSMIC-RAY

X-ray

ALLOCATIONSFREQUENCY

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S..

This chart is a graphic single-point-in-time portrayal of the Table of Frequency Allocations used by theFCC and NTIA. As such, it does not completely reflect all aspects, i.e., footnotes and recent changesmade to the Table of Frequency Allocations. Therefore, for complete information, users should consult theTable to determine the current status of U.S. allocations.

U.S. D

EPARTMENT OF COMMERCENATIO

NA

L TELECO

MMUNICATIONS & INFORMATIO

N AD

MIN

ISTRA

TION

MOBI

LE (A

ERON

AUTIC

AL TE

LEME

TERI

NG)

S)

5.68

5.73

5.90

5.95

6.2

6.52

5

6.68

56.

765

7.0

7.1

7.3

7.35

8.1

8.19

5

8.81

5

8.96

59.

040

9.4

9.5

9.9

9.99

510

.003

10.0

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11.1

7511

.275

11.4

11.6

11.6

5

12.0

512

.10

12.2

3

13.2

13.2

613

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13.4

113

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13.6

13.8

13.8

714

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14.3

5

14.9

9015

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15.0

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15.6

15.8

16.3

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17.4

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17.9

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19.9

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20.0

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21.0

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21.9

2422

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22.8

5523

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24.8

924

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25.0

0525

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25.0

725

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25.3

325

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25.6

726

.126

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26.4

826

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26.9

627

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27.4

127

.54

28.0

29.7

29.8

29.8

929

.91

30.0

UNITEDSTATES

THE RADIO SPECTRUM

NON-GOVERNMENT EXCLUSIVE

GOVERNMENT/ NON-GOVERNMENT SHAREDGOVERNMENT EXCLUSIVE

RADIO SERVICES COLOR LEGEND

ACTIVITY CODE

NOT ALLOCATED RADIONAVIGATION FIXED

MARITIME MOBILEFIXED

MARITIME MOBILE

FIXED

MARITIME MOBILE

Radiolocation RADIONAVIGATION

FIXED

MARITIMEMOBILE

Radiolocation

FIXED

MARITIMEMOBILE FIXED

MARITIMEMOBILE

AERONAUTICALRADIONAVIGATION

AERO

NAUT

ICAL

RADI

ONAV

IGAT

ION

Aeron

autic

alMo

bile

Mariti

meRa

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on(R

adio

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ons)

MARI

TIME

RADI

ONAV

IGAT

ION

(RAD

IO BE

ACON

S)Ae

ronau

tical

Radio

navig

ation

(Rad

io Be

acon

s)

3 9 14 19.9

5

20.0

5

30 30 59 61 70 90 110

130

160

190

200

275

285

300

3 kHz 300 kHz

300 kHz 3 MHz

3 MHz 30 MHz

30 MHz 300 MHz

3 GHz

300 GHz

300 MHz

3 GHz

30 GHz

AeronauticalRadionavigation(Radio Beacons)

MARITIMERADIONAVIGATION(RADIO BEACONS)

Aeron

autic

alMo

bile

Mariti

meRa

diona

vigati

on(R

adio

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ons)

AERO

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ICAL

RADI

ONAV

IGAT

ION

(RAD

IO BE

ACON

S)

AERONAUTICALRADIONAVIGATION(RADIO BEACONS)

AeronauticalMobile

Aeron

autic

al Mo

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RADI

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IGAT

ION

AER

ONAU

TICAL

RADI

ONAV

IGAT

ION

MARI

TIME

MOBI

LE AeronauticalRadionavigation

MOB

ILE (D

ISTR

ESS

AND

CALL

ING)

MARI

TIME

MOBI

LE

MARI

TIME

MOBI

LE(S

HIPS

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Y)

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LE

AERO

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ICAL

RADI

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NS)

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ISM – 40.68 ± .02 MHz

ISM – 24.125 ± 0.125 GHz 30 GHz

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17.7

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21.2

21.4

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This chart is a graphic single-point-in-time portrayal of the Table of Frequency Allocations used by theFCC and NTIA. As such, it does not completely reflect all aspects, i.e., footnotes and recent changesmade to the Table of Frequency Allocations. Therefore, for complete information, users should consult theTable to determine the current status of U.S. allocations.

300 MHz 3 GHz

30 GHz 300 GHz

cellular WiFi

note: log scale so even smaller over here

Gain and Aperture in mmWave

Smaller wavelength means smaller captured energy at antenna 3GHz->30GHz gives 20dB extra path loss due to aperture

Larger bandwidth means higher noise power and lower SNR 50MHz -> 500MHz bandwidth gives 10dB extra noise power

8

microwave noise bandwidth

mmWave noise bandwidth

microwave aperture

mmWave aperture

TX

RX

isotropic radiator

No

= kTeB

receive spectral density

receive aperture

Prx

=Ptx

4⇡R2

�2

4⇡

Gain and Aperture in mmWave

Smaller wavelength means smaller captured energy at antenna 3GHz->30GHz gives 20dB extra path loss due to aperture

Larger bandwidth means higher noise power and lower SNR 50MHz -> 500MHz bandwidth gives 10dB extra noise power

8

microwave noise bandwidth

mmWave noise bandwidth

microwave aperture

mmWave aperture

TX

RX

isotropic radiator

No

= kTeB

receive spectral density

effective receive

aperture

transmit antenna

gain

Prx

=Ptx

4⇡R2

�2

4⇡G

rx

Gtx

Gain and Aperture in mmWave

Smaller wavelength means smaller captured energy at antenna 3GHz->30GHz gives 20dB extra path loss due to aperture

Larger bandwidth means higher noise power and lower SNR 50MHz -> 500MHz bandwidth gives 10dB extra noise power

8

microwave noise bandwidth

mmWave noise bandwidth

microwave aperture

mmWave aperture

TX

RX

isotropic radiator

No

= kTeB

receive spectral density

effective receive

aperture

transmit antenna

gain

Prx

=Ptx

4⇡R2

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Gtx

Gain and Aperture in mmWave

Smaller wavelength means smaller captured energy at antenna 3GHz->30GHz gives 20dB extra path loss due to aperture

Larger bandwidth means higher noise power and lower SNR 50MHz -> 500MHz bandwidth gives 10dB extra noise power

8

microwave noise bandwidth

mmWave noise bandwidth

microwave aperture

mmWave aperture

TX

RX

isotropic radiator

No

= kTeB

receive spectral density

effective receive

aperture

transmit antenna

gain

Prx

=Ptx

4⇡R2

�2

4⇡G

rx

Gtx

Exploit gain from large antenna arrays

MIMO

Constraints in mmWave Inform Theory & Design

9

Baseband Precoding

Baseband Processing

1-bit ADC

1-bit ADC

ADC

ADC

1-bit ADCADCno rich scattering

efficient antennasfeed antennas

phase noise

mixed signal power consumption

RF Chain

RF Chain

RF Chain

Analog processing

Analog processing

Analog processing

Joint processing

quantized phase shifters insertion loss

beam tracking

array geometry

mobilityorientation

low gainlinearity

equalizationsynchronization

penetration loss

Constraints in mmWave Inform Theory & Design

9

Baseband Precoding

Baseband Processing

1-bit ADC

1-bit ADC

ADC

ADC

1-bit ADCADCno rich scattering

efficient antennasfeed antennas

phase noise

mixed signal power consumption

RF Chain

RF Chain

RF Chain

Analog processing

Analog processing

Analog processing

Joint processing

quantized phase shifters insertion loss

beam tracking

array geometry

mobilityorientation

low gainlinearity

Compounded by use of MIMO with 8 to 256 antennas or more

equalizationsynchronization

penetration loss

!

!

Why massive MIMO at below mmWave frequencies?

* Meaning below 10 GHz ** We sometimes call this microwave but technically

(apparently) microwave goes from 300 MHz to 300 GHz

Multiuser MIMO — What Happened?

11

supports up to 8 antennas @ BS

sensitive to scheduling algorithms

feedback becomes a huge bottleneck

due to FDD

performance with severe quantization favored by industry is dismal

impaired by interference

one or two antennas @ UE

can’t spatially multiplex many UEs

at once

Massive MIMO - Multiuser MIMO Reborn

12

64 antennas or more @ BS

requires a lot of space for the antennas

TDD avoids significant feedback overheads

performance depends on what CSI is available and how it is used

accounts for out-of-cell interference

massive MIMO comes with massive complexityspatially multiplex

tens of UEs at once

Issues in Massive MIMO

13

CSI Feedback for FDD Operation† * Quantized or analog feedback * Exploiting sparsity * Adaptive feedback techniques

Algorithms * Reducing complexity * Managing interference * Mobility in the channel

Base Station Implementation * Designing good arrays * Feeding antennas, port matching * Distributed antennas * Synchronization Protocols

* Quantized or analog feedback * Performance analysis * Exploiting sparsity * Protocols

† Current cooperation topic w/ H. Nikopour at Huawei in Ottawa !K. T. Truong and R. W. Heath, Jr., “Effects of Channel Aging in Massive MIMO Sys- tems,” Journal of Communications and Networks, Special Issue on Massive MIMO, vol. 15, no. 4, pp. 338-351, August 2013. Received the 2014 Journal of Communications and Networks Best Paper Award. !K. T. Truong and R. W. Heath, Jr., “Impact of Spatial Correlation and Distributed Antennas for Massive MIMO systems ,” (invited) Proc. of the Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, November 3-6, 2013.

Differentiating features of below mmWave and mmWave

Channel Differences: Conventional vs. mmWave

15

< 10 GHz WiFi or Cellular

mmWave WiFi

mmWave 5G

bandwidth 1.4 MHz to 160 MHz 2.16 GHz 100 MHz to 2 GHz

# antennas @ BS or AP 1 to 8 16 to 32 64 to 256

# antennas @ MS 1 or 2 16 to 32 4 to 16

delay spread 100 ns to 2 us 5 to 47 ns 12 to 40 ns

angle spread 1° to 60° 60° to 100° up to 50°

# clusters 4 to 9 < 4 < 4

small-scale fading Rayleigh Nakagami non-fading or Nakagami

large-scale fadingdistant dependent +

shadowing distant dependent + shadowingdistant dependent +

blockage

path loss exponent 2-4 2 LOS, 2.5 to 5 NLOS 2 LOS, 3.5 to 4.5 NLOS

penetration loss some varies possibly high

channel sparsity less more more

spatial correlation less more more

LOS: line-of-sight NLOS: non-line-of-sight Data synthesized from various sources

Some Differentiating Features

16

massive mmWave massive

beamforming digital analog or hybrid

number of simultaneous users more than 10 up to 4

blockage sensitivity low high

outage important no yes

orientation sensitivity low high

cell size macro or micro pico

network deployment low density higher density or hotspot

backhaul wired or out-of-band inband

Comparing sub-millimeter wave and millimeter wave

in terms of coverage and capacity

Approach for Comparison

18

Consider large network with randomly deployed BSs Use stochastic geometry to analyze SINR and rate distribution

Usual (boring) Poison point process model (no clustering, GPP, etc)

Uplink and downlink are different network, but w/ same density

!

Consider a large number of antennas at the base station TDD based massive MIMO w/ matched filtering

Incorporate differentiating features into the spatial correlation model

infinity of base stations and antennas creates challenges

[And11] J. G. Andrews, F. Baccelli, and R. K. Ganti, "A Tractable Approach to Coverage and Rate in Cellular Networks", IEEE Transactions on Communications, November 2011. [Hae13] M. Haenggi, Stochastic Geometry for Wireless Networks, Cambridge Press 2013. [Mar10] T. L. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., Nov., 2010.

performance analyzed for a typical user

large

infinite

small

Differences Included in the Analysis

19

< 10 GHz mmWave

small-scale fading correlated with high rankcorrelated with low rank, varies

with LOS or NLOS

large-scale fading distant dependent pathloss distant dependent with random blockage model and outage

network deployment low BS density high BS density

UE array configuration single antenna directional antenna with gain

# users served simultaneously higher (10 or more) few (limited by beamforming)

!

!

Massive MIMO Analysis

SINR Analysis of Massive Microwave

21

Channel estimate of -th BS to its k-th user

pilot contamination

M antennas at BS

Single antenna at MS

interference

inside-of-cell out-of-cell

inside-of-cell out-of-cell

SINR Analysis of Massive Microwave

21

Channel estimate of -th BS to its k-th user

pilot contamination

M antennas at BS

Single antenna at MS

interference

inside-of-cell out-of-cell

inside-of-cell out-of-cell

infinite # interferers

Use log-distance model for path loss gain A link of length d has path loss

Mean square of eigenvalues of is finite, i.e., More general than the finite maximum eigenvalue assumption [Hoy13] Ensure the rank of grows with the size of antennas M Intuitively assumes larger array sees more independent multi-path Reasonable assumption in rich-scattered microwave

Channel Model Assumptions

22

antennas at BS & single antenna at MS Channel vector modeled as

Path loss in power

Covariance matrix for small-scale fading

i.i.d. random vector

[Hoy13] J. Hoydis et al, “Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?” IEEE JSAC, Feb, 2013

SINR Convergence Results

23

T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, submitted to GlobalSIP, June 2014 Prior version available on Arxiv

SINR Convergence Results

23

Lemma 1 (even with correlation asymptotic orthogonality holds) When , , and .

T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, submitted to GlobalSIP, June 2014 Prior version available on Arxiv

SINR Convergence Results

23

Lemma 1 (even with correlation asymptotic orthogonality holds) When , , and .

T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, submitted to GlobalSIP, June 2014 Prior version available on Arxiv

Theorem 1 [Downlink Asymptotic SIR] When , the downlink SIR converges as . The CCDF of the asymptotic SIR approximately equals

SIR limited by pilot contamination

An increasing function of path loss exponent

SINR Convergence Results

Convergence with an infinite number of nodes is non-trivial Use Campbell’s them and factorial moment to prove convergence

Uplink SINR has the same asymptotic distribution Asymptotic rate are the same in downlink and uplink

23

Lemma 1 (even with correlation asymptotic orthogonality holds) When , , and .

T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, submitted to GlobalSIP, June 2014 Prior version available on Arxiv

Theorem 1 [Downlink Asymptotic SIR] When , the downlink SIR converges as . The CCDF of the asymptotic SIR approximately equals

SIR limited by pilot contamination

An increasing function of path loss exponent

SINR Simulations(1/2)

24

BS distributed as PPP Assume IID fading Avg. ISD: 1000 meters

Converges to the asymptotic bound

SINR Simulations(2/2)

25

Gain from large # of antennas

BS distributed as PPP Avg. ISD: 1000 meters

SINR grows as path loss exponent grows

!

!

mmWave Massive MIMO Analysis

SINR Analysis of Massive mmWave

27

T. Bai, R. Vaze, and R. W. Heath, Jr., ``Analysis of Blockage Effects in Urban Cellular Networks”, To appear IEEE Trans. Wireless Commun., June 2014 On arXiv. T. Bai and R. W. Heath Jr., “Coverage and rate analysis for millimeter wave cellular networks”, submitted to IEEE Trans. Wireless Commun., March 2014. On arXiv. M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, E. Erkip, “ Millimeter Wave Channel Modeling and Cellular Capacity Evaluation,” available on arXiv.

Interfering Transmitters

Associated Transmitter

Buildings

Typical Receiver

NLOS Path

LOS path

Standard massive MIMO @ BSDoes not explicitly incorporate beamforming

or hardware constraints

SINR Analysis of Massive mmWave

27

Sectored beamforming pattern model @ UE

Main lobe beamwidth

Main lobe array gainBack lobe gain

T. Bai, R. Vaze, and R. W. Heath, Jr., ``Analysis of Blockage Effects in Urban Cellular Networks”, To appear IEEE Trans. Wireless Commun., June 2014 On arXiv. T. Bai and R. W. Heath Jr., “Coverage and rate analysis for millimeter wave cellular networks”, submitted to IEEE Trans. Wireless Commun., March 2014. On arXiv. M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, E. Erkip, “ Millimeter Wave Channel Modeling and Cellular Capacity Evaluation,” available on arXiv.

Interfering Transmitters

Associated Transmitter

Buildings

Typical Receiver

NLOS Path

LOS path

Standard massive MIMO @ BSDoes not explicitly incorporate beamforming

or hardware constraints

Blockage + Outage Model

28

Blockage

stochastic building modelrandomly located buildings

LOS: K=0non-LOS

K>0

Exponentially decreasing LOS probability

Outage

S. Rangan, T. S. Rappaport, E. Erkip, “Millimeter Wave Cellular Wireless Networks: Potentials and Challenges”, available at http://arxiv.org/abs/1401.2560.

no outage (blockage)

outage (no signal) Received Signal Model

If not in outage * LOS with p(R) * NLOS with 1-p(R)

exponent proportional to building density

Use blockage model to determine LOS/ NLOS status Path loss exponent 2 in LOS and around 4 in NLOS for

Assume deterministic channel for LOS links !

!

Measurement shows small-scale fading has minor effects in mmWave Assume steering vectors for all LOS links asymptotically orthogonal Requires angles of arrival to have no overlap if using ULA at BSs

NLOS paths the same channel structure as in microwave cases NLOS links potentially have more multi-path

Channel Model Assumptions

29

Path loss in power

Directivity gain at MS

2

h(k)`n =

⇣�(k)`n A(k)

`n M⌘1/2

u(k)`n

Unit steering vector

2

h(k)`n =

⇣�(k)`n A(k)

`n M⌘1/2

u(k)`n

u(k)`n

SINR Convergence Results

30

* T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, to be submitted soon, prior version available on Arxiv

SINR Convergence Results

30

* T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, to be submitted soon, prior version available on Arxiv

Lemma 2 For a LOS link, .

2

h(k)`n =

⇣�(k)`n A(k)

`n M⌘1/2

u(k)`n

u(k)`n

h(k)⇤`n h(k)

`n /Mp.! �(k)

`n A(k)`n

SINR Convergence Results

30

* T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, to be submitted soon, prior version available on Arxiv

Lemma 3 For any two mmWave links,

Lemma 2 For a LOS link, .

2

h(k)`n =

⇣�(k)`n A(k)

`n M⌘1/2

u(k)`n

u(k)`n

h(k)⇤`n h(k)

`n /Mp.! �(k)

`n A(k)`n

SINR Convergence Results

30

* T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, to be submitted soon, prior version available on Arxiv

Lemma 3 For any two mmWave links,

Lemma 2 For a LOS link, .

2

h(k)`n =

⇣�(k)`n A(k)

`n M⌘1/2

u(k)`n

u(k)`n

h(k)⇤`n h(k)

`n /Mp.! �(k)

`n A(k)`n

Theorem 2 [Asymptotic mmWave DL SINR] The mmWave downlink SINR converges in distribution as

2

h(k)`n =

⇣�(k)`n A(k)

`n M⌘1/2

u(k)`n

u(k)`n

h(k)⇤`n h(k)

`n /Mp.! �(k)

`n A(k)`n

SINRDLd.!⇣�(1)00 A

(1)00

⌘2/

X

`6=0

�(1)`0 A(1)

`0

!2

.

SINR Convergence Results

Asymptotic SINR different from microwave due to channel structure Effects of noise vanishes in mmWave massive networks

Analytical expressions for asymptotic SINR distribution available*

30

* T. Bai, R. W. Heath, Jr., “ Asymptotic coverage and rate analysis in massive MIMO cellular networks”, to be submitted soon, prior version available on Arxiv

Lemma 3 For any two mmWave links,

Lemma 2 For a LOS link, .

2

h(k)`n =

⇣�(k)`n A(k)

`n M⌘1/2

u(k)`n

u(k)`n

h(k)⇤`n h(k)

`n /Mp.! �(k)

`n A(k)`n

Theorem 2 [Asymptotic mmWave DL SINR] The mmWave downlink SINR converges in distribution as

2

h(k)`n =

⇣�(k)`n A(k)

`n M⌘1/2

u(k)`n

u(k)`n

h(k)⇤`n h(k)

`n /Mp.! �(k)

`n A(k)`n

SINRDLd.!⇣�(1)00 A

(1)00

⌘2/

X

`6=0

�(1)`0 A(1)

`0

!2

.

3

−10 −5 0 5 10 15 20 250.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SINR Threshold in dB

SIN

R C

ove

rage

Asymptotic

102 antennas

103 antennas

Fig. 2. Optimal BS density with different LOS path loss exponent n.

Pm(T ) = 1� e

�2⇡�m

⇣A2

2 + e��A

�2(�A+1)

⌘

, (1)

A =

✓MrMtCNPt

�2T

◆1/↵N

. (2)

PM(T ) =

✓1 +

T

↵22F1(1, 1�

2

↵, 2� 2

↵,�T )

◆�1

. (3)

Pc(T,B) = P[(SINRM > T ) [ (SINRm > BT )] = PM(T ) + Pm(BT )� PM(T )Pm(BT ), (4)

R(T ) = W log2(1 + T )Pm(T,W ) (5)

�2= KW (6)

(1/W )

1/↵N (7)

Simulations (1/2)

31

Blockage model 1. LOS prob. 2. Avg. LOS range 200 meters 3. Avg. ISD: 200 meters 4. LOS path loss exponent: 2 5. NLOS exponent: 4 !No MS beamforming

Convergence to the asymptotic SINR in distribution

3

−10 −5 0 5 10 15 20 25 30 35 400.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SINR threshold in dB

Cove

rage P

robabili

ty

ISD 100 m

ISD 200 m

ISD 400 m

ISD 400 m +MS BF gain 6 dB

Fig. 2. Optimal BS density with different LOS path loss exponent n.

Pm(T ) = 1� e

�2⇡�m

⇣A2

2 + e��A

�2(�A+1)

⌘

, (1)

A =

✓MrMtCNPt

�2T

◆1/↵N

. (2)

PM(T ) =

✓1 +

T

↵22F1(1, 1�

2

↵, 2� 2

↵,�T )

◆�1

. (3)

Pc(T,B) = P[(SINRM > T ) [ (SINRm > BT )] = PM(T ) + Pm(BT )� PM(T )Pm(BT ), (4)

R(T ) = W log2(1 + T )Pm(T,W ) (5)

�2= KW (6)

(1/W )

1/↵N (7)

200

Simulations (2/2)

32

Blockage model 1. LOS prob. 2. Avg. LOS range 100 meters 3. LOS path loss exponent: 2 4. NLOS exponent: 4 5. In outage if link > 300 m !mmWave MS beamforming: 1. 6 dB gain 2. 90 degree beam width

MS beamforming improve SINR

Increasing BS density does not always increase SINR as there are more LOS pilot contaminators

Asymptotic SINR

!

!

Comparisons

3

−10 −5 0 5 10 15 20 25 300.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SINR threshold in dB

Co

vera

ge P

rob

abili

ty

ISD 200 m +MS BF gain 6 dB

ISD 400 m+ MS BF gain 6 dB

ISD 600m +MS BF gain 6 dB

Microwave: ISD 1000 m

Fig. 2. Optimal BS density with different LOS path loss exponent n.

Pm(T ) = 1� e

�2⇡�m

⇣A2

2 + e��A

�2(�A+1)

⌘

, (1)

A =

✓MrMtCNPt

�2T

◆1/↵N

. (2)

PM(T ) =

✓1 +

T

↵22F1(1, 1�

2

↵, 2� 2

↵,�T )

◆�1

. (3)

Pc(T,B) = P[(SINRM > T ) [ (SINRm > BT )] = PM(T ) + Pm(BT )� PM(T )Pm(BT ), (4)

R(T ) = W log2(1 + T )Pm(T,W ) (5)

�2= KW (6)

(1/W )

1/↵N (7)

Asymptotic Coverage Comparison

34

mmWave is worse in low SINR if base stations are not dense enoughBlockage model

1. LOS prob. 2. Avg. LOS range 100 meters 3. LOS path loss exponent: 2 4. NLOS exponent: 4 5. Outage if > 300 m !!!Microwave path loss exponent: 4 !mmWave MS beamforming: 1. 6 dB gain 2. 90 degree beam width

mmWave better in high SINR

3

−10 −5 0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

SINR threshold in dB

SIN

R C

ove

rag

e P

rob

ab

ility

Microwave 64 antennas

mmWave 16 antennas

mmWave 128 antennas

Fig. 2. Optimal BS density with different LOS path loss exponent n.

Pm(T ) = 1� e

�2⇡�m

⇣A2

2 + e��A

�2(�A+1)

⌘

, (1)

A =

✓MrMtCNPt

�2T

◆1/↵N

. (2)

PM(T ) =

✓1 +

T

↵22F1(1, 1�

2

↵, 2� 2

↵,�T )

◆�1

. (3)

Pc(T,B) = P[(SINRM > T ) [ (SINRm > BT )] = PM(T ) + Pm(BT )� PM(T )Pm(BT ), (4)

R(T ) = W log2(1 + T )Pm(T,W ) (5)

�2= KW (6)

(1/W )

1/↵N (7)

Coverage with Finite # of Antennas

35

mmWave blockage model 1. LOS prob. 2. Avg. LOS range 100 meters 3. LOS path loss exponent: 2 4. NLOS exponent: 4 !Mmwave 1. Avg. ISD: 200 meters 2. 4 users per cell 3. No MS beamforming !!Microwave 1. Avg. ISD 400 meters 2. 10 users per cell 3. path loss exponent: 4

Gain from larger # of antennas

mmWave better than microwave, possibly due to assuming smaller # of users

Training Overhead

Using OFDM symbol as training, max. # of simultaneous users**

36* Z. Pi. F. Khan, "A millimeter-wave massive MIMO system for next generation mobile broadband," In proc. of Asilomar, Nov. 2012 ** T. L. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Trans. Wireless Commun., Nov., 2010.

Given per user rate , cell throughput can be computed as

BW (MHz)

OFDM symbol time CP length Coherence

time

OFDM symbol# in a

slot

# of users per training symbol

Microwave (2 GHz) 30 71.5 4.76 500 7 14

MmWave* (28 GHz) 500 4.16 0.46 35 8 7

Training overhead Overhead from CP

Asymptotic Rate Comparison

37

Spectrum efficiency (bps/Hz)

# of users/cell % useful BW Cell throughput (Mbps)

ISD (m)

Rate per area (Mbps/km2)

Micro SISO 2.0 1 30*93.4% 56.0 400 446

Micro Massive MIMO

3.6 14 30*80.0% 1209.6 400 9626

Micro Massive MIMO

3.6 14 30*80.0% 1209.6 200 38522

MmWave Massive MIMO

5.2 4 500*77.8% 8229.1 200 208450

MmWave MS beamforming: 6 dB gain with 90 degree beam width

Asymptotic rate gain is substantial

20x

4x

5x

Rate with Finite Antennas

38

MmWave MS beamforming: 6 dB gain with 90 degree beam width

Still notably large gain with finite antennas

Spectrum efficiency (bps/Hz)

# of users/cellBW*

Overhead(MHz)

Cell throughput (Mbps)

ISD (m)

Rate per area (Mbps/km2)

Micro SISO 2.0 1 30*93.4% 56.0 400 446

Micro 64 antennas

1.2 10 30*80.0% 288.0 400 2292

Micro 64 antennas

1.2 10 30*80.0% 288.0 200 9172

MmWave 16 antennas

2.2 4 500*77.8% 3388.1 200 107850

MmWave 128 antennas

3.0 4 500*77.8% 4260.5 200 147072

20x

4x

10x10x

1.5x

Massive MIMO Rates with Different User Numbers

39

Spectrum efficiency (bps/Hz)

# of users/cellBW*

Overhead(MHz)Cell throughput

(Mbps)ISD (m)

Rate per area (Mbps/km2)

Micro 64 antennas

2.0 4 30*80.0% 192.0 400 1528

Micro 64 antennas

1.6 6 30*80.0% 230.4 400 2407

Micro 64 antennas

1.2 10 30*80.0% 288.0 400 2292

Micro 64 antennas

0.9 14 30*80.0% 302.4 400 2406

Micro 64 antennas

0.8 20 30*66.7% 320 400 2547

Micro 64 antennas

0.6 28 30*66.7% 336 400 2674

Micro 64 antennas

0.4 42 30*53.3% 269 400 2138

Cell throughput non-monotonic with user #

MmWave Massive MIMO Rates with Different User Numbers

40

MmWave MS beamforming: 6 dB gain with 90 degree beam width

Spectrum efficiency (bps/Hz)

# of users/cellBW*

Overhead(MHz)Cell throughput

(Mbps)ISD (m)

Rate per area (Mbps/km2)

MmWave 128 antennas 3.0 4 500*77.8% 4261 200 147072

MmWave 128 antennas

2.8 7 500*77.8% 6959 200 221510

MmWave 128 antennas

2.5 14 500*67.8% 11865 200 377670

Max. # of users limited by # of RF chains

Conclusion

Go Massive at mmWave if network dense

at lower frequencies if network sparse